viznut's amazing discoveries

[2007-06-12]

All Imaginable Things Exist

[Leibniz's medallion celebrating binary
numbers as the secret of creation]

According to Gottfried Wilhelm von Leibniz, we live in "the best of possible worlds". That is, our world is based on a minimal set of rules producing a maximal amount of "richness". In computational terms, it could be described as a very short computer program that outputs highly complex patterns.

The basic premise of a cosmological hypothesis called Digital Physics is that the whole universe is indeed digital and computable, perhaps something like a cellular automaton. The legendary computing pioneer, Konrad Zuse, was also a pioneer of this idea. And yes, this idea has a relationship with my earlier post about fitting a universe in a 4K intro.

One of my favorite scientists, J├╝rgen Schmidhuber, goes on to point out that, considering that our universe is computable, the shortest program that computes it is actually the one that computes every possible computable universe (with every possible set of physical constants and laws). Something like this, for example:

  for(n=0;;n++)
  {
    binaryString a = createStringOfZerosWithLength(n)
    do {
       universe = new Universe();
       universe.initializeWithProgram(a);
       universe.start();
    } while(++a); // goes thru all the binary sequences of length n
  }   

Assuming that this is the basis of our existence, then it is also the basis of the equally true manifestation of every imaginable universe, every imaginable life experience, every imaginable idea, et cetera. Even every imaginable variation of yourself and your life exists in an infinite number of permutations. So, in short, All Imaginable Things Exist.

What binds all these imaginable things together is not causality, but the fabric of computability, which, for instance, makes it possible to simulate smaller universes within a larger one. In our universe, we use computers to simulate all kinds of virtual worlds such as "games of life", and similarly, our universe is being simulated in an infinite number of larger universes. All of these simulations reflect the same "stand-alone" universe, or an "idea" thereof.

It is quite fashionable nowadays to extend computational concepts into something really big and profound, such as cosmology and metaphysics. However, I see nothing wrong with it - each generation finds its own ways for getting fascinated about the deep questions. And personally, as someone who has been influenced by bits and bytes since childhood, I get quite a lot of kicks from "computerish" philosophies like this.

[Information emanates from nothingness]

One of the philosophical aspects I like the most is the relationship of "profoundness" with information-theoretical complexity. That is, the fewer bits it takes to represent an idea (in algorithmic means or otherwise), the more profound the idea is. The most profound of all ideas, of course, is the one at the centre of All-That-Is, the one that cannot be defined by anything else that an empty string (zero bits, no information). Philosophical traditions across the world give different names to this idea: Tao, Logos, Ein Sof, Hen (The One), and so on.

According to the commentators of Yijing (I Ching), in the beginning there is Taiji (T'ai Chi), with no information content whatsoever. Taiji splits into two polarities (yin and yang), both identified by a single bit (or "yao"). Each of these splits in two, collectively creating four different two-yao combinations. The process continues, with each step doubling the number of combinations and increasing their description length by one bit. Short binary strings (especially the 3- and 6-bit combinations) represent all kinds of archetypes that govern All-That-Is.

But anyway, even though we might understand the basic principles behind existence, the infinitely massive infinite infinity that emanates from it is so cosmically vast that it escapes mortal understanding. And besides, that's the way I like it.