Physicists have a lot to say about what they perceive as “information.” They use mathematics that is even peculiar to them to describe it. (They are still, apparently, messing around with Claude Shannon’s bits, logarithms, uncertainty of communication, etc.) But really, what is it? Years ago, I came up with a “dimensional” way of answering the question. It was not elegant; and it went (almost) nowhere. The mathematical “real numbers” can be conceived as being “one dimensional.” That is, they describe quantities such as “how long,” “how heavy,” “how hot,” etc.
The most basic mathematical “functions” are two-dimensional — they are curves on a (flat) plane. The theory gets a bit messy here, since sketches made with soft chalk on flat canvases could just as well be called “functions.”
So real numbers are one-dimensional. “Basic” functions are two dimensional. Boolean values would be “in” or “out,” “yes” or “no,” or “true” or “false,” etc. Clearly they are zero-dimensional. They are not entities that have the quality of being “more” or “less,” They either “are” or they “are not.” This all makes clear sense, yet it goes nowhere by itself.
I used to work for the State of Connecticut, in the U.S.A. as a surveyor’s assistant, planning long highways. They were very long, and so we would have to take “earth curvature” into account. In ancient times, for ships sailing on the vast oceans, this was done with something called spherical trigonometry. Distances on our spherical earth were measured in degrees of arc, rather than in, say, meters. A spherical triangle is formed by the shortest distance (on a globe) of three points. Etc. If we ignored this earth curvature, roads from New York State would simply not quite meet up with roads from the State of Connecticut. That would be a very bad thing!
Now this is all absurd from the point of view of the ordinary land surveyor. He or she would do a “cadastral” (line-by-line) survey, which is concerned with pieced-together bits of evidence, such as stone walls, iron pipes driven into the ground, and sometimes, fences. It was all performed using precision instruments. But there was no thought at all given to “earth curvature!” It was taken for granted that the earth was basically flat, and it would be ridiculous take into account tiny distortions caused by earth curvature. I worked at jobs doing both types of surveying. But these ways of thinking, though perfectly logical, were completely incompatible! This means that, for human beings, two-dimensional information is fundamentally incompatible with three-dimensional information. Basically, three dimensional information cannot be faithfully represented in terms of two dimensional information. Yet, it is usually necessary to think of geography in terms of two dimensional information. The physical universe manages to operate with no difficulties arising from the discrepancies between a “flat world” and a “round world.” It is “monological”. Everything fits together, and there is no possibility of any contradiction between chemistry, physics, mathematics, logic, and so on. The universe “talks to itself only.” But nonetheless, operating on a small scale, human beings (and most everything else) would waste vast amounts of energy by trying to take notice of earth curvature. Is this perhaps a line of demarcation between the human and the rest of the universe? A human being has a brain that can negotiate discrepancies between incompatible systems of logic. The essence of sentience is that it has the ability to negotiate between inconsistent systems. Between the two dimensional and the three dimensional, for example.
There exist other incompatible systems in the world that must be reconciled. Human speech is not an “monological” process. That is, it is not at all like mathematics or physics. In monological systems, everything locks together into a totally coherent process. This has engendered a fallacy that has persisted for 2,500 years. Human speech is a “dialogical” (mediated) system, much like an advanced biological system. It is a system comprised of subsystems that are in fact somewhat incompatible, and which thus require the services of a computational apparatus (the human mind) to mediate their mutual interference.
Now, consider the biology of your physical being, for example: Your brain requires glucose constantly; it demands 25% of the ATP energy of your cells. But that glucose is rather toxic to most every other organ in your body. So the size of your brain is not so important as the size of your liver. Humans have huge livers to keep their blood free of neurologically disruptive chemicals, and they work with the pancreas to balance the insulin that keeps the brain running without the glucose in the bloodstream poisoning every other organ. This is not an monological system that runs automatically. This “dialogical” system is fundamentally unstable, and requires the mediation of many mutually interfering subsystems by a DNA/protein computer, which must run constantly to maintain a tenuous dialog.
The brain is another computational system whose main function is the mediation of mutually interfering subsystems. One of them is language. So, language is not amenable to ordinal proofs and corollaries. It can only be understood in terms of typology and “comprehensive closure” (an approximate, yet detailed and reasonably accurate “fitting of things together”). We can observe its organs and their interactions, but we will never arrive at proofs and corollaries.
The science of computing is merely at the threshold of becoming able to manage incompatible dialogical systems. For example, if a computer program is tasked with dividing three by zero, the machine could just “crash,” or it could “throw an exception,” which might be “handled” by some special sub-program. This sort of solution is often seen as awkward. In fact it is the first step toward the evolution of dialogical (sentient) systems.
Mutually inconsistent systems can sometimes co-operate via the implementation of stochastic methods. Decisions can be made by lackadaisical coin-tossing, but that will not usually give adequate results.
What we think of as “information” is really always the product of dialogical mediated systems, that are alive, or intelligent, or (sometimes) merely computational.
And the entire human enterprise of “science” has always been a never-ending attempt to represent information in the zero-dimensional form, manifested as written and spoken words.
(By clicking HERE you can read or write comments below.)