The transformation rules operating in a computer system are embodied in the computer’s software, which is run by the computer’s central processing unit (the CPU). The software instructs the CPU how to operate on its input information in a specified way. Built into the CPU are numerous logic gates (like AND, OR, and NOT gates) that transform sequential inputs of ones and zeros into further sequences of ones and zeros according to how input is fed into the CPU. Millions of such transformations occur each second, and the resulting output states (further strings of ones and zeros) can then be interpreted from outside the system. In other words, the context of human perception is needed to inject some meaning into the computer’s output. For example, a computer system might take some input from a keyboard, process it according to its program, and then display the words
Other formal systems are things like dreaded algebra and heavy propositional logic (input
Chess is a more common kind of formal system. In chess, the pieces are the individual symbols and the strings are the possible positions of those pieces. The game proceeds according to transitions of the initial state, whereby the initial configuration, or initial start pattern, changes into another configuration through the movements of the chess pieces. This is the same principle involved with computers, as they too work by processing information via transitions of an initial input state. Thus, the rules of chess represent a kind of software that dictates how state transitions are to proceed.
The transition from one state of an ongoing chess game to another is discrete, as with the operation of any formal system. A bishop does not half move; instead, it “jumps” from one position to another. Also, since a formal system like chess depends solely on the form of the symbols and strings relative to one another, it is irrelevant what the pieces are made of. Indeed, they need not even be “physical” at all, for most professional chess players are able to play the game in their heads alone. Though that will not do much for avid spectators of chess, it does highlight the fact that a formal system can be realized in many different types of medium. Indeed, a computer system can be made of old tin cans and bits of string. The crucial aspect is the way the system’s symbols relate to one another, regardless of the medium.
You could even take some people and use them to represent in binary code two numbers that you would like to multiply. Roughly symbolizing genital structure, the women could represent the number zero and the men the number one. After the two numbers have been transformed into a binary queue of men and women, one could multiply the two numbers by channeling the queue through a few logic gates operated by a couple of friends (instead of telling the binary people queue to go forth and multiply…). You could then take the output queue (the new pattern) and interpret the resulting encoded number, which, if you set up the system correctly, would correspond to the multiplication of the two original numbers. Agreed, a calculator app on a cell phone could have done the job more efficiently and with much less hassle, yet the point is that the calculator app itself works on the same principle, only it uses memory bits to embody the binary information. Formal systems like computers are therefore not tied to any particular substantiation.
Formal Systems and Language
Before we alighted on the notion of formal systems, I argued that not only was the Universe made of information, but that this information moved or flowed in a language-like way. I claimed that the elements in informational systems like DNA uttered their informative content in response to specific contexts, as if natural dialogues were unfolding. We have now reached the point where we can define language, in whatever mode, as a formal, and hence informational, system. Let me quote writer Paul Young, author of
All languages are form dependent. In spoken language, arbitrarily selected symbols are manipulated as units that can be interconnected or arranged only in specific relationships according to specific rules. It is the form (relations), whether semantic, syntactic, experiential, or contextual, of the elements of language, and not the matter of which they are constructed, from which the mind generates meaning; the physical symbols themselves embody no linguistic meaning…. It is neither the mass nor the energy content of the letters, words, sentences, and so on, whether expressed via mouth, pen and ink, stylus and wax, or computer printout, that contains the information in language, but their specific form or arrangement.{36}
I have gone one theoretical leap farther, however. Young refers to the so-called “matter of which they are constructed” with regard to the symbols of language. This “matter,” in my view, is itself composed of language-like elements within some formal system or another. This implies that there is only information; the Universe is built on formal informational systems like those of physics, chemistry, and biology, and all are embedded within one another to form an integrated continuum. They are formal systems because it is the form (that is, the pattern) of the elements, whether they are particles, atoms, molecules, or words, and their formal relations to one another that determine the role, meaning, and subsequent behavior of those elements.
The language-like system of particles represents the Universe’s most basic informational substrate. This system begets the language-like system of atomic elements. In turn, this system gives rise to the language-like system of chemistry, which itself leads to the language-like system of DNA. And so on right up to the substantiation of the language system of consciousness within our biological brains. Each language-like system of information utilizes its own kind of logic to express itself, namely the logic of physics, the logic of chemistry, molecular logic, the logic of genetics, bio-logic and, finally, the logic that underpins cognition. Each kind of logic gives rise to patterns that influence one another and that lead to more patterns, some of which produce, or come to embody, new systems of logic. Descartes was wrong; the dualistic mind/ body problem is an illusion. Formal systems consisting of language-like information constitute reality. Information in process is everywhere and everything.
Some Inside Information: Are We Output?
If the above reasoning is correct, the Universe must in a real sense be an ongoing computation in which its information content is being continually churned and processed so as to yield new forms and/or patterns of information. At any one moment the Universe is in a specific state or form. This state is processed according to the “rules of the Universe,” and another universal state is formed. And so on, from the moment of the alleged big bang to right now. The entire Universe can thus be considered a progressive state transitional computation, a kind of metaformal system continually expressing its creative potential. And, more profoundly, we are inside the computation. Or so it seems.
Is such speculation tenable? Could we really be locked inside a vast Matrix-like computation as though we were all but hapless subroutine prisoners, moving in time to some grand algorithmic dance? According to our foray into the nature of information and computational procedures, the suggestion that the Universe is a kind of computation would appear to be a spectacular probability, albeit a trifle claustrophobic, and an outrageous absurdity at the same time. We are so used to thinking of computers as neat boxes atop desks that we forget that they are formal systems that can, in principle, be embodied in anything. But, if we do take this fact into account, and if we also bear in mind that computers can manipulate all sorts of information, even going as far as simulating things like the solar system, then we might well be attracted to the idea of a computational Universe. Or am I merely resorting to the use of a convenient metaphor borrowed from our technological culture? If so, the metaphor might be useful but, ultimately, since it is temporal, its use will be limited until another, more useful metaphor becomes available.
