I was thinking about the evolution of eyes and such and whether they are odd contingent results of evolution on Earth or whether they are EASY for chemistry and biology to come up with...

It's a current question in evolutionary theory, for instance:

If you play the tape over again of evolution wold you get COMPLETELY different weird critters and morphologies as S. J. Gould posited in his Wonderful Life,

or would evolution converge on many similar structures, as Simon Conway Morris posits in his "Life's Solution: Inevitable Humans in a Lonely Universe"

Here we find out that the two are having something of a feud, and Conway Morris is a theist, besides.

more ideas on this dilemma: Lewin's book "Complexity: Life At The Edge Of Chaos"

Take eyes. are they unexpectedly difficult things to evolve or are they nearly inevitable consequences of the way biology, chemistry and light interacts? or to take it to the extreme: as Conway Morris posits, is human intelligence ALSO an inevitable consequence of the laws of phyics?

Odd thoughts and the gut response is: of course not! but then i started thinking of the classification of finite simple groups.

You set up a simple set of axioms for what constitutes a mathematical group. then you go exploring the space of all possible groups by messing around, kind of like how evolution explores morphospace, except that we can possibly be more mathematially thorough! In fact can we find ALL the possible kinds of groups? is the morphospace infinitely complex, dirt simple or somewhere in between?

The surprise came a few decades ago when it appeared that we COULD map out all the possible kinds of groups (actually we found all the finite simple groups, kind of like the prime factors of groups)! And what we found was that there was moderate complexity: 18 different classes, plus... some chaos: 26 different sporadic groups that did not fall into any of classes.

The sporadic groups are odd, HUGE and complex. the largest has: 808,017,424,794,512,875,886,459,904,961,710,757,005,754,368,000,000,000 elements!

How on earth did the simple definition of a group imply this interesting space of structures with just a LITTLE bit of chaos?

Description here (describes axioms for group, some examples you can work out, and pointers to the mathematical results):

finite simple groups

So i'm wondering... if you look at physics, chemistry and the basics of cell bio as the axioms for life, is the possible morphospace a huge infinte chaos, where anything is possible, or is it more manageable with just a little bit of chaos? And thus, maybe there is not a chaos of sensory organs possible, but a finite bunch of them with eyes, being one of the classes? Of course the corresponding classification of possible structures must be WAY HUGER than the classification of finite simple groups. And we also have to model how the historical process of evolution constrained by the specific conditions of a planet (which are in turn modified by the evolution of the organisms...) explores that morphospace!

Another process that might whittle down the regions of morphospace possible for evolution, is that only a very small fraction of it might be attractive orbits to the evolutionary dynamical system

Say, as Stuart Kaufmann finds in his random boolean networks

So, maybe eyes are not so surprising after all.

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