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On Wed, 30 Jul 2008 08:54:09 +0100, Invisible wrote:
>>> 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
Well, what fun would it be if I just agreed with you? ;-)
Jim
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On Wed, 30 Jul 2008 14:14:53 +0100, Phil Cook wrote:
> And lo on Tue, 29 Jul 2008 21:45:13 +0100, Jim Henderson
> <nos### [at] nospam com> 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?
Well, I'm talking about physical loss of "data bits", not about the use
of patterns to reconstruct it. The bit pattern is gone. :-)
> For an example of destroyed information tell me the equation I used to
> derive the answer of 9.
no. ;-)
Jim
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And lo on Wed, 30 Jul 2008 19:07:54 +0100, Mike Raiford
<mra### [at] hotmailcom> did spake, saying:
> 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.
Mistranslation of humour -
'I remember back in ye olden days using ye olden thing'
'What do you mean ye olden days? I'm still using ye olden thing!'
--
Phil Cook
--
I once tried to be apathetic, but I just couldn't be bothered
http://flipc.blogspot.com
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>> 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.
The idea is that if you had some super-machine that could somehow decide
whether any given Turing machine halts for a given input, you would
still be unable to tell whether this brand new machine halts for a given
input - using exactly the same proof as the original halting problem.
--
http://blog.orphi.me.uk/
http://www.zazzle.com/MathematicalOrchid*
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Jim Henderson wrote:
> Well, what fun would it be if I just agreed with you? ;-)
Damn it, that isn't even *logic*! :-P
--
http://blog.orphi.me.uk/
http://www.zazzle.com/MathematicalOrchid*
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Invisible wrote:
> The idea is that if you had some super-machine that could somehow decide
> whether any given Turing machine halts for a given input, you would
> still be unable to tell whether this brand new machine halts for a given
> input - using exactly the same proof as the original halting problem.
That's possible. But it certainly isn't obviously true. If the
super-computer isn't programmed in the usual way, or if (for example) it
can execute an infinite number of instructions in finite time, or if it
can travel back in time, or etc, I expect you'd have to think hard about
whether that gets around the technique the halting problem proof uses.
If your super-computer cannot, for example, have its programs
represented as input to itself (i.e., you can't create a universal
super-computer), then the halting problem isn't even *defined* for that
type of computer.
--
Darren New / San Diego, CA, USA (PST)
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Darren New wrote:
> That's possible. But it certainly isn't obviously true. If the
> super-computer isn't programmed in the usual way, or if (for example) it
> can execute an infinite number of instructions in finite time, or if it
> can travel back in time, or etc, I expect you'd have to think hard about
> whether that gets around the technique the halting problem proof uses.
>
> If your super-computer cannot, for example, have its programs
> represented as input to itself (i.e., you can't create a universal
> super-computer), then the halting problem isn't even *defined* for that
> type of computer.
I implicitly assumed that any machine that can't process it's own
program isn't worthy of the title "computer", that's all. ;-) But yes, I
see what you're saying.
As for being able to perform infinite instructions in finite time...
surely that just makes it even *harder* to predict what the machine will
od, no?
--
http://blog.orphi.me.uk/
http://www.zazzle.com/MathematicalOrchid*
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On Thu, 31 Jul 2008 09:18:43 +0100, Invisible wrote:
> Jim Henderson wrote:
>
>> Well, what fun would it be if I just agreed with you? ;-)
>
> Damn it, that isn't even *logic*! :-P
LOL!
Jim
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On Tue, 29 Jul 2008 22:29:26 +0100, Orchid XP v8 wrote:
> 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.
Absence of evidence is not evidence of absence. ;-)
>>> 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
Then we're even. ;-)
>> 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.
Again, 10 years ago, doing this was thought to be impossible.
>> 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...
I don't see how your statement follows mine....
Throughout history, mankind has claimed to have reached the end of
knowledge on all manner of topics, saying "there's nothing more to learn
here". In every instance (AFAIK), that's been proven wrong.
But now here, in the 21st century, we've finally exhausted the base of
knowledge? I don't think that's the case.
Jim
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Invisible wrote:
> I implicitly assumed that any machine that can't process it's own
> program isn't worthy of the title "computer", that's all. ;-) But yes, I
> see what you're saying.
So, your brain is weaker than a Turing machine? Cool.
It's the simplicity of the machines that make them amenable to
universality, not the complexity. Remember that the Von Neumann
architecture was a breakthrough.
> As for being able to perform infinite instructions in finite time...
> surely that just makes it even *harder* to predict what the machine will
> od, no?
Not if it can process its own input. Think about how the halting problem
works, and why... If the machine has unbounded state, it might run
forever without ever getting into the same state twice. But if you can
run the computer forever without it actually taking forever, then you
can say definitively "no, that machine never stops."
And a machine that can run an infinite number of instructions in finite
time *always* stops. ;-)
--
Darren New / San Diego, CA, USA (PST)
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