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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*
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And lo on Wed, 30 Jul 2008 14:48:57 +0100, Invisible <voi### [at] dev null> 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
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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)
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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.
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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] 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?
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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