 |
|
|
|
|
|
| |
| |
|
|
|
|
| |
| |
|
|
>> 1. Fermat claimed to have a proof, but to this day nobody knows what it was.
>
> Some people have the opinion that, regardless of being an exceptionally
> gifted mathematician, Fermat was simply wrong when he wrote that margin
> note.
That seems perfectly plausible to me...
Some have also speculated that Fermat spotted a "simple" proof that has
eluded the rest of the community for over 300 years. This seems rather
less plausible.
(The modern day proof could not possibly be the one Fermat had. Well, I
mean, unless he invented several entire branches of mathematics in his
head that day...)
Some folks think he might have had a broken proof similar to Cauchy, but
not realised it was broken. The margin note looks like an off-hand
remark, so maybe he didn't check it out too much... People certainly
make mistakes.
--
http://blog.orphi.me.uk/
http://www.zazzle.com/MathematicalOrchid*
Post a reply to this message
|
|
| |
| |
|
|
|
|
| |
| |
|
|
>> Unless quantum computing ever works some day, and it turns out to have
>> _fundamentally_ different capabilities, the halting problem will never
>> be solved.
>
> Quantum computing (today) doesn't even solve NP problems in P time, let
> alone non-computable problems. :-)
But you get what I'm saying. Maybe there is some fundamentally new
system that changes the rules, so to speak.
Even if such a system were to exist, you would still have a new,
generalised Halting Problem, and you're back to square one.
--
http://blog.orphi.me.uk/
http://www.zazzle.com/MathematicalOrchid*
Post a reply to this message
|
|
| |
| |
|
|
|
|
| |
| |
|
|
>> I don't know about you, but every time *I* look at either the GIMP or
>> PhotoShop, I can never figure out what magical trick I'm missing that
>> lets you do the impressive stuff everybody else does. To me, it just
>> seems to be a small set of pretty simple tools that don't appear to give
>> you much power to do anything.
>
> ie, they allow you to do the "impossible". ;-)
>
> (which is my point - don't let the limits of what you know - or what
> humankind collectively knows - define what is possible and what is not)
And my point - which you seem hell-bent on ignoring - is that there is a
difference between "we don't know if/how to do this" and "we know for a
fact that this is impossible". :-P
--
http://blog.orphi.me.uk/
http://www.zazzle.com/MathematicalOrchid*
Post a reply to this message
|
|
| |
| |
|
|
|
|
| |
| |
|
|
>> (Kinda amusing how not denying access to data is a "feature", eh?)
>
> http://www.fsf.org/blogs/community/antifeatures
Yeah, that's where I got the idea from. ;-)
--
http://blog.orphi.me.uk/
http://www.zazzle.com/MathematicalOrchid*
Post a reply to this message
|
|
| |
| |
|
|
|
|
| |
| |
|
|
And lo on Tue, 29 Jul 2008 15:42:40 +0100, Mike Raiford
<mra### [at] hotmail com> did spake, saying:
> Nicolas Alvarez wrote:
>
>> I definitely remember Windows 98 slowly redrawing the desktop as if it
>> was
>> raytracing the damned wallpaper, while the hard disk made horrible
>> insane-seeking noises.
>
> I remember that, too. I attributed it to the Wallpaper being somewhat
> dispensable, and being swapped to disk as soon as memory was being
> needed by the application.
What do the pair of you mean remember? I've still got a 98 machine here
that does just that if you dare to use more memory then is physically
present.
--
Phil Cook
--
I once tried to be apathetic, but I just couldn't be bothered
http://flipc.blogspot.com
Post a reply to this message
|
|
| |
| |
|
|
|
|
| |
| |
|
|
And lo on Tue, 29 Jul 2008 21:45:13 +0100, Jim Henderson
<nos### [at] nospamcom> did spake, saying:
> On Tue, 29 Jul 2008 09:10:38 +0100, Invisible wrote:
>
>>>> If the grains in the film reacted to colour in some currently
>>>> unreadable fashion and/or those alterations were transferred to the
>>>> photo itself then you could, in theory, recover colour from a B&W
>>>> photo or film by reading those imperfections.
>>>
>>> That's kinda what I'm thinking.
>>
>> ...so in other words, hypothetically the information might not be
>> "gone". If that were indeed the case, it is at least plausible that
>> somebody could possibly get it back, yes.
>
> Oh, the information could well be gone, but it could be reconstructed
> from the available data.
In that case the information hasn't really gone merely converted into
another pattern?
For an example of destroyed information tell me the equation I used to
derive the answer of 9.
--
Phil Cook
--
I once tried to be apathetic, but I just couldn't be bothered
http://flipc.blogspot.com
Post a reply to this message
|
|
| |
| |
|
|
|
|
| |
| |
|
|
Phil Cook wrote:
> For an example of destroyed information tell me the equation I used to
> derive the answer of 9.
...I can't *believe* you robbed me of the opportunity to say "what do
you get if your multiply six by nine?" :-o
--
http://blog.orphi.me.uk/
http://www.zazzle.com/MathematicalOrchid*
Post a reply to this message
|
|
| |
| |
|
|
|
|
| |
| |
|
|
And lo on Wed, 30 Jul 2008 14:48:57 +0100, Invisible <voi### [at] devnull> did
spake, saying:
> Phil Cook wrote:
>
>> For an example of destroyed information tell me the equation I used to
>> derive the answer of 9.
>
> ...I can't *believe* you robbed me of the opportunity to say "what do
> you get if your multiply six by nine?" :-o
Sorry I was thinking of a different book, in this case a Jasper Fforde
dealing with Nextian mathematics that does allow you to work out whether
the answer 9 is derived from 3+6 or 3*3, or something else entirely.
--
Phil Cook
--
I once tried to be apathetic, but I just couldn't be bothered
http://flipc.blogspot.com
Post a reply to this message
|
|
| |
| |
|
|
|
|
| |
| |
|
|
Invisible wrote:
>>> Unless quantum computing ever works some day, and it turns out to
>>> have _fundamentally_ different capabilities, the halting problem will
>>> never be solved.
>>
>> Quantum computing (today) doesn't even solve NP problems in P time,
>> let alone non-computable problems. :-)
>
> But you get what I'm saying. Maybe there is some fundamentally new
> system that changes the rules, so to speak.
That still won't solve the halting problem, because the halting problem
isn't defined in terms of this fundamentally new system.
It's like saying "integers are not closed under division", and then
saying "but we've discovered rationals!" Integers *still* aren't
closed under division, even if you invent rationals.
> Even if such a system were to exist, you would still have a new,
> generalised Halting Problem, and you're back to square one.
That's rather harder to say, really, since we by definition have no idea
what a program in this entirely new paradigm would look like. But I
suspect you're correct.
--
Darren New / San Diego, CA, USA (PST)
Post a reply to this message
|
|
| |
| |
|
|
|
|
| |
| |
|
|
Phil Cook wrote:
>
> What do the pair of you mean remember? I've still got a 98 machine here
> that does just that if you dare to use more memory then is physically
> present.
>
I haven't used 98 in years ... That's what I mean by remember.
Post a reply to this message
|
|
| |
| |
|
|
|
|
| |
