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in reply to Re: Evolving formulae
in thread Evolving formulae

The day we consign math to genetic algorithms, IMHO, is the day we stop understanding math.

I suppose that depends on two things -- first how well the programs are able to describe their new discoveries to us. This is the case for all of mathematics right now... just because you personally didn't solve some problem doesn't mean you can't understand the solution. Also when you do solve a problem it doesn't mean you can make everyone else understand.

Second, you (and everyone should do this excercise with us) need to decide whether you consider mathematics (or programming for that matter!) to be a discipline of creation or discovery. Either people are making this stuff up and it wouldn't be there otherwise, or we are just finding out what is already out there.

I personally am a discoverist!

Hmm... actually now that I think about it that second point could well be irrelevant. Who cares whether the algorithms are discovering mathematics or creating it? Oh well, its a fun thought anyway.

What does everyone think... are programs discovered or created?

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Re: Re: Re: Evolving formulae
by tsee (Curate) on Feb 28, 2004 at 08:42 UTC

    Personally, I prefer thinking of programs being created - I seem to work so much more productively that way ;)

    Fun aside, I think mathematics is neither completely human-created nor -discovered. It's a mixture of the two. Now, if Hilbert had been right and we could deduct everything from a created set of axioms, I'd say we created the axioms and discovered the rest.

    Unfortunately, Hilbert was wrong and on the grand scale of things, to me, mathematics is a steaming pile of dung if you consider that perfectly logical things contradict themselves. Thus, mathematics must have been created by humans.

    Steffen

      ... if you consider that perfectly logical things contradict themselves.

      I think there might be a flaw in your argument! :)

      Actually you have a wonderful point.