Re: Raatikainen's critique of Chaitin
From: Robin Chapman (rjc_at_ivorynospamtower.freeserve.co.uk)
Date: 09/08/04
- Next message: Thomas Mautsch: "Re: Weird Trigonometric Identity"
- Previous message: mina_world: "residue....-"
- In reply to: Craig Feinstein: "Re: Raatikainen's critique of Chaitin"
- Next in thread: Robin Chapman: "Re: Raatikainen's critique of Chaitin"
- Messages sorted by: [ date ] [ thread ]
Date: Wed, 08 Sep 2004 16:49:02 +0100
Craig Feinstein wrote:
> kramsay@aol.com (KRamsay) wrote in message
> news:<20040907203446.22164.00000631@mb-m05.aol.com>...
>>
>> |See a paper that I wrote http://arxiv.org/abs/math/0312309
>>
>> Oh, so you're the guy who wrote *that*? I think you should take some
>> time and try to learn how to do rigorous proofs. You don't come
>> anywhere near proving an independence result in that paper.
>
> That's not a valid criticism. It's a good paper and argument.
No and no.
> It is
> true that it is informal in some senses, but it is valid nevertheless.
No.
>>
>> |The reasoning in it is a little different than Chaitin's reasoning (I
>> |look at computational complexity while he looks at information
>> |complexity), but it comes to a similar conclusion.
>>
>> The reasoning is hugely different, in that his mathematics, at least,
>> makes sense.
>
> Again, not a valid criticism, because it doesn't say anything. It's
> just your opinion.
?
Are you now asserting that Chaitin's mathematics makes no sense?
>>
>> These hypotheses are treated for the time being as unproven but
>> probably true. I don't know what change in policy anybody would
>> recommend to the mathematical community concerning them. I don't
>> think giving up on proving them is a good idea; that would be
>> giving up way too easily. I believe the concensus is that at least
>> the Riemann hypothesis, Goldbach, twin primes, and the like will
>> someday be proved. I can imagine someone urging us to take them more
>> for granted, for example to quit worrying about what you can prove is
>> true without using the Riemann hypothesis. (Some estimates in number
>> theory are pubished in two cases, one for what they could prove
>> assuming the Riemann hypothesis or the generalized Riemann hypothesis,
>> one for what they could prove otherwise.) I don't think the saved time
>> would be worth hiding which hypotheses are being used, however.
>
> Again, that's just your opinion, just like some people believe that an
> angle can be trisected with a straight-edge and compass.
See
http://www.cut-the-knot.org/pythagoras/archi.shtml
>>
>> |See http://crd.lbl.gov/~dhbailey/expmath/
>> |I wouldn't be surprised if there is no deductive explanation for the
>> |picture there. One can only explain it using statistical arguments.
>>
>> I would be _very_ surprised if algebraic number theory was unable to
>> produce an explanation for the pattern:
>>
>> This is a plot of all roots of polynomials with coefficients
>> 1 or -1 up to degree 18. Coloration is by sensitivity of the
>> polynomials to slight variation around the values of the zeros.
>> The color scale represents a normalized sensitivity to the range
>> of values; red is insensitive to violet which is strongly
>> sensitive. The bands, quite clearly visible in the plot, are
>> unexplained.
>>
>> The important thing is that this group is busy discovering such
>> phenomena experimentally. Expecting not to be able to provide rigorous
>> explanations for them is very pessimistic.
>
> But perhaps realistic.
That's just your opinion (and we have seen how worthwhile
your opinions have).
-- Robin Chapman, www.maths.ex.ac.uk/~rjc/rjc.html "Lacan, Jacques, 79, 91-92; mistakes his penis for a square root, 88-9" Francis Wheen, _How Mumbo-Jumbo Conquered the World_
- Next message: Thomas Mautsch: "Re: Weird Trigonometric Identity"
- Previous message: mina_world: "residue....-"
- In reply to: Craig Feinstein: "Re: Raatikainen's critique of Chaitin"
- Next in thread: Robin Chapman: "Re: Raatikainen's critique of Chaitin"
- Messages sorted by: [ date ] [ thread ]
Relevant Pages
|
