**Followup to**: Building Something Smarter , Say Not "Complexity", That Alien Message

One of the Godel-inspired challenges to the idea of self-improving minds is based on the notion of "complexity".

Now "complexity", as I've previously mentioned, is a dangerous sort of word. "Complexity" conjures up the image of a huge machine with incomprehensibly many gears inside - an *impressive* sort of image. Thanks to this impressiveness, "complexity" sounds like it could be explaining *all sorts* of things - that *all sorts* of phenomena could be happening because of "complexity".

It so happens that "complexity" also names another meaning, strict and mathematical: the *Kolmogorov complexity* of a pattern is the size of the program code of the shortest Turing machine that *produces the pattern as an output*, given unlimited tape as working memory.

I immediately note that this mathematical meaning, is *not* the same as that intuitive image that comes to mind when you say "complexity". The vast impressive-looking collection of wheels and gears? That's not what the math term means.

Suppose you ran a Turing machine with unlimited tape, so that, starting from our laws of physics, it simulated our whole universe - not just the region of space we see around us, but all regions of space and all quantum branches. (There's strong indications our universe may be effectively discrete, but if not, just calculate it out to 3^^^3 digits of precision.)

Then the "Kolmogorov complexity" of that entire universe - throughout all of space and all of time, from the Big Bang to whatever end, and all the life forms that ever evolved on Earth and all the decoherent branches of Earth and all the life-bearing planets anywhere, and all the intelligences that ever devised galactic civilizations, and all the art and all the technology and every machine ever built by those civilizations...

...would be 500 bits, or whatever the size of the true laws of physics when written out as equations on a sheet of paper.

The Kolmogorov complexity of just a *single* planet, like Earth, would of course be much* higher* than the "complexity" of the entire universe that contains it.

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