Invisible wrote:
>>> My point is still that you can't reover what isn't there any more.
>>>
>>
>> Right, but the information is still there, and so it is recoverable.
> 
> Heh. Next thing you'll be telling me that you can take a photograph that 
> has faded to a plain yellow sheet of paper and somehow "recover" the 
> image that used to be on it. :-P
> 

I have seen a originally black&white photograph (from somewhere of 20th 
century beginning, 1920 oslt), which got just scanned and printed with 
color printer - and it actually did got some colors. You could see the 
color on persons face as well as she was wearing a blue dress. That was 
something that really amazed me.

-- 
Eero "Aero" Ahonen
    http://www.zbxt.net
       aer### [at] removethiszbxtnetinvalid

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> All I know is that when I take a dark image and try to make it brighter, 
> it comes out hopelessly noisy.

That is probably because you took it with a camera that is already 
hopelessly noisy, of course brightening it digitally is just going to 
amplify the noise too.

Try playing about with a better photo, (googling "photo" is a start!), 
darken it by a factor of 4, then lighten it back to its original.  Hardly 
any noise visible.

Post a reply to this message

>> All I know is that when I take a dark image and try to make it 
>> brighter, it comes out hopelessly noisy.
> 
> That is probably because you took it with a camera that is already 
> hopelessly noisy, of course brightening it digitally is just going to 
> amplify the noise too.

Well, my camera *is* quite noisy. (More precisely: my camera takes very 
dark pictures unless used in insanely bright lighting conditions, or on 
a very long exposure.) I quickly learned that there is really no point 
attempting to take the beer-like shots it takes and make then viewable. 
All you get is signal noise.

But then, isn't film inherantly noisy too? And especially a scanned 
image, complete with dust and a rough surface...

> Try playing about with a better photo, (googling "photo" is a start!), 
> darken it by a factor of 4, then lighten it back to its original.  
> Hardly any noise visible.

Heh, not even DCT artifacts? :-P

-- 
http://blog.orphi.me.uk/
http://www.zazzle.com/MathematicalOrchid*

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> But then, isn't film inherantly noisy too?

Not really, not in the way digital image sensors are.

> Heh, not even DCT artifacts? :-P

No, just some banding in the sky due to you effectively losing the last 2 
least significant bits of data.

BTW, on a lot of digital cameras now you can save your images in "raw" 
format, which is usually 12-bit per channel.  That way you can make your 
colour/contrast/brightness adjustments and still have the full 8-bit output 
possible without any loss of a bit or two.

Post a reply to this message

>> But then, isn't film inherantly noisy too?
> 
> Not really, not in the way digital image sensors are.

Really? I thought film was well-known for being grainy at low light 
levels...

>> Heh, not even DCT artifacts? :-P
> 
> No, just some banding in the sky due to you effectively losing the last 
> 2 least significant bits of data.

I'll have to try it at some point I guess.

> BTW, on a lot of digital cameras now you can save your images in "raw" 
> format, which is usually 12-bit per channel.

My camera isn't that expensive.

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

-- 
http://blog.orphi.me.uk/
http://www.zazzle.com/MathematicalOrchid*

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> Really? I thought film was well-known for being grainy at low light 
> levels...

Yes, but a cheap film camera with ISO100 loaded will display orders of 
magnitude less noise compared to even a moderately priced digital camera.

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

But the data never exists as a whole in the first place in cheap cameras. 
The demosaic/compression chip will work on groups of lines at a time and 
spurt them out to the file-write buffer.  If you tried to simply pass the 
raw data through you'd need a much bigger buffer and possibly faster 
file-writing electronics (unless you're happy to wait 3x-6x longer for each 
write).

Also they would need to include some RAW conversion software with the 
camera, which needs writing.

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"scott" <sco### [at] scottcom> a écrit dans le message de news: 
48884e9a$1@news.povray.org...
>
> But the data never exists as a whole in the first place in cheap cameras.

Actually it does exist, at least in Canon cameras. There's even a hack to 
get the RAW data instead of the JPEG.
http://www.oyonale.com/blog/2008/03/hacking-cheap-canon-camera.html

>Also they would need to include some RAW conversion software with the 
>camera, which needs writing.

I guess that Canon wrote RAW converters for its SLR models. Also, they 
bundle a mountainload of crappy, useless "utilities" with the camera anyway, 
so it's not like they're lacking developers. Really, this is a case study of 
hardware being deliberately crippled through software for marketing reasons.

G.

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And lo on Thu, 24 Jul 2008 10:21:19 +0100, Invisible <voi### [at] devnull> did  
spake, saying:

>>> But then, isn't film inherantly noisy too?
>>  Not really, not in the way digital image sensors are.
>
> Really? I thought film was well-known for being grainy at low light  
> levels...

Depends on the film, if I take a good photo using ISO200 film at 1/60th of  
a second I can can get the same exposure with the less grainy ISO100 by  
shooting at 1/30th or even ISO50 for 1/15th. Of course leaving the shutter  
open that long may not be what I want so I could switch to ISO400 for  
1/120th.

The larger the ISO the larger the grains in the film that react to light  
so the grainier it gets. Digital cameras don't have grains though, they  
have fixed-sized sensors. So to emulate the sensitivity they just up the  
gain and well you know what happens when you do that for tiny sensors.

-- 
Phil Cook

--
I once tried to be apathetic, but I just couldn't be bothered
http://flipc.blogspot.com

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On Thu, 24 Jul 2008 08:57:40 +0100, Invisible wrote:

>>> My point is still that you can't reover what isn't there any more.
>>>
>>>
>> Right, but the information is still there, and so it is recoverable.
> 
> Heh. Next thing you'll be telling me that you can take a photograph that
> has faded to a plain yellow sheet of paper and somehow "recover" the
> image that used to be on it. :-P

Even more impressively, they've been able to colour films that were 
originally shot in B&W.

http://en.wikipedia.org/wiki/Film_colorization

Jim

Post a reply to this message

On Thu, 24 Jul 2008 10:21:19 +0100, Invisible wrote:

>>> But then, isn't film inherantly noisy too?
>> 
>> Not really, not in the way digital image sensors are.
> 
> Really? I thought film was well-known for being grainy at low light
> levels...

Depends on the film speed and camera characteristics.

>>> Heh, not even DCT artifacts? :-P
>> 
>> No, just some banding in the sky due to you effectively losing the last
>> 2 least significant bits of data.
> 
> I'll have to try it at some point I guess.
> 
>> BTW, on a lot of digital cameras now you can save your images in "raw"
>> format, which is usually 12-bit per channel.
> 
> My camera isn't that expensive.
> 
> (Kinda amusing how not denying access to data is a "feature", eh?)

You're not the first to make this observation.  For some cameras, there's 
actually alternate firmware you get get that enables this on low-end 
cameras that don't expose RAW data to the end user.

Jim

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Jim Henderson wrote:

> Even more impressively, they've been able to colour films that were 
> originally shot in B&W.
> 
> http://en.wikipedia.org/wiki/Film_colorization

Yeah, but only with human intervention. You don't just press a button 
and out pops an image with colours that correctly match the original.

-- 
http://blog.orphi.me.uk/
http://www.zazzle.com/MathematicalOrchid*

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>> But the data never exists as a whole in the first place in cheap cameras.
>
> Actually it does exist, at least in Canon cameras.

That's because they probably use the same hardware in lots of different 
cameras. Again it's all about cost, cheaper to use an existing solution that 
is slightly more than they need, rather than to develop a new one.

> Really, this is a case study of hardware being deliberately crippled 
> through software for marketing reasons.

It's not marketing reasons, it's purely financial reasons, to make maximum 
profit.  Say it costs Canon $100 to make each camera, whether crippled or 
not.  You have two options:

Option 1: Sell just one model for $150 and make $50 profit on each camera

Option 2: Sell a crippled version for $125 and a non-crippled one for $200. 
If you choose those two prices correctly, you will make more profit.

Companies realise that option 2 is likely to make them much more profit, you 
get sales from all the people who couldn't afford $150 before, plus you get 
sales from people who think that because it's $200 it must be better than a 
$150 camera from another company, and obviously it's better than your $125 
you are selling.

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On Thu, 24 Jul 2008 16:13:21 +0100, Invisible wrote:

> Jim Henderson wrote:
> 
>> Even more impressively, they've been able to colour films that were
>> originally shot in B&W.
>> 
>> http://en.wikipedia.org/wiki/Film_colorization
> 
> Yeah, but only with human intervention. You don't just press a button
> and out pops an image with colours that correctly match the original.

As the original is B&W, that doesn't make sense...

But colourization technology has advanced somewhat since the earliest 
films (and in all honesty, the earliest colourized films that I saw were 
pretty crap anyways).

But even with colour correction in cameras, the best results usually 
involve human intervention.

Jim

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>> Yeah, but only with human intervention. You don't just press a button
>> and out pops an image with colours that correctly match the original.
> 
> As the original is B&W, that doesn't make sense...

I meant you can't just give a machine a BW picture of a tree and have it 
automatically know to turn it green. That's impossible. You must have a 
human there, and they must know what the hell the colours are supposed 
to be.

-- 
http://blog.orphi.me.uk/
http://www.zazzle.com/MathematicalOrchid*

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"scott" <sco### [at] scottcom> a écrit dans le message de news: 
48889cb8@news.povray.org...
> Companies realise that option 2 is likely to make them much more profit, 
> you get sales from all the people who couldn't afford $150 before, plus 
> you get sales from people who think that because it's $200 it must be 
> better than a $150 camera from another company, and obviously it's better 
> than your $125 you are selling.

Some of the crippled features only exist in uncrippled form in the high-end, 
much more expensive SLRs, that have specific hardware features (namely the 
abiility to have different and much better lenses and the SRL system itself) 
that cater to different people. Both lines of products do not compete with 
each other: they're different markets (with a small line of "bridge" cameras 
filling the gap). If Canon had left RAW support in the point-and-shoot 
digicams, that would not have prevented power users to buy SLRs.

In the end it surely comes down to money and I'm pretty sure that they ran 
simulations about this, but the true rationale still looks like real 
marketing to me: Canon judged that a digicam belongs to a market segment 
that doesn't need (or even understand) RAW support and other fancy high-end 
features, so they took those features off of the list to keep their product 
lines neatly separated.

G.

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On Thu, 24 Jul 2008 18:29:54 +0200, Gilles Tran wrote:

> If Canon had left RAW support in the
> point-and-shoot digicams, that would not have prevented power users to
> buy SLRs.

It isn't so much that they didn't leave the support in, they disabled it 
specifically in the lower-end cameras.  At least according to what I've 
read.

Jim

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On Thu, 24 Jul 2008 17:00:48 +0100, Invisible wrote:

>>> Yeah, but only with human intervention. You don't just press a button
>>> and out pops an image with colours that correctly match the original.
>> 
>> As the original is B&W, that doesn't make sense...
> 
> I meant you can't just give a machine a BW picture of a tree and have it
> automatically know to turn it green. That's impossible. 

I don't know that to be the case.  Again, a case of one's ability to 
fathom how something like that is done doesn't translate to "there's no 
way it could possibly be done".

> You must have a
> human there, and they must know what the hell the colours are supposed
> to be.

Maybe.  Maybe not.  Depends on how advanced the technology is.  It 
certainly isn't an *easy* problem to solve, I'll grant that.  
Impossible?  Smarter people than me have figured out how to do things I 
thought weren't possible.

"Any sufficiently advanced technology is indistinguishable from magic."

Jim

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>> I meant you can't just give a machine a BW picture of a tree and have it
>> automatically know to turn it green. That's impossible. 
> 
> I don't know that to be the case.  Again, a case of one's ability to 
> fathom how something like that is done doesn't translate to "there's no 
> way it could possibly be done".

It's a basic premise of signal processing that you cannot recover data 
that isn't there any more. Shannon's theorum and all that.

Whether you can *fake* something that "looks" right is another matter. 
But *recover*? No. Impossible.

-- 
http://blog.orphi.me.uk/
http://www.zazzle.com/MathematicalOrchid*

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On Thu, 24 Jul 2008 20:24:51 +0100, Orchid XP v8 wrote:

>>> I meant you can't just give a machine a BW picture of a tree and have
>>> it automatically know to turn it green. That's impossible.
>> 
>> I don't know that to be the case.  Again, a case of one's ability to
>> fathom how something like that is done doesn't translate to "there's no
>> way it could possibly be done".
> 
> It's a basic premise of signal processing that you cannot recover data
> that isn't there any more. Shannon's theorum and all that.
> 
> Whether you can *fake* something that "looks" right is another matter.
> But *recover*? No. Impossible.

At least as far as we know today.

A couple centuries ago, people also believed that if someone's heart 
stopped beating it couldn't be restarted and they were dead forever.  We 
know that to not be the case in all circumstances today.

If you take a photo of something out of focus, you could never recover 
the original picture again, right?

Wrong.  http://refocus-it.sourceforge.net/

Pretty cool plugin.  Even 5 years ago, something like this would have 
been thought to be totally impossible.

Jim

Post a reply to this message

>> It's a basic premise of signal processing that you cannot recover data
>> that isn't there any more. Shannon's theorum and all that.
>>
>> Whether you can *fake* something that "looks" right is another matter.
>> But *recover*? No. Impossible.
> 
> At least as far as we know today.

Right. And the fact that a mathematical proof of its impossibility 
doesn't matter either, right?

How many years do you think it will be before somebody solves the 
halting problem, or develops a lossless compression algorithm with an 
infinite compression ratio?

> If you take a photo of something out of focus, you could never recover 
> the original picture again, right?
> 
> Wrong.  http://refocus-it.sourceforge.net/
> 
> Pretty cool plugin.  Even 5 years ago, something like this would have 
> been thought to be totally impossible.

I've always thought that, logically, this ought to be possible in 
principle. I mean, defocusing is basically a convolution, so it should 
be possible to deconvolute it to some degree... (Similarly with echo 
cancellation.)

-- 
http://blog.orphi.me.uk/
http://www.zazzle.com/MathematicalOrchid*

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On Thu, 24 Jul 2008 21:31:19 +0100, Orchid XP v8 wrote:

>>> It's a basic premise of signal processing that you cannot recover data
>>> that isn't there any more. Shannon's theorum and all that.
>>>
>>> Whether you can *fake* something that "looks" right is another matter.
>>> But *recover*? No. Impossible.
>> 
>> At least as far as we know today.
> 
> Right. And the fact that a mathematical proof of its impossibility
> doesn't matter either, right?

Mathematical proofs have been proven wrong before, you know.

> How many years do you think it will be before somebody solves the
> halting problem, or develops a lossless compression algorithm with an
> infinite compression ratio?

Who knows?  Technology evolves over time.  Even 10 years ago, the idea of 
having a computer the size of a notebook that was as powerful as a then-
current Cray supercomputer?  Yet here we are.

Can they be solved using current computing technologies?  Probably not.  
Can they be solved with something that makes our current technology look 
like a toy?  Possibly.  Who knows?

>> If you take a photo of something out of focus, you could never recover
>> the original picture again, right?
>> 
>> Wrong.  http://refocus-it.sourceforge.net/
>> 
>> Pretty cool plugin.  Even 5 years ago, something like this would have
>> been thought to be totally impossible.
> 
> I've always thought that, logically, this ought to be possible in
> principle. I mean, defocusing is basically a convolution, so it should
> be possible to deconvolute it to some degree... (Similarly with echo
> cancellation.)

My point, though, is that there are people - even exceptionally smart 
people - who say "no way no how is 'x' ever going to be possible" and 
they're proven wrong.  Maybe not in their lifetimes, but who's to say 
what's really possible?

Jim

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>> Right. And the fact that a mathematical proof of its impossibility
>> doesn't matter either, right?
> 
> Mathematical proofs have been proven wrong before, you know.

Yes - but it's really extremely rare. Especially for very simple proofs. 
The ones that turn out to be wrong are usually the highly complex ones.

>> How many years do you think it will be before somebody solves the
>> halting problem, or develops a lossless compression algorithm with an
>> infinite compression ratio?
> 
> Who knows?  Technology evolves over time.  Even 10 years ago, the idea of 
> having a computer the size of a notebook that was as powerful as a then-
> current Cray supercomputer?  Yet here we are.
> 
> Can they be solved using current computing technologies?  Probably not.  
> Can they be solved with something that makes our current technology look 
> like a toy?  Possibly.  Who knows?

See, that's just it. The halting problem is unsolvable in a theoretical 
computer with an infinite amount of memory, allowed to run for an 
infinite amount of time. It's not a question of computers not being 
"powerful enough", the problem is unsolvable even theoretically.

Unless quantum computing ever works some day, and it turns out to have 
_fundamentally_ different capabilities, the halting problem will never 
be solved.

The impossibility of a lossless compression algorithm with an infinite 
compression ratio doesn't even depend on the model of computing used; it 
is a trivial exercise in logic.

> My point, though, is that there are people - even exceptionally smart 
> people - who say "no way no how is 'x' ever going to be possible" and 
> they're proven wrong.  Maybe not in their lifetimes, but who's to say 
> what's really possible?

And *my* point is that some things are "impossible" because nobody has 
yet figured out how, while other things are "impossible" because they 
defy the laws of causality. And there's a rather bit difference.

-- 
http://blog.orphi.me.uk/
http://www.zazzle.com/MathematicalOrchid*

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On Thu, 24 Jul 2008 22:07:08 +0100, Orchid XP v8 wrote:

>>> Right. And the fact that a mathematical proof of its impossibility
>>> doesn't matter either, right?
>> 
>> Mathematical proofs have been proven wrong before, you know.
> 
> Yes - but it's really extremely rare. Especially for very simple proofs.
> The ones that turn out to be wrong are usually the highly complex ones.

True.  But as I said, not *impossible*.  I don't like absolutes when it 
comes to things like this; people who think in absolutes usually limit 
themselves, and also tend to have a very jaded view of the world.

To borrow a line from Patriot Games:  Shades of grey.  The world is 
shades of grey.

>>> How many years do you think it will be before somebody solves the
>>> halting problem, or develops a lossless compression algorithm with an
>>> infinite compression ratio?
>> 
>> Who knows?  Technology evolves over time.  Even 10 years ago, the idea
>> of having a computer the size of a notebook that was as powerful as a
>> then- current Cray supercomputer?  Yet here we are.
>> 
>> Can they be solved using current computing technologies?  Probably not.
>> Can they be solved with something that makes our current technology
>> look like a toy?  Possibly.  Who knows?
> 
> See, that's just it. The halting problem is unsolvable in a theoretical
> computer with an infinite amount of memory, allowed to run for an
> infinite amount of time. It's not a question of computers not being
> "powerful enough", the problem is unsolvable even theoretically.

Using current thinking about how computers work.  If/when the computer 
science geniuses crack true AI, then the halting problem can be solved, 
can it not?  Can not humans evaluate the halting problem, at least in 
limited cases?

If you only thing in terms of turing machine-style computers, then you're 
absolutely right.  But turing machines are not (or rather, may not be) 
the end-all be-all of computing for the rest of the life of the universe.

> Unless quantum computing ever works some day, and it turns out to have
> _fundamentally_ different capabilities, the halting problem will never
> be solved.

*Bingo*, that's my point.  There's that "unless" phrase.

> The impossibility of a lossless compression algorithm with an infinite
> compression ratio doesn't even depend on the model of computing used; it
> is a trivial exercise in logic.

Again, someday we may have really exceptional AI that can figure this 
stuff out, not based on current computing technologies.

> And *my* point is that some things are "impossible" because nobody has
> yet figured out how, while other things are "impossible" because they
> defy the laws of causality. And there's a rather bit difference.

Sure, but solving the halting problem or properly colouring a photo that 
started in black and white is not something that defies the laws of 
causality.  It merely defies our technological abilities at this time.  
It's true that it may never be solved, but if there's one thing humanity 
has proven through the ages is that we usually can find a way - we just 
have to think in ways we haven't thought before.

After all, two thousand years ago, the earth was flat because nobody 
could comprehend the idea that it wasn't.  Well, I say nobody - there 
were some who did, and they were branded as heretics and in many cases 
they were killed for it.  Turns out they were right.

Be a heretic. :-)

Jim

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> If Canon had left RAW support in the point-and-shoot digicams, that would 
> not have prevented power users to buy SLRs.

Maybe for most of them, but I'm sure there are a group of people who had to 
strech their budgets etc to just be able to afford the cheapest Canon with 
RAW support.  If Canon offered RAW in their cheap models, they would surely 
lose some sales of the more expensive models.

But like you say, I'm sure they worked all this out with simulations and 
market research etc before making a decision, there is no way their finance 
department would have allowed it otherwise ;-)

Post a reply to this message

>>> Mathematical proofs have been proven wrong before, you know.
>> Yes - but it's really extremely rare. Especially for very simple proofs.
>> The ones that turn out to be wrong are usually the highly complex ones.
> 
> True.  But as I said, not *impossible*.

Not impossible, no.

Also, taking a shattered piece of glass and throwing the pieces at each 
other in such a way that the individual atomic laticies just happen to 
line up perfectly and you end up with the original, unshattered piece of 
glass is perfectly "possible", it's merely "unlikely".

...unlikely enough that no sane person bothers worrying about it. 
Similarly, the proof of the impossibility of an infinite compression 
ratio is *so* absurdly trivial that the chances of it being wrong are 
vanishingly small.

There are far more elaborate proofs that *might* be wrong - the four 
colour map theorum immediately leaps to mind - but when one speaks about 
a proof so simple it can be stated in a few sentences... it's really 
astonishingly unlikely to be wrong.

> I don't like absolutes when it 
> comes to things like this; people who think in absolutes usually limit 
> themselves, and also tend to have a very jaded view of the world.
> 
> To borrow a line from Patriot Games:  Shades of grey.  The world is 
> shades of grey.

Well... that's very nice, but unless somebody proves that the laws of 
logic as currently formulated have some really deeply *fundamental* flaw 
[in which case all of mathematics and science as we currently understand 
it is completely wrong], the halting problem isn't going to be disproved 
any time soon.

>> See, that's just it. The halting problem is unsolvable in a theoretical
>> computer with an infinite amount of memory, allowed to run for an
>> infinite amount of time. It's not a question of computers not being
>> "powerful enough", the problem is unsolvable even theoretically.
> 
> Using current thinking about how computers work.  If/when the computer 
> science geniuses crack true AI, then the halting problem can be solved, 
> can it not?  Can not humans evaluate the halting problem, at least in 
> limited cases?

Let me be 100% clear about this: NO, even human beings CANNOT solve the 
halting problem. (I have a simple and easy counterexample to this.)

It is not a question of "not having good enough AI". It's a question of 
"there is a proof of a dozen lines or so that shows that no Turing 
machine program can ever exist which solves this problem".

> If you only thing in terms of turing machine-style computers, then you're 
> absolutely right.  But turing machines are not (or rather, may not be) 
> the end-all be-all of computing for the rest of the life of the universe.
> 
>> Unless quantum computing ever works some day, and it turns out to have
>> _fundamentally_ different capabilities, the halting problem will never
>> be solved.
> 
> *Bingo*, that's my point.  There's that "unless" phrase.

I would like to point out that even if you assume that some hypothetical 
device exists which can easily solve the Turning machine halting 
problem, there is now a *new* version of the halting problem (namely, 
does a program for this new machine ever halt?) which will still be 
unsolvable. And if you design a new machine that can somehow solve even 
this new "super-halting problem", you just end up with a 
super-super-halting problem. And so on ad infinitum.

The halting problem is not a consequence of the exact way a Turing 
machine works. It is a very basic consequence of simple logic, and 
applies to any hypothetical detministic machine. (That's WHY it's such 
an important result.)

>> The impossibility of a lossless compression algorithm with an infinite
>> compression ratio doesn't even depend on the model of computing used; it
>> is a trivial exercise in logic.
> 
> Again, someday we may have really exceptional AI that can figure this 
> stuff out, not based on current computing technologies.

Intelligence - artificial or not - isn't the problem. It's not that 
nobody can work out *how* to do it, it's that IT'S IMPOSSIBLE.

Now if we were talking about some phenominon of physics, there would be 
at least some degree of uncertainty - we might be wrong about one of the 
"laws" of physics. There could be some edge case we don't know about 
yet. (E.g., Newton's laws of motion aren't quite 100% correct.)

But we're talking about simple logic here. Unless there is some fatally 
dire flaw in our ability to comprehend logic [in which case, we're 
basically screwed anyway], infinite compression is entirely impossible, 
and always will be. It's not about current computer technologies; this 
is impossible for any deterministic technology that would hypothetically 
exist.

>> And *my* point is that some things are "impossible" because nobody has
>> yet figured out how, while other things are "impossible" because they
>> defy the laws of causality. And there's a rather bit difference.
> 
> Sure, but solving the halting problem or properly colouring a photo that 
> started in black and white is not something that defies the laws of 
> causality.  It merely defies our technological abilities at this time.

This is precisely my point: Solving the halting problem DOES defy the 
laws of causality. It is NOT just a problem of technology. It is a 
problem of "if this algorithm were to exist, it would cause a logical 
paradox, regardless of the technology used".

-- 
http://blog.orphi.me.uk/
http://www.zazzle.com/MathematicalOrchid*

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scott wrote:
>> If Canon had left RAW support in the point-and-shoot digicams, that 
>> would not have prevented power users to buy SLRs.
> 
> Maybe for most of them, but I'm sure there are a group of people who had 
> to strech their budgets etc to just be able to afford the cheapest Canon 
> with RAW support.  If Canon offered RAW in their cheap models, they 
> would surely lose some sales of the more expensive models.
> 
> But like you say, I'm sure they worked all this out with simulations and 
> market research etc before making a decision, there is no way their 
> finance department would have allowed it otherwise ;-)
> 
> 

There is also the cost that Canon would have associated if they did 
leave RAW support enabled on the point-and-shoot cameras. That being the 
cost price of tech support and returns from people who just do not 
understand that format. JPEG is pretty well understood, to the extent it 
needs to be, by people who just want to take a snap shot and email it to 
the family. RAW formats aren't. Simple reason, Windows doesn't 
automatically open the picture in preview, and if they just emailed the 
RAW file to someone that person probably would not be able to open it.

I'd guess that Canon worked that information into their market research 
before they did anything, as well.

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And lo on Thu, 24 Jul 2008 20:31:59 +0100, Jim Henderson  
<nos### [at] nospamcom> did spake, saying:

> On Thu, 24 Jul 2008 20:24:51 +0100, Orchid XP v8 wrote:
>
>>>> I meant you can't just give a machine a BW picture of a tree and have
>>>> it automatically know to turn it green. That's impossible.
>>>
>>> I don't know that to be the case.  Again, a case of one's ability to
>>> fathom how something like that is done doesn't translate to "there's no
>>> way it could possibly be done".
>>
>> It's a basic premise of signal processing that you cannot recover data
>> that isn't there any more. Shannon's theorum and all that.
>>
>> Whether you can *fake* something that "looks" right is another matter.
>> But *recover*? No. Impossible.
>
> At least as far as we know today.

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.

-- 
Phil Cook

--
I once tried to be apathetic, but I just couldn't be bothered
http://flipc.blogspot.com

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Phil Cook wrote:

>>> Whether you can *fake* something that "looks" right is another matter.
>>> But *recover*? No. Impossible.
>>
>> At least as far as we know today.
> 
> 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.

Now *that* at least makes sense, hypothetically.

-- 
http://blog.orphi.me.uk/
http://www.zazzle.com/MathematicalOrchid*

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scott wrote:
>> 16 colours out of 16, verses 32 out of 4,096? Seems like a fairly big 
>> difference to me. ;-)
> 
> Yeh saying that, we've been stuck at 2^24 out of 2^24 for a while now... 
> ;-)

Wasn't the Parhelia that board that did 10 bits per channel, back around 
2004?  It also offered tri-monitor support for "surround gaming", or 
something.

I know people claim you can't tell the difference with more bits, but 
honestly I still see banding in "truecolor" (ie 8 bits per channel) images.

I can't wait for the day that double precision colors become mainstream, 
and DACs offer 16 or 32 bits per channel in the display :)

...Chambers

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Chambers wrote:

> I know people claim you can't tell the difference with more bits, but 
> honestly I still see banding in "truecolor" (ie 8 bits per channel) images.

My laptop is 24-bit graphics modes. However, the physical display 
hardware only supports 16-bit colour, and does dithering in hardware to 
produce the rest. The end result is, obviously, horrid.

[But then my laptop's LCD is horrid anyway. No matter where you put your 
head, only 50% of the display is visible at any time - the other 50% 
shows up in negative. Talk about narrow viewing angle...!]

I can well understand somebody looking at a "24-bit image" on this 
16-bit display and concluding that 24-bits is insufficient. But 
honestly, on every *real* 24-bit display I've seen, there is no evidence 
of banding at all. Hell, my sister has a gigantic 42-inch LCD TV in her 
front room, and I'm watching digital TV and playing COD4 on a PS3, all 
in 24-bit colour, and it looks damned *perfect*.

(...and then there are those people who claim to be able to tell the 
difference between 44.1 kHz and 48 kHz digital audio - despite the 
proven scientific impossibility of this feat.)

-- 
http://blog.orphi.me.uk/
http://www.zazzle.com/MathematicalOrchid*

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Invisible <voi### [at] devnull> wrote:
> My laptop is 24-bit graphics modes. However, the physical display 
> hardware only supports 16-bit colour, and does dithering in hardware to 
> produce the rest. The end result is, obviously, horrid.

  The end result would often be more horrid without the dithering. The
second image at http://en.wikipedia.org/wiki/Ordered_dithering is a rather
good example of how dithering can actually help the quality of the image,
even if the dithering algorithm is braindead simple.

-- 
                                                          - Warp

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>> My laptop is 24-bit graphics modes. However, the physical display 
>> hardware only supports 16-bit colour, and does dithering in hardware to 
>> produce the rest. The end result is, obviously, horrid.
> 
>   The end result would often be more horrid without the dithering.

Undoubtably so. But all the dithering in the world can't really compare 
to having propper shades. (Unless the spatial resolution is *very* high. 
This is how printers get away with it...)

-- 
http://blog.orphi.me.uk/
http://www.zazzle.com/MathematicalOrchid*

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On Fri, 25 Jul 2008 11:13:52 +0100, Phil Cook wrote:

> And lo on Thu, 24 Jul 2008 20:31:59 +0100, Jim Henderson
> <nos### [at] nospamcom> did spake, saying:
> 
>> On Thu, 24 Jul 2008 20:24:51 +0100, Orchid XP v8 wrote:
>>
>>>>> I meant you can't just give a machine a BW picture of a tree and
>>>>> have it automatically know to turn it green. That's impossible.
>>>>
>>>> I don't know that to be the case.  Again, a case of one's ability to
>>>> fathom how something like that is done doesn't translate to "there's
>>>> no way it could possibly be done".
>>>
>>> It's a basic premise of signal processing that you cannot recover data
>>> that isn't there any more. Shannon's theorum and all that.
>>>
>>> Whether you can *fake* something that "looks" right is another matter.
>>> But *recover*? No. Impossible.
>>
>> At least as far as we know today.
> 
> 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.

Jim

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On Fri, 25 Jul 2008 09:28:11 +0100, Invisible wrote:

>>>> Mathematical proofs have been proven wrong before, you know.
>>> Yes - but it's really extremely rare. Especially for very simple
>>> proofs. The ones that turn out to be wrong are usually the highly
>>> complex ones.
>> 
>> True.  But as I said, not *impossible*.
> 
> Not impossible, no.

Well, there you go. :-)

> Also, taking a shattered piece of glass and throwing the pieces at each
> other in such a way that the individual atomic laticies just happen to
> line up perfectly and you end up with the original, unshattered piece of
> glass is perfectly "possible", it's merely "unlikely".
> 
> ...unlikely enough that no sane person bothers worrying about it.
> Similarly, the proof of the impossibility of an infinite compression
> ratio is *so* absurdly trivial that the chances of it being wrong are
> vanishingly small.
> 
> There are far more elaborate proofs that *might* be wrong - the four
> colour map theorum immediately leaps to mind - but when one speaks about
> a proof so simple it can be stated in a few sentences... it's really
> astonishingly unlikely to be wrong.

True.  But unlikely != impossible.

>> I don't like absolutes when it
>> comes to things like this; people who think in absolutes usually limit
>> themselves, and also tend to have a very jaded view of the world.
>> 
>> To borrow a line from Patriot Games:  Shades of grey.  The world is
>> shades of grey.
> 
> Well... that's very nice, but unless somebody proves that the laws of
> logic as currently formulated have some really deeply *fundamental* flaw
> [in which case all of mathematics and science as we currently understand
> it is completely wrong], the halting problem isn't going to be disproved
> any time soon.

Maybe.  But then again, throughout history there are examples of really 
fundamental things needing to be adjusted.  Knowledge continues to grow.

>>> See, that's just it. The halting problem is unsolvable in a
>>> theoretical computer with an infinite amount of memory, allowed to run
>>> for an infinite amount of time. It's not a question of computers not
>>> being "powerful enough", the problem is unsolvable even theoretically.
>> 
>> Using current thinking about how computers work.  If/when the computer
>> science geniuses crack true AI, then the halting problem can be solved,
>> can it not?  Can not humans evaluate the halting problem, at least in
>> limited cases?
> 
> Let me be 100% clear about this: NO, even human beings CANNOT solve the
> halting problem. (I have a simple and easy counterexample to this.)
> 
> It is not a question of "not having good enough AI". It's a question of
> "there is a proof of a dozen lines or so that shows that no Turing
> machine program can ever exist which solves this problem".

This is the problem, though:  The assumption is that computing will 
always use a Turing model, like I said.

>> If you only thing in terms of turing machine-style computers, then
>> you're absolutely right.  But turing machines are not (or rather, may
>> not be) the end-all be-all of computing for the rest of the life of the
>> universe.
>> 
>>> Unless quantum computing ever works some day, and it turns out to have
>>> _fundamentally_ different capabilities, the halting problem will never
>>> be solved.
>> 
>> *Bingo*, that's my point.  There's that "unless" phrase.
> 
> I would like to point out that even if you assume that some hypothetical
> device exists which can easily solve the Turning machine halting
> problem, there is now a *new* version of the halting problem (namely,
> does a program for this new machine ever halt?) which will still be
> unsolvable. And if you design a new machine that can somehow solve even
> this new "super-halting problem", you just end up with a
> super-super-halting problem. And so on ad infinitum.

Maybe.  It's hard to say that that would be the case, because the future 
is unknowable.

> The halting problem is not a consequence of the exact way a Turing
> machine works. It is a very basic consequence of simple logic, and
> applies to any hypothetical detministic machine. (That's WHY it's such
> an important result.)

Maybe the halting problem was a bad example to illustrate my point; the 
bottom line on my point still stands, though.  What's "impossible" 
yesterday became an everyday occurrence.  It was "impossible" that the 
solar system was heliocentric a thousand years ago.  Today, it's common 
knowledge that that is untrue.

>>> The impossibility of a lossless compression algorithm with an infinite
>>> compression ratio doesn't even depend on the model of computing used;
>>> it is a trivial exercise in logic.
>> 
>> Again, someday we may have really exceptional AI that can figure this
>> stuff out, not based on current computing technologies.
> 
> Intelligence - artificial or not - isn't the problem. It's not that
> nobody can work out *how* to do it, it's that IT'S IMPOSSIBLE.

Using today's technologies, maybe.  Again, we don't know what the future 
holds.  It is impossible to use paper in transistors.  Or is it?

> Now if we were talking about some phenominon of physics, there would be
> at least some degree of uncertainty - we might be wrong about one of the
> "laws" of physics. There could be some edge case we don't know about
> yet. (E.g., Newton's laws of motion aren't quite 100% correct.)
>
> But we're talking about simple logic here. Unless there is some fatally
> dire flaw in our ability to comprehend logic [in which case, we're
> basically screwed anyway], infinite compression is entirely impossible,
> and always will be. It's not about current computer technologies; this
> is impossible for any deterministic technology that would hypothetically
> exist.

Not necessarily in our ability to comprehend logic, but perhaps in our 
ways of understanding how to process it.

>>> And *my* point is that some things are "impossible" because nobody has
>>> yet figured out how, while other things are "impossible" because they
>>> defy the laws of causality. And there's a rather bit difference.
>> 
>> Sure, but solving the halting problem or properly colouring a photo
>> that started in black and white is not something that defies the laws
>> of causality.  It merely defies our technological abilities at this
>> time.
> 
> This is precisely my point: Solving the halting problem DOES defy the
> laws of causality. It is NOT just a problem of technology. It is a
> problem of "if this algorithm were to exist, it would cause a logical
> paradox, regardless of the technology used".

There again, maybe I chose a poor example to illustrate my point.

Jim

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>> 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.

-- 
http://blog.orphi.me.uk/
http://www.zazzle.com/MathematicalOrchid*

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>> There are far more elaborate proofs that *might* be wrong - the four
>> colour map theorum immediately leaps to mind - but when one speaks about
>> a proof so simple it can be stated in a few sentences... it's really
>> astonishingly unlikely to be wrong.
> 
> True.  But unlikely != impossible.

You realise that it's completely possible that at one point today you'll 
try to swallow a mouthful of water and accidentally inhale it, right? 
People actually *die* like this. But I don't see you worrying about it - 
because it's rather unlikely. And yet it is many, many times *more* 
likely than somebody solving the Halting Problem.

>> Well... that's very nice, but unless somebody proves that the laws of
>> logic as currently formulated have some really deeply *fundamental* flaw
>> [in which case all of mathematics and science as we currently understand
>> it is completely wrong], the halting problem isn't going to be disproved
>> any time soon.
> 
> Maybe.  But then again, throughout history there are examples of really 
> fundamental things needing to be adjusted.  Knowledge continues to grow.

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.

>> Let me be 100% clear about this: NO, even human beings CANNOT solve the
>> halting problem. (I have a simple and easy counterexample to this.)
>>
>> It is not a question of "not having good enough AI". It's a question of
>> "there is a proof of a dozen lines or so that shows that no Turing
>> machine program can ever exist which solves this problem".
> 
> This is the problem, though:  The assumption is that computing will 
> always use a Turing model, like I said.

And like I have explained multiple times, the problem isn't the Turing 
model. Even if we assume some as-yet unknown technology with miraculous 
[but not unlimited] powers, we still have an unsolvable problem. That's 
what is so significant about the Halting Problem. (I mean, face it, what 
*practical* use does HP have? None. It's importance is that it 
demonstrates that some problems are unsolvable.)

>> I would like to point out that even if you assume that some hypothetical
>> device exists which can easily solve the Turning machine halting
>> problem, there is now a *new* version of the halting problem (namely,
>> does a program for this new machine ever halt?) which will still be
>> unsolvable. And if you design a new machine that can somehow solve even
>> this new "super-halting problem", you just end up with a
>> super-super-halting problem. And so on ad infinitum.
> 
> Maybe.  It's hard to say that that would be the case, because the future 
> is unknowable.

You're missing my point: It doesn't *matter* that we can't know the 
future. Simple logical deduction demonstrates that ANY machine we can 
construct will have the same problem, REGARDLESS of how it works.

> Maybe the halting problem was a bad example to illustrate my point; the 
> bottom line on my point still stands, though.  What's "impossible" 
> yesterday became an everyday occurrence.  It was "impossible" that the 
> solar system was heliocentric a thousand years ago.  Today, it's common 
> knowledge that that is untrue.

Once again, you are talking about science.

In science, it is always possible that some "fact" could turn out to be 
partially or wholely wrong. We think we know how the universe works, but 
we could always be wrong about something.

Mathematics is different. Not quite as different as was originally 
believed, but still. In mathematics, we can construct absolute truths 
which will never be disproven until the end of the universe itself. The 
only question mark is the reliability of the human mind.

For sufficiently complicated proofs, it becomes not merely possible but 
*plausible* that some mistake could exist. For sufficiently simple 
proofs, we can be absolutely certain that only a fundamental flaw with 
renders all of mathematics invalid could disprove the theorum.

In summary: Science can never have absolute truths. Mathematics can.

>> Intelligence - artificial or not - isn't the problem. It's not that
>> nobody can work out *how* to do it, it's that IT'S IMPOSSIBLE.
> 
> Using today's technologies, maybe.  Again, we don't know what the future 
> holds.  It is impossible to use paper in transistors.  Or is it?

Making transistors out of paper is a question of physics - a branch of 
science. Infinite compression ratios is a question of mathematics. 
Therein lies the critical difference.

>> This is precisely my point: Solving the halting problem DOES defy the
>> laws of causality. It is NOT just a problem of technology. It is a
>> problem of "if this algorithm were to exist, it would cause a logical
>> paradox, regardless of the technology used".
> 
> There again, maybe I chose a poor example to illustrate my point.

I'm not sure what your point is.

If your point is that science is sometimes wrong, or at least needs to 
be amended, then I agree. If your point is that widely held beliefs are 
sometimes wrong, then I also agree. If your point is that every proven 
mathematical result could actually be wrong, then I completely disagree.

-- 
http://blog.orphi.me.uk/
http://www.zazzle.com/MathematicalOrchid*

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Invisible wrote:
>>> Yeah, but only with human intervention. You don't just press a button
>>> and out pops an image with colours that correctly match the original.
>>
>> As the original is B&W, that doesn't make sense...
> 
> I meant you can't just give a machine a BW picture of a tree and have it 
> automatically know to turn it green. That's impossible. You must have a 
> human there, and they must know what the hell the colours are supposed 
> to be.
> 

Right. The restorations shown in the posts above did require some human 
intervention. The one of the baby (me) in the gold chair gave some weird 
blotchiness in the gold color, so that had to be cleaned up, basically 
using a colorization technique.

But, generally human intervention is required to do the best at 
correction and restoration. I can't just push a button that says "Fix 
cracks", I have to at the very minimum tell it where those cracks are 
that I want fixed.

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.

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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.

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Jim Henderson wrote:

> 
> Wrong.  http://refocus-it.sourceforge.net/
> 

Ooh, new toy! Could prove to be very useful!

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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.

-- 
http://blog.orphi.me.uk/
http://www.zazzle.com/MathematicalOrchid*

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Invisible wrote:

> 
> All I know is that when I take a dark image and try to make it brighter, 
> it comes out hopelessly noisy.
> 

As you push those low RGB values up, values in-between maintain their 
relationship by scaling. You're also scaling the baseline noise of your 
camera. S/N ratio is still the same, the only difference is that there 
was very little signal to begin with. You might be able to stretch this 
a small amount, using a noise reduction algorithm, but this will eat 
details, which you have very little of, so the image will be soft and 
begin to show artifacts. You could also take advantage of human 
perception of color and smooth the color channels, which will reduce the 
apparent color noise, you'll still have luminance noise, but this is 
generally regarded as more pleasant than chroma noise.

Also, with 8 bit images, the risk of posterization becomes greater the 
more drastic the changes. You only have 32 levels to work with in an 
image that is underexposed by 3 stops. (which would be rather dark) as 
opposed to 256 levels had the image been properly exposed in the first 
place. Now, lets say you have an image that had been recorded in 12 
bit-- which is common in most digital SLR's, though 14bit is becoming 
more common-- , now that same image has 512 levels, therefore on current 
displays and print technologies, there really is no posterization. This 
gives a much greater lattitude when performing color adjustments.

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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 was more likely happening is as applications are opened, and worked 
with, more memory is needed, and the least recently used block happened 
to be the wallpaper.

You minimize a few windows, The desktop is made visible again, 
Explorer's paint routine for the background is executed, it hits the 
image, and gets a page fault, Windows then gets that page from memory, 
GDI draws a bit of the image, hits another page fault, etc... until the 
image is painted in, All the while paging out more data from other apps 
to draw the background. These other apps may need the data just paged 
out, and so begins the harddrive-pounding swap.

Adding more RAM usually resolved the problem. ;) 3MB in a 16MB memory 
space is an awful heavy load on memory for something like a pretty 
background. (Based on a 1024x768 32bpp screen, not unheard of in those days)

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On Tue, 29 Jul 2008 09:12:12 -0500, Mike Raiford wrote:

> Jim Henderson wrote:
> 
> 
>> Wrong.  http://refocus-it.sourceforge.net/
>> 
>> 
> Ooh, new toy! Could prove to be very useful!

It's not easy to use, and documentation is thin - but I've found it 
useful as well.

Jim

Post a reply to this message

On Tue, 29 Jul 2008 09:23:54 +0100, Invisible wrote:

>> True.  But unlikely != impossible.
> 
> You realise that it's completely possible that at one point today you'll
> try to swallow a mouthful of water and accidentally inhale it, right?
> People actually *die* like this. But I don't see you worrying about it -
> because it's rather unlikely. And yet it is many, many times *more*
> likely than somebody solving the Halting Problem.

Have you calculated the odds of both? ;-)

We're not talking about comparative probabilities.  Impossible means *no* 
chance of it ever happening.

>> Maybe.  But then again, throughout history there are examples of really
>> fundamental things needing to be adjusted.  Knowledge continues to
>> grow.
> 
> 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.

>> This is the problem, though:  The assumption is that computing will
>> always use a Turing model, like I said.
> 
> And like I have explained multiple times, the problem isn't the Turing
> model. Even if we assume some as-yet unknown technology with miraculous
> [but not unlimited] powers, we still have an unsolvable problem. That's
> what is so significant about the Halting Problem. (I mean, face it, what
> *practical* use does HP have? None. It's importance is that it
> demonstrates that some problems are unsolvable.)

<sigh>  We're going in circles here....

>> Maybe.  It's hard to say that that would be the case, because the
>> future is unknowable.
> 
> You're missing my point: It doesn't *matter* that we can't know the
> future. Simple logical deduction demonstrates that ANY machine we can
> construct will have the same problem, REGARDLESS of how it works.

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.

>> Maybe the halting problem was a bad example to illustrate my point; the
>> bottom line on my point still stands, though.  What's "impossible"
>> yesterday became an everyday occurrence.  It was "impossible" that the
>> solar system was heliocentric a thousand years ago.  Today, it's common
>> knowledge that that is untrue.
> 
> Once again, you are talking about science.
> 
> In science, it is always possible that some "fact" could turn out to be
> partially or wholely wrong. We think we know how the universe works, but
> we could always be wrong about something.
> 
> Mathematics is different. Not quite as different as was originally
> believed, but still. In mathematics, we can construct absolute truths
> which will never be disproven until the end of the universe itself. The
> only question mark is the reliability of the human mind.

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.

> For sufficiently complicated proofs, it becomes not merely possible but
> *plausible* that some mistake could exist. For sufficiently simple
> proofs, we can be absolutely certain that only a fundamental flaw with
> renders all of mathematics invalid could disprove the theorum.
> 
> In summary: Science can never have absolute truths. Mathematics can.

Sometimes the devil is in the details (and how detailed your data is).

>> Using today's technologies, maybe.  Again, we don't know what the
>> future holds.  It is impossible to use paper in transistors.  Or is it?
> 
> Making transistors out of paper is a question of physics - a branch of
> science. Infinite compression ratios is a question of mathematics.
> Therein lies the critical difference.

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.

>>> This is precisely my point: Solving the halting problem DOES defy the
>>> laws of causality. It is NOT just a problem of technology. It is a
>>> problem of "if this algorithm were to exist, it would cause a logical
>>> paradox, regardless of the technology used".
>> 
>> There again, maybe I chose a poor example to illustrate my point.
> 
> I'm not sure what your point is.

That I chose a poor example.

> If your point is that science is sometimes wrong, or at least needs to
> be amended, then I agree. If your point is that widely held beliefs are
> sometimes wrong, then I also agree. If your point is that every proven
> mathematical result could actually be wrong, then I completely disagree.

I believe that's just a limitation of our understanding of things as they 
are now.

Jim

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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.
> 

There are lots of tools, though. Some are quite sophisticated, such as 
the aforementioned healing brush. Layers, masking and blend modes are 
also quite powerful features.

If you look at the brush tool in PS, it's extremely powerful, pressure 
sensitive, can create brush strokes that splatter and scatter, etc, PSE 
is significantly neutered, though and had much less options on the brush 
tool.

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>> 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.

I can think of any number of results in *science* that were widely 
believed to be true but turned out not to be. But mathematics is different.

>> You're missing my point: It doesn't *matter* that we can't know the
>> future. Simple logical deduction demonstrates that ANY machine we can
>> construct will have the same problem, REGARDLESS of how it works.
> 
> 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...

> 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.

>> Making transistors out of paper is a question of physics - a branch of
>> science. Infinite compression ratios is a question of mathematics.
>> Therein lies the critical difference.
> 
> 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.

>> If your point is that science is sometimes wrong, or at least needs to
>> be amended, then I agree. If your point is that widely held beliefs are
>> sometimes wrong, then I also agree. If your point is that every proven
>> mathematical result could actually be wrong, then I completely disagree.
> 
> I believe that's just a limitation of our understanding of things as they 
> are now.

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

-- 
http://blog.orphi.me.uk/
http://www.zazzle.com/MathematicalOrchid*

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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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