A personal journey

Religion and myself, a complicated story

I was raised catholic. I actually did follow catechism until I was around 15/16 years old. Mostly because of the pressure my mother exerted on me. As for every teaching I followed during my childhood I was really listening when I was there, but not much more. I acquired a theological formation without having deep thought about it. I thought it was part of life like taxes or death. As I grew up, reaching adulthood, the parental pressure became less present and I simply stopped my “religious” life beyond christmas mass or ceremonies like burrial or baptisms in my family. But lately religion came back to my life from the most unexpected circumstances and I don’t really know what to do about that. Believe it or not it all ignited when I started giving course of computability theory and was having theoretical thoughts about consciousness.

---

Unlike the theory of relativity or quantum mechanics, the fundamental results of computability have not reached the large public. I am constantly amazed by public discussions that sounds like talking about perpetual motion in this regard. There are very fundamental results that are even stronger than the ones of relativity and quantum mechanics because they are mathematical results. No experience may ever invalidate them. Maybe they are harder to grasp than physical theories because they are about how we think and communicate our thoughts beween humans and not about objects.

Computability theory can be seen as a mathematical study of language. It studies what can be written down following logical rules and using symbols. It turns out that most of the results of this field are negative results: there are things you simply can’t do when playing with symbols and following rules. I will not get into details in this article. One iconic (actually it is more than just iconic) result of impossibility is the so called halting problem. It is not possible to have a program P that takes as input another program Q such that P answers “yes” or “no” whether or not a program Q will eventually stops. This problem may look peculiar but is in fact deeply linked to logic and thinking. An intuitive way to see it is as follows: How can you disprove a theorem? Think at a theorem like “Every even number greater than 4 is the sum of two prime numbers” (known as Goldbach’s conjecture). One way to link the fact this theorem is true or not (at the time of writing no one has a proof) is to consider a program that is searching for counter-examples. If this program runs forever, it means that there is no counter-example and ultimately that the theorem is true. Otherwise, if the theorem is false, one day the program will halt by finding a counter-example. The links between computability and logic are more complex than that (arithmetical hierarchy is an entry point to this fascinating field) but it is enough to have a sense of what is going on.

Now you may ask yourself: what is the link between those remarks and religion? Patience we are halfway through. There is another point to develop first: how computability tells us things about epistemology in a broader sense.

The example that I presented make a link between purely mathematical results and computability. But there is more. For whatever theory you make about the world, this theory has to be computable. Indeed, what is the interest of a theory in which you cannot actually compute things? Such a theory behaves like a magical spell. You need to be able to compute predictions in your theoretical model to match those predictions with the actual results of the experiments. So the link becomes evident: if there are things you can’t compute, it ultimately means that there are strong limits on the scientific way to talk about the world (namely what is not computable). And this is not mere philosophical speculation. The undecidability of the spectral gap is just one concrete example.

Long story short, whatever you will produce as physical theory, most of what happens in the world has no “reason” with relation to this theory. That is if you understand “reason” as having a theory that would “explain” this phenomenon. Explaining meaning that you have a more economical way to describe the phenomemon than the phenomenon itself (eg you just need initial conditions plus the theory and by computation you recreate the phenomenon). There is simply no way around this fact. It is even more established than the impossibility of the perpetual motion. Because this impossibility is not a mathematical theorem, but a logical consequence of some physical postulates that are maybe wrong at the end of the day : they have not yet been proven wrong but who knows? We do not elect the laws (if there are such things in the first place) of nature, while we define the rules of logic. For instance before relativity it was not clear that it was impossible to move faster than light. And maybe a new physical theory will go beyond that one day. You can’t say this about mathematical results that do not rely on how the objective world behave.

Now the natural question is: can we know more than what just science tells us about the world? This is where religion appears.

Religion as a category of knowledge

The type of knowledge I am going to talk about is the knowledge that works in real world and has passed the test of time while not having a scientific explanation (ie a testable theory in which the phenomenon can be dealt with from an abstract point of view). I will refer to this type of knowledge as functional truths.

The typical examples of functional truths are provided by myths and religions. One way of understanding those type of old stories is to consider them as collections of stories that have been transmitted through generations: useful ones have survived, useless ones have disappeared. Moral values, indications on what is, and how to have, a “good” life are examples of such truths.

Backward causality

Functional truths are typically ideas that go backward from a causality point of view. Indeed usually causality is the attempt to describe the present as a function of the past. Moral values, political decisions, etc., go the other way around: in some sense they are self-fulfilling prophecies. It is because you expect some future event to take place that you modify the present by adopting some behaviors. It looks like as if it is the future that is the root cause for the present.

This land of knowledge is very slippery because there is nor internal (coherence), nor external (reality check in the form of properly defined experiences), surveillance mechanisms working as a guardingrail. The worst part being that it cannot be proved that a particular kind of knowledge belong to this tier. From a computability point of view it is the equivalent of the Post’s theorem: if two complementary sets are semi-decidable, then each set is in fact decidable.

In particular it means that one cannot hope to make a theory out of them. And even if, at some point, an explanation is found, there is no warranty that this is the “right explanation”. A concrete example is given by the jewish food law forbidding the simultaneous consumption of milk and meat. Nowadays it is thought that calcium makes the absorption of iron more difficult. Moreover, due to the endemic presence of Malaria in this part of mediterrannea, there were selective pressures leading to a higher prevalence of thalassemia than average. Indeed, thalassemia offers some kind of protection against Malaria. But on the other hand people having thalassemia suffers from anemia and have iron deficiencies. Thus in this context it looks logical to set up this kind of dietary law. The theory I presented is maybe a valid explanation of this old jewish diet rule. But other explanations could also be valid:

• Maybe it was just a rule to enforce ingroup/outgroup distinction.

• Maybe it is because a large part of this population is lactose intolerant and it makes digestion easier for them.

• Maybe it is a mix of those explanations or even something else we don’t have any clue about.

• Maybe there is no more “valid” explanations than : it is due to luck (which is a way to characterize our ignorance).

The point is: we will never know for sure why (if there is a why) this rule has been edicted and preserved. Moreover, there is no hope to have a “rationnal” explanation meeting the standard of a scientific proof one day regarding this issue. Because, at the end of the day, it is a law that has been layed down by human beings, not a law of nature. And this law has been passed among generations for different purposes.

Functional Truths are not Subjective

An important point is that one cannot build the functional truth type of knowledge on his own. Indeed, they are ideas that need to be tested over very long periods of time to prove their usefulness. Typically many generations are required, and the longer the test of the idea the more one can rely safely on it. So even if you profer an idea of this type, a rule of thumb that you have hard time to justify in other way that “it looks like it works”, you will never know, or have a proof, of their effeciency. It is in this sense that they are different from other type of knowledges.

Undecidability and Relativity in Practise

Functional truths are products of the interactions between humans. They are ideas vetted by adoption rate and adequation to the context in which they are used. Other typical instances are human institutions: they are ideas that emerge from societies. Their validity may change over time contrary to physical laws of nature. This can lead to an absence of consistency which is somehow used by atheists as a proof that religions are not relevant. Let us reconsider the example of the jewish dietary rule regarding meat and milk. It could be the case that it is simply for environmental reasons that it is a useful rule. Therefore, there is no contradiction if in another region of the earth, where environmental pressure is not the same, that other dietary rules are edicted more in accordance with local peculiarities. Actually, what would appear as suspicious would be that religious beliefs were homegeneous around the world, and across time.

On one hand, from a computability perspective, functional truths correspond to undecidable phenomenons. It looks like the Goldbach’s conjecture but from a practical/real point of view. You cannot find meaningful counter examples but yet cannot exhibit a theory of why such rule is correct. On the other hand, from a historical/sociological point of view, functional truths are context dependent laws that may only be valid in some specific contexts.

Time as the only guardrail

The fact that such knowledges take the form of revelations is also not surprising: since there are no real “explanations”, they have to be taken for granted. This idea is well captured by the saying “God works in mysterious ways” which is not as sarcastic as one may think at first, but as a reflection of undecidability/incompletness phenomenons.

This land of knowledge brings the risk of misunderstandings, because in the absence of safeguards, attempts (which ultimately is not possible either to prove or disprove such kind of knowledge) to build theories may spiral out of control leading to religious wars. The other danger is to have a relativistic approach to the idea of truth by extending this category to all human knowledge.