A Mathematician's Approach to Evolution Theory

Discussion in 'General Science & Technology' started by Eugene Shubert, Aug 28, 2015.

1. Eugene ShubertValued Senior Member

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David Hilbert was a powerful mathematician. For example, Albert Einstein, after spending eight years trying to derive the equations of General Relativity, even with the help of many geometers, got nowhere until he explained his “grand problem” to David Hilbert. Hilbert spent six months studying Einstein’s “grand problem” and then solved it in two weeks’ time.

I’m not aware of Hilbert saying anything about evolution but I suppose that most mathematicians here are Darwinists. I wonder what would be the result if professional mathematicians, with the assistance of knowledgeable Darwinists, tried to formulate their understanding of biological evolution in the style of Hilbert’s mathematical philosophy of physics.

The following brief illustration of Hilbert’s mathematical philosophy should suffice for the purpose of understanding my question:

“If geometry is to serve as a model for the treatment of physical axioms, we shall try first by a small number of axioms to include as large a class as possible of physical phenomena, and then by adjoining new axioms to arrive gradually at the more special theories. ...The mathematician will have also to take account not only of those theories coming near to reality, but also, as in geometry, of all logically possible theories. He must be always alert to obtain a complete survey of all conclusions derivable from the system of axioms assumed.” http://aleph0.clarku.edu/~djoyce/hilbert/problems.html

"Species change and the fittest, the most adaptable and the most prolific variants have the greatest chance of survival."

My question therefore is this: What should be the next incontestable axiom (i.e., incredibly well-verified empirical observation) to adjoin to the preceding one?

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3. OnlyMeValued Senior Member

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This statement seems to contain an inherent contradiction! If the information in the sentence is accurate in terms of time, it took Hilbert six months and two weeks!

The rest of your post seems to be leading with insufficient information provided to answer the last question. It sounds to me as though you have a hidden agenda, which should likely not.., be posted in the Physics & Math forum. I am guessing because I don't follow your posts, but maybe philosophy or some where in religion/religious philosophy...? Doesn't sound like math or physics.

5. krash661[MK6] transitioning scifi to realityValued Senior Member

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umm this is only partially correct.

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8. Eugene ShubertValued Senior Member

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As I said, David Hilbert was a powerful mathematician. And if you were to study his scientific philosophy, you would realize that Hilbert's vision of a unified science called for placing all the true sciences under mathematics. So for the purposes of this thread, I was asking a mathematical question.

"In my school, the brightest boys did math and physics, the less bright did physics and chemistry, and the least bright did biology. I wanted to do math and physics, but my father made me do chemistry because he thought there would be no jobs for mathematicians." — Stephen Hawking.

"Scientists are explorers. Philosophers are tourists." — Richard P. Feynman.

And you think that tourists are qualified to understand and answer my question?

Last edited: Aug 28, 2015
9. originIn a democracy you deserve the leaders you elect.Valued Senior Member

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Well, then either you were wrong 5 years ago or your memory is faulty, because what you are saying now is certainly not accurate.

10. Eugene ShubertValued Senior Member

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Why are you so certain?

11. originIn a democracy you deserve the leaders you elect.Valued Senior Member

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I just happen to be reading about that particular interaction between Einstein and Hilbert yesterday in the most recent edition of Scientific American.

12. Eugene ShubertValued Senior Member

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As I said, "I wonder what would be the result if professional mathematicians, with the assistance of knowledgeable Darwinists, tried to formulate their understanding of biological evolution in the style of Hilbert’s mathematical philosophy of physics." So I want to hear from mathematicians that understand Darwinian evolution.

13. QuarkHeadRemedial Math StudentValued Senior Member

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Leaving aside the trivial point that any observation is by definition empirical (hence you employ a linguistic redundancy), you seem not to understand the difference between an axiom and an observation.

14. Eugene ShubertValued Senior Member

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For most of the 20th century, it was an undisputed belief among knowledgeable academics that Hilbert derived the field equations first and also helped Einstein along the way. That was only contested recently after someone mutilated a key paragraph of Hilbert's page proofs. Obviously, the mutilation was done by an Einstein worshiping physicist. There are many suspects. See Corry, Renn and Stachel Fingered as Likely Suspects in the Mutilation of David Hilbert's Page Proofs.

15. Eugene ShubertValued Senior Member

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Not all observations are provable or verifiable by experience or experiment. Mathematicians have the audacity to select whatever axioms they want, provided that it leads to underpinning an intricate structure that generates results. I will accept any reformulation of ancient ideas that rattles the cages of those imprisoned by unnecessary traditions a sufficiently good result.

16. originIn a democracy you deserve the leaders you elect.Valued Senior Member

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It is clear that Hilbert helped Einstein tremendously in formalizing his field equations. Hilbert may well of derived the complete equations first (by a day or two), but Einstein publicly presented them first.
I think that it is safe to say and that without the collaboration of Hilbert and Einstein together it would have been many more years before the field equations were formalized.
So can we now get back to your attempt to show that God does not approve of evolution?

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17. Eugene ShubertValued Senior Member

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"Species change and the fittest, the most adaptable and the most prolific variants have the greatest chance of survival." I'm happy to take that as an axiom. Would you like to answer the question of the opening post?

18. danshawenValued Senior Member

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How about: "The environment may also change, and this may be random, or result from stress applied on other biota that are a result of a successfully evolved species." or simply: "Evolution is always a work in progress; today's successful adaptation may be tomorrow's failure and lead to extinction."

I don't believe this process is one that lends itself to easily fit into a mathematical description like Hilbert's axiomization. Why should it? Evolution is not something that is based on something as orderly as geometry. It is more akin to chaos with survival as a moving target that obeys few axioms or uniform rules, like performing shotgun integration on a target that not only moving, but keeps changing its shape.

Just like any other tool we use, the more finely tuned the adaptation, the less adaptable it will be to a change of rules.

The only adaptation that breaks all these apparently random evolutionary rules is the one that makes us care about each other enough to model each other's behavior. That was a masterstroke of evolution that has yet to be duplicated by other species to the extent that we do it on this planet. Whether it occurred by accident or by design, it's a pretty hard survival strategy to beat. It gave us science because we can model the way that subject behaves as easily as if it were the behavior of a person. It also gave us religion and a means for modeling the behavior of whatever it is that resulted in our creation. Whether this belief is based on objective reality or not is not really important.

Last edited: Aug 28, 2015
19. Eugene ShubertValued Senior Member

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All that I'm asking for is the underpinning of an intricate structure that supports and defines Darwinian evolution. It could be that Darwinian evolution is completely trivial.

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20. krash661[MK6] transitioning scifi to realityValued Senior Member

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actually einstein was presenting his theory, hilbert was in the audience, said to himself, i can solve that theories eq, they both worked on it. hilbert came up with it within a same time frame as ensien. hilbert said, it's einstein's theory, credit him.

21. OnlyMeValued Senior Member

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Just mentioning a mathematician and physics does not make any of your opinions or questions suitable for the Physics & Math forum.

I don't know where it really belongs but not here.

22. DywyddyrPenguinaciously duckalicious.Valued Senior Member

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In the Cesspool, where ALL of Eugene's posts belong.

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23. Eugene ShubertValued Senior Member

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Not exactly, but it is true that Hilbert was extraordinarily generous to Einstein.

At a gathering of mathematicians, Hilbert asked:

"Do you know why Einstein said the most original and profound things about space and time that have been said in our generation? Because he had learned nothing about all the philosophy and mathematics of time and space." P. Frank, Einstein – His Life and Times, p. 206.

I believe that this statement should be interpreted according to David Hilbert's philosophy of physics. In essence, Hilbert believed that "physics is too difficult for physicists" and that mathematicians should take it over. Isn't it obvious that Hilbert is chiding mathematicians for having no interest in his mathematical challenge to axiomatize all of physics?

Here is another famous Hilbert quote, referring to the general theory of relativity, that I also interpret as Hilbert chiding mathematicians for their disinterest in physics:

"Every boy in the streets of Gottingen understands more about four-dimensional geometry than Einstein. Yet, in spite of that, Einstein did the work and not the mathematicians."