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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
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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