22 January 2015

Compressibility, law and known facts to memorize

David Deutsch begins his book entitled The Fabric of Reality stating that the meaning of “to know everything is known” is equal “to understand” the world, but it doesn’t mean the knowledge of every isolated fact. We are far from a theory of everything which would be able to explain how our World works, but it “distinctly less fantastic than the idea that one person could memorize every known fact.” [p. 3]
It is not a surprise to found ourselves in a Universe which can be at least partially interpretable by laws –perhaps a primitive form of life could be able to evolve without a kind of predictability, but an intelligence able to interpret the World surely not. A kind of compressibility is the feature which allows to use shorthand to calculate the reality from certain pieces of information (i.e. a planetary orbits). Opposite to it, a string is random if we cannot present a representation of it which is shorter than the original sequence (Barrow: New Theories of Everything 2007, p. 11.).
Having studied a special musical instrument named lyre the Pythagoreans concluded that the reality ruled by numbers, and because of their intellectual heritage we regard self-evident that the description of the nature is compressible thanks to the numbers. It is not questionable that this mathematics based method proved to be really efficient to describe some aspects of reality.
On the other hand, there are incompressible things: i.e. it is trivial that there is no a shorter version for a poem which is equal to it, and it is a particular feature of the Universe that it can be divided into a compressible and an incompressible part.
Obviously, not “every known fact” mentioned by Deutsch is mathematically non-accessible, but our World’s another feature the proportion of the rules and the data we should memorize is unequal.
There are so few rules that some scientists hope to reduce all of them to a super formula. As it was mentioned earlier, the existence of intelligent life prescribes the existence of a very huge amount of data, since the evolution of thinking required billion years, and a long period of time means many events.
But on the one hand, why was it a so slow process? On the other hand: why do not exist many-many more laws even comparable in amount to the “every know facts?” Is it a requirement of a biofil Universe or only an accident?

And a concluding remark: we can draw up a categorization based on the relationship between "rules" (circa compressibility) and "data". Obviously the fifth subcategory is the most interesting where the efficiency of rules is determined either by a nonlinear function or changes randomly.


efficiency example
1. perfect (theoretically) compressible macro physical laws
2. zero poem, human society's evolution, etc.
3. less and less efficient over time meteorology
4. more and more efficient calculation by iterations
5. different patterns determines the effectifiency in time than the third or fourth subcategory ?

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