Part III : Explaining metaphysics

(Part I - Part II - - Part IV)

Abstract: The main metaphysics issues such as the mind-matter duality, and the foundation of morality, will be adressed here as a genuine field for reason and science, thus dismissing the widespread belief that this would be impossible. (fate, and the explanation and refutation of religious faith, especially Christian faith, will be discussed in Part IV)

For the presentation of a dualist ontology leading to an introduction to quantum physics, the first hints (on the foundations of mathematics and the non-algorithmicity of the mind) started in Part II, (sections "Understanding infinity" and "the nature of the mind"), then the presentation continues below (from section "Types of existence").

This page is still under development, but the quantum physics part is already complete (except figures)

How might any religious subject escape science ?

What is religion about ? Religion is about providing concepts about a reality of concern for the life of people, not directly perceived but connected to our lives and perceptions, so as to satisfy their need to understand life, and provide a form of guidance on what to do or how to think that may better lead to happy results for oneself and/or for others.

We explained in the previous part what science is about.

Science is about finding truths on complex issues as reliably as truths can be found without science on obvious things. It is about understanding the accessible world, discovering patterns and connections between our perceptions, so as to be able to predict what perceptions are more likely to come in the context of other perceptions and decisions; thus giving clues on what decisions can better lead to wanted results. And this understanding develops through intermediate concepts that represent aspects of reality (the predictive power of these concepts can be seen as an image of elements of reality causing these effects).

We don't need science to know that chocolate and strawberries are sweet, that night is dark, or that fun, friendship and love are good. So, these truths are "not scientific". They aren't either beyond science, but they come before it: they are are immediately perceptible, and don't require any mystical revelation to be discovered either.

Science cannot exactly predict the weather, earthquakes, what time the phone will be ringing, and many other things - but no other method than science can do it better (with possibly minor, very rare and impractical exceptions on some issues). We cannot access their full range of causes, nor do we have the computer power to make any exact weather forecast a week in advance even if the underlying laws are theoretically known. Thus, the very existence and knowledge of exact underlying laws is rather helpless and irrelevant here. Good approximations of such laws suffice.

Finally, what is the problem ? The problem is, how the hell could anyone fail to notice that the issues addressed by religious doctrines are directly and naturally a particular case and an integral part of what science can handle.
How could anyone say that issues dealt with by religions are not scientific questions, and is there anything true in these arguments ? Let us check these people's claims, what sort of a difference could they see between these two fields, that might be used to justify for such a difference.

One important argument seems to be, that science cannot explain feelings, nor predict them by putting them into equations.
Indeed, as we previously explained, the mind's behavior cannot be predicted through formulas, as it does not follow any mathematical determinism.
However, is it really a problem ?
The assessment of happiness, in good approximation, is readily available to our senses, not requiring any mystical revelation either, so that this does not constitute any relevant limit of science that an alternative form of truth inquiry could usefully overcome.

Thus, how can the absence of any theoretical reference of an exact mathematical law supposed to determine feelings (and even the fact that such a mathematical law does not exist), make any serious difference here ?
It is really necessary to recall that the work of reason and science does not require any a priori full knowledge of the ultimate laws that determine everything ? On the contrary, the scientific research has usually been to start from observations, for guessing more and more clues on how do things happens, what do the outcomes depend on, and what the underlying laws may look like.

So, what religious question might escape science ? All we need to start a scientific research, is observations.

Do we have observations concerning happiness ? Well, yes. The perception of one's own happiness or sadness, is one of the most direct perceptions that can be. What about perceiving the feelings of others ? Some may guess more or less such things, rightly or wrongly. However, it is not so hard to get a good approximation of this parameter, just by asking them the question.

The causes of happiness are generally perceptible things too. People can be happy or sad depending on what happens to them. In case it may depend on their thoughts, these can be expressed as well.
It may sometimes happen that some people become happy or sad for no visible cause (even by themselves), however this is a marginal case. So, happiness is roughly determined by events, which are themselves partly random (we shall discuss later what it means) and partly determined by a large system of visible causes and actions.

Issues on life after death ? Collections of NDE testimonies as already available online, provide more reliable and complete information than any religion ever did.

In fact, most religious claims, by the way they connect to life, are in average as verifiable (and falsifiable) than most other scientific fields. Sometimes such verifications would be very hard to make, however such a difficulty is no way specific to religious questions. Many traditional objects of scientific research are quite hard to check by logic, observation or experimentation as well.
So, the main difficulty that makes such a scientific inquiry on religious claims harder than those on more traditionally scientific subjects, is the problem of how to start deciding to seriously undertake the research by decently rational people. Just as the the surest way to lose a war is by not send any soldier to the battle.

Morality as a scientific field

Morality is about what actions can lead to a highest expectable global happiness.
This field of inquiry might be split into two questions.

One question is, what are the logical connections (causalities) by which someone's actions influence effective circumstances or other situations that people will face.
The second question is how these circumstances will affect their happiness.

Since all these things (actions, circumstances and happiness) are observable, and the very object of morality is how actions influence happiness in this way, this suffices to make morality a genuine field of science.
This call for considering morality as a science, and more precisely, for the same reason, that it must be a consequentialist (utilitarian) view, has ready been made by other authors, especially by Sam Harris. Unfortunately, while he had the merit to have claimed it loud by repeating and reexplaining this same remark over and over again, it is a pity that he hardly went any further in the effective study of this field. But we are going to present an effective start of such a work here. And the obsessive repetition of a single elementary principle without going further, is a philosopher's mania rather than a scientific work.

So, let's go a little further. We said, the issue can be split into 2 questions. Let's have a look at the second one: how do circumstances affect happiness ?
One may assume this question to be obvious, and its answer as directly accessible to our senses, just as we said that the measure of happiness is directly accessible to our senses: to know what someone needs for being happy, it would suffice to ask the question : "What do you need to be happy ?"

Assuming this measurement tool to be correct and thus focusing on the first question (what actions can better lead to specified concrete consequences) as the hard part, the science of morality is reduced to something quite practical, far from the mysteries of psychology, a field where scientific methods can fully apply as all the relevant elements and causality relations are, in principle, accessible to our senses and understanding (and, just like in any other sciences, the only problem is that they are very complex). This may be seen as encompassing all applied sciences for how their specifications of how to produce specific individual tools and objects. But a crucial aspect is how actions from several, many or all individuals can connect and interact together to globally lead to such wanted outcomes.
This is the field of economics and politicial science.
In this sense, the science of morality is quite old, and already took note of readily available solutions.

Concretely, a typical solution to find out and provide what objects people may best need for their daily life, is to put them in a supermarket and let them choose what to buy. But this would only address the needs currently satisfiable by buying something, which are not all needs.
Anyway, supermarkets are but a particular case of a general principle of self-help that already works in many areas (and more reasearch can be done to still extend its efficiency to more areas), so that  the self-awareness of one's needs (if correct) motivates the actions that lead to the optimized consequences (with no need of any explicit measure of individual or collective welfare by outside observers).

Economic and political sciences are dealing with the global flow of actions as resulting from everyone's strive for their respective goals, and how well this all leads to the accomplishments of the expressed goals. So, these fields can in good approximation be considered as synonymous to the science of morality. Or, they can be seen as another aspect of the same more general science. This more general science is the science of how politico-economical systems and individual actions in these systems affect a sort of global sum of the satisfaction by everyone of their respective wants.
Inside it, the political and economic questions are to compare these satisfactions as depending on the system or the policy, for a fixed set of behaviors; while the morality questions are to compare the effects of different possible behaviors of an individual inside a fixed politico-economic system.

Sometimes both questions may coincide, when individuals have the power to change the system or policy.

In other ways, we can consider morality as more general than economics, as it includes the consideration of all actions and their consequences (including among people who interact informally, maybe because they know each other well, disregarding the formal rules of the more global society), while economics and politics deal more specifically with the only actions that go through collective formal processes (markets...) and are concerned with the formal rules of society as a whole.
However, as I already explained in other texts and will develop in Part IV, new economical and political solutions can be developed through technology, extending their usefulness beyond their traditional scopes, so as to make the economic and political fields nearly as general as morality.

So, the problem with economics and political science is that they are currently far from perfect and need to be further worked on.

Now let's come back to the second morality question (what do people need), that we suggested to dismiss as trivial : this is the "self-responsibility hypothesis" assuming everyone's needs to be expressed by their respective intentions or wills (opinions about one's own needs). For practical purposes, economic theories often hold this self-responsibility hypothesis as true.

Now, is it possible to disagree with the self-responsibility hypothesis, and build a morality system over some negations of it ? Such a view is paradoxical as it presents a conflict of opinions: it puts forward an opinion about people's needs that is in conflict with their respective opinions about their own needs. This view is quite bold as requires :
How can this be ?
We can observe three methods (conceptions of other's needs and their associated "solutions") that have already developed on a large scale:  the Socialist method, the Buddhist method, and the Christian/Muslim method.

The Socialist method involves 3 ingredients: a fool, a doctor and a coercion system.
The doctor's role is to define the fool's needs in contradictions with the fools'own opinions (wants).
The role of the coercion system is to keep the fool's life under the doctor's control.
However there is a limit to this system, as the doctor is but a human just like the fool, and thus can be mistaken as well. As the doctor's errors would lead his will to harm the fool's needs (while the fool's foolishness only harms himself), this is rather called madness.
Thus its reliability somehow requires 2 more ingredients: a meta-doctor and a meta-coercion system.
The role of the meta-doctor is to find out whether the doctor is sane or mad.
The role of the meta-coercion system is to give the means for the meta-doctor to defeat the coercion system ifever the doctor is found to be mad.
Examples such coercions already in force:
So, the doctor's role is usually played by the government, the meta-coercion system is given by democracy (assumed to be enough, but quite miserable in practice), so that the meta-doctors more or less coincide with the fools themselves. This way of closing the chain of doctors and coercion systems into a loop, saves us from the need to specify meta-meta-doctors with meta-meta-coercion systems and so on ad infinitum. But it turns out when following the chain of dependencies of the socialist coercion system, that after its "democratic" meta-coercive system, it has two meta-meta-coercive systems, one is constitutional, and the other one is educational, thus only differing from the Buddhist method by the compulsory nature of public education.

With the Buddhist method (or rather, a method more or less followed by many religions), the fool is called a "disciple", the doctor a "Master", and the coercion method is purely dialectic. It goes as follows:
  1. The Master claims to have got a direct perception of the naked reality (called Awakening, Enlightenment or the like) while the disciple would be living in illusion;
  2. The disciple starts trusting the Master more than his own senses;
  3. The Master claims that the satisfaction of desires leads to suffering;
  4. The disciple, trusting this, makes a tabula rasa of his own wills.
Here again, the meta-doctor is the disciple himself, who is free to follow the master of his choice, or to follow none and keep his own mind, as Buddhism is tolerant and openly acknowledges the diversity of ways and the disciple's personal responsibility in making his own choices (so as to save the Master from any responsibility in case his guidance would be wrong). (But other religions with a similar method don't so liberally recognize the value of this meta-coercion system).

Note that such a method develops more as a sefish than a moral work, as most of the work is the one done by the disciple to change his own will for the sake of some assumed better personal happiness.

The Christian/Muslim method is the simplest. The fool (pious person) just needs to express his wishes to God in prayer. Then if these wishes don't happen to be fulfilled, he will conclude that they were not God's will.

No coercion system is needed, as God is assumed to be omnipotent anyway (or to say it otherwise, God's will is redefined as the outcome of the vacuous coercion system identified as destiny), so that even the attempt to wonder what this coercion system could be, would be condemned as blasphemy (a doubt towards God's omnipotence).
For the same motive of blasphemy prohibition, no meta-doctor can be tolerated either.

Now let us sum up the whole field of research in morality by the list of the main questions it is made of, some of which will be later examined in more details:
  1. What is the range of goals that should be seeked for, and their respective importances: human happiness, animals happiness, God's happiness (through worship or anything else), afterlife purposes, environmental preservation
  2. How valid are the above traditional methods to correct the expression of needs, from their natural form to any more correct expression of the real needs (specifying the direct circumstancial conditions of happiness);should such corrective methods be abandoned or further worked on, and can such methods be done sufficiently correctly and obtain worthy enough accomplishments compared to the coercitive works and collateral damages associated with risks of errors and other perverse effects (with the people's tries to avoid this coercion)
  3. By which means and towards which forms can and should the system be changed, and what laws would need to be adopted, either now or in later circumstances or systems. For example, can a system help to "make people more rational" by better informing them on what intermediate purposes they should follow to more efficiently serve their expressed ultimate needs ; how morally efficient can be works to improve the system, as compared to works to develop personal moral actions inside the existing system(s);
  4. As innovations and revolutions (hopefully towards better systems) cannot go on forever but will have to converge to some form or stability sooner or later, and anyway cannot be everybody's task, what are the main features of morality issues (the right rules, principles...) to be expected in the world, first in some near future, then in some ultimate system, in terms of one's actions in a fixed system (out of exhaustion of the needs for improving the system) - because the very purpose of legal systems is to forbid evil actions and try to prevent them from happening.

Types of existence

Now let's directly come to the "deepest" questions.
We said (in Part II), science is not essentialist, which means that it does not systematically require to refer to any know ultimate cause or law, not to specify the "deep nature" (essences) of its objects, for developing its knowledge, as such essences are usually irrelevant. It can be satisfied with raw observations first, then successively more accurate approximative models involving intermediate levels of reality, rather than any ultimate nature of things. Because its main work is about complexity and the exploration of the many ways how things may interact with each other.

Nevertheless, rational thinking is not afraid of essences either, whenever this may be relevant, as it could already successfully explore relatively deeper and deeper essences of physical systems through chains of successively more accurate theories.

Now the point of metaphysics is to discuss the essences of everything; there is no reason why logical positivism could not be applied to it too.
Historically, logical positivists happened to claim that metaphysics is empty, and should be rejected from science. However, this may be understood as a denunciation of the irrational way in which metaphysics has been traditionally handled by philosophers.
Indeed it can be amazing how debates went on and on so long between atheists, deists, religious apologists and philosophers, and it all remained a so miserable fuss of misunderstanding lacking a clear definition of the most basic concepts and the most basic claims about which agreements and disagreements can take place. For example, their debates for or against the existence of God, lacked a clear definition for "God" or for "existence of God". They even seemed to miss the fact that the question "does God exist" hardly makes any sense, as God is not supposed to be an object like other objects, so that the very qualification of "existence" should not apply to God in the same way as it could apply to objects - another understanding of the very concept of existence would need to designed for it.

But if approached more rationally, metaphysics can indeed become a meaningful scientific subject.

Here is a proposition how to do it.

First, let us note that the words "existence" and "reality" are roughly synonymous, and when saying that "something exists", the thing and its existence cannot be separated either : an existence can only be considered as applying to something, and there is no thing without existence.

Now, if things and existence are one and the same, what is that ?

The nature of material objects in our universe has been largely understood by physicists through quite amazing mathematical theories, so that the "unreasonable effectiveness of mathematics" for physics has been celebrated. So, even if not everything is mathematical, the world of mathematics deserves serious consideration here.

The field of mathematics comes with its own objects, and its existence claims on these objects.
Some philosophers debated whether mathematical objects are real, and whether mathematics is an exploration of a reality, or a construction of the mind or anything else, but opposite views added up and did not end to an official agreement (just as philosophers don't resolve any question anyway).
But usually for mathematicans, the debate is rather empty. When they study mathematics, they hold the universe of objects of their study as real, and it works as such. Well not all is clear, but the undeterminacy fuss does not have the same status as what philosophers are discussing. The foundation of mathematics has been studied as a branch of mathematics, and could resolve the main "philosophical debates" on the nature of mathematics, from a mathematical viewpoint.

Some philosophers mistakenly assumed a prior (though undefined) fixed concept of "existence" or "reality", before wondering whether it applies to mathematical objects (universes, truths...). But as the concept of existence is inseparable from its contents, so there is no preexisting standard concept of "existence" separated from mathematics, to be compared with mathematical objects. In other words, no a priori sense can be made of the question "Are mathematical objects real ?" for wondering what the answer is.

Instead, just as mathematical objects have their own nature, so they have their own type of existence, that should not be confused with other, more familiar types of existences. In other words, there are several separate concepts (types) of "existence" or "reality", each to come up after the respective types (natures) of the objects they apply to (even if connections can be found between these types). Namely, these may be classified into mathematical existence, physical existence and concious existence (though this classification is approximative and will have to be refined later).

Note that the physical existence is something relative: specified objects are only present at a given time and place.

Some characters of mathematical existence

Mathematical existence has its margin of relativity too. An illimited range of theories can be considered, including "theories of all mathematics", with each their range of possible universes where they can be interpreted. A claim of existence of an object is relative to a theory and a universe of objects in which this theory is interpreted.
So, the limits of mathematical existence are fuzzy, but the fuzziness of these limits remain internal to the field mathematical existence, and completely unrelated to (unaffected by) any other type of existence.
More precisely, the fuziness (relativity) of the mathematical existence, comes from the infiniteness of the systems that are considered to exist or not. On the other hand, the mathematical existence of finite systems (of specified limited size) enjoys an objective character, independent of any decent choice of a theory of mathematics and its interpretation.

Despite its relativity, the mathematical existence of infinite systems cannot be dismissed because it is somehow guaranteed by Gödel's completeness theorem. This theorem is at least as essential to the foundations of mathematics as the more famous incompleteness theorem. In fact, the incompleteness theorem only owes its higher popularity to its much more pleasant character in the eyes of the irrationalist propagandists who influence public opinion, as well as the biased sensitivity of the public itself who hates mathematics and is so fond of any excuse to praise stupidy and irrationality over reason.

The completeness theorem roughly says that for any theory without contradition, there exists a mathematical universe described by this theory.
At first sight, it may seem to contradict the incompleteness theorem; however there is no contradiction between them once understood more precisely, in ways that won't be detailed here.

So, it provides for the real existence of infinite systems (as many theories require their universe of objects to be infinite). Of course, as no theorem can provide for infinities out of no infinity, the completeness theorem requires an assumption of infinity in order to apply.
But the required infinity assumption is rather weak: it only needs the infinite list of all finite systems (to fix the idea, we can say: the infinite set of all natural numbers). But this assumption is already required to make sense of the premise of the theorem: a contradiction must be a finite system of symbols. Thus, the concept of a "theory without contradiction" involves the infinity of searches for any finite contradition that might be produced by the theory. It would be hard, indeed, to grant existence to every finite system but not to the whole infinite set they form (unless we might mean that every natural number exists inside reality, but this reality of all natural numbers would not itself "exist"...).

And this mathematical existence of infinite systems, while hardly deniable, keeps a margin of relativity in a way too complex to be summed up here (we already gave hints about this...).
However, this relativity margin does matter for us, as we are only concerned in practice with finite systems, whose mathematical existence is objective. Indeed, as will be explained later, the currently known laws of quantum physics are expressed in mathematical terms that somehow only depend on finite systems (and the successive approximations they give, like the computation of a real number, in a way we shall specify later), and thus inherite their objectivity. (And our conciousness has no full access to infinity either.)

Other types of existence

Now the question is: is there any other type of existence, that is, another type of object, outside the mathematical ones ? We mentioned about the physical and the concious existences. Do they differ from mathematical existence ?
Such a difference is hardly deniable. Could anyone mistake oneself with a mathematical object (in other words, one's own existence with a mathematical existence) ?

The status of physical existence is much more subtle, because unlike concious being, physical objects are not aware of their own existence. How to make sense of such an existence, and be sure that the physical type of existence "really exists" ? In fact, we can't. Instead, we shall explain that only the concious and mathematical existences are primitive types of existence, while the physical existence emerges as a combination (or intersection) of both.

But first of all, we need to examine (and refute) another view, widespread among atheists, according to which conciousness emerges out of physical reality, so that concious existence would be mere fruit or particular case of physical existence.

Such a view would first require some primitive type of physical existence, not reducible to mathematical existence. Or would it ?
Just imagine the idea of a universe where everything can be mathematically described, as well as its evolution laws. No matter whether "it exists" or not in a familiar sense, it does exist anyway in a mathematical sense, in the form of its encoding as a very big number (a string of information expressing the detailed configuration of all its parts). No matter how astronomically big this number is, it mathematically exists. Thus, so does mathematically "exist" the universe it encodes.

The problem is, this type of existence is much too large. With it, a universe in which an exact copy of myself would be walking on Mars, would be existing as well (since an encoding number for it could be defined and thus give it an existence). Morality would make no sense, as every possible state of happiness or suffering of every possible living being, would "exist" just the same, so that no initiative can help to make one of these states more "real" than another state. By the way, in such conditions, there would be no point connect someone's existence to a specific universe. Instead, each person would have copies of oneself inside astronomical numbers of universes. It would make no sense to ask "What is there on Mars" because your present existence (as a mathematical object) would be crossing multitudes of existing universes where the Mars planet would be configured differently.
There would be no problem for such a strange view of existence to be "mathematically conceivable". However, we also easily notice that some deep intimate convictions in ourselves, a feeling of our own existence, rejects that. There has not be something more to our existence, than a mathematical one. But what can this be ?

To a large extent, physical objects have a mathematical form. Can different types of existence be applicable to the same objects ? More precisely, can mathematical objects be given another type of existence than the mathematical one ?
Let's imagine this. Whatever "the cause" may be, consider that, among the too numerous universes that mathematically exist, only one or a relatively small number of them, would have the priviledge of another sort of "real existence", that others wouldn't. But... what would be making the difference between a universe that exists, and a universe that does not exist ?
Imagine this difference to come in a sort of arbitrary way, such as a magic gift from elsewhere. What might this be ? Imagine this to be a purely mathematical data. It could just be given by a formal list of existing universes (or contents of this universe) written in some divine book. Yes, but... such a divine book would be only one among an astronomical number of books that mathematically "exist" as well. Such a conventional data cannot bring any effective and more interesting type of existence than the mathematical one it had in the first place. 
Now, materialists usually assume this reality to be some physical one, that first makes the universe real disregarding the presence of conciousness inside. Then, they assume that consciousness may eventually appear in such a universe as an emergent phenomenon.

The problem is, a "physical existence" attributed to the universe, may be attributed to its most elementary particles, in the fundamental interaction processes between them, or to the universe this forms as a whole, but would have no special consideration towards any specific type of emerging phenomenon there, than to any other type of emerging phenomenon. No particular type of emerging phenomenon could have any special existence status. Instead, all emerging phenomena would be mere mathematical properties of the processes occuring there.

Even if some sort of physical existence is basically attributed to the universe, no structures emerging from mathematically predictable processes (that may include randomness) taking place there, can have any other existence than a mathematical one.

This is because the "physical existence" is only attributed to fundamental aspects of the universe, not to any emerging properties from them.
From the same mathematical laws, the same emerging processes occur in many physically inexistent universes as well. So, just imagine (or mathematically consider the existence of) a human being that only exists mathematically inside physically non-existing universes. Being determined by the same mathematical laws (at least in very good approximation), he would still strongly believe in his own existence just as we do, wouldn't he ? Still, this belief would be false. But, as our own belief in our real existence is an effect of our behavior that just follows the same laws, and this belief turns out to be mistaken "most of the time" (in all non-existing universes), what the hell could ensure this belief to be more true in our case ?
Does the question of the physical or concious existence, even have any meaning beyond mathematical existence ? Or should this very issue that there may be another type of existence than the mathematical one, be dismissed as empty, "not even wrong" ? If not, why ?

So, even though this argument may be considered subjective and not absolutely rigorouslogical argument, I cannot consider conciousness as a process emerging from complex phenomena following any mathematical laws, that would inherit its existence (and the "feeling of existence") from a physical existence.

This argument moreover confirms the first argument we presented in Part II against a mathematical determination of the mind.

Now that concious existence is accepted as a fundamental type of existence, let us examine some of its main properties.

The features of concious existence

Let us recall the main features of concious existence, and add a few complements.

The objects of this existence (the "concious objects") are more precisely concious events: perceptions, ideas, choices, feelings... No two concious events can be identical (in other words, none ever identlcally occurs more than once).
This type of existence cannot be dissociated from the concept of time.

Time is an order relationship (or preorder) between all concious events. In other words, this is a concept that specifies for any two concious events A and B, whether or not "A happens before B", and for any 3 events A, B and C, if A happens before B and B before C then A happens before C.
This relationship can also equivalently be called "B happens after A", or "A influences B" or "A is in the memory of B", "A exists for B".
In fact, all this should rather be talked about in the past: "happened". because every concious event only exists from the viewpoint of later events, and we cannot talk about events that do not exist yet.

Moreover, no event can happen both before and after another (unless they are simultaneous, which may happen of course if we have several perceptions together).

The existence of every concious event is half relative, half absolute. First it is relative, as it does not exist yet as long as it did not happen. But after it happened, its existence will remain fixed forever, and accumulates "in memory". Indeed every event has an infinite future, that does not exist yet but will come progressively to existence in its time. To say it otherwise, the future is not specified (we don't know it) before it happened. Some information about it can be more or less predictable, but predictions can't be perfectly exact.

The contents of memory can be hard to reliably check, and may eventually seem to be lost. This impression can be strong. Even in many cases, memory contents may seem to be completely lost (especially of dreams, or of past lives under an assumption of reincarnation). This means that the behaviors seem to not depend on these past events, and can be understood separately from them to an excellent approximation. However, this strong approximation is "only an appearance". Many NDE testimonies confirm that all the past contents of life remain "somewhere" in memory anyway, no matter if we seem to have forgotten them.

Moreover, here is another argument to support the idea that, though somehow hidden, the memory of the concious past keeps existing somewhere intact. Imagine it was not, and that, instead, this memory only consists of something like a computer memory that can be arbitrarily written or modified. This would especially the case in a materialist view where memory would merely consist in configurations of brain cells.
In this case, nothing would prevent external influences to rewrite or make up this memory completely. Imagine this: what if you did not really live the life you think you lived but all your body and brain with all its memory has just been built up by some superintelligent aliens 5 minutes ago. Would that be that possible ? If materialism was true, or if in any other way it was possible to arbitrarily modify or make up concious memory, then you would have no reliable evidence that anything you remember ever really happened to you.
Instead, something deep in your mind leads you to hold as an evidence that your memory can't all be faked. Then, the act of giving this intuition the status of an effective evidence as it naturally suggests, requires to admit that memory is of a sort of unalterable nature. Namely, that this memory contains the effective evidence, or we can say, the reality itself, of the remembered events.

The fact that every event is affected by the whole of its past, confirms (or contributes) that no two events can be identical (as they don't have the same past).

All these properties of concious existence appear very different from those of ordinary finite mathematical objects (but they do have strong similarities with those of infinite mathematical systems as viewed in high level works on the foundations of mathematics, and possibly also with computation theory).

The Turing test

It has been long said that metaphysics is not scientific because it is unfalsifiable.
But here is a claim expressing a good deal of metaphysics, that is clearly falsifiable, as is precisely a specification of the experiment what would falsify it :

Artificial Intelligence can never pass the Turing test

The idea of the Turing test, is to investigate the question "Can machines think like humans". This is done by trying to develop software aimed to imitate human thought. The quality of this imitation is assessed by human judges taking through computers (instant messaging) with the candidate (human or program trying to imitate human replies), and trying to guess if the replies come from a human or a program. We would say that the program passes the test if it can fool the judge into believing it is a human.

It is so falsifiable that a number of researchers are already working hard trying to refute it, with a deep conviction that they will succeed someday.
It is reported that some judges have already been fooled, mistaking computers for humans. But this is because the test has not been hard enough: too short exchange of messages, lack of imagination by judges to provide meaningful challenges. So, the claim here, is that under harder conditions of sufficiently long and imaginative conversations (for the length, say for example, 2 hours of phone conversation), the chances for machines to be mistaken as humans will remain unsignificant.

If you want other falsifiable claims expressing the same metaphysical position in other ways, here are some:
The claim that AI cannot pass the Turing test, is related to the deep natural intuition which makes solipsism unsustainable.
Namely, if it was possible to simulate human behavior by a program in a convincing way, then a person in an environment (real or virtual) showing other people's behaviors produced by this program, would have the same impresion as in the normal environment showing the real behaviors of other humans. In this case it would not be possible for someone to tell whether visible people, have anything more than a mathematical existence (as objects of computation of this program). This would make solipsism sustainable.

But if computers can't imitate humans, then the human character of other's behavior is what provides the intuitive evidence of their reality as peer conciousnesses.
Well, is it really a proof ? Such a kind of proof may sound strange. After all, it's nothing else than a set of information. How can a mere set of information, which is a mathematical object, prove anything about a non-mathematical existence ? It's because the chances to produce this information without concious means were unsignificant. Mere mathematical means would have almost surely produced irrealistic results. And, as the observer is concious and there can't be astronomical numbers of observers and tries at the disposal of the experiment, it's rather unlikely to manage producing any case of delusional impression of existence of a concious being, out of mere random or other mathematical tricks.

Let us go a little further. Admitting that the precise behavior of appearing people (in interaction with oneself) suffices to bring the evidence of their existence, as this behavior could not have been imagined by a nonconcious being. What about the possibility for a concious being to invent this behavior instead ? Indeed it could do better... at first sight.
But after a much longer interaction, the realism of this imitation would fade out. To remain fully realistic in the long run (even in the mere sense of how to fool one human observer into this impression), the author of this imitation would need to be God, and to imagine these characters so precisely, that this imagination would give these characters a real existence inside his imagination, feeling himself their feelings.

These remarks that a full knowledge of oneself (or one soul) is equivalent to a union with God, may seem to give credit to some religious and spiritual teachings promoting introspection as a way to God.

However plausible this idea may sound at first sight, we should remain very cautious, and not believe anything without proof.
The problem is, the theoretical principle that a higher form of conciousness (encompassing many individual conciousnesses into a whole) may exist, does not give any clues how to reach it, ifever any way to it really exists at our disposal. Our earthly cognitive abilities may not suffice to properly guess what such a way should look like. Any claims of such a thing must be taken with great care, and serious verifications.
Fortunately, we have more than mere guess to study the question.
If there is a way to any form of spiritual enlightenment, and if it is not too hard to make it, some people may have reached it already. But then, they should be able to bring verifiable knowledge out of this experience.
Therefore, the scientific method is fully relevant to check the validity of any such claims.
But before entering this question, let us explain the nature of the physical universe first.

The nature of the physical universe

Let's come now to examine the nature of the physical universe.

As we said, fundamental physics had great successes in the 20th century. While there are still some very difficult problems to put the known laws together into a fully consistent mathematical whole that would provide details on some of the most extreme phenomena, the laws underlying ordinary matter are now already quite well-established. Namely, the physical aspects of biological processes, starting from chemistry, and where the familiar cases of mind-matter interactions do occur, are fully expressed by quantum theory.
This theory already explains how mind-matter interaction can take place, and what status it gives to physical reality, as a composite or intermediate sort of reality between the concious and mathematical ones.

Unfortunately, many physicists with a materialist philosophical positions failed to get the message. While trying to understand it in a materialistic manner look for different interpretations of this theory, by none was satisfying. Consequently, many considered quantum theory as deeply paradoxical, or even incomprehensible.
The situation has been described by physicist John Baez as follows:

"How should we think about quantum mechanics?  For example, what is meant by a "measurement" in quantum mechanics?  Does "wavefunction collapse" actually happen as a physical process?  If so, how, and under what conditions?  If not, what happens instead?

Many physicists think these issues are settled, at least for most practical purposes.  However, some still think the last word has not been heard.  Asking about this topic in a roomful of physicists is the best way to start an argument, unless they all say "Oh no, not that again!".  There are many books to read on this subject, but most of them disagree."

On the other hand, the interpretation of quantum theory expressing the mind/body dualism (see also there) was already put forward by some of the founders of quantum theory (who are also physics Nobel Prize laureates):
"In many philosophies, the conscious mind is seen as a separate entity, existing in a realm not described by physical law. Some people claim that this idea gains support from the description of the physical world provided by quantum mechanics. Parallels between quantum mechanics and mind/body dualism were first drawn by the founders of quantum mechanics including Erwin Schrödinger, Werner Heisenberg, Wolfgang Pauli, Niels Bohr, and Eugene Wigner. (...)
Quantum mechanics made some dualist ideas about the mind/body problem acceptable again within mainstream science."

So, why has this interpretation become progressively so unpopular among physicists since the discovery of quantum physics ? One of the main reason seems to be that it has been hijacked by a number of popular authors (Quantum mysticism, New Age and New Thought movements) who mixed it with a lot of nonsense (some crackpot theories and irrationalist ideologies), while they don't even understand quantum theory themselves, in order to give their propaganda an illusion of scientific credibility. 
The situation was made even messier by the presence of some famous genuine physicists (Brian Josephson, Fritjof Capra...) who followed the same path, of promoting this interpretation of quantum theory while taking other supposedly related positions that may be dismissed as closer to crackpot or irrationalist attitudes than to science.
Other scientists came to be fed up with such nonsense even when coming from peer physicists. Thus, when trying to defend science and reason, they had to oppose these caricatural and indefensible versions of this interpretation of quantum theory and/or its supposedly associated deviations and ideologies, thus driving them to reject the original concept altogether.

So, I perfectly agree with the objection of many physicists against many spiritual writers'attitude who misuse quantum theory to support some spiritual claims while it in fact doesn't, and while no proper understanding of quantum physics is included in the argument.
Thus, in order to keep proper rationality standards, the below presentation of the relations between quantum theory and metaphysical concepts of mind/matter duality, will seek clarity, precision and conceptual minimality (abstaining from any unnecessary speculative claim), and include a simplified but mathematically accurate presentation of quantum physics, which will this way appear as less paradoxical than its reputation says.

To say very roughly, the nature of the physical existence (the deep nature of physical entities) can be defined in this way:

The physical universe is the trajectory of a visit of conciousness inside the mathematical universe.

This explains how the physical world combines a mathematical description with a non-mathematical type of existence. Conciousness visiting the mathematical world, makes a choice of which path it will visit. But this way of choosing a specific path (physical universe) does not affect the path itself (it does not make up any intrinsic difference to universes that "exist" as compared to those who don't). This "choice process" and what the physical universe consists in, is but a behavior conciousness, a matter of how concious perceptions evolve.

However, while this may seem to agree with some spiritual teachings at a fundamental level, caution should be kept on what practical consequences may result, as many fuzzy reasonings made by spiritual authors, often lead to nonsense far from reality. The fact that reality is ultimately made of thoughts, does not imply that thoughts can control reality just by the force of fancy, that all problems can be resolved just by denying their existence and multiplying pious dreams and good intentions. For example, the past cannot be changed, no matter how regrettable it is or how if we wish to cancel it.
Also, for mysterious reasons, we can notice that the commitment of conciousness to keep following the started path, is a very heavy one : our universe is very, very big, with very many living beings coming after each other and continuing the same adventure for many millions of years, as well as (probably) in many planets in the universe. This submits concious experience to heavy constraints from a complex network of influences: concious choices, mistakes, random events and diverse causalities. 

It turns out that the laws of physics are made of different concepts and theories connected together, describing different aspects of physical reality.
But more precisely, the concepts forming quantum theory, are split into two quite different conceptual layers expressing different paradigms or types of existence.

  1. The more "fundamental" layer of physics can be qualified as "purely mathematical", and is deterministic. It represents the mathematical space which is open to the visit of conciousness, offering a wide range of freedom to the visit; but it does not deal with the concept of reality as we normally understand it. It ignores any concept of a difference between a universe that exists and one that doesn't, and thus gives the same existence status to monstruous quantities of possible universes (even if we restricted considerations to those with fixed laws and values of the physical constants, as these can't vary between different parts of the same universe). It contains a mathematical model of time, but this model of time, being purely mathematical and contained in a fixed mathematical world, does not have the living essence of time. As a dead model of time without substance, it is symmetric with respect to the exchange between past and future. All the ongoing research in particle physics is dedicated to refining the details of this fundamental layer. 
  2. The upper layer of reality, on the other hand, can also be called the "metaphysical" or "thermodynamic" layer. Its speaks about the concept of reality and the uniqueness of our universe (disregarding the possible real existence of other universes...), and is time-dissymmetric. It deals with the specific manner in which conciousness can (and is likely to) proceed its visit in the mathematical world. It is non-deterministic, and apart from its non-determinism, all its properties are deduced from the "fundamental" layer of physics, by logical rules that are mysterious in principle but happen to be simple, clear and unambiguous in practice, thanks to emergent properties from quantum physics that make the effective predictions from this mysterious process independent of any choice of the precise way in which it may be parachuted. All its properties except one: its time-dissymmetry. As a dissymmetric law cannot be deduced from a symmetric one (at least not in this specific case), this dissymmetry is in fact parachuted into the laws of physics, from the fundamental time-dissymmetry of conciousness which we just described.
Let us enter the precise description of all these things.

Classical probabilities

The laws of quantum physics are fundamentally probabilistic. Thus, to understand them, we need to express probabilistic laws of evolution. The presentation will take place in two steps.

In the first step, we will develop a mathematical expression of the most general case of classical probabilistic laws of evolution for material systems, out of elementary logic.

In the second step, we will specify how quantum theory is obtained as a modification from these classical laws (how quantum probability differs from classical probability), and deduce how it explains some famous "paradoxes" of quantum physics.

Let us start with an elementary expression of the most general case of a classical probabilistic law of evolution.
Such a law is expressed in a way that conforms to the following list of features and conditions; it will apply to any material system at any other time and place, provided it is known to start inside the same list of initial states, and the amount of time Dt and the external conditions are the same:

1) We have a list A of n possible states a among which some material system at a given time t, is assumed to be; 

2) After the amount of time Dt (so, at the later time t'= t+Dt), we have another list B of m possible states b among which the system will be.

3) To every a in A and every b in B, a positive real numbers p(a,b) is assigned.

4) These numbers satisfy the condition: for every a in A, the sum of all p(a,b) among all b in B, is equal to 1.  (Thus, p(a,b) ≤1 for every a,b).

5) The number p(a,b) is the probability that the system will be in the state b at time t' in the case it happened to be in the state a at time t.

Note that the last of these features is fundamentally different from the first four: the first four are purely mathematical claims, while the last one is metaphysical. Indeed there is something irreducibly metaphysical in the very concept of probability, expressing something from the concious type of existence that cannot be reduced to purely mathematical concepts, even though it is a very incomplete account of the concious type of existence.

The metaphysical nature of the concept of probability can be seen by developing the different ideas contained in it:
Such a succession of different versions (contents) of reality along time, is a proper feature of the concious type of existence, as opposed to the mathematical one (some mathematical tools can represent some aspects of this concept but not all). From the concious type of existence, the concept of probability also inherits its dissymmetry with respect to the exchange between past and future.
You may have noted that, while purely mathematical, the above rule 4) is not symmetrical either; however, in the case of quantum physics, this condition (or what it will be come in the context of quantum theory) will be ensured by a time-symmetrical law.

Now, this concept of a probabilistic law of evolution is rather awkward, by its way of mathematically ruling the features of a non-mathematical type of existence for mathematical objects.
It may be considered coherent from a logical viewpoint, but does not fit all the non-mathematical aspects of the concious existence that it involves.
There are in fact two problems here:
  1. No mathematical law can ensure by itself the production of a concious existence. Concious perceptions can be absent from the location of the system at time t', therefore reducing the final state to a mere mathematical status, made of a superposition of the different possible states at time t', rather than as a unique state; by such superpositions, the physical system can keep evolving by itself until the final result will eventually be perceived later.
  2. It hardly means anything to say that the evolution of a given system has obeyed a given probability law. All what can precisely be checked is whether the observed final state indeed had a non-zero probability, as resulting from the initial state according to a given law. Any other claim requires to check a large number of repetitions of an experience, and to hope that the unlikely event of large deviations of statistical observations from "the true probability law" won't happen.
We shall come back to the second point later, as it provides a starting concept for parapsychology.
Now let us expand the first point further.

Probabilistic states

As a probabilistic superposition of states of a physical system can be obtained as a still unobserved outcome of a probabilistic evolution from a fixed initial state, we can consider further evolutions of the system starting from such superpositions.

Finally, probabilistic combinations of states will be considered as possible states of a physical system in their own right, aside the list of "pure states" that we initially assumed to be the possible states of the system. Then, predictions of results from these evolutions will be considered as depending on these more general cases of initial states, in a way that extends and is deducible from the probabilistic law that governed the evolution out of "pure states".

Let us represent such probabilistic states in a geometrical form, starting from the simplest cases.

The simplest interesting case is made of the combinations of 2 available "pure" states we shall denote here X and Y. Probabilistic combinations of them are represented by the real numbers p and p' which are the probabilities for the system to be respectively in the state X or Y. These numbers are positive and satisfy p+p'=1.

In the plane of coordinates (p,p'), this set of all states combining of X and Y, is represented by the points of the segment whose ends are the points (1,0) and (0,1), which can be identified as X and Y themselves (a system that has probability 1 of being in the state X, is in the state X). Any other point S of coordinates (p,p') inside this segment, is the barycenter of the two points X and Y with respective weights p and p'. In other words, for any positive numbers p and p'=1-p, if you put a ball of mass p at point X (1,0) and a ball of mass p' at point Y (0,1), then the gravity center of the whole will be at the point of coordinates (p,p').

The same constructions can be done with any higher number of pure states: with 3 states, the set of points of coordinates (p,p',p") such that all p,p' and p" are positive and p+p'+p"=1, is a triangle.  With 4 states we obtain a tetrahedron.

The general concept of a classical probabilistic state of a system, has the following properties:
Recommanded readings : Barycentric coordinate system - stochastic matrix

Now, let's come back to the evolution of a physical system, from a list A of n possible states to a list B of m possible states. How does it operate on the probabilistic states ? The numbers p(a,b) form the matrix of a linear transformation from the n-dimensional space with coordinates labeled by initial pure states, to the m-dimensional space with coordinates labeled by final pure states.
This linear transformation sends the symplex in the first space (defined by the equations: sum of coordinates = 1; all coordinates  ≥ 0) into the symplex defined the same way in the final space.

Considering the affine spaces of respective dimensions n-1 and m-1, each defined by the equation (sum of coordinates = 1) containing these simplexes, this transformation is an affine transformation from the one to the other; affine transformations are the transformations that preserve barycenters.

Let's take an example : n=m=3.
Each of this symplex is a triangle; and the evolution defines an affine transformation sending the first triangle into the second triangle. The images of vertices of the first triangle are any 3 points inside the second triangle, and determine the whole transformation. 

The justfication for the preservation of barycenters can be understood easily, as barycenters are a fundamental structure of these spaces: for any points X,Y,Z in one such probability space, no matter whether they are pure or not, any time we may need to consider a system that has respective probabilities p,p',p" to be either in state X,Y or Z, this can be summed up by saying that the state of this system is the barycenter of X,Y,Z with weights p,p',p".

Measurements

After having explained how the unobserved probabilistic evolution of systems can be geometrically expressed as a deterministic evolution of abstract points representing probabilistic states, let us now describe the expressions of concious observations of these states according to this geometric representation.

Coming back to the definitions we started with, and considering a system of n possible states, we can consider the case of a complete measurement, with n possibilities of perceptions corresponding to each of the n pure states of the system. So, if the system was in one of the n pure states then the perception would be determined with certainty; while it is undetermined with specific probabilities to give one or another result if the state of the system is not pure.
 
In practice, we usually don't have the chance to directly perceive by conciousness the state of physical systems. Instead, we use measurement apparatus that interact with the systems, then our body interacts with the measurement apparatus (or if we consider the direct vision of a system, then the eyes play the role of the measurement apparatus...). Anyway, let us assume that the measurement apparatus are convenient enough so that once the measurement on the system is made, the result will be ready for reading.

Thus we can describe the measurement process as a physical evolution from the observed system into a set of possible final states of the measurement apparatus. We already explained how physical evolution takes place. Then the convenience of the measurement apparatus consists in the fact that we can distinguish its pure states from each other with certainty (measure its state completely in the above sense). We forget for now how the measured system becomes after measurement, and will come back to it later.

This measurement result does not give much of the respective probabilities of the final states. Instead, it only specifies one of this states. What information does this give about the initial system ? It only gives a hint about the probability to have got the result we got. This can be interpreted as an indirect measurement of each of the previous intermediate states of the system during its evolution before it was measured.

This is expressed in the form of a long matrix multiplication, that gives the probability of a result as depending on the initial state:

Proba = L M E' E S
where:
S = initial state (column)
E = matrix of a first evolution of the system
E' = matrix of a second evolution of the system (any number successive evolutions can be inserted)
M = matrix of the measurement process (last evolution, into a final state of the measurement apparatus)
L = row matrix expressing the perceived result of the measurement, with one 1 and zeros, for example (0 1 0 0).

The matrix multiplication is associative:

Proba = L(M E' E S) = (L M)(E' E S) = (L M E') (E S) = (L M E' E)S

So, the observation L of the state (M E' E S) of the measurement apparatus, can be interpreted as the observation (L M) of the final state (E' E S) of the system, or as the observation (L M E') of the intermediate state (E S) of the system, or as the observation (L M E' E) of the initial state S of the system.

While the evolution determines the successive probabilistic state of any system from the past into the future, a final measurement retrospectively provides measurements of previous states.
Each linear form defined by the row matrices L, L M, L M E' and L M E' E takes values between 0 and 1 on the corresponding symplex. This is equivalent to saying that all its coefficients are between 0 and 1 (these are the respective probabilities to obtain the result starting from each pure state).

Finally, we have a sort of duality between probabilistic states and perceptions (=results of measurements), where states go forward in time while perception can be defined to apply retrospectively. While they are very different in reality, they may be somehow considered to be mathematically symmetric when exchanging the past and the future, but... it depends. More precisely, this symmetry only concerns perceptions not yet done (which are still in the future of conciousness), when it still makes sense to wonder what will be the probability of a result (because the probability of a result already obtained is 1). When a measurement is done, the result becomes past and modifies the state of the system.

Just like states, some possible perceptions are pure (with only one nonzero component), giving full information on the system, while others are impure (with several nonzero components).

This duality does not seem very symmetrical in the general case of classical probabilistic evolutions we are studying here, and has some problems.
For example, the previous states can be retroactively revised based on the final measurement (However we should be careful that these are not any concious retrocausalities, as previous perceptions remain unchanged in concious memory).
But these revised states do not naturally evolve with certainty towards this very measurement finally obtained.
However, we will see that in some aspects (but not all aspects), quantum theory is more symmetrical about this.

The concious (metaphysical) time should not be confused with the physical time. The concious concepts of "before" and "after" a measurement, mean before / after we know what is the result of the measurement, and do not always fit with the physical time when an apparatus interacts with a system to measure it. In the same way, concious perception should not be confused with physical perception defined as a measurement by physical interaction with a measuring apparatus).

Non-disturbing measurements

We first introduced impure perceptions retroactively in a way that destroys the system. But the same sort of impure perceptions can be operated by interaction with a measuring apparatus without disturbing the system. More precisely, in a way that preserves the pure states of the system (but the impure ones won't be preserved).

Consider a system with 3 possible states, and a probability state is given by its barycentric coordinates (p1,p2,p3). Let it interact with a measuring apparatus that will have the respective probabilities a,b,c to give a result "yes" while preserving the state if the system was respectively in each of the 3 pure states (and thus the respective probabilities 1-a, 1-b, 1-c to give the result "no").

What will be the state of the system after the measurement (in a concious sense) if the result is "yes" ?
The total probability to get "yes" is: p = a.p1 + b.p2 + c.p3.
Before we knew it, for each possible state, the probability to get it together with "yes" was (for each of them) a.p1, b.p2 and c.p3.
Once we know that we got "yes", the new probabilities are (a.p1/p), (b.p2/p) and (c.p3/p).

What is the effect on the triangle of probability states ? It maps it into itself, preserving it globally, and preserving each vertex, but the interior points are not fixed, as it is moved by a projective transformation.

Projective transformations are familiar to our intuition as they usually occur when a figure in a plane is viewed from space and represented in perspective in another plane, so as to appear the same when the latter plane is viewed from the right point. To specify a projective transformation, all we need is to choose the horizon line (the line that will go to infinity) in the original plane, and once it is moved to infinity, the remaining possible movements are affine transformations. 
This horizon line is the line defined by the cancellation of the denominator in the expression of the transformation. This denominator is p (the probability to get "yes").

So, the above formula of what happens to the state during the non-disturbing measurement, by the fact of finding that it gives "yes", can be described geometrically by saying that it is the only projective transformation which sends the zero probability line (a.p1 + b.p2 + c.p3 = 0) to infinity, and which preserves each of the 3 pure states.

Another characterization, is that this is the only projective transformation which preserves each of the 3 pure states (vertices of the triangle), and which moves the center of the triangle, to the point that is the barycenter of vertices with weights a,b,c.

But if we both measure and disturb the system, then this can produce any projective transformation from the triangle of initial states into the triangle of final states.

Before continuing, let us tell more about the duality between states and measurements.

In a state, the sum of coordinates is 1, while for a measurement, every coordinate is ≤ 1 and the sum can be anything but in fact it does not matter: we can multiply it all by an arbitrary positive real number,  so as to make the sum = 1 if we wish : it only changes the whole probability of having got the measurement result we got, but in the case we already got it, the information obtained on the system is the same, and only depends on the zero probability line (which remains fixed when the probability is multiplied by a constant).

So, if by mere convention we fix the sum of components of the perception = 1, then this perception can be also represented as a point of a new triangle.

This new triangle T* of perceptions, represents the set of all straight ligns outside the triangle T of states. The vertices of T*, which are the pure perceptions, represent each of the 3 edges of T (in the role of zero-probability lines), while each edge of T* represents the set of all lines meeting T at precisely one given vertex.

As the set of all possible perceptions (straight lines around a symplex) also forms a symplex, just like for states we shall call

While the evolution defines successive affine transformations for triangles T from the past into the future, the retrospective information given by a final measurement, successively defines (for the dual triangles T*), projective transformations preserving the center (from the future into the past). Because the center is the perception that does not give any information on the system, thus is equally uninformative all time long.

Correlation

Consider 2 physical systems forming together a big system.
Each pure state of the big system consists in the case when each of the subsystems is in a specified pure state. Thus, the number of possible states of whole system is the product of those of each subsystems.
All other states are combinations (barycenters) of them.

For any state of the big system, we can consider the probabilistic state of one subsystem while ignoring the other. But a measurement of the one (and knowing the result) affects the state of the other.

Every combination of states of the system is represented by a matrix, what we will call the correlation matrix where the raws and colums correspond to the pure states of each subsystem (and all coefficients are positive).

As we explained previously, matrices with positive coefficients define projective transformations from a symplex into another. The matrices of evolution we previously considered, satisfied more conditions, that forced properties on these projective transformation (being affine on the one way, preserving the center in the other way). But the correlation matrix has no more such conditions, so that the projective transformation defined by it, does not have any such further requirement to satisfy. But what does this transformation operate on ?

In fact, this is the projective transformation mapping the perceptions symplex A* of one subsystem (dual to its states symplex A), into the symplex B of states of the other: having got a perception on the one, gives an information about the other and thus modifies its (probabilistic) state (which represents what we know of it); and its transpose, maps the symplex B* of perceptions of the latter, into the symplex A of states of the former.

This transformation, maps the center of B* (the uninformative perception on the second system), into the element of A which expresses what the first system looks like while ignoring the second; and similarly when the roles of both systems are exchanged.

Thus in correlations between two or more systems, a measurement result of one affects the statistical state of all others. This change may be seen as both affecting the future of the measured system, and of the other ones, as related by going "backwards" in time, from the measurement through the past "common cause" of the states of all systems (by retrospective revisions of the initial state), and from that point then forward in time. But this is merely an interpretation: a possible mathematical representation of things where the question of "what is real" need not make much sense.

Principles of quantum theory

We can obtain the basic principles of quantum theory, from the classical probabilistic concepts we just developed, by slight modifications and specifications, as follows (you may ask "Why are things this way ?" well, we just know that they are this way because experience has confirmed it countless times) :
Indeed consider the simplest example, n=2 : any point inside the sphere can be obtained as a barycenter of 2 "pure states", that is, points one the sphere. These are the 2 intersections of the sphere with any line going through the point. You can see that any point of the sphere fits with one of these possible decompositions.

Let us focus on this case n=2 to examine how things work there in more details.

The spin 1/2

The most natural case of a physical system with "2 possible states", is the spin 1/2 of a particle. The simplest and most common example of a particle with 2 states due to its spin 1/2 is the electron, so that we will fix the discussion on it, but some other particles such as the proton (hydrogen kernel), the neutron, and some other atoms, kernels or ions, have this property too (it does not matter whether a particle is elementary or not).

What is a spin ? The first idea for describing a spin, would be that of a rotating ball that must keep rotating because of the conservation of angular momentum. However a rotating ball has too much details that an electron does not have: we can draw a mark on the ball and see it moving around; the ball may stop spinning and become at rest, or spin at different speeds.
The electron, on the other hand, has no such details: it cannot stop spinning, and has no mark on its face that can be seen moving around. Its spin state only consists in the data of its angular momentum, and thus remains constant in time as long as it is not modified by interaction with the environment (namely, by the magnetic field). For any system, the momentum can only vary by integers (to multiply by the Planck constant). The electron has only 2 possible values of the momentum, ± 1/2, thus with a difference of 1.
In order to measure the spin of an electron and getting one of both possibilities (clockwise vs. counterclockwise), we first need to choose the direction of the axis around which this spin will be measured. And the probabilities of results will of course depend on the axis chosen (as a continuous change of possible choice ending up in exchanging both ends, will of course exchange both probabilities).

Before choosing an axis, any electron's spin is naturally in some state. Like any angular momentum, it is a pseudo-vector. This means it belongs to a 3-dimensional vector space, but its representation as a vector in our space depends on a convention of orientation of space, and is reversed when we change this convention. For example, the angular momentum of the Earth can be represented by a vector towards the North pole, but a representation by a vector towards the South pole would be an equally possible convention. We just have to fix the convention once for all.

So, once this space orientation convention is fixed, the ball B of all spin states of an electron, whose surface is the sphere S of pure states, is figured by a ball in space.

Spin measurement

Let us describe measurements of this spin.
As before, each possible perception (measurement result) goes with a probability calculated as an affine function from B to real numbers, and more precisely into [0,1]. It can be any such function. So, it can be represented geometrically by the data of both parallel planes P0 and P1 where this affine function, extended to the whole space, would take the values 0 and 1 (so, outside B, and having B between them).
In the case of a binary (yes/no) measurement, the other possible perception has the complementary probability (so that the sum is 1), represented with P0 and P1 exchanging their roles.

Now that we have specified "what is to be measured" (the probabilities of measurement results as depending on the initial state), what can be the state of the system after the measurement ?

In fact, we don't know how it goes precisely for a quantum state when it is directly perceived by conciousness. What we can describe is the situation when a measuring apparatus interacts with a system, and lets the result of the measurement appear in a macroscopic way, where its description can be summed up (approximated) in the form of classical probabilities that we first presented.
The reason for caring to refer to a physical measurement process rather than a purely concious perception, is that in quantum physics there is not such a thing as a non-disturbing measurement.
All perceptions we could have of physical systems, were proceeded through physical measurement processes that disturbed the systems in a way that is precisely predicted by the theory, as an effect of the physical processes making the measurement. The final perception is done by a macroscopic observer, where the means to detect such a disturbance have become inaccessible.
But in a first time, let us ignore the details of the physical processes involved in the measurement, and just assume that they are used. They will be explained later.

Instead of a non-disturbing measurement, we have the concept of a least-disturbing measurement. Let us describe its effects geometrically, for the spin of the electron.

The simplest case is the case of a complete measurement, that is where the probability 0 and 1 planes are tangent to S at two opposite points. This measurement collapses the spin onto the point of tangency which is the only pure state having the probability 1 of giving the observed result. As the two possible measurement results collapse the spin onto 2 opposite points, this is why we say that the "number of possible states" of the spin is 2.
In fact, this collapsing effect works for any pure perception of the spin, that is, whenever P0 is tangent to the sphere, disregarding whether P1 is also tangent or not, and so collapses the spin onto the maximum probability point (opposite to the 0 probability one).

Indeed, we already explained with classical probabilities, that the meaning of a perception, and thus its effect on the state of the system, does not change if the function that gave the probability of reaching it, was multiplied by a constant.

In this sense, just like in the classical case, the set of all perceptions has the same geometrical shape (a ball) as the set of all states (and this correspondance also works for any other "number of states"). To see this, you just need to divide the probability function of a perception, by its value at the center of S, which will thus become 1 (and divide again the result by 2 if you want it to give a meaningful probability, with values in [0,1] over the sphere). In a cartesian coordinates system (for the 3-dimensional space containing the sphere), you just need to reinterpret the coefficients (a,b,c) of this function (x,y,z) -> ax+by+cz+1, as the coordinates of the perception in a space of perceptions.

In other words, a perception, as specified by its zero-probability plane outside the sphere, will be represented by the point inside the sphere, on the line from the center and orthogonal to the plane, and at a distance from the center which is the inverse of the distance of the center to the plane (if the sphere has radius 1), and on the opposite side.
This way, each perception is represented by the point where it sends the center of the sphere (the totally undetermined state) according to its least-disturbing effect.
Each pure perception is figured as the element of the sphere where it has its maximal probability, while others are figured inside it.

So, there are many other possible sorts of least-disturbing measurements: binary measurements where one possible result collapses the spin while the other doesn't; or where none does; measurements with arbitrary numbers of possible results, with arbitrary respective probability functions on B, provided that they are positive, affine, and that their sum is 1 all over B.

Now let us describe the non-collapsing case, that is where P0 is not tangent, but away from S. Then the effect is that of a projective transformation of the space that sends P0 to infinity, and globally preserves B and S : each pure state becomes another pure state.
Only two pure states remain fixed (in the least-disturbing case): those that were nearest and furthest to P0. 

(These projective transformations of the 3-dimensional space that preserve a sphere, are also those acting on the set of speeds considered as relatively to different observers according to Special Relativity theory: the elements of the sphere define the speed vectors whose length correspond to the speed of light, thus expressing the fact that going at the speed of light, is a property that does not depend on the movement of the observer that measures this speed.)

We can see here that the concept of non-perturbing measurement cannot make sense in general: not all pure states (points of the sphere) can be preserved in such a projective transformation. Only two can, and so must be specified to make sense of the "non-perturbing" claim.

Popular accounts of quantum physics mention the Heisenberg inequalities. One of these inequalities say that the position and the momentum of a particle cannot be both determined, and the more precisely one of these quantities is known, the less the other is.
What we just explained about the spin, already presents such an indetermination: it is neither possible to measure nor predict the spin of the electron along several axis at the same time.

Energy and evolution

The evolution of a physical system is determined by the energy differences between its possible states.
We will describe the situation in the case of the spin of the electron, but the same law applies to any other system as well. The explanation will be based on some concepts of classical mechanics. Many concepts of classical mechanics are no more valid in quantum theory, however some properties like those we will mention here, still apply somehow and can help to understand the situation intuitively.

The electron has a magnetic moment associated to its spin. This means that it behaves like a little magnet with the same orientation as its spin. Like any magnet, its interaction with an external magnetic field gives it a potential energy that is minimal when the magnetic moment is aligned with the magnetic field, and maximal when they are opposite. When the magnetic moment is not aligned with the magnetic field, the magnetic field exerts a torque on the magnet, which in the case of ordinary magnets pushes them towards the minimum energy configuration, aligned with the field. But the axis of the electron's spin is not like a fixed object that is turned in the way forces push to turn it. Instead, as it is defined by the angular momentum, the torque exerted by the magnetic field produce a gyroscopic precession of this spin around the direction of the magnetic field.

Now let us express the situation in the terms of quantum physics.

One of the Heisenberg inequalities says that the energy and the time cannot be both determined. Thus, whenever the energy of a system has an exact well-defined value, nothing can happen to it along time.

The spin has two possible states, and thus two possible values of the energy (when the environment is classically fixed). Each of both pure states of the spin along the direction of the magnetic field, has a well-defined value of the energy. For any other state of the spin, the energy in undetermined.
The measurement of the energy of the electron, coincides with the measurement of its spin along the direction of the magnetic field.
These two pure states of well-defined energy remain fixed in time, and give the axis of the rotation of the set B of all spin states along time.
The frequency of this rotation is proportional to the difference of energy between both possible values of the energy. This rotational movement of the spin, being also a rotation of the magnetic momentum of the electron which affects the surrounding magnetic field, generates an electromagnetic wave. This is the frequency of the photon emitted by the electron, by which it will lose its energy in the long term, and reach its state of lowest energy.
But to say this, means that we don't consider the spin of the electron as an isolated system anymore.

The photon

The quantum theory of electromagnetism is very complex with strange properties, but here we will focus on the simple case of a single photon with a well-defined frequency and propagating in a unique direction,

Like the electron, the photon has a spin, also called polarization, whose number of possible states is 2, even though the two values of its angular momentum are no more ±1/2 but ±1. Unlike the electron whose spin could be mesured along any axis in space, the spin of the photon is only defined with respect to the axis which is the direction of propagation. Still, it is possible to measure this spin along any other direction of its abstract sphere of states, but the  (below described) correspondance between these abstract directions and our usual space-time differs from the spin 1/2 case; while the angular momentum that a photon may carry with respect to other directions, takes the form of the spatial configuration of the wave (position and direction of propagation) and will not be discussed here.

We can first understand the polarization in the case of a classical electromagnetic wave: this is a transverse wave, which means that the oscillation of the electric field is perpendicular to the direction of propagation (and the magnetic field too, which at every point of space-time, coincides with the electric field turned 90° around the direction of propagation).

On the abstract sphere of states of the photon's polarization, let us mark 6 points, configured like the centers of faces of a cube containing this abstract sphere; as a cube defines a coordinates system, so these points are expressed by their 3 coordinates.
Imagine that the photon propagates horizontally, so that the oscillation of the field happens in a vertical plane.

Let us also represent in the last column of the following table, another case of a 2-states system: the two possible states of the electromagnetic field that correspond to the undetermined presence of a given circularly polarized photon.

Abstract Position Coordinates Polarization type for a photon Possibly absent circular photon
Left (-1,0,0) Linear, horizontal Electric field to the left
Right (1,0,0) Linear, vertical Electric field to the right
Front (0,-1,0) Linear, diagonal Electric field to the top
Back (0,1,0) Linear, other diagonal Electric field to the bottom
Top (0,0,1) Circular clockwise One circular photon
Bottom (0,0,-1) Circular counter-clockwise Zero photon

(The situation would be the same for the presence/absence of an electron as here with a photon, except that there is no direct measurement possible for this system in any other direction of that sphere than the presence/absence direction, in contrast with the case of the photon where such a measurement can be done in terms of the electric field. In other words, unlike the photon, it is not possible to "see" any oscillation in the electron, despite the fact that such an oscillation somehow exists relatively to some contexts such as the double-slit experiment, see below)

Note that in the case of the pssibly absent photon, the electric field oscillates circularly at the frequency usually said to be the frequency of the photon, because each of both poles of the sphere (one photon/zero photon) has a different well-defined energy, which makes the sphere of states rotate around this axis at the frequency defined by the energy difference, which is the energy of the photon.

Also note that we have a nice correspondance between the sphere of spin states of the electron precessing in the magnetic field, and the sphere of states for the undetermined presence of a photon: this is the way the electron comes down to its minimum energy level by emitting a photon and thus transferring its state to it.
We described the case of the circularly polarized photon. It is what would be emitted by the spin of the electron in the direction of the magnetic field, in the case the photon would be detected in this direction, as the rotation of the electric field follows the rotation of the spin.

But the photon is emitted in all directions, so that if we only try to detect it in one direction, we may not get it as it may be going to another direction instead. In other words, the detection of the photon in a direction is correlated to its non-detection in another direction.
So, let us consider a photon detector all around the electron, with a way out in some angular area around the direction of the magnetic field.
The fact that no photon is detected around, defines a partial measurement with respect to the initial spin state of the electron: it is the sure outcome if the electron was already in its minimal energy level, but it also has a chance to be so if it was in the maximal energy level, as the photon can go by the exit (circularly polarized). Thus this case of absence of any photon emitted in other directions, makes a physical evolution defined by a projective transformation from the initial spin state of the electron to the final state of presence/absence of the circular photon emitted in the direction of the magnetic field; this transformation maps pure states into pure states.

Or, if we don't wait enough time to let the electron come down to its minimum energy level for sure, then the presence of an emitted photon will be correlated with the remaining spin state of the electron.

Let us now examine the concept of correlation in quantum theory.

Quantum Correlations

Let us recall the description of correlation in the classical probabilistic theory:

Consider a classical n-states system, whose states space A has dimension n-1, correlated with an m-states system, whose states space B has dimension m-1.
Each correlated state is expressed by a projective transformation from the (n-1)-dimensional set A* (dual set to A) of all possible perceptions of the first system, into B; which can be equivalently expressed by a projective transformation from B* (perceptions of the second system) into A.
The set of all such correlated states had dimension nm-1, as the global system is an nm-states system.

Now with quantum theory, the situation is very similar:
An n-states system aside an m-states system, together form an mn-states system, as it is possible to distinguish there mn distinct pure states by measurements with certainty (which means that any two from such a list are clearly distinct, being 2 opposite points of the sphere of states they are forming). And distinguishing n states on the one and m states on the other, is a way to make such a distinction of nm states on the global system.

Now, the states sets A and B of these systems have respective dimensions n²-1 and m²-1. The set AB of all (correlated) states of the global system, has dimension n²m²-1. Each one is represented by a projective transformation from A* into B, or equivalently from B* into A.

Let us call classically correlated state, any state (element of AB) which can be obtained as a barycenter of a list of uncorrelated states, where an uncorrelated state is defined by a pair (a,b), of states in A and B (corresponding to the limit sort of "transformation" that collapses A* onto b and collapses B* onto a).

There are 3 differences between classical and quantum correlations:
  1. The set of projective transformations from A* to B has the same dimension n²m²-1 as AB, and AB is included there, but some of its elements (projective transformations mapping A* inside B), do not belong to AB (they do not express physically possible states of the system).
  2. The set of classically correlated states has the same dimension n²m²-1, and is included in AB, but is not all AB: some physically possible correlations cannot be obtained as a classical correlation. Bell inequalities are inequalities satisfied by all classically correlated states, but not always by other elements of AB.
  3. In particular, the set of pure states in AB has dimension 2mn-2, while its subset of uncorrelated pure states (a,b) where a is pure in A and b is pure in B, has a lower dimension, sum of the dimensions of variations of a and b: (2m-2)+(2n-2)=2m+2n-4. Thus, most pure states of AB are correlated but can't be classically correlated, because classically correlated states can't be pure.
Let us describe the simplest case of quantum correlated systems: the case n=m=2, incarnated as the spins of two electrons.


A pure correlated state naturally appears in the form of an electron pair. Indeed an electron pair is a 1-state system, thus pure. But both electrons there are together. In order to obtain a system made of two subsystems (electrons), we first need to separate both electrons from the pair. This is done by spatially introducing a separation (a wall or the like), and checking that exactly one electron is present on each side, without disturbing the system any further.

So, after the separation, we have a system made of 2 subsystems, which is in a pure correlated state. Both spins are opposite, no matter the common direction in which they will be measured.
The corresponding projective transformation from A* to B is very simple: it is the central symmetry of the sphere.

As this central symmetry maps the center into the center, the first measurement of any of these spins has probability 1/2 for each of its both possible results. And whatever is the result, the knowledge of this result collapses the state of the other electron's spin onto the opposite point.

Then, what other pure correlated spin states are there ?
An easy way is to take the one we got, and modify it by simply rotating one of the spins (by a magnetic field). This way, the possible relations we will get between the spins, will be anyone defined by the composition of a central symmetry with a rotation, so, any indirect isometry (around the center of the sphere).

More generally, all pure correlated states are represented by all projective transformations that map the sphere of pure perceptions of one spin, to the sphere of pure states of the other spin, and reversing the orientation.

We can describe their whole set as follows: the pure correlated states of spins, are those mapping the sphere of pure perceptions of the one, onto the sphere of pure states of the other, and reversing the orientation.

This reversing of the orientation is required: the projective transformations preserving the sphere but also preserving its orientation, do not define any physically possible state of spin correlation.

To understand what these transformations look like, we can study the orientation-preserving transformations instead (as both cases are exchanged by central symmetry).
These are conformal transformations of the sphere: they map circles on the sphere to other circles, because circles are the intersections of the sphere with planes in space, and projective transformations of the space map planes into planes. Those who are not isometries, are expanding some side of the sphere and shrinking the opposite side.
It is possible to understand these transformations of the sphere, by considering a sphere taken on picture in perspective, and reinterpreting the same picture of the sphere as if it was viewed from different distances to the sphere, or viewed from infinity.

Now, inside the quantum 4-states shape of all states of a system of 2 electrons'spins, let us consider its the particular 2-states sphere, of the states between (↑,↓ ) and (↓,↑). That is, all the states that have probability 1 of being "either (↑,↓ ) or (↓,↑)".
We can represent these two states (↑,↓ ) and (↓,↑) as the poles (north and south) of this sphere.  Then, what is its equator made of ?
It is made of all negative isometries of the sphere that exchange ↑ with ↓.
The central symmetry is one of them. To get all others, you just need to apply a rotation around the vertical axis. In particular, the one opposite to the central symmetry, is the reflection with respect to the horizontal plane.

Generally, any two correlated states defined by (negative) isometries of the sphere, can be completely separated by a measurement after some interaction between both spins, if an only if these two isometries differ by composition by an axial symmetry.
So, while the 4 states  (↑,↓ ), (↓,↑), (↑, ↑) and (↓,↓) are a possible set of completely distinct 4 pure states generating the whole quantum 4-states shape of all states of correlated spins, another possible list of completely distinct pure states, is made by 4 isometric correlated states differing from each other by compositions by axial symmetries around all 3 axis of a cartesian coordinates system.

Whatever the choice of such a list, the isobarycenter of these 4 states, or global center of this quantum 4-states shape, is the uncorrelated state given by the centers of each sphere of spin.
When applied to this center, any pure state has a probability 1/4 to be obtained.
In particular, the measure of presence of a pure correlated state, such as the one of central symmetry s (from a pair of electrons), has this probability 1/4.
When applied to the state defined by the transformation ks for any real number k, its probability is the affine function of k. that gives 1 for k=1 and gives 1/4 for k=0. Thus it cancels for k=-1/3 (the state -s/3, the dilation with ratio 1/3), thus a mere combination of "the 3 remaining states"), and k cannot go lower (dilations with ratios higher than 1/3 can't be reached).
(The state -s/3 can be obtained as a classical correlation too... but as the possibilities of classical correlations don't depend on the sign, they can't make a k higher than +1/3 either, so that the state s, that exists in quantum systems, is quite far from reach by classical correlations)

The failure of local realism

Let us give an example of a thought experiment (not exactly done as a real experiment, but many similar experiments have been done, so that it is expected to work as well), expressing how the predictions of quantum theory cannot be explained by ideas of classical correlation.

Imagine a pair of 2 crosses, prepared using a pure correlated state (that you can guess from the below described consequences), first attached together, oriented like x and +, so that they form a star with 8 vertices. On each of these 8 vertices is a bulb.
One experimenter keeps the + on Earth; another one takes the x with him to Mars.
Each experimenter is free to wait any amount of time, then, at any time, decide to select one of both axis of his cross (disregarding whether both experimenters do their selection of axis in either order or simultaneously; no communication is possible between them, especially if they are simultaneous, as no information can go faster than light).
As soon as each experimenter selects one axis, one and only one of both bulbs at the ends of this axis lights on.

Then, no matter whether the experimenters have any strategy or not regarding the time and choice of the axis they will select, there are 85% chances that the two vertices that light on (one on the Earth, the other on Mars) had been neighbours before separation.

If you want an "explanation" (by a classical correlation), assuming that observations are mere discoveries of a previously unknown but existing reality, then you cannot do better than a 75% probability of having neighbour vertices light on. This 75% is obtained by preparing the crosses so that the vertices that would light on if their axis is selected, were 4 consecutive ones - but we don't know which ones yet.
But a 85% chance cannot be explained in terms of an observation from a local hidden reality that was merely unknown.

This paradox contributes to the idea that, not only randomness is a fundamental physical property, but also that the measurement results that quantum theory presents as random, are not a mere consequence of a local "lottery machine", but has some hidden links to measurement results made at distance.

If there was an absolute conception of time, in the sense that among any two events there would always be one before the other, then such a strange phenomenon could be understood as follows:
The first measurement done affects the state of the whole universe, so as to influences the result of the measurement by the observer of another object correlated with the first, and thus explains the correlation.

But the theory of special relativity ensures that, as far as the laws of physics are concerns, if two events can't be connected by a signal with speed slower than or equal to the speed of light, then they are causally unrelated: it makes no absolute sense to say which one precedes the other, as it would depend on the observer calculating their respective times (in other words, simultaneity is relative). And if the one could influence the other, then the latter could influence the former as well (because the same laws apply for another observer who sees them as being in the other time order), thus leading to possible contradictions just like when trying to change the past.

So, no information can go faster than light; and the quantum correlation, while suggesting a sort of interconnectedness between distant places, does not provide any means to transmit information faster than light - as it is only a correlation, treated by quantum theory as being of the same nature as classical correlation. But that is only what the laws of physics are saying. As these laws cannot describe conciousness, this does not say whether conciousness can share information faster than light. As I don't know of any evidence for answering this, I will leave the question open.

The double-slit experiment

Let us now explain this famous experiment that expresses the strangeness of quantum physics with its wave-particle duality.

Consider a photon going towards a plate with two slits.
It may be stopped by the plate, or go through the slits.
To simplify, let us assume that the case when the photon is stopped by the plate, is detected and eliminated from consideration.

The state of the electromagnetic field in each slit, is undetermined, in between the presence and the absence of the photon. The global system of both slits, is in a pure state of correlation of the slits.
And it is located "in the middle" between both states defined by (1 photon, no photon) and (no photon, 1 photon). Let us denote C the circle of points of the sphere "in the middle" (the equator) between them (taken as poles).

We have explained what are such "equatorial" points, elements of C: they are correlated states defined by an indirect isometry between both abstract spheres of presence/absence of the photon, exchanging the presence of the photon in the one, with the absence of the photon in the other.
Therefore, both equators are just following each other. Points of these equators correspond to different orientations of the electric field. Different elements of C give different correspondances between the electric fields of both slits: they say how much delay separates their oscillations (how late is one's oscillation with respect to the other). One whole way around C, makes this time difference change up to one whole period, coming back to the initial correspondance.

The photon has been sent to the slits from one specific direction, thus specifying the element of C involved (the phase difference between the slits).

After the slits, we have a screen with many points that are sensitive to the photon. So we have a measurement with many possible results (which point of the screen will detect the photon).
Each of these results consists in the pure perception of a point of C. (The barycenter of these many points of C has to be the center of that sphere, for this to be a possible measurement.)

If we could detect which slit the photon was in (distinguish between (1 photon, no photon) and (no photon, 1 photon)), this would be a measurement along the axis of C (orthogonal in space), and would collapse the state of the system onto either (1 photon, no photon) or (no photon, 1 photon). It would no more be at its position on C. its probability of being detected by this measurement, thus as a pure perception characterized as coming from some point of C (=whose probability cancels at the opposite point), is half the probability for this point by this perception (=its maximum probability).

Further remarks on the double slit experiment

In principle, this experiment can be proceeded with any particle, however it becomes more and more difficult (sensitive to disturbance) as its mass increases. The biggest "particle" so far on which it has been made and interferences have been observed, is the fullerene (C60) molecule.

Instead of having a continuous range of possible positions of detections of the particle, corresponding to all points of C, it is possible to redesign the experience to have only two possible results, correponding to diametrically opposite positions in C. This is an experience with photons going through mirrors and semi-reflecting mirrors (I forgot the reference).
So, a photon has a probability 1/2 of going through either path; if from only one path it would have a probability 1/2 of ending in either of possible final locations; but with this way of keeping both possibilities of paths, it can only reach one destination; but if a modification is done on one of these paths to inverse its phase, this operates a 180° turn of C so that the photon can only end up to the other destination. Strange conclusion: by only affecting the path of statistically half of the photons, the destination of all photons is changed !
See also my further explanations of quantum physics in this discussion, some explanations about the wave/particle duality and the classical approximations of quantum physics by classical mechanics.

How are measurements physically proceeded (in principle)

Let us now explain how the laws of quantum physics allow measurements to be proceeded, finally reducing quantum states into classical probabilistic states at a macroscopic level.

The interaction of a 2-states system we want to observe with a measurement apparatus, will end up to produce correlated states of the system with the apparatus. 

We described above the sphere of correlated states between (↑,↓ ) and (↓,↑).
By just rotating one spin, we get a similar sphere of correlated states between (↓,↓ ) and (↑,↑), (and similarly to adapt to the chosen direction of measurement).

Assuming that the measurement apparatus was initially in a known pure state, the sphere of initial states of the system, will evolve into such a sphere of correlations, with ↓ evolving into (↓,↓ ), and ↑ into (↑,↑) (where one component represents the state of the measurement apparatus, and the other represents the state of the system after measurement).

This would operate the complete observation of the system that would collapse it into the perceived state... if we could observe the state of the measurement apparatus.
So, how to do it ? The advantage of the measurement apparatus, will be that it will let its state appear macroscopically, which means that it will will make many copies of its state in the same way. Such copies are faithful for copying the wanted classical bit of information: whatever the state we can have in the sphere of states between (↓,↓ ) and (↑,↑), ifever the first component is measured in the intended direction (↑ or ↓), then the possible result ↑for one copy will collapse the other copy to ↑ too, while the other possible result ↓ on one copy will collapse the other copy to ↓ too. And their respective probabilities properly reflect the wanted observation.

Moreover, even without the intervention of a concious observer, the mere fact of losing one of the copies away in the environment, suffices to collapse the sphere of possible initial states, by projecting it (orthogonally) onto its diameter, which represents the segment of classical probabilistic states between the 2 possible results we wanted to measure.

The cases of impure measurements, can be obtained by some other ways of mapping the sphere of the object's initial state, into a correlated state with the measurement apparatus. This is completed by the same exact copying procedure for the obtained bit of information as in the exact case.

Thermodynamics

Quantum physics, as we just described, is quite more time-symmetrical than the general case of a classical probabilistic theory. The dual properties for the transformation of the states set, of being affine and center-preserving, are both satisfied by this evolution (defined by a rotation). The physical evolution of a system can be mathematically defined as detemined both forwards and backwards in time from any specified state at a given time. Both ways are similar, and the computation of the "future of the past" (and vice versa) from any given present state, gives back the same state.

Entropy at the macroscopic level

However, in practice at the macroscopic level, we also know that many familiar physical processes are irreversible. This irreversibility is measured by a physical quantity, entropy, that is preserved and transfered (like energy) during reversible processes, but is created (and can locally decrease only by flowing away) during irreversible processes. For example, life on Earth, involving many irreversible processes, can thrive mainly thanks to the entropy evacuation process consisting in infrared radiation from Earth to outside space (to interstellar and then intergalactic space), which can thus be seen as a gigantic entropy bin. Indeed, infrared carries quite more entropy than the similar amount of energy given by sunlight, by which this energy initially arrived to the Earth. Namely, the temperature of a system is defined by the ratio energy/entropy of any small quantity of heat that can go to it or from it. In fact, a "quantity of heat" is just a mixture of energy an entropy, that can flow from a place to another, whatever the physical form, either direct contact or radiation. The radiative heat can be understood as the heat (thermic agitation) of the electromagnetic field. For example, the temperature of sunlight (its ratio energy/entropy) is the temperature of the surface of the Sun it comes from.
Heat flows from hot objects to cold ones (as hot objects emit more heat than cold ones), so that, with the same energy, this heat increases its entropy as it reaches places of lower temperature.
In fact, warmer objects emit both more energy and more entropy. In the case of an ideally black object (that absorbs the light of all wavelengths), this radiation for every temperature T is made of an energy flow proportional to T4 while the entropy flow is proportional to T3. 

Most of the entropy of the universe is made of the giant black holes at the galactic centers. This expresses the fact that the fall of matter into black holes, contributing to their growth and thus to entropy creation, is the most violently irreversible process ever.

Apart from black holes, the most dominant form of perceptible entropy in the universe (not considering the entropy of practically undetectable particles: dark matter, neutrinos, gravitons...) is made of the light (and other electromagnetic radiations) in the intergalactic space. But most of the entropy of this radiation consists in the cosmic microwave background, while all light emitted from all stars, whether or not it is cooled down through interstellar clouds, remains quite smaller, even in terms of energy, as compared to this rest from the big bang.

Let us now explain the nature of entropy, and how it is created by some irreversibile processes emerging at the macroscopic level, despite the time-symmetry of the laws of quantum physics that these irreversible processes come from at a fundamental level.

The nature of entropy

While entropy creation is not a fundamental process (as there is no irreversible process at the fundamental level), it is possible to give a definition of entropy, even for small (microscopic) systems.

The entropy of the state of a quantum system, can be expressed in successively more precise ways, as follows: In fact, there is something fuzzy and relative in the definition of entropy, as the above 3 definitions don't always agree, and these discrepancies will progressively explain how entropy can be created.

If a system is in a pure state that we know, then when measuring the system in the same direction, we know in advance what will be the result. In this case, we don't have any prior ignorance on what the result will be. The quantity of information still needed to inform about the result is empty: the entropy is zero.

In the case of a 2-states system, thus whose states set is a sphere, then the maximum possible entropy of this system is 1 bit. Because the result of a complete measurement that would be made on the system, (that would collapse it into a pure state), would take one bit (binary digit) of information.

To tell it another way, a 2-states system can store one bit of information maximum. If we store a bit there, then, as it is only interested insofar as the same information is not also stored elsewhere, then the environment does not know the value of this bit. This ignorance, if it considers both possibilities as equally likely, is a way to view the state of the system as being the center of the sphere, in between both possibilities.

However, a state that is neither pure nor in the center, has its entropy somewhere in between. So, a quantity of information can be a number of bits somewhere between zero and one bit. This happens for a bit whose two values don't have the same probability. Indeed, if you have a file of many such bits, then there is a way to compress the file that will give it a shorter average length (a most often shorter length, though there is a small risk this will make it longer).

Quantities of information can be measured for example in any basis. We are familiar with decimal expressions for numbers, while computers are familiar with bits, or byte, where 1 byte (that specifies a number among 256 = 28 possibilities) = 8 bits. As n bits can specify a possibility among N=2n, this means that a possibility among N (a number between 0 and N-1), is specified by a number n of bits that is the binary logarithm of N. But if written in a decimal form, or in any other basis, the logarithm should be taken in that other basis. So, finally, the entropy of a system that has a state among N equiprobable possiblitites, has entropy ln(N). But if the possibilities have different probabilities then the entropy is lower.

For example, consider a system that may be among 3 states with probabilities 1/2, 1/4 and 1/4.
Its entropy is 1.5 bit, because it takes one bit to specify with one bit whether it is in the first state or in either of the other 2 states, then there is a 50% chance that another bit is needed to distinguish between the last 2 states. But if the probabilities were all 1/3 then the second bit would be more likely required, hence a bigger entropy: taking account of the real probabilities of 1/3 each with a ternary digit, gives an entropy ln(3)= 1.098, while an improper representation by one bit and a half of 3 equiprobable states has entropy (1/3)ln(2)+(2/3)ln(4)= 1.155, and one bit a half in its proper case of probabilities 1/2, 1/4, 1/4 has entropy (3/2)ln(2)=1.039.

How is entropy created

While entropy creation is not a fundamental process, it happens in practice at the macroscopic scale for reasons that become more and more significant as the consideration is extended to larger and larger scales (for larger and larger systems of many particles that have large available space for their movement, which are better and better approximations of our large universe), thus with larger numbers of possible states, but can already be understood in a fuzzy sense in the case of the 2-states systems we described, in the following ways:

The origin of the time orientation

While there is no time dissymmetry in the fundamental evolution laws for the states of physical systems, the time dissymmetry that appears in the entropy creation "process", can be understood as being parachuted into physics by the "a priori conditions" that conciousness puts in the choice of which states the physical systems are in. Namely, the present state of physical systems must be assumed as fixed in a unique way by the past history (only). If the previous state of the universe (at any fixed past time) was not in some sense "completely known", then there would be "no reason" able to specify the probability for being now something than something else compatible with the observations that happened since, just as (with the inverse time orientation) there is still "no reason" why the future state of the universe will be that where this or that perceptions happened, that are given nonzero probabilities.

The entropy creation process can be roughly described as a process of evolution from a system with a number N of possible states, into a system with a much larger number N' of possible states, where the N states evolve into the space of N' states with near certainty, and are "dissolved" in it (distinctions with the other states there are no more accessible to observation in practice). But what we take the final observable system of N' states and compute the inverse evolution ? Then, for a reason of numbers, the probability to get back among the initial N states is extremely small. A still larger set of more than N' possibilities is needed, including the N first ones.
But then, how can we know from the present state in the N' set, that the past state of the system was more probably among the first N than among the others that the theory "retro-predicts" from the present observed state ?
We could say: because if it was others, then it would probably not have evolved into what it is now.
But this argument requires to assume that, inside this larger set, the previous state of the system was only possibly oriented towards "previously observable" directions, and did not have a "hidden purity" precisely designed to make it much more probably evolve towards what it is now.

These considerations seem to confirm that the reasoning which explains the thermodynamic time orientation (irreversible entropy creation), requires the assumption that the present state of the universe is completely determined by past observations.
This would mean that conciousness was already there and observed the universe since its beginning (the big bang).
However, this reasoning is not very rigorous (as it is quite metaphysical...), so its status as a "proof" remains subject to personal opinion.

To help making an informed opinion, the following scientific clues on the subject can be mentioned:
    1. the "possible entropy" (log of the total number of states into which matter might potentially evolve); 
    2. the entropy as it is (the "measure of our ignorance" on the state of the universe); 
    3. the total information that has been received from concious perceptions of matter (the "measure of our knowledge" on the universe, even if we forgot most of it).
A naive objection to the idea that the backwards evolution from a state of higher entropy (but the same energy) would correspond to a warmer big bang, is the law of energy conservation. But this law only appears as a "constant energy" in the case of an isolated systems with a fixed volume, which is not the case of the expanding universe. Here in the present universe, matter emits radiation (above the temperature of the cosmic microwave background) from nuclear energy coming from the fact that the energy of the Big Bang had largely separated protons and neutrons, putting them in the form of hydrogen and helium that can make nuclear reactions in stars. A reversed evolution from this would emit light that would increase its energy by blueshift (inverse of the cosmological redshift), giving the involved supplementary energy.

Global History

But let us now present an overview of our universal history starting from the big bang, as science could discover.
Most of this information was extracted from various Wikipedia articles (before noticing there is a short and a long summary of the history of life on Earth; something about cosmic inflation is from my familiarity with general relativity).

The Universe is about 13.75 billion years old, starting with the "Big Bang" (a period of expansion starting by initially extreme and decreasing densities and temperatures). Current theories cannot account for any exact origin of time, but give a good description of what happened after a very short time (small fraction of a second) after it.

Cosmic Inflation: the first process of observable importance, that swept away all observable traces of what could happen before. In this period, most of the (very high) energy density (or mass density, which is the same by E=mc2) was of a form characterized by a high negative pressure. This negative pressure has a gravitational effect of accelerating the universal expansion in a roughly exponential manner, according to general relativity, multiplying the size of the universe by large numbers.
(The naive idea that, without gravitation, a positive pressure accelerates expansion like in an explosion, while a negative one would slow it down, only applies to a limited system surrounded by void, with its boundaries accelerating inwards or outwards by the difference between the internal pressure and the external void; such an effect cannot apply to the big bang because of the uniformity of the universe that has no such orientation of inwards and outwards; instead, only gravitation applies, as it is not a force but a determination of the space-time curvature).
This form of energy has the property of keeping its density during expansion, rather than diluting it (just as an elastic gathers potential energy during its extension, or a bubble keeps its surface density of capillar energy while expanding; this energy needs not come from anywhere because the conservation of energy only applies locally, while the universal expansion is a global process).
The precise field/particle responsible for the inflation has not been identified yet by particle physicists; still, predictions made out of known physical principles applied to the inflation hypothesis have already been verified by different observations. This explains the approximate uniformity of the universe at the largest scales (that became too far away for causally connecting and regularizing later), and the small inhomogeneities at the origin of the large scale structures of the cosmos (collapse of matter into galaxies and galaxy clusters).
Inflation ends when all that energy converts into "ordinary" particles and forms of energy, with positive pressure (photons and speedy particles), thus slowing down again the expansion and diluting the energy density faster than the density of ordinary particles (photons lose their energy by Doppler effect, while speedy particles reduce their speed by the relativity of speed between different regions).

Big Bang nucleosynthesis. starting 3 minutes after the big bang (when the temperature was low enough to not immediately break away any composite nucleus), lasting 17 minutes (until the temperature was too low for fusion to occur - to be compared with the nearly 15 minutes of mean lifetime of free neutrons): Nuclei heavier than hydrogen formed, leaving about 1/4 th of the number of nucleons (or mass of ordinary matter if we forget other forms of energy : dark matter, photons, neutrinos, and kinetic energy) into Helium-4, while about 3/4 remained as Hydrogen-1.

Recombination (380,000 years after the big bang): The temperature of 3000 K is cool enough to let electrons and nuclei form atoms. The space becomes transparent to radiation, releasing what is now the Cosmic Microwave Background (whose temperature decreased to the current value of 2.725 K by Doppler effect during expansion). Ordinary matter at that time (hydrogen and helium) was about 4×10-22 times the mass density of water, that is about one atom per 5 mm3.

Reionization (400 million years after Big Bang). New sources of energy appear and break again atoms into nuclei and electrons, but the density is now low enough to leave the space rather transparent. These can be quasars (matter falling into galactic black holes) and/or Population III stars (very massive stars, thus with short lifetime, that were the only ones which could be formed first, in the absence of the heavy atoms).

Oldest known star of the Milky Way: 13.2 billion years ago (500 million years after the Big Bang).

Globular clusters formed about 12.7 billion years ago (1 billion years after the big bang).

Thin Disk of the Milky Way (8.8 ± 1.7 billion years ago)

Formation of the Solar System began 4.57 billion years ago, from a big molecular cloud, after one or more massive star(s), with thus short lifetime, first formed and exploded in supernovae, giving heavy elements and compressing the region of the cloud, making possible the creation of the solar system.

Moon's formation 4.527 ± 0.010 billion years ago, probably by a giant impact between the Earth and a Mars-size planet, that also inclined the rotation axis of the Earth and gave the Earth a very fast rotation (a day of 6 hours instead of 24). This rotation later slowed down by transmission to the Moon's orbit (initially close to the Earth) through tidal interaction.

Late Heavy Bombardment: period of intense meteorite impacts (began about 4.1 Ga, and concluded around 3.8 Ga). From Wikipedia: "no consensus yet exists as to its cause. One popular theory postulates that the gas giant planets migrated in orbit at this time, causing objects in the asteroid belt and/or Kuiper belt to be put onto eccentric orbits that reached the terrestrial planets.

Note that the Sun's luminosity progressively increases in time. It is now 30% brighter than it previously was. This needs to be balanced by other processes, mainly a decrease of atmospheric concentrations of CO2 and other greenhouse gases (which were initially abundant), to make it possible for water to keep existing in liquid form meanwhile. This will mainly take place in 2 ways: deposit of calcium carbonate (CaCO3) in the oceans, and photosynthesis.

Last universal common ancestor between all current living forms on Earth (Bacteria, Archaeas, animals and plants; except viruses): some 3.5 to 3.8 billion years ago

Photosynthesis started about 3.5 billion years ago

Cyanobacteria making oxygenic photosynthesis (producing O2), may have appeared 3 billion years ago (or between 2.8 and 3.7 billion years ago).

Great Oxygenation Event (2.4 billion years ago): The oxygen produced by cyanobacteria, could finally remain in the atmosphere, after organic matter and dissolved iron were saturated and could no more capture it. This resulted in a massive extinction of anaerobic organisms for which oxygen was toxic; but also in the appearance of an ozone layer that would open the possibility for life outside the ocean; and the possibility to get more energy for organisms able to use O2 in their metabolism.

Huronian glaciation (2.4 to 2.1 billion years ago): the Earth was covered with ice, which may be due to the disappearing of methane (consumed with oxygen).

Eukariotic cells appeared 1.7-2 billion years ago by integrating bacteria that could use O2 for metabolism, in the role of mitochondria.

First multicellular organisms (1 billion years ago) while the lineages of animals, fungi and plants were separated; molecular evidence suggests that fungi colonized land at that time (while procariotes had done it already around 2.6 billion years ago). Plants started photosynthesis by integrating cyanobacteria in the role of chloroplasts.

(Ma = million years ago)

More Snowball Earth periods (intense glaciations) would have occured around the times of 750, 710 and 640 Ma

Cambrian explosion : life seemed to complexify a lot around 530 Ma. This would include the development of complex eyes, shells, skeletons (with the emergence of vertebrates) and exoskeletons - unless these were what made possible a better preservation of fossils, that our ability to detect the presence of life diversity depends on. The earliest fossil crustaceans date from about 513 million years ago

Oldest fossils of land fungi and plants date to 480–460 Ma

Arthropods on land around 530-450 Ma. (Arthropods were well pre-adapted to colonize land, because their existing jointed exoskeletons provided protection against desiccation, support against gravity and a means of locomotion that was not dependent on water).

Ordovician–Silurian extinction event (End Ordovician or O-S) (450-440 Ma, at the Ordovician-Silurian transition). Two events occurred that killed off 27% of all families and 57% of all genera.[6] Together they are ranked by many scientists as the second largest of the five major extinctions in Earth's history in terms of percentage of genera that went extinct.

The first tetrapods evolved from fish (380 to 375 Ma)

Late Devonian extinction (360-375 Ma) near the Devonian-Carboniferous transition. A prolonged series of extinctions eliminated about 19% of all families, 50% of all genera[6] and 70% of all species.

Plants evolved seeds (360 Ma) which dramatically accelerated their spread on land.

The Karoo Ice Age (360 to 260 Ma, named after the glacial tills found in the Karoo region of South Africa where evidence for this ice age was first clearly identified). The Earth during this time was covered with an immense degree of vegetation compared to earlier times, causing a long term increase in planetary oxygen levels and reduction of CO2 levels that resulted in this ice age.

The amniotic egg evolved (340 Ma), which could be laid on land, giving a survival advantage to tetrapod embryos. This resulted in the divergence of amniotes (most terrestrial vertebrates) from amphibians.

Divergence of amniotes, between the Synapsids (ancestors of mammals, also called "mammal-like repliles"), which started to dominate, and the Sauropsids (other reptiles) 310 Ma.

Supercontinent Pangea formed 300 Ma (?) (after a long story of continental drifts alternating supercontinents and separations of continents).

Sauropsids split: as for those still existing today, the ancestors of turtoises diverged first, then quite later (at the end of the Permian period) came a split between Lepidosauromorpha (ancestors of lizards and snakes) and archosaurs.

Marine reptiles from different origins started developing and will take an important place until the Cretaceous extinction (65 Ma).

Permian–Triassic extinction event (End Permian - 250 Ma at the Permian-Triassic transition). Earth's largest extinction killed 57% of all families and 83% of all genera (53% of marine families, 84% of marine genera, about 96% of all marine species and an estimated 70% of land species). On land, it ended the primacy of Synapsids. The cause of this extinction remains unclear.

Archosaurs split soon after, between  Avemetatarsalia (ancestors of pterosaurs and dinosaurs, and thus of birds) and Crurotarsi (ancestors of crocodiles).

Dinosaurs (230 Ma) appeared by diverging from other Archosaurs.

Pterosaurs (220 Ma), earliest vertebrates known to have evolved powered flight, appeared. Pterosaur fossils have been found on every continent. At least 60 genera of pterosaurs have been found to date, ranging from the size of a small bird to wingspans in excess of 10 metres (33 ft).

Triassic–Jurassic extinction event (End Triassic) - 205 Ma at the Triassic-Jurassic transition. About 23% of all families and 48% of all genera (20% of marine families and 55% of marine genera) went extinct. Many of the dinosaurs were spared and soon became dominant among the vertebrates, as most of the other groups of early archosaurs (like aetosaurs, ornithosuchids, phytosaurs, and rauisuchians) were killed. These losses left behind a land fauna mainly made of crocodylomorphs, dinosaurs, mammals, pterosaurians, and turtles.  Mammalian were small, but their lines began to separate.

Pangaea broke up (180 - 200 Ma) into Laurasia on the north, and Gondwana on the south. 

Gondwana broke up (167 Ma) into East Gondwana and West Gondwana.

Archaeopteryx, a dinosaur traditionally considered one of the first birds (probably close to their ancestors but not among them), lived around 150 Ma

Flowering plants : first evidence to 132 Ma

Eutherians (ancestors of placental mammals, which is the main branch of mammals) diverged from metatherians (ancestors of marsupials), while prototherians (ancestors of monotremes) had already diverged before. The earliest known fossil eutherian, was found in Asia, and is dated to about 125 Ma.

Confuciusornis (125 to 120 Ma) is a genus of primitive crow-sized birds, more advanced than Archaeopteryx (same remark).

West Gondwana split (130 - 110 Ma) into South America and Africa, opening the South Atlantic Ocean
East Gondwana split between (India-Madagascar-Seychelles) that began to move northward, and (Australia-Antarctica-New Zealand), but some connections with Africa will still exist later.

Later, competition with birds drove many pterosaurs to extinction and the dinosaurs were probably already in decline, when came:

Cretaceous–Tertiary extinction event (End Cretaceous or K-T extinction, 65 Ma), which may have been caused by the impactor that created Chicxulub Crater on the Yucatán Peninsula. About 17% of all families, 50% of all genera and 75% of species went extinct, including Pterosaurs, all non-avian dinosaurs, most avian dinosaurs, and many other animals.
This left the space for mammals to diversify and grow larger.

Last common ancestor of primates: 63 Ma, as Strepsirrhini (which are the only primates of Madagascar, also present in South-East Asia and Africa) split from the main branch.

Laurasia split (about 60 Ma), separating Eurasia from (Greenland + North America).

Indian plate collided with Asia (45 Ma) while Australia separated from Antarctica

Split between humans and chimpanzees at 5 or 7 Ma

The Quaternary glaciation, or current ice age, marked the start of the Quaternary period, about 2.58 million years ago when the spread of ice sheets in the Northern Hemisphere began. Since then, the world has seen cycles of glaciation with ice sheets advancing and retreating on 40,000- and 100,000-year time scales.

Homo genus appeared then (while the ancestors of the common chimpanzee and the bonobo split from each other).

Quaternary extinction and Holocene extinction: the Quaternary period saw the extinctions of numerous predominantly larger species (megafauna), many of which occurred during the transition from the Pleistocene to the Holocene epoch (around 12,000 years ago). Among the main causes hypothesized by paleontologists are natural climate change and overkill by humans.

Homo erectus migrated from Africa around 2.0 million years ago, and dispersed throughout much of the Old World, especially in Asia, until they probably went extinct about 70,000 years ago.

Homo neanderthalensis lived in Europe from about 400,000 to 30,000 years ago. They were strong hunters, mainly (but not completely) carnivorous, thus more depending on fauna for their subsistence than homo sapiens.

The last glacial period (most recent glacial period within the current ice age) started approximately 110,000 years ago.

The Toba supereruption occurred between 69,000 and 77,000 years ago at Lake Toba (Sumatra, Indonesia), and it is recognized as one of the earth's largest known eruptions. This supervolcanic event may have plunged the planet into a 6-to-10-year volcanic winter

A bottleneck in human evolution probably resulted from this eruption. The homo sapiens population was reduced to a group of 10,000 or even a mere 1,000 breeding pairs in East Africa. An important final step of the cultural development of homo sapiens, as seen in the more sophisticated technology and artwork, happened in that period (between 100,000 and 50,000 years ago).

Homo sapiens conquered the world in several waves quickly after this bottleneck, causing an extinction of Neanderthals on their way (except for a little interbreeding between roughly 80,000 and 50,000 years ago in the Middle East, resulting in 1–4% of the genome of people from Eurasia having been contributed by Neanderthals).

End of the last glacial period 10,000 years ago.

Parapsychological issues and paradoxes

The problem of evil : what's wrong with the universe

When studying the universe in its different aspects, we face a problem:

When considering the first principles of existence,  it all looks like the universe should be deeply good, and that everything should be wonderful there.

However, experience shows that many things there are going wrong, many people suffer, many people are in deep error, and many crimes and abuses are made and profitable.
If we just try to imagine how things should be just by pure thoughts, reasonings, we can make some deductions on what to expect about things. Namely, that the world should be fair, joyful and harmonious. But these expectations do not fit observations.

So we are in a strange universe where first principles cannot properly explain some important observations. Can they ?

If theory and experience seem to contradict at first sight, then we need to examine each in more details, and check every seemingly contradicting argument and observation in all their aspects one by one, to separate the true from the false everywhere. If it is not very carefully, then contradictions should vanish, because... the universe is real and the truth cannot contradict itself.

But this will turn out to be quite hard, and even more paradoxical than could be expected at first sight.

As there are problems that not all is going well in the universe, then we do need to understand exactly what is going wrong and why, and what solutions can be found.
Just pretending that things are going right would not help.
A general trend among "spiritual people" is to view things in such ways that it makes them feel good by insisting that, according to them, some kinds of things would be going well. In such a way, they reject the cause of troubles onto some other aspects of things, that they are less disturbed to see as going wrong.

Their motivation for interpreting the causes of troubles as coming from something rather than something else, can have several causes:

It can be feelings; but this is only a subjective feeling that makes them more sensitive to something than something else, so that they feel better by seeing the causes of troubles as coming from something than something else. But other people's sensitivity can be oriented otherwise, so that a view that better satisfies someone may make someone else feel worse. For example, some people like to imagine that God makes things good and that troubles come from people's bad hearts or bad actions. This can help bring them good feelings towards God, but also be quite unfair and insulting towards their fellow humans (and even sometimes to themselves).

But it can also be some sort of logic and reasoning, as it seems, so as to make their worldview coherent enough to their satisfaction of having the impression that they understand the world rather well.

In principle, logic and reasoning cannot contradict reality. The problem comes with naive and approximate reasoning, of a kind that satisfies many people and seems logical to them, but that would not stand careful scrutinity, and whose conclusions can happen to be refuted by more careful research (reasonings and observations).

Ultimately, what is needed and good, is not to believe something something rather than something else just because it feels well, or because it helps to praise God. Rather, it is to objectively check and understand more precisely how things are, so as to not make mistakes about how to help solve problems, and to not making any innocent person feel guilty for having done the right thing just because such false accusations would help some other people to feel good.

Let us start with a famous example of a debate:

Darwinism vs. Creationism or Intelligent Design

Are the laws of physics fine-tuned for life ?

A natural guess, when considering that the universe is ultimately created by and made of conciousness, is that it would be fine-tuned and designed for life.
So we have to examine this guess.

Let us start the consideration with the laws of physics. They form very remarkable and wonderful theories indeed, so that it would be quite hard to imagine a universe made of more elegant laws. But these laws are formed with a number of seemingly arbitrary choices of structures among other conceivable possibilities, as well as a list of seemingly arbitrary constants, for which we currently have no explanations.

How well-designed for life is that ?

A first parameter to consider (so obvious that some forget it) is the number of dimensions: we are in a space-time with 4 dimensions, divided into 3 space dimensions and 1 time dimension, together forming a Minkowski space that is very similar to Euclidean geometry (making time be somehow like space, despite the fact that it does not feel so in everyday experience).
The fact there is only 1 time dimension, is required by the properties of concious existence, that we previously described.
But, why does our space have 3 dimensions, rather than another number ?
In fact, roughly the same laws of physics (general relativity and quantum physics) could apply to space-times with other numbers of space dimensions (and even with other numbers of time dimensions). However, these would not be suitable for life by any similar means to those that we are familiar with:
What about other parameters in the laws of physics, which seem arbitrary ? Some authors have claimed that they would be remarkably fine-tuned for life. Victor Stenger disagreed. Precisely, he considered how would a universe behave with other values of the main physical constants in some range around their value in our universe, and found that such variants could be suitable for life as well (if the modifications of the constants are "not big"). But someone replied. Let us leave this debate to specialists... (random example of debate on the subject)

The scientific consensus for natural evolution

Now admitting the laws of physics with all its constants as fixed, what about the emergence and evolution of life: has the evolution of live been guided in a concious manner, with some plan on where it is going ?
This is a serious question, where purely philosophical expectations would lead to see it as highly plausible.

So, in terms of pure thinking and expectations, the idea of intelligent design could have been a plausible idea. However, this idea has to be compared to observational evidence.
A lot of evidence on how life evolved, has been gathered by biologists and paleontologists.

From this evidence, a large consensus has emerged among them, that the genetic evolution of life has all the characteristics of being the result of blind natural selection processes, with no observed significant trace of remarkable guidance from a mysterious origin (not to speak about young-Earth creationist views that have no plausibility at all - as Christian preachers once had trouble trying to evangelize the Chinese who had an older record of ancient history than the creation time claimed by the Bible).

References:

Statement of the scientific consensus by the American Anthropological Association

Level of support for evolution

"99.9 percent of scientists accept evolution".
the scientific community considers intelligent design, a neo-creationist offshoot, to be unscientific,pseudoscience, or junk science
...
a coalition representing more than 70,000 Australian scientists and science teachers issued a statement saying "intelligent design is not science" and calling on "all schools not to teach Intelligent Design (ID) as science, because it fails to qualify on every count as a scientific theory"

The same article mentions a variable level of support for evolution among religions.
There has even been official support for evolution by religious bodies:

According to V. Stenger (physicist and skeptic)
"Only abysmal self-complacency can see in Man a reason which Omniscience could consider adequate as a motive for the Creator. The Copernican revolution will not have done its work until it has taught men more modesty than is to be found among those who think Man sufficient evidence of Cosmic Purpose."

Misconception of science :"Scientists Have an Atheist Agenda"
"Just because no scientific study has indicated the presence or need for a deity in the universe does not mean that this was the intent of the work. It may be true scientific study in general has the overwhelming lack of indication that the universe has any outside influence, but that does not mean that is what scientists wanted to believe."

Searching for the Watchmaker

The difficulties debating the subject - scientific illiteracy problems

I recently saw a Christian Web site (I guess there may be many like this) speaking about science, and trying to argue that Intelligent Design would be a scientific position, while Darwinism would be non-scientific.

That site tried to explain that Intelligent Design would be falsifiable while Darwinism would not.
How funny.
I happened to hear from Christians at some times a number of claims against Darwinism (even made with a tone of mockery against Darwinism) arguing about the Missing Links (e.g claiming that no intermediate forms between apes and humans could be found), or that some complex organs such as eyes are so "well-designed" with all parts necessary for the working of the whole, so that it could not have appeared by mere chance and natural selection.
Such claims are so well falsifiable, indeed, that they have already been fully refuted, for example by the discovery of explicit explanations of the evolutionary development of the eye step by step, with each step being selected as it brings a better ability.

The consensus of the scientific community for natural evolution, is remarkable in front of oppositions by otherwise dominating ideologies, not only on the right but also on the left (but these "right" and left" sides can be understood as similar religions taking the same side of the real opposition, that is the side of feelings and a priori value judgements against reason, and the side of popular stupidity against intelligence).

It would be rather pointless to try to answer all anti-darwinist arguments in much details. Who do they think they are ? Do they claim to teach scientists about what is science ? Do they think that 99.9% of biologists are ignorant about their own field or about what is science ? Who are they trying to convince ? If such a few pages made of a couple of childish "arguments" will succeed to confort their ignorant Christian readers in their feelings and desires to believe that Darwinism is stupid and that their faith in Jesus makes them much more clever scientists than the professional ones, can this "success" ever have anything to do with the truth ?
(see also about the fundamental misconception "Scientists Are Arrogant, But They Can’t Know Everything")

Seriously, whatever may be their arguments or what I would try to answer, would not change the very heavy trend of what emerged from the huge amount of observational evidence in biology: that, given the available evidence, the only rational position that can resist is the Darwinian position, while Intelligent Design happens to be an irrational position, in the sense that to persist giving it any credit (as many ignorant people do) against the available evidence, happens to require quite irrational attitudes.

But no matter the refutations, anti-darwinists carefully keep ignoring the experience of how often their claims happened to be refuted, and keep claiming to make much wiser predictions on future discoveries than scientists.

In fact, the continuing public opposition to Darwinism is mainly based on a great deal of ignorance of the existing evidence: (from wikipedia)
A 1997 study found that fewer than 20% of Americans possessed basic scientific literacy and a People for the American Way poll found that less than half (48%) of those polled chose the correct definition of evolution from a list. In 2006, New Scientist reported that almost 2/3 of Americans believe they share less than half their genes with "monkeys", when in fact the figure is between 95–99% depending on the primate and comparison method

Thus, a majority of very ignorant people who politically support (through the Republican Party...) an educational system marked by scientific illiteracy, as well as a litterature with some complelety indefensible pseudo-scientific claims that conveniently give an illusion of scientific credibility for their religious creeds, suffices to explain the social persistence of this nonsense, disconnected from all existing evidence.

But to those who still think they would have arguments against Darwinism...this is a too big and hard subject for making it possible to give here a significant account of all the arguments that can be said. A summarized presentation may not be able to give it justice, while anti-scientific propaganda may be the strongest.

As reported here (about attempts by proponents of intelligent design, at inserting "critical analysis" of evolution in some curriculum, but in a way that perverts the debate):
" The good feelings didn't last long. Early this year, a board-appointed committee unveiled sample lessons that laid out the kind of evolution questions students should debate. The models appeared to lift their examples from Wells' book Icons of Evolution. "When I first saw it, I was speechless," says Princehouse.(...)
After months of uproar, the most obvious Icons-inspired lessons were removed. But scientists remain furious. "The ones they left in are still arguments for special creation - but you'd have to know the literature to understand what they are saying. They've used so much technical jargon that anybody who doesn't know a whole lot of evolutionary biology looks at it and says 'It sounds scientific to me, what's the matter with it?'" says Princehouse. "As a friend of mine said, it takes a half a second for a baby to throw up all over your sweater. It takes hours to get it clean." "

However, let's try.

The evidence from poor design

Moreover, it even happens that our eyes are not as well-designed as they could be, as there does exist other animals with better designed eyes than our own: Octopus has better designed eyes than vertebrates, and Mammals have lost the tetrachromatic vision, which other terrestrial vertebrates (birds, reptiles...) inherited from the first tetrapods.
Also, a large part of the genome in humans and many other organisms, is made of a lot of wasteful copies of the same genes whose only function is to multiply the number of their copies inside this genome (or otherwise promote itself during reproduction) - a property which is considered to have been inherited from some primitive virus that settled in its host durably in early evolutionary times.

Some more examples of bad designs (among many other possible examples) are in the Argument from poor design page (against the existence of God).
Other examples are given by the many cases of extinct species: what were they designed for ? Were they designed for extinction ?

The evidence from human-driven evolution

In fact, it's not very difficult to debunk the main naive thesis put forward by opponents of evolution, that consists in disbelieving the theoretical possbility for all those "wonderful" complex functionalities in living organisms, to have emerged out of mere random mutations and natural selection. Somehow we may consider this question to be a "purely mathematical" question, as it is mathematically rather well-defined (except for the concious behavior of animals, which can be driven out of the equation by restricting the consideration to the evolution of plants), but of course the difficulty is its astronomic complexity, as it involves the processes occuring all over the planet during about 1 billion years, which is most probably too big even for the most powerful of our supercalculators to simulate. Without the possibility of effectively operating such a simulation, different people might keep diverse and opposite convictions according to their personal feelings (intuitions) about "what the rational view must be", each one considering one's own view as the reasonable one, and dismissing the opposite view as blind faith, but with no easy objective way to decide whose intuition is right.
However we do have some hints out of experience. The accessible experience is not as big as the whole history of life, but it is already significant. I want to point out the experience of the documented evolution of species that occured under the human control since humans took over the planet, especially agricultural species and pets (to not speak about the extinction of many species exterminated by humans for different reasons - species that God designed for being finally exterminated, probably). Examples among many others: yellow bananas appeared in the 19th century and need human intervention to survive because they have no seeds; dogs evolved into quite diverse races under the human control after a common origin; bacteria developed resistance to antibiotics... Improvements are even perceptible during a farmer's lifetime (which is why they bother caring about selecting their animals).

Very important positive changes occured by natural mutation with just an artificial selection by human control.
Would anyone claim that this evolution was mysterious, beyond explanation, and requiring some supernatural intervention ? Hardly so. Mutations were natural; humans did not choose them. These species had a much longer evolution, before being domesticated, where they were not a priori designed for humans. It is the hand of man operating the selection, that changed them into this "design" (for human convenience; or inconvenience, in the case of bacteria).
This happened in a very short time (centuries, millenia or tenths of millenia...) relatively to the history of life (hundreds of million years): less than 1/1000 of it.

Thus, why the hell should we dismiss the plausibility for natural selection to have driven evolution towards the many complex useful features for survival that we observe, considering it had over 1000 times more time for this, than the already dramatic evolution towards human convenience which we admit to have been the natural consequence of human selection over natural mutations ?

The convenience of scientific research ?

Admittedly, there are other viewpoints about why to see Intelligent Design as an irrational idea.

For example, this argument against Intelligent Design. states the following point among others:

"Yet it's fundamental to the philosophy of intelligent design: I don't know what this is. I don't know how it works. It's too complicated for me to figure out. It's too complicated for any human being to figure out. So it must be the product of a higher intelligence(...) How presumptuous it would be for me to claim that if I can't solve a problem, neither can any other person who has ever lived or who will ever be born.
Science is a philosophy of discovery. Intelligent design is a philosophy of ignorance. You cannot build a program of discovery on the assumption that nobody is smart enough to figure out the answer to a problem. "

Indeed it could have been much more problematic to develop scientific research and knowledge on how life could develop on the Earth if the evolutionary process received an important deal of influence from supernatural intervention.
Fortunately for scientists (and very unfortunately for the very many miserable lives of animals that had a hard time during this long and painful evolutionary process), this is not the case.

Natural evolution and the mind-matter duality

Not a spiritual evolution

A common misunderstanding of natural evolution among spiritual people, is to interpret it as similar to or identified with some idea of "spiritual evolution". Namely, something that would feel like an educational process, an adventure of discovering, experiencing, taking lessons and choosing to change one's behavior out of lessons learned.

Somehow, we might indeed make such a parallel, and notice that it indeed behaves this way. However, this is only valid in a very metaphorical sense. Just an abstract mathematical comparison, which has some operational status of a comparison in the eyes of mathematicans and other scientists. However, this comparison would fatally become a disastrous misunderstanding when reaching the minds of spiritual people, because the very concept of what is a similarity, has a very different meaning to them than to scientists.
This misunderstanding comes from the fact that spiritual people approach any concept in an essentialist framework, in terms of how it feels and what it is ultimately made of; while scientists approach concepts in non-essentialist, structural terms.

Namely, natural (or artificial) selection, is a mere material process only "educating" the NDA, and has no f***ing care for the souls (feelings and wishes) of the individuals at stakes.
For example, if along centuries, pigs grow fatter, and cows evolve into having bigger and bigger udders that give more and more milk, it's not because cows are following a spiritual educative path towards a better self-fulfilment (nor even towards a higher empathy for humans) where they discover that having a bigger udder makes them feel better, but because the selection process that is forced upon them from the outside, happens to preferably reproduce this feature.

Immaterial souls neither require nor produce intelligent design

Now that we presented both the defense of mind-matter duality and darwinan evolution without intelligent design, this combination will seem odd to many readers, as few are the authors that promoted it. And I admit that it also sounds odd to me.
Still, careful consideration shows no direct contradiction between these claims.

As has been observed in Near Death Experiences and other paranormal experiences, it is possible for our mind as well as other spiritual entities, to visit this universe (and also leave it) without any material support such as a brain. Therefore, there is no reason to think that conciousness ever had to wait for the emergence of humans (or other animals of importance) for being here to observe the development of life and interact with it. This possiblity does not oblige conciousness, that was here and eventually incarned into biological organisms, to have any well-designed, long-term plans on where this evolution would be all heading.

Indeed: we don't have ourself any long-term plans about where life will be heading in the next hundreds of million years, and we are not dedicating our concious efforts on this issue by any means. And anyway, having such plans would be pointless, because... the future does not exist yet, and cannot be predicted with certainty. But for the same reason, why should (and how could) the actions of concious beings on Earth in the previous hundreds of million years ago, have cared for us by any means ? They didn't.

Once admitted that the incarnation of souls in biological organisms along evolution does not necessarily produce traces of intelligent design in the many generic characters for health and ability that have been studied, what about the development of the brain that governs this mind-matter duality itself: did it require any intelligent design, or could it be produced by blind darwinian evolution too ?

I think, there is no problem either for blind darwinian evolution to have produced these opportunities of mind-matter interaction with their observed characteristics.
First, because there is no problem to imagine that nervous systems could develop based on their selective advantage even with no soul incarned; while souls passing by could occasionally play with the quantum indetermination of the behavior of these system, as a primitive form of incarnation
Second, because there are a number of indications (from "spiritual healings") that the mind can directly interact with and affect some biological systems other than nervous systems.

So, there is no problem to imagine that some primitive forms of incarnations of souls in biological organisms could start at some time in the ancient history of life on Earth, with organisms that could work (survive and reproduce) by themselves but that souls may occasionally influence.
Some species may have developed characteristics where this interaction took more and more importance in the behavior of these organisms, and where it could have provided a selective advantage.
Souls there could have started to play the game of taking part in such interactions, just because it was a funny adventure to guide these organisms to their survival.
We have explained that conciousness has unique abilities to behave in some sort of creative, intelligent ways that cannot be imitated by mere mathematical calculations (which organisms with a nervous system but no souls could be able of). This explains how interactions with souls can give organisms a decisive selective advantage over other organisms that would not host any souls.

Progressively, natural selection favored the characteristics of this mind-matter interaction such that the mind became "enclosed" in the body, attached to it with hardly any means to get out of it or travel outside it, and thus with the impression of being identified with this body. This is because this is the way to oblige the soul to be most careful about protecting the survival and reproductive interest of the body, in a merciless jungle where characters of universal selflessness (or abilities to "leave the battle" by curiosity for visiting something else) would defeat the reproductive advantage of the bodies that would have them.

Now if you ask: which are the organisms that host souls ? Well, I don't know. I guess that all vertebrates do, but I can't tell about the case of insects and other arthropods. So what ? Rational thinking does not consist in pretending to have answers to every question.
Still if I really had to make a guess whether insects have a soul or not, I would say yes, for the following reason. When I was a child, I sometimes happened to play with a fly, pulling its legs and wings apart. And you know what ? I felt bad at doing so.

Darwinian selection may be seen as a form of empirical method for developing complex structures able to cope with a huge lot of many situations that may happen, both to the body and to the soul, and which could hardly have been predicted in avance by pure theory - even if can be deplored as so wasteful.

However, there is another aspect of the situation, which makes the combination of mind-matter duality and absence of intelligent design, more heavily paradoxical.

The problem is that, it would not even require any grand visionary plans, nor any wonderful miracle, for a higher power (God, or the community of spirits not currently incarned, or anything like this) to push the evolution forwards to the greater good, in a way that would generate effective traces of intelligent design in the evolution of life on Earth.
All it would take from such a higher power, is a combination of common sense, elementary observations, discipline and morality, such as we humans are already largely capable of.

The method would simply consist, for souls considering to find incarnations in embryos, in "boycotting" the organisms with clear genetic defects, while judging these defects on the clearly visible troubles of health or behavior resulting from them - whatever the way these troubles may be assessed. This would give a boost to evolution, by completing natural selection with a sort of intelligent selection. Even if it was not very intelligent, it could already have effects.

If such things happened, they should be observable, not only by their results as faster evolutionary progress in the ancient past than could be naturalistically expected, but also as still happening now. There should be many cases of sterility or miscarriage correlated with circumstances that would justify them on moral grounds. This should particularly happen in cases of overpopulation, so as to prevent the risks of environmental crisis that overpopulation could generate.

But this not what we observe. No such correlation between sterility (or miscarriage) and any visible, justifiable circumstances could be observed. Genetic defects keep spreading. Overpopulation happens unstopped, the same with humans as with animals that reproduce so quickly that they devastate their environment and all end up in starvation. Bad people and criminals have no less children (that often inherit these bad behaviors) than good people.

So many things happen as if the universe was governed by blind natural forces with no influence from any concious intelligence. But, is everything really natural ?

Skeptics and paranormal phenomena

The question of the presence of paranormal phenomena (or miracles) is a very tough debate. The study of these phenomena developed as a scientific field, that is parapsychology, which came to be somehow officially accepted as a science when the Parapsychological Association became affiliated to the American Association for the Advancement of Science in 1969. Among researchers in this field, a sort of consensus more or less emerged, that some proofs of existence of supernatural phenomena are present, but they are usually very tenuous (with casual exceptions) so that it is not possible to provide as clear and simple proofs as many skeptics are usually requiring, but a long study in the field is required to figure out the existing evidence.

It is very hard to give a proper account of the situation of this debate (how scientific has the field of parapsychology developed, what evidence is there and how valid is it), not only because of the scarcity of the proofs and the hardness to check them, but also because irrational attitudes are widespread on both sides. 

I spent quite a time reviewing the situation of the debate in France. Here is my full report but I only wrote it in French too. To roughly sum up:

There is only one research organization on parapsychology in France, Institut Métapsychique International (IMI), which is recognized as public interest organization but hardly has any public support, and roughly no recognition of its views by any other organization. (So, thorough debates usually have to refer to the data produced outside France as evidence for psi)

Instead, the views of the skeptics groups ("Zététique") are strongly supported by the academic system and other official scientific organizations.

The founding organization of the whole French skeptical movement (Cercle Zététique) was more and more discredited and finally self-dissolved, as the leading and finally remaining few members were the most sectarian.
Members who left as they were not happy with its methods formed other groups, but inherited its ill-informed claims and its biased methods.
One of them is the Laboratoire de Zététique, an official laboratory in the University of Nice, directed by the founder of the Cercle (Henri Broch), and officially supported by 2 French Physics Nobel laureates, both dead but still put forward as honorary members.

The other, less official but the least sectarian and thus most respectable, thus with the maniest members, is the Observatoire Zététique, based in Grenoble. So they have basically the same ideology from the same guru (Broch) but make a difference by their "soft attitude".
Smaller groups and independent skeptical webmasters also exist.
The Observatoire made clear its independence to not be mistaken with the others'sectarism, and prefers to not put forward its divergence with the other groups, but all is explained in its forum.

The whole ideology of the Zététique groups is that they are not interested in the paranormal for itself, but made the choice to focus on paranormal claims (preferably the most crazy and incredible ones, or their own caricatural interpretation of them) as a toy model for a pedagogical project of teaching the scientific method to a large public. But the practical effect of doing so is a dogmatic, ideological fight against all paranormal claims across society through unserious investigations only; and their discrepancy with science is particularly manifested by their amateurist, demagogic approach of the scientific method (which one web site of a small zététique group claims to be applicable by a child) - while of course keeping the conclusion fixed by "science".

The Skepticism pole of IMI's student group, whose members had to remain anonymous to avoid any sort of personal attacks, hold a blog and made a lot of contributions to many online discussions. Finally they set up a web site to debunk the claims of the Zététique movement.
By taking the time to review some of the many debates across forums and blog comments, it is striking how more rational and convincing (while remaining very polite and civilized) is the argumentation of these critics, as compared to the visible dogmatism, sectarism, amateurism and paranoia of the skeptics, which has been widely discredited anyway as such across any forum not hosted by them nor by any "officially scientific" organization.

Ironically, I even happened to find a lot of similarities between the attitudes of these "skeptics" and those of Fundamentalist Christianity, as well as with some aspects of Postmodernism, (both movements which skeptics officially claim to be radically opposed to), and which are not shared by mainstream science. In other words, by such a long, rich and extensive set of various rationality criteria, it happens that "Scientific Skepticism" falls on the side of irrationality together with its irrational "best ennemies" of religious fundamentalism and posmodernism which it is most similar to, while the whole of mainstream science generally falls on the opposite side (rationality).

So, the official support to the French skeptics groups and ideology is all a kind of Emperor's new clothes.

Examples of irrational features and symptoms of irrationality that are common between skepticism and (at least some of the other irrational movements such as) religion, pseudo-science and crackpot movements but differ from mainstream science:
On the other side, unfortunately, the community of paranormal believers (if we may call it so) did not properly manage to draw a separation from irrationalists and crackpots as well as the rest of the scientific community; some still mistake skepticism with mainstream science, and assume that in order to "fight" their "ennemies" that are skeptics, they would have to oppose the scientific community too, by making alliance with all possible other ennemies of mainstream science.
These ennemies of mainstream science, can be religions or paranoid cranks with their conspiracy theories accusing scientists to be dogmatic, close-minded and to censor new (crackpot) ideas.

What they didn't notice is that by developing such alliances, they are just ridiculizing their points in the eyes of scientists (just like skeptics are ridiculizing the scientific method in the eyes of any witness of paranormal phenomena).

Here is a long explanation that I wrote about how a pro-paranormal site, which claims to be scientific, fails to stand rationality standards, and thus discredits itself in the eyes of scientists.

Some aspects of the problem have already been pointed out in an article in IMI's site:

"To finish with some clichés: parapsychologists would be marginal, while skeptics would be the official representatives of science. And what if it were the contrary ?

(This text is an introduction to the lecture given by Pierre Lagrange January 28, 2005 at IMI)

I will want to consider two points during this presentation. The first is how all actors, whether favorable to the study of parapsychology or against this study, present the debate. In their view, this debate would oppose a parapsychology at the margins of science that would be barred from becoming a normal science because of the opposition of skeptics, integrated with the institution. But if you look at the situation as it stands, we notice that it is parapsychology, particularly through the Parapsychological Association, that belongs to the institution, while the skeptics are those gathered in associations outside the establishment. It is therefore not a controversy for the admission of a discipline but a controversy between scientists (parapsychologists) and science consumers (the rationalists) who are skeptical towards the interest for society of obtained results, as often happens (GMOs, nuclear energy etc.). Thus why do even parapsychologists accept reports on the controversy that do not correspond to reality and promote the discourse of skeptics ? That is an enigma.

But this puzzle does not come alone. In fact, I think it is related, at least in France to another very powerful speech in parapsychology circles. Indeed, for decades, endless controversies always occured following the terms imposed by rationalists. Thus parapsychologists scramble to meet the requirements of proof raised by rationalists rather than rely on the normal scientific practice and seek in the plurality of scientific practices the allies they would need. And this discourse on evidence taken from rationalists (that has the disadvantage of being by definition impossible to satisfy) is coupled with a lack of real practice of the discipline. However, it is difficult to accept that rationalists are such a great danger when we see that parapsychology has scientific societies such as the PA, newspapers referees and symposia. Nothing prevents French parapsychologists to use these tools but the frequent argument is that rationalists prevent their work. Isn't this argument a bit weak ? Also if you look back in time there were other times, especially in the early 50s with Robert Amadou, when parapsychology has created the conditions for a debate without worrying constantly of the only rationalist opponents (...) By focusing on rationalists, parapsychologists today give the impression of wanting to support them at all costs by refraining to find elsewhere relays to build an identity for research in parapsychology (...) we may wonder if rationalists would be an ally for some actors that otherwise would be obliged to produce facts, to show they have something to say. But as long as this sterile controversy lasts they can pose as oppressed and pretend that they are prevented from producing facts..."

So, finally, what evidence for the paranormal can be found ?
Personally, what I found most striking and meaningful as an evidence of the existence of spiritual realities beyond our physical universe, is the study of near death experiences,

A sketch of this evidence is listed there. Well, I'm a bit ashamed of suggesting this list, because it is far from accurate: it contains quite a number of redudancies, exaggerations and flawed arguments. Its way of pretending to be stronger than it really is, does not support its credibility.
However, some of its arguments are valid.
Here is an opposite view on the subject (sorry I did not take the time to check it in details)

As another example, here is an interview with Cardiologist and NDE Researcher Dr. Pim van Lommel.
(discussed here). Other interesting interviews can be found in the Skeptiko site.
Unlike antiscientific ideas such as creationism, intelligent design or other irrationalities, and to the surprise of many skeptics, belief in the paranormal does not decrease with education. (contrary to other antiscientific views such as creationism).

Differences in paranormal beliefs across fields of study

Former skeptic

Let us give an example of the irrationality of skeptics.
In any of their argumentative texts (that I know of) against the reality of the perceptions out of the body in near death experiences, skeptics have put forward the observation that these perceptions were "reproduced" by drugs or special stimulations of the brain, or the like. They presented this as an evidence that out of body perceptions were hallucinations, by arguing that the "natural" NDE were the same perceptions as these stimulated ones, and assuming that these stimulated ones are mere hallucinations, that would be a "model" of hallucination for the spontaneous NDEs.

A rational argument based on an observation, when addressing a competition between 2 worldviews (once assumed that these worldviews are well-defined enough as concerns the observation being discussed), is a matter of how it affects the ratio of probabilties between these views, whatever the a priori ratio of probabilities that one could give them.

As we explained with classical probabilities, the effect of an observation on the competition between two hypothesis, consists in a multiplication of the ratio of their probabilities by p/p' where p is the probability for the observation to have given the perceived result under one hypothesis, and p' the one under the other hypothesis. Thus it can significantly promote one hypothesis, only if the probability of the oberved result under the other hypothesis is close to zero.

In particular, in order for the observation of "out of body sensations" under drugs or specific brain stimulations, to be an argument against the "real out of body" interpretation of NDEs, this would require this result to have a probability close to zero under this hypothesis.

But, under the "real out of body" interpretation of NDE, there is absolutely no surprise that such experiments on the brain can really drive the soul out of it and thus produce real out of body perceptions in this way.
Strangely, when putting forward their experience of stimulated out of body perception as a "model" for NDE, they did not even consider any question of how it can be at odds or not with the real out of body hypothesis. So they did not contradict either that its probability for their observation can be 1. In fact, all they showed is their a priori unability or unwillingness to dare thinking about the view they are claiming to oppose.

Conclusion: skeptics are ridiculizing themselves by their way of showing that they don't even understand how to assess the weight of a rational argument based on an observation.

Now, it's a pity that among all testimonies of out of body perceptions, it seems none has been recorded in "fully controlled" circumstances in order to remain undeniable, though the situation as seen by the involved people is already sufficiently clear to make doubt unreasonable.
Let us just make a few remarks:
Indeed, the question of afterlife is, in principle, much more interesting for so many people (with many people on both sides of the controversy, each conviced to have some evidence on their side), than the quest for the Higgs boson, and is no less accessible to scientific inquiry. Therefore I see no reason why the amount of resources dedicated to the former remains so ridiculously smaller than the one for the latter.

Beyond probabilities

Quantum theory gives probabilities for physical phenomena, but the behavior of the mind, as we explained, does not conform to any probability law. This means that there is a sort of concious law that has "preferences" among the possible behaviors allowed by the physical probability laws, that concious beings will follow. This can be expressed by saying that "understanding conciousness" reduced the entropy of the behavior of concious individuals, as compared to the observation of the same behavior without this understanding.
More generally, understanding the world means to find an interpretation of the world that reduces the entropy of the observations made there. In other words, to find an optimized compression format for the data of the observation. Such a definition of an optimized compression format, may either be mathematical or non-mathematical. Of course, compression formats usually implemented in computers are mathematical ones, but non-mathematical compression formats are conceivable too. For example, some people communicate with SMS in a very abreviated form, so that other people, eventually with some efforts, can "uncompress the message" (understand what the message means), but it would not be possible to make a program that would reliably uncompress such abreviation into the correct full words they are meaning.

I think that the world (particularly the concious behavior) is neither absolutely deterministic, but probability laws don't make absolute sense either. Instead, there is a sort of free will. What is free will ? Well, we don't know, and maybe we will never know, as there can't be a complete understanding of it.
However, even when something is deeply beyond any possibility of complete understanding, does neither mean that it is absolutely wonderful, nor that it would escape all understanding.
Rather, it can often happen that, in their free will, people commit many errors ; some miserable errors can be expectable, and some non-material causalities (such as, losing one's love or staying without love makes one depressed) can be uncurable.

But, if an understanding is not a mathematical one, then what can it be, and does it really make sense ? Well, this is a very hard question. And different people may have different sensibilities, so that they would have different distributions of a priori probabilities between worldviews. Indeed, inside an astronomically long list of "possible wordviews" that may be conceived, they can't be a priori equally likely: some can be seen as much more plausible than others, even before any observation. It all depends on the way you want to group them: if 1000 possibilities are "as likely as" a million others, does it mean that each of the first group is as likely as each of the second group (so that we have 1/1000 chance to be in the first group), or does it mean that we have 1/2 chance to be in either group ? These are different possible ways of compacting the information saying in which world we are.

When we don't understand the world yet, we don't know how to "make sense" of it. So, how to compress the information about it. Then, as we gather more information, this starts to "make sense", we discover better ways to compress it. But good compression formats, that can "understand" a lot of information as "explained by" a smaller quantity of causes or "explanations", require to be themselves specified in some compression format. And the problem, is how heavy is the quantity of information necessary to specify this compression format. The heavier it is, the less good is the explanation it provides.
We can see this by expressing the compression format as a program, and put this program together with the compressed file, thus forming as self-extracting file (a program whose execution produced the wanted file).
But we might also consider this as rephrasing the problem, but not fundentally changing it: it is not possible to process the self-extraction of the file unless there is an a priori knowledge of the computer language in which this program has been written. We may as well reinterpret the whole self-extracting file with its program, as being ultimately the data of the compressed file, while considering the language interpreter (that can run the program), to be the ultimate program that will uncompress this file.

But, the total size of the self-extracting file depends on how and in which language the extracting program has been written; in the same way as the size of a compressed file depends on the compression format.
And, as the choice of a computer language is somehow arbitrary, it also does not make absolute sense to say how complex is a specification of a compressing format (it is more complex or "looks more arbitrary" when written in a language than in another).
 
In other words: without a lot of observational data that have different probabilities to occur as depending on different ways the world might be, it would be hopeless to try to argue which worldview is more likely than another worldview: it would remain irreductibly subjective.
This subjectivity (assessment of how complex or arbitrary is something) is especially important for non-mathematical forms of understanding.
It even occurs in the context of strictly mathematical definitions. We just explained it about the arbitrariness of computer languages in which compressing programs can be written, but there is more to it.

Some works on the foundations of mathematics, especially by G. Chaitin, have established that there is randomness in pure mathematics too. For example, we might consider the series of decimals of pi (or other irrational numbers), as a series of random digits. Such considerations have been intuitively summed up by saying that "some mathematical claims are true just by chance".

Let us present one of his most amazing discoveries: "No file larger than a certain size can be provably minimal" (where "minimal" = impossible to compress as a shorter self-extracting file)
In other words, for any sufficiently large quantity of information, we have no way to refute the possibility for all this information to be "explained" by a smaller quantity of information. This proposition looks strange, because it seems to reduce infinitely many different possibilities into a finite number of cases (expressed by self-extracting files smaller than a given size).

How can this be ? This is, in fact, a variant of the incompleteness theorem, playing the same way on the difference of viewpoints between "successive times" in the foundations of mathematics.

The proof of the theorem roughly goes as follows.
The idea is to explicitly write down a program (self-extracting file) A, whose instructions say the following:

Program A = [Search for all possible proofs of mathematical propositions (e.g. formal consequences of the ZF set theory), until you discover a proof of a proposition of the form "B is not the output of A" for whatever file B; then, give this B as output].

(More technical details must be included in the program to be able in this way to speak about itself)
 
In fact, this program A will run eternally without ever giving any output. Because, if it happened to give an output B, this would mean that a proof has been discovered of the proposition "B is not an output of A", which is false. It would be such a pity to have a proof of a false claim.

Now that we know that this program cannot stop to give any output, this knowledge is not accessible (it cannot be proved) in the same formal system that is involved in the proof. Its unability to provide any output, means that there cannot be any proof of a proposition of the form "B is not the output of A" for whatever file B. This is the result that we have announced.

Consequently, for any series of random events, the belief in the existence of (unspecified) laws determining these events is unfalsifiable.

Now, back to quantum physics, we may wonder: why is it that the behavior of lifeless systems obeys the probabilities given by quantum theory (or is at least very close to this) while the behavior of humans and animals is largely influence by free choice away from these probabilities ? I have a suggestion of an explanation, though I can't say if it is the right one or not:
The random effects of quantum processes happening in the brain, are first perceived by only one soul, therefore giving this sould the chance to "choose" the perceived results. But random results of measurements in lifeless system, have many copies sent at the speed of light in all directions, thus not giving the way to let any unique concious observer be the absolutely first observer (because of the relativity of simultaneity between possible perceptions by many distant observers). Well, we may say the delay given by the transmission at the speed of light to the observer is too short to be meaningful, but there are "much bigger" delays before the measurement in converted to a visible result, and between the arrival of the light in the retina and the transmission of the signal to the brain where it is finally perceived.

No reason to dump reason

We don't know how the spiritual universe (where we go after death) looks like. Is there any physics of what happens there ? Does it have any sort of physical connection with our universe ? Do visual perceptions there (light...) have any similarity of nature with the light of our physical universe (which we do understand by quantum physics) ? What happens to conciousness there ? Why do some souls stay here to haunt houses ? Is there a hell ? If yes, what does it look like, what brings people there, and for how long ?
These are so many questions that are very hard to answer, for lack of observational data. We have some hints from near death experiences. In particular, it presents strong indications of the existence of reincarnation (as some other sorts of observations can show too), but anyway not immediate or not systematic, as shown by the meetings with dead relatives, that show they are not reincarnated at that time.
Also, it says that we are our own judges on our life, that we review (maybe not in all cases ??) for our instruction, not really as a "judgement" in some negative sense, but a sort of objective perception, not focused on judging, but which makes us feel the effects of our deeds on others.
Maybe, by studying NDE more closely, some progress can be made in the understanding of afterlife.

However, I would not dare to make any precise claim about afterlife that would be just a guess not be based on sufficient evidence, for the following reason.
As it seems, it goes beyond our imagination. Thus, if we try to imagine something by the mere naive means we usually have at our disposal, most probably we would have it wrong, as it would be still very different.

Some authors tried to imagine something. For example, they would describe a physics for the spiritual universe.
I think such a try is much too risky, because the laws of physics are mathematically expressed, while spiritual realities have mainly a non-mathematical nature. They try anyway, but to make it different from the physical things (as it should), their only method is to take any well-established fact and claim the contrary.
For example, in particle physics, no known particles can go faster than light, and the impossibility of information transmission faster than light has been deduced from special relativity (as time loop contradictions would come otherwise) ? Then, just because there is a mystery of non-locality with quantum observations as expressed in the EPR paradox, let us imagine particles that go faster than light: such particles must be very spiritual.
Entropy is increasing ? Let's imagine a space where entropy decreases, such a space must be very spiritual.
Self-proclaimed defenders of reason promote a materialistic philosophy ? Let's reject reason, this attitude must be very spiritual.
Everybody is walking on their feet ? Then let's walk on our hands, this way of walking must be very spiritual.
Everybody is thinking with their heads ? Let's think with our feet, this way of thinking must be very spiritual.

Well, sorry, I don't believe in the relevance of such extravagance contests, as any choice of something to deny will be quite arbitrary anyway, and just taking a known concept to turn it upside down will remain too similar in nature with its claimed opposite, in order to be a serious candidate of a breakthrough.
That a careful rational imagination is currently not enough to figure out things properly, does not give any more credance to a foolish imagination.

When we don't know something, there might be so many possibilities that may be or not be imaginable, that a try of a guess not supported by due evidence would have no decent chances to have anything to do with the truth. Thus the best way may be to just give up trying to guess anything, and keep examining the data (testimonies or other considerations), until some evidence might appear on some specific questions.

Indeed, the fact that a question currently appears too hard for us and that we don't currently have readily available data to orient us to an answer, does not mean that it would be of a radically different nature, something fundamentally beyond reason. The power of reason does not have any clear and precise limits, and a question that appears beyond its reach at a time might turn out to be solvable later (may it be through testimonies of NDEs, deliberate out-of-body experiments, or anything else).
Thus, the scientific attitude is to just admit that one does not know something at a given time, but keep searching in hope it can be resolved later, may it take centuries (a quite short period of time comparted to the history of life on Earth).

This is to be strongly contrasted with the religious attitude that consists, towards any hard or unobvious question, in claiming : "Alleluia ! this is beyond the reach of reason and science, therefore a miracle in the exclusive domain of faith and divine revelation (and more precisely, mine...)"

Notes on spiritual dimensions

Let's just make a few remarks about possible connections between physics and spiritual realities.

Consider visual perceptions of the environment in out of body experiences.
Such perceptions would be made possible by the ability of conciousness to perceive matter. This can be either a perception of matter, or a perception of physical light, since light and matter are but two cases of physical systems, well described by our physical theories, and that can interact together.
Contrary to what some authors might think, I see no likeliness in the idea that wide perceptive abilities that experiencers may have of our physical landscape, would be any hint that these perceptions would take place as viewed from another dimension. Indeed our usual visual abilities are highly dependent on the presence of the physical light that "takes a picture" of objects, and makes this picture perceivable at a distance.
In order to receive this picture, we need to remain inside our usual 3-dimensional space (+1 time dimension). We could not have such a visual perception from outside this space. Otherwise this would not be based on our physical light but another, unphysical sort of light that has no reason to take any picture of our physical objects in the way that the physical light does.
Inside our space, the out of body visual perceptions of physical objects, insofar as they are based on physical light, can make use of many more wavelengths of the electromagnetic spectrum that those of our humanly "visible" light: it should be possible to perceive the ultraviolet and infrared too (to name just those carring most of the energy in usual conditions).

Then, when experiencers "enter the tunnel" or other such spaces differing from our usual space, suddenly lose all visual perception from our space. This is coherent with the idea that they left our space.
But does it mean that they also left all concern of the physical laws of our universe altogether ?
This is a hard question.
Indeed it still looks like there are still in a sort of space. But our space-time with its geometry, is a part of physics. The geometry of our universe (space and time) is in close interaction with the material contents, according to Einstein's theory of gravitation (general relativity). We have explained that time is a property of conciousness. So, if time is influenced by matter, it means that, in its time perceptions, conciousness is also influenced by the events of our material universe, as long as its stays inside our space. And as our space-time is linked with matter in our universe, is time (and maybe space) outside our universe, following any law or influence of a similar sort ? As there is a time (and maybe space) connection between this world and the beyond, can there be any other sort of physical connection too ?

Conciousness can travel outside our space, as it seems. Still, the travelling distance seems to be finite, as it takes a finite and quite limited time to go there and come back to life here. The speed of this travel might be very fast, but can it be faster than light ? First, can this question make any sense ? It would make sense if there was a way to measure distances outside our physical space. This is far from obvious.
Still, there might be a way to give a sense to this.
In our physical space, there is an available definition of distance, once admitted a measure of time intervals, based on the fact that no information can go faster than light: just measure how much time must be waited on Earth when a signal goes from Earth to Mars and then back to Earth. This measures the distance between Earth and Mars.
We can give up much of our physical laws and still make sense of the question concerning spiritual realities.
But this depends whether the limitation of speed for transmission of information, still holds in the spiritual universe; or on the contrary, is it sometimes possible to reliably transmit information faster than light between locations of our physical space through parapsychological means ?
Sorry I don't have the answer to this question. I just know that such a faster than light transmission, would mean to break the relativity princple (the idea that the speed is relative, as is the case for physical phenomena) when it comes to parapsychological phenomena, and such a claim would need some observational evidence to be supported.

If faster than light travel (or information transmission) as measured in our space, is possible for souls, then it makes it hard or perhaps impossible to define any concept of space and distance as a fundamental character of the universe of conciousness.
But if this speed limitation holds for souls then the concept of distance can be extended to the universe of conciousness, while the limitation of speeds by the speed of light would hold by definition of times and distances, just the same as is expressed in our laws of physics.
It would make sense to ask "how far from Earth" is some space beyond, through the "tunnel", as defined by the minimum time it takes to wait on Earth from the departure of the soul from Earth and it arrival back to Earth.
As NDEs usually only take mere minutes, and the way through the tunnel may even be considered shorter, maybe seconds, this means that the space beyond being visited, is "closer" to Earth, than are other planets of our solar system (which are several light minutes away from Earth).
Does it make sense ? Well, not so bad. After all, if that trip drove us away from the galaxy, there would be too many risks to land on the wrong planet when trying to come back ;)
Also, reincarnation stories usually speak about past lives on the Earth, not on any other planet. This does not exclude the possiblity of life on exoplanets and travels of souls between them, but distances are so big that it might "waste time" for souls that might prefer keeping connections with a not too old universe, rather than making big travels to other planets that would make them skip an interval of age of the universe (even if they would not have to wait this time in their own perception, according to the twin paradox).

Are the "tunnels" specific places inside some larger space (that may be of dimension higher than 3, though perceptions strangely seemed to remain 3-dimensional), or do they only exist to provide "artificial" bridges between otherwise spatially (physically) independent places (universes), with even no existence of a space beyond their width ?

There is a lot of work ahead for future researchers...
Part I: moral comparison of science and religion - Part II: Explaining reason and science - Part III - Part IV : explaining and refuting religions

Back to main page