 |
|
|
|
|
|
| |
| |
|
|
|
|
| |
| |
|
|
>> Show me one single mathematical result which was *proven* to be true,
>> and verified independently by a large number of mathematicians, and
>> subsequently turned out to actually be false.
>
> The most obvious answer I can provide (but I don't know how many
> confirmed the proof) is Fermat's Last Theorem - at least from my read, it
> was proven for n=3 in the 10th century, but the proof was later
> invalidated.
>
> A correct proof was later constructed in the mid-20th century, again,
> from what I understand.
See, now from what I understand,
1. Fermat claimed to have a proof, but to this day nobody knows what it was.
2. In the intervining several centuries, various proofs have been put
forward. Some special cases were successfully proven. Some proofs put
forward were quickly shown to be incorrect.
3. Recently a group of related mathematical proofs finally settled the
matter.
I am not aware - despite possessing a book detailing the entire history
of Fermat's Last Theorum - of any proof that was widely held to be
correct for a long time before being found wrong. All the incorrect
proofs were discovered to be incorrect fairly quickly.
It's easy for one person to make a mistake. (I saw a very neat example
of this actually...) It's rather rarer for a large body of
mathematicians to all fail to spot a flaw. Usually once a theorum gets a
propper peer review, you can state the validity or otherwise of the
proof with a pretty high degree of confidence. [Depending on how complex
the proof is, of course...]
One of the reasons the Four Colour Map "proof" is not widely accepted is
that it's just about impossibly to peer review it properly. Obviously
the authors think it's correct, but nobody can easily check it, so it
could actually be balony. [Regardless of whether the thing it's trying
to prove is actually correct or not.]
>> And I suppose next you'll be telling me that some day, some future
>> technology might enable us to find a sequence of chess moves whereby a
>> bishop can get from a black square to a white square, despite it being
>> trivially easy to mathematically prove the impossibility of this...
>
> You're still missing my point....
You're still missing *my* point. :-P
>>> And yet you agreed with another post in this thread that said that
>>> something was possible. Look at the refocusing capabilities of some of
>>> the tools for that to reconstruct detail in blurred images. Blurring
>>> is lossy compression, yet being able to recover that data isn't
>>> impossible; that's been proven.
>> Hey, guess what? Blurring isn't compression. It might *look* like it is,
>> but it isn't.
>
> My point is that there's plenty of examples where raw data is lost but it
> can be reconstructed.
Blurring doesn't actuallly "lose" nearly as much data as you'd think.
That's why it can be mostly reversed.
>> Sure. And no doubt some day we'll discover that 2+2 isn't actually 4. I
>> won't hold by breath for that though. :-P
>
> Well, who knows? There are ancient civilizations that had no concept of
> zero. The introduction of imaginary numbers didn't come along until the
> late 1500s. Up until that point, sqrt(-1) was undefined.
>
> Who knows what we don't know about mathematics even today?
If I were you, I'd be far more worried about the sky falling - it's
about as logically plausible...
--
http://blog.orphi.me.uk/
http://www.zazzle.com/MathematicalOrchid*
Post a reply to this message
|
|
| |
| |
|
|
|
|
| |
| |
|
|
Orchid XP v8 <voi### [at] dev null> wrote:
> 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.
There's some evidence of this. IIRC, Fermat provided proofs for the cases
n=3 and n=4 some time *after* he wrote that margin note. Why would he do
that if he had a simple proof for *all* values of n?
The most logical explanation is that Fermat was wrong, realized it
himself some time after, and then proceded studying his own theorem
further by, among other things, giving proofs for n=3 and n=4. He simply
didn't go back and erase the margin note (maybe he just forgot about it).
--
- Warp
Post a reply to this message
|
|
| |
| |
|
|
|
|
| |
| |
|
|
Invisible wrote:
> (Kinda amusing how not denying access to data is a "feature", eh?)
http://www.fsf.org/blogs/community/antifeatures
Post a reply to this message
|
|
| |
| |
|
|
|
|
| |
| |
|
|
scott wrote:
>> Well... it looks fine to me, that's all I'm saying. ;-)
>
> But "fine" is nowhere near what you see in real life. While there is
> still an obvious gap between real life and what you can reproduce, there
> will no doubt be improvements in the future.
"But this is HDTV. It's got better resolution than the real world."
Post a reply to this message
|
|
| |
| |
|
|
|
|
| |
| |
|
|
>> 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] hotmailcom> 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
|
|
| |
| |
|
|
|
|
| |
