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>> Whether you can *fake* something that "looks" right is another matter.
>> But *recover*? No. Impossible.
>
> Or, you find another source for the missing data.
Yeah, but that wouldn't be "recovering" the data, that would be getting
it from another source. ;-)
--
http://blog.orphi.me.uk/
http://www.zazzle.com/MathematicalOrchid*
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>> 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.
It just amused me that a 33 MHz machine would struggle so much to draw
16 colour graphics when my puny little 7 MHz Amiga could draw 32 colour
graphics instantly, and at higher resolutions...
...and then, like I said, the Amiga's hardware stood still for 10 years.
Kinda lost the edge after that.
--
http://blog.orphi.me.uk/
http://www.zazzle.com/MathematicalOrchid*
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Orchid XP v8 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. :-)
--
Darren New / San Diego, CA, USA (PST)
Helpful housekeeping hints:
Check your feather pillows for holes
before putting them in the washing machine.
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Jim Henderson wrote:
> This is the problem, though: The assumption is that computing will
> always use a Turing model, like I said.
No, computing doesn't today using a Turing model, and the Halting
problem applies to many more computing models than the Turing model.
The Halting problem isn't solvable. If you come up with a new computing
model that "solves" it, what you're solving isn't the halting problem
any more.
It's like arguing "Maybe 2+2 will equal 6 some day, if 2 turns into 3."
But if 2 turns into 3, you're not longer adding 2+2.
The halting problem is a precisely defined mathematical construct. Maybe
newer computing models might conceivably obsolete the implications of
the halting problem, but they won't actually negate its proof. (In the
same sense, that computers are far faster may obsolete the problems
caused by some algorithms taking O(N^3) instructions, but that doesn't
make the algorithm take fewer instructions.)
--
Darren New / San Diego, CA, USA (PST)
Helpful housekeeping hints:
Check your feather pillows for holes
before putting them in the washing machine.
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scott wrote:
> But "fine" is nowhere near what you see in real life.
I'm pretty sure it is. Try going to where you took that photo, looking
at the wall, and without moving your eyes, see if you can see the
details in the clouds. Then look at the clouds, and without moving your
eyes, see if you can see the detail on the wall.
Even medical X-Rays only use 12 bits of greyscale.
--
Darren New / San Diego, CA, USA (PST)
Helpful housekeeping hints:
Check your feather pillows for holes
before putting them in the washing machine.
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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.
Kinda like rebuilding a RAID-5 array using parity data.
Jim
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On Tue, 29 Jul 2008 18:17:34 +0100, Orchid XP v8 wrote:
>>> Scientific facts have been found to be incorrect. There are far fewer
>>> examples of mathematical truths which have needed to be adjusted. And
>>> there are vanishingly few examples of widely accepted *proofs* that
>>> turn out to be wrong - it tends to be things lots of mathematicians
>>> "think" are true that eventually turn out to be disproven.
>>
>> Exactly my point, but with a narrower focus. Things lots of *people*
>> "think" are true sometimes/frequently/often turn out to be disproven.
>
> 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.
>> It's simple logical deduction that unless I have a screwdriver, I can't
>> drive a screw.
>>
>> Until you realise that the screw has a hex head and an allen wrench
>> will do the job just as nicely.
>>
>> *Sometimes* all you need is a new tool. Sometimes the new tool hasn't
>> been invented yet.
>
> 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....
>> I think it's a mistake to say "we know all there is to ever know about
>> 'x'". There have been many points in history where humankind has made
>> such declarations about many things - including mathematics - and it
>> has turned out that we'd only scratched the surface. It's the height
>> of hubris to assume we can't learn anything new.
>
> I'm not claiming that nothing new can be learned - I am saying that, at
> least in mathematics, learning new things doesn't invalidate what we
> already know.
Except that it can. That was demonstrated in the example I provided
above - proof done, proof invalidated, new proof done again. Will the
new proof be invalidated? Probably not, but who's to say it never will
be?
>> 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.
> 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?
Jim
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On Tue, 29 Jul 2008 11:42:47 -0700, Darren New wrote:
> Jim Henderson wrote:
>> This is the problem, though: The assumption is that computing will
>> always use a Turing model, like I said.
>
> No, computing doesn't today using a Turing model, and the Halting
> problem applies to many more computing models than the Turing model.
>
> The Halting problem isn't solvable. If you come up with a new computing
> model that "solves" it, what you're solving isn't the halting problem
> any more.
>
> It's like arguing "Maybe 2+2 will equal 6 some day, if 2 turns into 3."
> But if 2 turns into 3, you're not longer adding 2+2.
>
> The halting problem is a precisely defined mathematical construct. Maybe
> newer computing models might conceivably obsolete the implications of
> the halting problem, but they won't actually negate its proof. (In the
> same sense, that computers are far faster may obsolete the problems
> caused by some algorithms taking O(N^3) instructions, but that doesn't
> make the algorithm take fewer instructions.)
Well, like I said, perhaps I chose a bad example - I should stick to
things I know, maybe. :-)
Jim
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On Tue, 29 Jul 2008 18:18:16 +0100, Orchid XP v8 wrote:
>>> Whether you can *fake* something that "looks" right is another matter.
>>> But *recover*? No. Impossible.
>>
>> Or, you find another source for the missing data.
>
> Yeah, but that wouldn't be "recovering" the data, that would be getting
> it from another source. ;-)
Which is often what data recovery *is* - reconstruction based on
available data.
Jim
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On Tue, 29 Jul 2008 15:19:10 +0100, Invisible wrote:
> Mike Raiford wrote:
>
>> You have PS elements, right? Find a picture that's scratched and use
>> the healing (or spot healing) brush on the scratches. The brush looks
>> like a bandage. I know the tool exists in Elements. I use a lot of
>> Clone and Heal, often both to get the results. I should upload a copy
>> of the layers palette of the images to give you an idea as to how much
>> is really involved.
>
> 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)
Jim
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