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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>> 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*

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Orchid XP v8 <voi### [at] devnull> 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

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Invisible wrote:
> (Kinda amusing how not denying access to data is a "feature", eh?)

http://www.fsf.org/blogs/community/antifeatures

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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."

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