The Formal Mystery
P. J. [Science]

The Formal Mystery

Any study begins scientific starting from the moment (and inasmuch as) it loses its anthropocentric character. That is, our notions and the forms of expression are treated in science as extraneous to the content of our knowledge, which could as well be arranged in any other way, still referring to the same natural things and events. I do not say that this cognitive attitude to nature is the only possibility, and it is not necessarily right, or always preferable; but this is how science works, and we respect its place in the whole of the human culture.

With this intentional objectivity, scientific research requires a highly developed capacity of abstraction and demands a regular critical reassessment of its basic principles, to prevent inadvertent recurrence of the primitive anthropomorphism. For a human being, it is not easy, to stop sitting in the center of one's personal universe and agree that somebody else might look at it from a different angle. As we all know, some steps in that direction took many centuries and a lot of courage, and even heroism. Today, most scientists agree that the humanity is a tiny spot in the magnificent picture of the Universe, existing on a local scale in no way comparable to the cosmological measures. When, in a billion years (or, rather, much sooner), the human race will be entirely exterminated by the next metagalactic cataclysm, there will be nobody to deplore it. However, we still take a very tender pride in our artificial toys and fancy ourselves the discoverers of the ultimate truths of an imperishable value.

Well, in a way, each portion of knowledge refers to an objective situation that can be reproduced in an infinity of contexts in different respects. That is, our knowledge (however imperfect) contains absolute truth; otherwise, it just would not be knowledge. However, this does not mean that we can always guess what we actually know. Consciousness is different from mere awareness, and self-consciousness is very different from mere consciousness. People invent many useful things (including scientific theories), but they don't need to care for the reasons, as long as it just works the right way. Some things are used to produce other things; then yet another thing is to assist the production of the means of production, and so on. One can never judge until trying the new tool; however, neither failure nor success can serve as a decisive argument, since there are no universally applicable tools, and utterly useless inventions can find a quite unexpected niche, as it happened so many times in the history of the humanity. That is, as long as our practical activity runs on, we can be sure that we have learnt something about the world; but we can be as sure that the form of our knowledge (science) is a very approximate expression of what we know, and it will certainly be replaced by a more appropriate formulation later on.

That is exactly where a human scientist tends to slough in anthropocentrism. Besides the already mentioned gnoseological diversity, there is a strong psychological bias. One cannot be entirely honest towards one's dear creatures; we like them as they are, and their obvious drawbacks get lovingly reinterpreted as signs of perfection. With those millennia of incessant effort to set up the scientific method, how can we be wrong after all? Well, Babylonians and Romans were as fond of their tables for operating with what they considered big numbers; still, that kind of math is out of any relevance nowadays. The founders of mathematical analysis were debating its different formulations; today, the very calculus is often treated as old-fashioned and obsolete, while physicists savor the cuisine of the abstract algebra (to fade in the face of a new formalism to come).

Philosophically naive scientists are apt to identify the form of their science with its object. They develop notions and concepts to describe a specific application area; the inner relations between them are to explain a range of observable regularities. However, these notions and concepts only represent certain practical aspects of the application area; they never refer to any real objects. A trivial mathematical example: we can enumerate various collections of objects with natural numbers, but there is no such thing as a natural number as such, and a correct scientific theory would be very careful to ensure that different enumerations are indeed commeasurable within its application area. Three bananas and three years of prison are only equivalent in a very special sense; while we can formally add three and three to get six, one will have to work hard to practically demonstrate the sum of bananas and time. This example might seem too simplistic in view of the higher arithmetic, but it has to do with the childish belief of modern physicists that their ability to combine space and time in an invariant quantity (the interval) means physical equivalence.

By the way, in law, if one crime is punished with three years of prison, and another crime is punished the same way, the total for a criminal condemned for the both will hardly ever be six years; the legal law of penalty accumulation is far from the plain mathematical sum. The same holds for many economic calculations as well. When apparently commeasurable quantities do not sum up, this usually means that there is a qualitative difference that does not allow direct summation; that is, the units of such quantities only nominally coincide, with the same word used to denote practically different things. No allow combination of such quantities, we need to construct a higher-level framework containing them as limit cases.

Popular literature is replete with all kinds of superfluous identifications. Similarly, when, say, biologists borrow some ideas from physics, they do not need studying physics in depth; popular accounts of physical research are enough for productive metaphors. However, in such adoption, lack of physical intuition may lead to exaggerating formal aspects to the detriment of objective analysis. For example, we read in a paper on neurophysiology: "Any flow of energy may arrange things." I have fed this phrase to some of my scientific acquaintances and obtained an illustrative picture: putting aside the weird wording, physicists generally agree with this statement and admit that it could be taken for a starting point for further discussion. Isn't it a hidden concession to anthropocentrism? Indeed, the situation is exactly converse: we characterize certain kinds of motion (which manifests itself as rearrangement of things) with the notion of energy flow. Things move as if there was a kind of flow; but this abstraction does not move or arrange anything. Taking abstract ideas for real things is a philosophical illusion known as objective idealism. With such a background, scientific study is to eventually degrade into mystical phantasy. earing to be more general than their former unifications. Of course, such hierarchical conversion in science means scientific revolution—but who can be sure that the present picture of world is already complete and shaped forever?

[Science] [Unism]