Evolution of Knowledge
Eugene Wigner in his famous essay ‘the unreasonable effectiveness of mathematics in natural sciences’, raises a question on whether mathematical concepts used to explain concepts in science are ‘uniquely appropriate’ or not, he says:
‘The first point is that mathematical concepts turn up in entirely unexpected connections. Moreover, they often permit an unexpectedly close and accurate description of the phenomena in these connections. Secondly, just because of this circumstance, and because we do not understand the reasons of their usefulness, we cannot know whether a theory formulated in terms of mathematical concepts is uniquely appropriate. We are in a position similar to that of a man who was provided with a bunch of keys and who, having to open several doors in succession, always hit on the right key on the first or second trial. He became skeptical concerning the uniqueness of the coordination between keys and doors.’
This same question can be raised on the unique appropriation of any scientific theory proposed to explain our observations in nature. We have no way to be sure if the idea presented is the only, or the most appropriate or even an accurate explanation of the phenomenon it explains. It is common knowledge that theories presented in science are always open to revision and even hard-core theories, belief on whom is often the basis of much research and progress in science often turn out to be non-credible in time.
If the history of science could be divided into epochs, each epoch would represent a general underlying belief on how nature works. For millennia people believed that matter was made of four essential components, water, fire, soil and air, and it seems that for them this theory served well in explaining how everything in the world works.
The evolution of human knowledge is an essentially social phenomenon. Ideas and belief held on those ideas pile up upon one another, and with time and lots of record-keeping the older layers are exhausted by the new, more detailed ones. Every new discovery and concept does not work in isolation, rather it may spark several new discoveries or ideas, even in fields that do not seem to be related at first glance. And what really drives thinkers to look for more and conceptualize more are – inconsistencies.
As it happens, every time with more observations, thinkers find that the previously held ideas have some inconsistencies, especially when an effort is made to explain new observation in those old premises. The Jain of India and the Greeks in the 4th and 5th centuries BC, independently came upon the belief that matter was made of indestructible, immutable ‘atoms’ surrounded by ‘void’ and these atoms combined to form all the different things. This was a great theory and explained the world and everything in it perfectly and agreed with experiments for many centuries. Then in the 1870s cathode rays were discovered that proved the existence of a negative charge, which led to the discovery of electron and eventually a theory was put forth by Bohr in 1922 that suggested an atom built up of a nucleus and successive orbital shells of electrons.
And eventually this theory also became inconsistent with findings of the quantum realm. Now the theory of wave-particle duality was proposed and it was proposed that the atom and even its components do not exist all the time but are in some kind of a spooky state and only come to existence when detected. Has it been the case that more and more we attempt scrutiny of the objects of nature, the more and more we are forced to discard the shells of matter from around it, so that at the end the ultimate reality would be left as something more of the subjective realm and less of the objective one. It seems that the evolution of ideas in science have led us to paint around us a universe more and more subtle than before.
Having to shed off so much of what we believed to be hard-core truths in science has made us all skeptical towards the solidity of any theory we arrive at and we face the question of whether to keep on looking for the absolute theory that we crave for and the belief of which drives us through all the hard work of experimenting and theorizing or should we admit that the more we unveil truth the more we will find it to be farther away from us. But what does not let us stop in our pursuit for more knowledge is one belief, shared in the scientific community, it is the belief that all of nature works upon a very simple law, a law that controls all laws and all cycles of nature, and unveiling that law, that ‘ultimate reality’ will eventually deliver humanity the bliss it deserves.
Coming back to the question of being uniquely appropriate, one could question, if the way scientific thinkers have sought to resolve the mysteries of nature by introverting to subtle solutions was the only ways those mysteries could have been solved or was it the inclination of the human thought as a whole, to seek into such answers. This leads us to confront the question of what the nature of knowledge itself is. Is knowledge a string of progressive events? Is knowledge a single fabric among infinite others that could warp reality into phenomenon? Or is knowledge a field of possibilities, seemingly void, and erupting into existence only occasionally when questioned?
If indeed human knowledge has a life of its own, though feeding entirely upon our grey cells, it does show a trait unique to life itself, that surely it evolves. And the methods of its evolution have, just like other life, been somewhat spontaneous, probabilistic and unpredictable.
The zeitgeist theory proposes that in the accumulative presence of much new observations, when older theories start showing inconsistencies, unique heroic individuals, "great scientists" or "geniuses", are able to enter from the old to the new realm of reality. But this theory has been opposed by the hypothesis that most scientific discoveries and inventions are made independently and more or less simultaneously by multiple scientists and inventors.
Robert Merton, who founded the sociology of science, explains ‘multiple independent discovery’ as the phenomenon of simultaneous discovery of a phenomenon by two or more scientists working independently. For instance Newton, Leibniz and others independently formulated calculus in about the same decade. Oxygen was discovered by Carl Scheele, Priestley, Lavoisier and others independently at the same time, and the history of science is filled with such multiple events. The idea of ‘multiple events’ soon led thinkers to the question if knowledge evolves with the same evolutionary principle by which life supposedly evolved from species to species by mutations in the smallest units of life, the DNA.
It was thought that perhaps like the DNA carries information from generation to generation, there may be a cultural unit called a meme that carries ideas from mind to mind, and this ‘sharing’ would carry forward the evolutionary process of the thought. But discoveries being ‘independent’ implies that those ideas were not shared between those men until there publications. This would make the need of a theory that can describe the evolution of knowledge, not just as a social phenomenon, but as a temporal phenomenon too.
Like Bolyai said to his son Janos, ‘When the time is ripe for certain things, they appear at different places in the manner of violets coming to light in early spring’, which means that the human thought, as a whole, is bound to stumble upon discoveries, when their time is come. That perhaps the pace of discovery, with all the prerequisites that will be accumulated in the way, has been preset in nature for the genus homo, with respect to time. And the fact that different minds come on the same solution for a prevailing issue also indicates the possibility that the way human thought would respond to issues is fashioned and preset.
But there is yet another astonishing behavior of the evolution of knowledge; which was presented in the theme of Wigner’s essay on ‘unreasonable effectiveness...’ – in the first place, it is the surprise how and why nature and the human thought share the same language – that of mathematics – and secondly how is it that many times mathematics that is developed with no specific explainable phenomenon in mind and just for the sake of the math, turns out to be exactly the math required later to explain new observations.
Mario Livio explaining this issue in his article says that there is an active and a passive facet of the unreasonable effectiveness, the active face is that ‘at least some of the laws of nature are formulated in directly applicable mathematical terms. The mathematical entities, relations, and equations used in those laws were developed for a specific application. Newton, for instance, formulated the branch of mathematics known as calculus because he needed this tool for his equations of motion’. And ‘the passive effectiveness, on the other hand, refers to cases in which abstract mathematical theories had been developed with absolutely no applications in mind, only to turn out decades, or sometimes centuries later, to be powerfully predictive physical models’. Like as Wigner said ‘Max Born noticed that some rules of computation, given by Heisenberg (to explain quantum mechanics), were formally identical with the rules of computation with matrices, established a long time before by mathematicians’.
Along with science and in general with all knowledge being unreasonably effective in explaining nature, and the fact that a scientific explanation and the math needed to articulate it, usually appear as close to each other in time as to be able to catch up, hint as if nature is fulfilling the prerequisites and fashioning the way forward for science – there is also the fact that many times nature fulfils these prerequisites in a rather spontaneous and unpredictable way. This is precisely the reason for some discoveries to be able to make quantum leaps, taking mankind form one paradigm of reality to another. This happens when most of scientific research and activity is going rather smoothly upon a paradigm based on certain basic ‘suppositions’ about matter to be true, and even though many observations are not fitting those ‘suppositions’, thinkers are not ready to discard the basic ‘suppositions’ rather it is easier for them to doubt their observations. Yet only some thinkers are forced to re-think upon those basic suppositions, meaning that when going-forward is being hindered to such a level, their rebellious souls are ready to think out-of-the-box and suddenly something that was previously thought to be a no-go way of thinking clicks in their minds as the very right way forward, and this bold way of thinking lead to the abandonment of the basis ‘truths’ for finer ones. So the supposition that atoms are indestructible is abandoned for a subatomic model and that also is later abandoned for a supposed probabilistic model. And this re-thinking of the basis, leaps us into completely newer paradigms of nature. But again, the need of this re-thinking, combined with the courage and novelty required and the seeming serendipity of suddenly waking up at a solution that had not been in the focus at all – all this makes it look spontaneous.
This also brings us to the query, how the human mind is able to ‘suppose’ a basic, general model about the nature of matter and how that ‘supposed’ model prove to be so effective for so much advancement in science. And then a new model is supposed and it is even more effective. Surely the supposed models have not been laid upon mere imagination, rather they are always bound to satisfy the known facts of that time, yet one must be weary of the ‘fact’ that our foundations are laid upon ‘suppositions’. And this makes unreasonable effectiveness even deeper, like rooted in the structure of our thought.
One must also ponder upon the fact that even though we keep changing the paradigm of our thinking into more sophisticated ones, the older paradigms do not simply cease to exist, rather they remain to be true at a certain level of certainty. The Quantum paradigm does not simply wipe off the Newtonian paradigm, both work in their own range, hinting that nature can be observed at different levels, levels that may be different facets of the same whole yet work on sets of rules that seem to be entirely disjoint and different.
Wigner’s using of the phrases ‘unexpectedly close and accurate description’ and ‘because we do not understand the reasons of their usefulness’, make us contemplate on to what measure our mathematical formulas and their related scientific theories are ‘not accurate’ and in what way we ‘cannot understand the reasons of their usefulness’. For instance if we take the very common example of Force=mass x acceleration, we do appreciate the fact that the heavier and the faster a thing is moving the harder it is going to hit something, but looking at each component of the equation we may realize that the mass of an object and the force the object would exert on something it hits are two disjoint phenomenon that seemingly have nothing in common, nor are they measured in similar units and nor are they convertible into each other. In terms of simple logic, we say 2balls x 3balls = 6balls, but 6balls cannot equal 2bats x 3hats, unless they are actually taken to that absolute acceleration where they can shape-shift and remain at both ends of the equation all the time.
The real dilemma with science and related math is however the fact that most of the entities that we talk of with surety and belief are such that they are known to us only by observable effects that they produce, but of what those entities really are, we know little. Like we know what ‘force’ is by the effect it makes on other things, we say that it is ‘a push or pull on an object’, but what it is in itself, we have no clue of. Furthermore when we define force to be equal to the product of mass and acceleration, we are not telling of something intrinsic to force but its relation to other entities. Likewise with ‘gravity’, which is also a force acting upon all things around us, but what the source of gravity is or what, if any, properties the supposed carrier of gravity called the ‘graviton’ holds, we know nothing of, all we know is the effect this unknown thing coming from an unknown place has upon us. The earlier ‘supposition’ that the source of the gravity of the earth, as a force, is in its core has been rendered obsolete with Einstein’s general relativity, which describes gravity not as a force but as a consequence of the curvature of space-time caused by the uneven distribution of mass/energy – which makes it perhaps the resultant ‘consequence’ of everything in the Universe. Again we see that the two ideas negate each other but both are also correct and practicable in their own paradigms. And again we find that we have bounced from one accurate description to another, yet we have no clue as to what the ‘reasons of their usefulness’ is, when we are clueless about any intrinsic properties of the entities we are talking of.
Perhaps knowledge will always be clueless of the intrinsic properties of objects and happenings in nature. Because knowledge is the ‘idea’ thought by the mind, about the ‘effects’ detected by the senses, from a ‘source’ we name the object. So knowledge can be said to be the second derivative effect produced by the source, it is the effect of the effect. Yet what the ‘source’ produces and what the mind produces in reaction to that, are mutually disjoint and altogether non-similar, or at least we have no means to find out either the intrinsic properties of the mind or of the object, what we are sure of is perhaps only the effects or the effects of the effects.
The mind records the effects it observes in the form of unit ideas, and with it intrinsic abilities of shuffling, recombining and structuring the units, produces complex ideas – ideas that the thought can appreciate, that mean something to the ‘thinker’. And this appreciation and meaning we have for an idea makes the value of the idea, it makes it rational, it makes it true and it makes it a belief, whether backed by empirical evidence or in search of empirical evidence as yet.
So knowledge evolves from paradigm to paradigm as it peels off the crude ways with which it had been perceiving objective reality. The same object, the same earth, the same sky, but the way we were looking at it all this time was so wrong – more tools and more discovery aid us in seeing the same things so clearly now. Yet the clarity is only in our perception, we are able to capture more and more effects in a wider and wider range and with those increased realization of effects we refine the ideas, which are effects produced by those effects. As Russell said in his essay on Ethics, “In this, as in all philosophical inquiries, after a preliminary analysis of complex data we proceed again to build up complex things from their simpler constituents, starting from ideas which we understand though we cannot define them, and from premises which we know though we cannot prove them”. Simply because our knowledge is, at its basis, rested upon ‘assumptions’ about the things we see, maybe like the simple assumption that the object I have in my hand is an apple, now what could be simpler than that, it’s a truth we know as a fact, yet the apple is what ‘we see’ of the thing, not what the ‘thing-in-itself’ may know itself to be.
Regarding the amount of knowledge we have compared to what knowledge really can be in its wholeness, we might think that our Evolution of Knowledge is a mere jumping from one face of infinity to another, but only within the bounded limits of effects detected by our sensual detectors. These limited effects are spontaneous, unpredictable and far-apart clues that merely help us complete the already possessed introvert picture of the Universe that is imprint in the framework of our thought-system – because this knowledge, that we intrinsically possess, that actually guides and fashions our journey towards discovery, ‘knows’ the very ‘basic assumptions’ about life and the Universe as simple as we know for a fact that ‘I have 2 pencils in my hand’ or ‘robbing and lying are bad things’ even when we do find instances when we may find them not to be so.
Perhaps then, this ‘common sense’ knowledge is the bunch of keys in the hand of the man who is to open the doors; this very simple tool is the key with which we can open upon us the doors of paradigm after paradigm and is the only tool that will open these doors. And the simplicity of this tool and its assumptious nature will always amaze us of the giant leaps it is able to take in the evolution of human knowledge.