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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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>> 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] dev null> 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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>> 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.
That seems perfectly plausible to me...
Some have also speculated that Fermat spotted a "simple" proof that has
eluded the rest of the community for over 300 years. This seems rather
less plausible.
(The modern day proof could not possibly be the one Fermat had. Well, I
mean, unless he invented several entire branches of mathematics in his
head that day...)
Some folks think he might have had a broken proof similar to Cauchy, but
not realised it was broken. The margin note looks like an off-hand
remark, so maybe he didn't check it out too much... People certainly
make mistakes.
--
http://blog.orphi.me.uk/
http://www.zazzle.com/MathematicalOrchid*
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>> 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.
Even if such a system were to exist, you would still have a new,
generalised Halting Problem, and you're back to square one.
--
http://blog.orphi.me.uk/
http://www.zazzle.com/MathematicalOrchid*
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>> 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
--
http://blog.orphi.me.uk/
http://www.zazzle.com/MathematicalOrchid*
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>> (Kinda amusing how not denying access to data is a "feature", eh?)
>
> http://www.fsf.org/blogs/community/antifeatures
Yeah, that's where I got the idea from. ;-)
--
http://blog.orphi.me.uk/
http://www.zazzle.com/MathematicalOrchid*
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And lo on Tue, 29 Jul 2008 15:42:40 +0100, Mike Raiford
<mra### [at] hotmail com> did spake, saying:
> 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 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.
--
Phil Cook
--
I once tried to be apathetic, but I just couldn't be bothered
http://flipc.blogspot.com
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And lo on Tue, 29 Jul 2008 21:45:13 +0100, Jim Henderson
<nos### [at] nospam com> did spake, saying:
> On Tue, 29 Jul 2008 09:10:38 +0100, Invisible wrote:
>
>>>> If the grains in the film reacted to colour in some currently
>>>> unreadable fashion and/or those alterations were transferred to the
>>>> photo itself then you could, in theory, recover colour from a B&W
>>>> photo or film by reading those imperfections.
>>>
>>> That's kinda what I'm thinking.
>>
>> ...so in other words, hypothetically the information might not be
>> "gone". If that were indeed the case, it is at least plausible that
>> somebody could possibly get it back, yes.
>
> Oh, the information could well be gone, but it could be reconstructed
> from the available data.
In that case the information hasn't really gone merely converted into
another pattern?
For an example of destroyed information tell me the equation I used to
derive the answer of 9.
--
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:
> 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] nospam com> did spake, saying:
>
>> On Tue, 29 Jul 2008 09:10:38 +0100, Invisible wrote:
>>
>>>>> If the grains in the film reacted to colour in some currently
>>>>> unreadable fashion and/or those alterations were transferred to the
>>>>> photo itself then you could, in theory, recover colour from a B&W
>>>>> photo or film by reading those imperfections.
>>>>
>>>> That's kinda what I'm thinking.
>>>
>>> ...so in other words, hypothetically the information might not be
>>> "gone". If that were indeed the case, it is at least plausible that
>>> somebody could possibly get it back, yes.
>>
>> Oh, the information could well be gone, but it could be reconstructed
>> from the available data.
>
> In that case the information hasn't really gone merely converted into
> another pattern?
Well, I'm talking about physical loss of "data bits", not about the use
of patterns to reconstruct it. The bit pattern is gone. :-)
> For an example of destroyed information tell me the equation I used to
> derive the answer of 9.
no. ;-)
Jim
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And lo on Wed, 30 Jul 2008 19:07:54 +0100, Mike Raiford
<mra### [at] hotmail com> did spake, saying:
> Phil Cook wrote:
>
>> What do the pair of you mean remember? I've still got a 98 machine
>> here that does just that if you dare to use more memory then is
>> physically present.
>>
>
> I haven't used 98 in years ... That's what I mean by remember.
Mistranslation of humour -
'I remember back in ye olden days using ye olden thing'
'What do you mean ye olden days? I'm still using ye olden thing!'
--
Phil Cook
--
I once tried to be apathetic, but I just couldn't be bothered
http://flipc.blogspot.com
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>> But you get what I'm saying. Maybe there is some fundamentally new
>> system that changes the rules, so to speak.
>
> That still won't solve the halting problem, because the halting problem
> isn't defined in terms of this fundamentally new system.
>
> It's like saying "integers are not closed under division", and then
> saying "but we've discovered rationals!" Integers *still* aren't
> closed under division, even if you invent rationals.
>
>> Even if such a system were to exist, you would still have a new,
>> generalised Halting Problem, and you're back to square one.
>
> That's rather harder to say, really, since we by definition have no idea
> what a program in this entirely new paradigm would look like. But I
> suspect you're correct.
The idea is that if you had some super-machine that could somehow decide
whether any given Turing machine halts for a given input, you would
still be unable to tell whether this brand new machine halts for a given
input - using exactly the same proof as the original halting problem.
--
http://blog.orphi.me.uk/
http://www.zazzle.com/MathematicalOrchid*
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Jim Henderson wrote:
> Well, what fun would it be if I just agreed with you? ;-)
Damn it, that isn't even *logic*! :-P
--
http://blog.orphi.me.uk/
http://www.zazzle.com/MathematicalOrchid*
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Invisible wrote:
> The idea is that if you had some super-machine that could somehow decide
> whether any given Turing machine halts for a given input, you would
> still be unable to tell whether this brand new machine halts for a given
> input - using exactly the same proof as the original halting problem.
That's possible. But it certainly isn't obviously true. If the
super-computer isn't programmed in the usual way, or if (for example) it
can execute an infinite number of instructions in finite time, or if it
can travel back in time, or etc, I expect you'd have to think hard about
whether that gets around the technique the halting problem proof uses.
If your super-computer cannot, for example, have its programs
represented as input to itself (i.e., you can't create a universal
super-computer), then the halting problem isn't even *defined* for that
type of computer.
--
Darren New / San Diego, CA, USA (PST)
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Darren New wrote:
> That's possible. But it certainly isn't obviously true. If the
> super-computer isn't programmed in the usual way, or if (for example) it
> can execute an infinite number of instructions in finite time, or if it
> can travel back in time, or etc, I expect you'd have to think hard about
> whether that gets around the technique the halting problem proof uses.
>
> If your super-computer cannot, for example, have its programs
> represented as input to itself (i.e., you can't create a universal
> super-computer), then the halting problem isn't even *defined* for that
> type of computer.
I implicitly assumed that any machine that can't process it's own
program isn't worthy of the title "computer", that's all. ;-) But yes, I
see what you're saying.
As for being able to perform infinite instructions in finite time...
surely that just makes it even *harder* to predict what the machine will
od, no?
--
http://blog.orphi.me.uk/
http://www.zazzle.com/MathematicalOrchid*
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On Thu, 31 Jul 2008 09:18:43 +0100, Invisible wrote:
> Jim Henderson wrote:
>
>> Well, what fun would it be if I just agreed with you? ;-)
>
> Damn it, that isn't even *logic*! :-P
LOL!
Jim
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On Tue, 29 Jul 2008 22:29:26 +0100, Orchid XP v8 wrote:
> I am not aware - despite possessing a book detailing the entire history
> of Fermat's Last Theorum - of any proof that was widely held to be
> correct for a long time before being found wrong. All the incorrect
> proofs were discovered to be incorrect fairly quickly.
Absence of evidence is not evidence of absence. ;-)
>>> And I suppose next you'll be telling me that some day, some future
>>> technology might enable us to find a sequence of chess moves whereby a
>>> bishop can get from a black square to a white square, despite it being
>>> trivially easy to mathematically prove the impossibility of this...
>>
>> You're still missing my point....
>
> You're still missing *my* point. :-P
Then we're even. ;-)
>> My point is that there's plenty of examples where raw data is lost but
>> it can be reconstructed.
>
> Blurring doesn't actuallly "lose" nearly as much data as you'd think.
> That's why it can be mostly reversed.
Again, 10 years ago, doing this was thought to be impossible.
>> Well, who knows? There are ancient civilizations that had no concept
>> of zero. The introduction of imaginary numbers didn't come along until
>> the late 1500s. Up until that point, sqrt(-1) was undefined.
>>
>> Who knows what we don't know about mathematics even today?
>
> If I were you, I'd be far more worried about the sky falling - it's
> about as logically plausible...
I don't see how your statement follows mine....
Throughout history, mankind has claimed to have reached the end of
knowledge on all manner of topics, saying "there's nothing more to learn
here". In every instance (AFAIK), that's been proven wrong.
But now here, in the 21st century, we've finally exhausted the base of
knowledge? I don't think that's the case.
Jim
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Invisible wrote:
> I implicitly assumed that any machine that can't process it's own
> program isn't worthy of the title "computer", that's all. ;-) But yes, I
> see what you're saying.
So, your brain is weaker than a Turing machine? Cool.
It's the simplicity of the machines that make them amenable to
universality, not the complexity. Remember that the Von Neumann
architecture was a breakthrough.
> As for being able to perform infinite instructions in finite time...
> surely that just makes it even *harder* to predict what the machine will
> od, no?
Not if it can process its own input. Think about how the halting problem
works, and why... If the machine has unbounded state, it might run
forever without ever getting into the same state twice. But if you can
run the computer forever without it actually taking forever, then you
can say definitively "no, that machine never stops."
And a machine that can run an infinite number of instructions in finite
time *always* stops. ;-)
--
Darren New / San Diego, CA, USA (PST)
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Jim Henderson wrote:
> Absence of evidence is not evidence of absence. ;-)
Sure it is. It's not proof of absence, of course, but it's stronger
evidence than not.
http://www.overcomingbias.com/2007/08/absence-of-evid.html
> But now here, in the 21st century, we've finally exhausted the base of
> knowledge? I don't think that's the case.
The problem is that you're confusing math with physics. In math, yes, we
have exhausted the base of knowledge of the halting problem. The halting
problem goes like this:
Assume A. Assume B. Assume C. Therefore D.
You're arguing "maybe assumption B is counterfactual." That doesn't
disprove the halting problem. It doesn't mean you can solve the halting
problem. It merely means the halting problem doesn't apply to your
current situation.
Indeed, one of the assumptions required for the halting problem to hold
(namely, unbounded storage) is *known* to be impossible to realize in
this universe (or at least normally assumed to be impossible even by
people who understand the halting problem). That *still* doesn't mean
the halting problem is "solved".
Math isn't physics.
--
Darren New / San Diego, CA, USA (PST)
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On Thu, 31 Jul 2008 09:24:30 -0700, Darren New wrote:
> Jim Henderson wrote:
>> Absence of evidence is not evidence of absence. ;-)
>
> Sure it is. It's not proof of absence, of course, but it's stronger
> evidence than not.
>
> http://www.overcomingbias.com/2007/08/absence-of-evid.html
>
>> But now here, in the 21st century, we've finally exhausted the base of
>> knowledge? I don't think that's the case.
>
> The problem is that you're confusing math with physics. In math, yes, we
> have exhausted the base of knowledge of the halting problem. The halting
> problem goes like this:
>
> Assume A. Assume B. Assume C. Therefore D.
>
> You're arguing "maybe assumption B is counterfactual." That doesn't
> disprove the halting problem. It doesn't mean you can solve the halting
> problem. It merely means the halting problem doesn't apply to your
> current situation.
>
> Indeed, one of the assumptions required for the halting problem to hold
> (namely, unbounded storage) is *known* to be impossible to realize in
> this universe (or at least normally assumed to be impossible even by
> people who understand the halting problem). That *still* doesn't mean
> the halting problem is "solved".
>
> Math isn't physics.
Now my brain hurts. ;-)
Jim
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>> I am not aware - despite possessing a book detailing the entire history
>> of Fermat's Last Theorum - of any proof that was widely held to be
>> correct for a long time before being found wrong. All the incorrect
>> proofs were discovered to be incorrect fairly quickly.
>
> Absence of evidence is not evidence of absence. ;-)
It *is* evidence. It isn't proof, but it is evidence.
Somebody having a proof that everybody thought was right but actually
turned out to be wrong would make for pretty dramatic reading in a book
which is basically a dramatisation of the history of FLT. Of course, the
researchers could have missed something though...
>> Blurring doesn't actuallly "lose" nearly as much data as you'd think.
>> That's why it can be mostly reversed.
>
> Again, 10 years ago, doing this was thought to be impossible.
Emphasis: Thought.
There is a difference between something being "thought" and something
being mathematically "proven". A very significant difference.
Cryptographers "thought" that public key cryptography was impossible,
and where astonished when somebody actually invented it. However, note
that nobody ever *proved* that PKC was impossible, people just *assumed*
it would be. Very Big Difference.
>> If I were you, I'd be far more worried about the sky falling - it's
>> about as logically plausible...
>
> I don't see how your statement follows mine....
Your "logic" seems to be "absolutely anything is possible". That
includes the sky falling down. Which is about as likely as the Halting
Problem being incorrect - but, obviously, far more serious. I don't know
about you, but *I* would rather be wrong about some theorum than have
chunks of sky fall on my head!
> Throughout history, mankind has claimed to have reached the end of
> knowledge on all manner of topics, saying "there's nothing more to learn
> here". In every instance (AFAIK), that's been proven wrong.
>
> But now here, in the 21st century, we've finally exhausted the base of
> knowledge? I don't think that's the case.
In mathematics, learning generally consists of discovering new things,
and rarely involves finding out that old things were wrong. (Although
you have to carefully draw a line between *facts* which have been
proven, and *ideas* about mathematics. The latter can and do change, the
former are forever.)
--
http://blog.orphi.me.uk/
http://www.zazzle.com/MathematicalOrchid*
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>> I implicitly assumed that any machine that can't process it's own
>> program isn't worthy of the title "computer", that's all. ;-) But yes,
>> I see what you're saying.
>
> So, your brain is weaker than a Turing machine? Cool.
This is not exactly news. A Turing machine has unbounded memory,
remember? ;-)
> It's the simplicity of the machines that make them amenable to
> universality, not the complexity. Remember that the Von Neumann
> architecture was a breakthrough.
Uh... wuh?
>> As for being able to perform infinite instructions in finite time...
>> surely that just makes it even *harder* to predict what the machine
>> will od, no?
>
> Not if it can process its own input. Think about how the halting problem
> works, and why... If the machine has unbounded state, it might run
> forever without ever getting into the same state twice. But if you can
> run the computer forever without it actually taking forever, then you
> can say definitively "no, that machine never stops."
>
> And a machine that can run an infinite number of instructions in finite
> time *always* stops. ;-)
Really? And by "infinite" do you mean Aleph0, Aleph1, or some larger
cardinallity? ;-)
--
http://blog.orphi.me.uk/
http://www.zazzle.com/MathematicalOrchid*
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>> ...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.
That sounds like an "interesting" mathematical system. (And not an
entirely implausible one, actually.)
By the way... 6 * 9 = 54? I'm confused now! o_O
--
http://blog.orphi.me.uk/
http://www.zazzle.com/MathematicalOrchid*
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Orchid XP v8 wrote:
> By the way... 6 * 9 = 54? I'm confused now! o_O
Yes it is.
"...something is fundamentally wrong with the universe..."
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"Invisible" <voi### [at] dev null> wrote in message
news:4885bf1a$1@news.povray.org...
> Today, anybody with sufficient technical bent can easily sit down with a
> computer and cut CDs of their music, or burn DVDs of their graphics and
> animations. It's not even expensive any more.
>
> We are truly living in the future, my friends...
Yep, and even possible serious gamemakers can do it for free*. I've got
to say that CryTek's CryEngine2/(Sandbox2) is fantastic!
*Free to produce mods, levels, etc., but it would cost you your arm or
two to use commercially. £500 Grand +, I think... :/
And yet... I would consider that good money well spent if I had the
inclination to use such a program with a NEW (read: idea) game that would
sell millions. ;) Wouldn't we all...
~Steve~
>
> --
> http://blog.orphi.me.uk/
> http://www.zazzle.com/MathematicalOrchid*
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Ooh... I'm right at the bottom of this long thread!
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St. wrote:
> Ooh... I'm right at the bottom of this long thread!
Yah - I'm on top. ;-)
[How often do I get to say that??]
--
http://blog.orphi.me.uk/
http://www.zazzle.com/MathematicalOrchid*
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>> Today, anybody with sufficient technical bent can easily sit down with a
>> computer and cut CDs of their music, or burn DVDs of their graphics and
>> animations. It's not even expensive any more.
>>
>> We are truly living in the future, my friends...
>
> Yep, and even possible serious gamemakers can do it for free*. I've got
> to say that CryTek's CryEngine2/(Sandbox2) is fantastic!
I have absolutely no idea how to do that.
I see a bunch of guys used the Source engine to build a game called
Dystopia. It's set in a dystopian future and features gameplay that
alternates between the real world and a Tron-like "cyberspace". It's a
slightly naff game, but far better than anything I could have built!
More recently another group of people used Source to build a very
different game called Insurgency. This is your hyper-realistic US
Marines vs Iraqi insurgents battlefield game. And when I say
hyper-realistic, there is no crosshair on the screen. You walk at about
1.5 MPH. It's almost impossible to know what's going on. And as soon as
you get near a combat zone, you instantly drop dead due to a single
sniper bullet. (In other words, it is absolutely no fun at all, just
like a real war.)
Yet another group of people are working on a complete conversion of the
original Halflife game. (Although the initial artwork - which impressive
- deviates too far from the original for my liking.)
I have absolutely no idea how in the game of God any of this is
possible. But people have done it, so it *must* be possible...
--
http://blog.orphi.me.uk/
http://www.zazzle.com/MathematicalOrchid*
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"Orchid XP v8" <voi### [at] dev null> wrote in message
news:48976fd4$1@news.povray.org...
> St. wrote:
>> Ooh... I'm right at the bottom of this long thread!
>
> Yah - I'm on top. ;-)
>
> [How often do I get to say that??]
Heh, you know that patience is a virtue, right? ;)
And you do know that when you're 56 years old with 2+ kids with their own
children, (your grand-children), you won't... won't... remember me typing
the above... ?
<sniff - the internet is bad>
~Steve~
>
> --
> http://blog.orphi.me.uk/
> http://www.zazzle.com/MathematicalOrchid*
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"Orchid XP v8" <voi### [at] dev null> wrote in message
news:48977221$1@news.povray.org...
>>> Today, anybody with sufficient technical bent can easily sit down with a
>>> computer and cut CDs of their music, or burn DVDs of their graphics and
>>> animations. It's not even expensive any more.
>>>
>>> We are truly living in the future, my friends...
>>
>> Yep, and even possible serious gamemakers can do it for free*. I've
>> got to say that CryTek's CryEngine2/(Sandbox2) is fantastic!
>
> I have absolutely no idea how to do that.
Getting Crysis = free editor. Play around in the editor and listen to
what the 15 year olds (ha, and older!) ;) have to teach on the forums. OR,
you have FarCry installed, yes? Well, CryEngine1 is available with that
game. Look on your disc for SandBox1 and have a play! Just mess around with
it for fun! Here's my first vid (Crysis) on YT:
http://www.youtube.com/watch?v=zjaxyfTW3UY
This shows how slow my comp is, but man, it was fun! About 180 Korean
trucks falling from the sky... blissfull destressing. :)
>
> I see a bunch of guys used the Source engine to build a game called
> Dystopia. It's set in a dystopian future and features gameplay that
> alternates between the real world and a Tron-like "cyberspace". It's a
> slightly naff game, but far better than anything I could have built!
>
> More recently another group of people used Source to build a very
> different game called Insurgency. This is your hyper-realistic US Marines
> vs Iraqi insurgents battlefield game. And when I say hyper-realistic,
> there is no crosshair on the screen. You walk at about 1.5 MPH. It's
> almost impossible to know what's going on. And as soon as you get near a
> combat zone, you instantly drop dead due to a single sniper bullet. (In
> other words, it is absolutely no fun at all, just like a real war.)
Oh, trust me, it is just like a real war (in a game experience at
least). I said to my son only last night, "What would you do if you were
ordered to go to the front line to save your country?" He said, "I'd fight".
I then said that he'll be killed fairly soon. No comment from him, and a
despondant face to match. Me? Stuff the war. I'd be around the back sniping
them if possible. I know for a fact that I wouldn't adhere to war 'rules'
whatever I might do. I'd do my best though for my country of course.
>
> Yet another group of people are working on a complete conversion of the
> original Halflife game. (Although the initial artwork - which impressive -
> deviates too far from the original for my liking.)
>
> I have absolutely no idea how in the game of God any of this is possible.
> But people have done it, so it *must* be possible...
Yes, it's true, people have done it, including myself. I'm about a month
away from publishing my first Crysis level, (the first in a series of three,
hopefully), and even though I've published many PoV-Ray images to the world,
it's scaring the crap out of me to upload my map. Really.O-O
~Steve~
> --
> http://blog.orphi.me.uk/
> http://www.zazzle.com/MathematicalOrchid*
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Orchid XP v8 wrote:
> I have absolutely no idea how in the game of God any of this is
> possible. But people have done it, so it *must* be possible...
The one I appreciated most was Thief 2X, a full 15-level (or so) new
game, with new story, characters, weapons, loot, levels, etc for the
engine in Thief 2. All done as a free fan mission.
Doubly impressive if you know how hard Thief's editor sucks.
--
Darren New / San Diego, CA, USA (PST)
Ever notice how people in a zombie movie never already know how to
kill zombies? Ask 100 random people in America how to kill someone
who has reanimated from the dead in a secret viral weapons lab,
and how many do you think already know you need a head-shot?
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>> I have absolutely no idea how to do that.
>
> Getting Crysis = free editor.
Getting the Source SDK = free download. I've even downloaded it. And
several similar things like it for other games. (Most notably, there was
a thing called Quake Object Oriented Level Editor or "QOOLE".)
What can I say? I just can't figure out how to produce anything
worthwhile. :-(
> Oh, trust me, it is just like a real war (in a game experience at
> least). I said to my son only last night, "What would you do if you were
> ordered to go to the front line to save your country?" He said, "I'd fight".
> I then said that he'll be killed fairly soon. No comment from him, and a
> despondant face to match. Me? Stuff the war. I'd be around the back sniping
> them if possible. I know for a fact that I wouldn't adhere to war 'rules'
> whatever I might do. I'd do my best though for my country of course.
I know some people who have really been snipers. As in, they've killed
actual people during an actual war.
They don't talk about it much...
>> I have absolutely no idea how in the game of God any of this is possible.
>> But people have done it, so it *must* be possible...
>
> Yes, it's true, people have done it, including myself. I'm about a month
> away from publishing my first Crysis level, (the first in a series of three,
> hopefully), and even though I've published many PoV-Ray images to the world,
> it's scaring the crap out of me to upload my map. Really.O-O
Yeah, but... throwing together a new map is one thing, but building an
entire new game... where do you get all the texture data from? Where do
you get all the sounds from? How to you design weapons? How do you
construct an AI engine? How do you do all of this with a few people in
their spare time?? It boggles the mind...
--
http://blog.orphi.me.uk/
http://www.zazzle.com/MathematicalOrchid*
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Invisible wrote:
> It all sounds a bit silly today. We tak such things for granted.
>
> We are truly living in the future, my friends...
When you think about it, it's kind of like the industrial revolution...
The industrial revolution transformed the way mankind lives and works.
It altered the economy forever. Fortunes were made and lives were
ruined, and the world has never been the same since. You can argue about
whether all these changes were for good or ill, but none can deny that
society was transformed. Things which would hitherto have been
considered impossible because quite ordinary.
But nobody really even thinks about the industrial revolution now.
Because it's *happened*. It's *over*. We're *here* now.
I guess it's the same with the digital entertainment revolution - nobody
really thinks about it any more because it's old news now.
Heh, I'm old enough to remember actual green screens. Computers that
tried to play "music" by making beeps. Images that were a mass of
multicoloured square blocks. The idea of a computer *so powerful* that
it could show pictures that looked almost photographic seemed
mind-blowing and futuristic.
Today, it's a mundane reality. Sure, you can now play a movie on your
computer as well as on your TV. And how is that really different? It
turns out that once you get over what a neat idea it is, the reality
isn't so different to VHS.
Actually, at the weekend I was reading an article in Amiga Format. This
was the April 1994 issue, and they're talking in hushed tones about a
visionary new technology dubbed "Full Motion Video" (FMV).
The article goes on to explain that since it's now possible to store
computer data on a CD (something they call a "CD-ROM"), in theory you
could be able to store a computer animation on there. And since the
Amiga can produce near-photographic image quality... hey, what if you
could put a *movie* onto a CD??
Ah, but there's a catch. One frame of high-quality video takes up about
1 MB of space - and you need 25 of them for a single second of video.
That gives us a transfer rate of 25 MB/s, which *wildly* exceeds what
any known CD drive is capable of.
(By my arithmetic, a CD gives you 10 MB/min, so 60x faster would be 10
MB/s, and another 2.5x faster would be 25 MB/s. So we need a drive that
spins at 180x normal speed. IIRC, normal CD speed is 500 RPM, so that's
90,000 RPM. The *centrifuge* in our lab doesn't spin that fast. Hell, my
*car* doesn't rev that high! The disk would surely shatter due to the
extreme centrefugal forces...)
But there's a bigger problem than transfer speed: 650 MB / 25 MB/s = 26
seconds of video (!!!), without any sound. Who the hell is going to
bother putting together a high-end system so they can play 26 *seconds*
of video on their computer?
It is crystal clear at this point that the storage requirements *must*
be reduced. The data has to be compressed somehow. But as soon as you do
that, the difficulty is finding a way of compressing the data so that it
can still be UNcompressed fast enough for realtime playback. This is a
serious problem.
Apparently Phillips has come up with a new device called the CD-I, which
usees the "white book standard". This basically means you take your
movie, downsample it to half resolution (so it's roughly 400x300
pixels), and then encode it using a newly-developed system known as
"MPEG". You then put this on a CD-ROM.
Trouble is, the latest high-end Amigas had MPEG decoding software, but
would only manage maybe 3-4 FPS at low resolutions. This is clearly
insufficient for FMV! But then there was the Amiga CD32.
For those that don't know, the Amiga CD32 is an Amiga 1200 with a CD-ROM
drive, built in the shape of a games console. (There's no keyboard or
mouse, for example.)
Most of the games released for it were actually just Amiga 1200 games
with a CD soundtrack added. But a small few actually took advantage of
the awesome storage capabilities of a CD-ROM. (Remember, previously
games came on 720 KB floppy disks!)
In this same issue of AmigaFormat, I read an issue for a game called
"Microcosm". Due to some sci-fi plot that isn't actually that
interesting, you get put inside a space ship, miniturised, and injected
into somebody's body to fight off a hord of robits inside the guy. In
other words, basically you fly down organic-looking tunnels shooting things.
I don't have the magazine in front of me now, but the final summary read
something like
"This may not be the most playable game ever, but it doesn't even
matter. This game is the future. And it's here right now. GET IT!"
The best screenshot I can find is this:
http://www.lemonamiga.com/games/screenshots/full/microcosm_(cd32)_20.png
The graphics were comparatively realistic. Certainly little like this
had been seen before. Most games were either cartoonish platforms, or a
few were very slow, jerky 3D things with giant polygons, point lights
and no surface texturing. *This* looked almost real.
(In solomn truth, it's actually just a 2D game with a prerendered 3D
background loop playing behind it. But it *looks* impressive. And it's
only possible to fit that much animation data in due to the cavernous
space on a CD-ROM.)
It was also intercut with smooth video sequences:
http://www.lemonamiga.com/games/screenshots/full/microcosm_(cd32)_03.png
Certainly it's nothing compared to what we have today, but back then
seeing bits of jerky motion on a *computer* was astonishing.
Anyway, getting back to FMV... There was a [very expensive] card for the
Amiga CD32 that allows it to play any White Book compliant CD movie.
Phillips were apparently very surprised when they found out about this.
But they seemed pleased. "I think anybody who does with producing a
proprietry format has the wrong idea. We need a common format to
stimulate adoption."
(Anybody who remembers the HD-DVD/BluRay feasco surely cannot doubt
these words!)
The FMV card was reputedly about £300. It basically consists of some
custom MPEG decoder hardware. The magazine mentions how "it takes many
months of running time on the latest supercomputers to convert video to
MPEG format". But, "amazingly", it makes the data fit onto a CD and play
back even within a CD's limited transfer rate.
The article is of course liberally decorated with screenshots from an
Amiga playing various movies. I've never heard of CD-I or the White Book
standard, but apparently quite a number of titles were actually released
for it.
The pictures don't actually look bad at all. If anything, the only real
problem is the very low spatial resolution. They all look kinda fuzzy
and out of focus, and very pixelish. (Remembe, this is 400x300 pixel
resolution!) But the *colour* seems completely perfect. There is no
*hint* of the MPEG artifacts you often see at high compression ratios.
When did DVDs come out? I don't actually know the answer to that, but it
seems like comparatively recently. To think that the Amiga was already
*doing* this stuff, for real, way back in 1994 seems quite impressive to
me. Not that it apparently got very far...
How are things different today? Well today we have DVDs, which are just
like CDs except with significantly more storage capacity. That means you
don't have to downsample the video to make it fit on a disk.
But more importantly, today a cheap PC can decode MPEG completely in
software, and the CPU is *idling* during this task. It's *easy*! And I
think that's the key thing. The computer power necessary for realtime
video decompression is now commonly available, which is why you can go
to Tesco and buy a DVD player for £20. Hell, you couldn't buy a *VHS*
machine for that price! EVER!
(I guess all those complicated robotic parts for spooling the tape and
so forth were just inherantly expensive to make. A DVD player just needs
a few motors, a laser, and a computer with some software. It's quite
easy really...)
--
http://blog.orphi.me.uk/
http://www.zazzle.com/MathematicalOrchid*
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"Invisible" <voi### [at] dev null> wrote in message
news:48980a4a$1@news.povray.org...
>>> I have absolutely no idea how to do that.
>>
>> Getting Crysis = free editor.
>
> Getting the Source SDK = free download. I've even downloaded it.
Yes, I've got it too, but don't use it. You only need the SDK if you want
to produce a 'mod' - i.e., provide a new weapon, or game strategy, etc. But,
you still need the disc to see and play your level, right?
You've got FarCry, so try it some time with their editor. ;)
Get some of those FatBoys and Trigens out and have a war with loads of
grunts! :)
And
> several similar things like it for other games. (Most notably, there was a
> thing called Quake Object Oriented Level Editor or "QOOLE".)
Never heard of that, although I knew there was an editor.
>
> What can I say? I just can't figure out how to produce anything
> worthwhile. :-(
Ah, well, I thought exactly the same. Then I played, and played and
played with the editor and just came up with 'anything' that works. Gave it
a name, and that was my eventual year long project.
> Me? Stuff the war. I'd be around the back sniping
>> them if possible. I know for a fact that I wouldn't adhere to war 'rules'
>> whatever I might do. I'd do my best though for my country of course.
>
> I know some people who have really been snipers. As in, they've killed
> actual people during an actual war.
Lol at me ranting. ;) I don't know what I'd be like really, all I know
is that I wouldn't be on that front line to get shot at, (who the f*** would
in their right mind!) I admire snipers, they have a tough job to do. I have
no idea what it's like to be a real sniper, but boy, these games do come
close I think. If you're playing Crysis, when you're slightly out of range
from the enemy sniper and he gets close with his shot by a few inches, you
can hear the whizz of that bullet pass your ear, (and see it via the trail),
now imagine that in real life!
>
> They don't talk about it much...
No, and I wouldn't either. It's a hard thing to do.
>
>>> I have absolutely no idea how in the game of God any of this is
>>> possible. But people have done it, so it *must* be possible...
>>
>> Yes, it's true, people have done it, including myself. I'm about a
>> month away from publishing my first Crysis level, (the first in a series
>> of three, hopefully), and even though I've published many PoV-Ray images
>> to the world, it's scaring the crap out of me to upload my map.
>> Really.O-O
>
> Yeah, but... throwing together a new map is one thing, but building an
> entire new game... where do you get all the texture data from? Where do
> you get all the sounds from? How to you design weapons? How do you
> construct an AI engine? How do you do all of this with a few people in
> their spare time?? It boggles the mind...
There are some clever kids out there, (and older guys), that's for
sure. AI engine? No idea. (Well, programming, obviously, but what, and how,
I wouldn't know). Textures? PS. Weapons (and everything else for a 'new'
game) - a modelling program.
Simple as that. ;) But you don't really need to do any of that for
your first map in Crysis, it's all there and configurable in the editor.
Takes some playing with to get right, but it works. I've tested my map loads
now, but I still need to get the saves in the right positions and get the
ending right.
Btw, this is me DE-STRESSING in Crysis. 180(ish) Korean trucks falling to
the ground:
http://uk.youtube.com/watch?v=zjaxyfTW3UY
Notice how slow it is on my 6600GT. ;) I'll do a daytime version
soon... ;)
~Steve~
>
> --
> http://blog.orphi.me.uk/
> http://www.zazzle.com/MathematicalOrchid*
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Invisible wrote:
> Yeah, but... throwing together a new map is one thing, but building an
> entire new game... where do you get all the texture data from? Where do
> you get all the sounds from? How to you design weapons? How do you
> construct an AI engine? How do you do all of this with a few people in
> their spare time?? It boggles the mind...
Minus the AI engine, that sounds like building a POV-Ray scene. And people
do it in their spare time.
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"Nicolas Alvarez" <nic### [at] gmail com> wrote in message
news:489a6bf8@news.povray.org...
> Invisible wrote:
>> Yeah, but... throwing together a new map is one thing, but building an
>> entire new game... where do you get all the texture data from? Where do
>> you get all the sounds from? How to you design weapons? How do you
>> construct an AI engine? How do you do all of this with a few people in
>> their spare time?? It boggles the mind...
>
> Minus the AI engine, that sounds like building a POV-Ray scene. And people
> do it in their spare time.
Yes, just an hour or two here and there, and maybe a full weekend if
you're inclined, and a year later you've got yourself a map. (In my case
that is. Some of these young guys can produce professional maps in like - a
couple of months or less!)
~Steve~
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Orchid XP v8 wrote:
> stbenge wrote:
>> Thank goodness for the open-source movement!
>
> Yeah - I'm still puzzled by all that. The Amiga had a strong "shareware"
> scene, but I'm puzzled by this sudden new craze of giving away
> fully-supported commercial-grade software (sometimes that *was*
> commercial!) for free. It suddenly seems to be the "trendy" thing to do,
> and I'm not really sure how that happened.
It makes sense when your primary source of revenue comes from service
contracts. Give away the thing you're servicing / supporting, and
suddenly you've a lot more potential customers.
...Chambers
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St. wrote:
> <sniff - the internet is bad>
But it's also good for lots of things!
...Chambers
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