Everything is a big subject. Yet modern scientists believe they have stumbled upon a key which unlocks the mathematical secret at the heart of the universe: a discovery that points them towards a monumental "Theory of Everything" which will unite all the laws of nature into a single statement that reveals the inevitability of everything that was, is, and is to come in the physical world.
Can we hope to give ultimate explanations of the Universe? Is there a Theory of Everything and what could it tell us? And just what would such a theory actually encompasse?
Science is predicated on the belief that the universe is algorithmically compressible and the modern search for the Theory of Everything is the ultimate expression of that belief, a belief that there is an abbreviated representation of the logic behind the Universe's properties that can be written down in finite form by human beings.
Only very rarely have ambitious scientists attempted to construct a theory of physics which would unite all the disparate and successful theories of different forces of nature into a single coherent framework from which all things could be in principle be derived.
The current breed of candidates for a title of a "Theory of Everything" hope to provide an encapsulation of all the laws of nature into a simple and single representation.
The theory of Everything seeks to provide us with the ultimate directory of all possible changes. The guiding principle in the search for this all controlling formula is that it must be a single law, not a collection of different pieces. Identifying this over-arching symmetry, if it does indeed exist, and is manifest in a form that is intelligible to us may be the nearest thing we could get to discovering the "Secret of the Universe"
But it may be that physical reality, even if it is ultimately mathematical, does not make use of the whole of arithmetic and so could be complete. It could lie within one of the decidable branches of mathematics that are not as rich as arithmetic.
The lessons learned here is that mathematical axioms are more like initial conditions for natural laws than we might have suspected. Indeed, it is the hope of some that they may turn out to be the same: that the ultimate assumptions for the theory of everything are those required for logical consistency.
It will become clear that some prescription for initial conditions is crucial if we are to understand the observed universe. A Theory of Everything needs to be complemented by some such independent prescription which appeals to simplicity, naturalness, economy, or some other metaphysical notion to underpin its credibility.
The only radically different alternative would seem to lie in a belief that the type of mathematical description of natural laws we have come to know and love - that of casual equations with starting conditions - is just an artifact of our own preferred categories of thought and merely an approximation to the true nature of things.
The dualistic view that initial conditions are independent of laws of nature must be reassessed in the case of initial conditions for the universe as a whole. If the Universe is unique - the only logically consistent possibility then the initial conditions are unique and become in effect a law of nature themselves.
We would expect the things could be perfectly unified in some sense, so that the laws and the ultimate particles of Nature that they govern are married together in a union of perfect and unique intercompatibility.
"...if reductionism means that all notions for complexity must be sought at a lower level, and ultimately in the world of their most elementary constituents of matter, then reductionism is false, Instead, as we might expect to find novel types of complex origination, at each level, as we go from the realm of quarks to nucleons to atoms to molecules to aggregates of matter.
We have seen that a naive reductionism that would seek to reduce everything to its smallest constituents pieces is misplaced. If we are to arrive at a full understanding of complex systems especially those that result from the haphazard workings of natural selections, then we shall need more than current candidates for the title "Theory of Everything" have to offer. We need to discover if there are general principles that govern the development of complexity in general which can be applied to a variety of different situations without becoming embroiled in their peculiarities,
Perhaps there exist a whole set of basic rules about the development of complexity which reduce to some of our simpler laws of nature is situations where the level of complexity is essentially nil .. If such rules do exist, then they are not like the laws which the particle physicists seek. But is there any evidence that such principles exist?
A collection of 1027 protons, neutrons, and electrons may be all that a desk-top computer is at some level, but clearly the way in which those sub-atomic particle are put together, the way in which they are organized, is what distinguishes the computer from a crowd of 1027 separate sub-atomic particles.
The longed-for theory of Everything promises to provide the final discovery after which all physics will become the refinement of its content, the simplification of its explanations. At first, "The Theory" will be intelligible only to the afficionados, then later to a wider circle of theoretical physicists. Next it will be presented in ways that make it accessible to scientists dedicated to other persons. Eventually it will appear on t-shirts. At all stages of this process, it will be believed that the route from the complicated to the transparently obvious is a path toward the "true" picture of Nature.
The question of the existence of a 'Secret of the Universe' amount to discovering whether there is some deep principle from which all other knowledge of the physical world follows.
Some seekers after the Theory of Everything would seem to be hoping that the uniqueness and completeness of some particular mathematical theory will make it the only logecally consistent description of the world and this will transform it from being a synthetic to an analytic statement.
So, today, perhaps the image of the Universe as a computer is just the latest predictable extension of our habit of thought. Tomorrow, there may be a new paradigm. What will it be? Is there some deep and simple concept that stands behind logic in the same manner that logic stands behind mathematics and computation?
Science is most at home in attacking problems that require technique rather than insight. By technique we mean the systematic application of a sequential procedure - a recipe. The fact that this approach to the world so often bears fruit witnesses to the power of generalization.
Nature uses the same principle again and again in different situations. The hallmark of these reapplications is their mathematical character. The search for the Theory of Everything is a quest for the technique whose application could decode the message of nature in every circumstance. But we know there must exist circumstances where mere technique will fail.
There is no magic formula that can be called upon to generate all the possible varieties of these attributes. They are never fully exhaustible. No program or equation can generate all beauty or all ugliness: indeed there is no sure way of recognizing either of these attributes when you see them. The restrictions of mathematics and logic prevent these prospective properties falling victim to mere technique even though we can habitually entertain notions of beauty or ugliness. The prospective properties of things cannot be trammeled up within any logical Theory of Everything. No non-poetic account of reality can be complete
There is no formula that can deliver all truth, all harmony, all simplicity. No Theory of Everything can ever provide total insight, for to see through everything would leave us seeing nothing at all.
Barrow discusses the search for a Theory of Everything and what such a theory encompasses. . He calls for a deep, general and transparently obvious principle, which is simple, natural and economical. It must be a single framework, a logically consistent, intercompatible and general principle which is capable of algorithmically compressing the physical Universe.
Barrow concludes his book with a surprise statement, "There is no magic formula...No Theory of Everything can ever provide total insight for to see through everything would leave us seeing nothing at all."
Barrow is correct as far as he goes. No particular theory can explain everything in general, no theory of science can explain all of science. But Barrow is incorrect if he assumes the book is closed. What about a theory of how everything works? Such a theory would not be difficult to find. If we assume that everything works the same way, then anything could tell us how everything works. What is it that is common to everything?
I chose the common coin to first grasp this concept. I knew that a coin has two sides, or so everyone said, but I thought there must be more than just "two sides to every coin" and indeed there is: the side that holds everything together also exists so there are really three, not two, sides to every coin. It should be noted here that the idea of two parts does not always mean only two parts. Two parts happens to be the minimum of parts, obviously, and two parts will always have a relationship if they are parts of a whole. Thus the simplest machine always has three parts. Is this the key we need to unlock all locks? It is the relationships that are common to all parts. Relationships are common to everything, so a language of relationships must speak to everything. Relationships are usually verbs, gerunds, based on action rather than identity. Relationships are the core of mathematics, the foundation of science, and essentially the whole of art, music and love. All of these can (only) be explained in terms of relationships.
Interestingly, this principle is not new. Indeed, it can be found as far back as 600 B.C. when Lao Tzu spoke of it in Chap. 42 of the Tao Te Ching. In modern terms, Information theory is similar but, again, one of those particular theories. A clue was provided by physicist Gerard t'Hooft in the May, 1980 Scientific American, in which he described the standard elementary particle theories like so: "What may be more important, all the theories of the four forces have the same general form."
Once understood, this "principle" becomes "transparently obvious".