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"Real-world problems are simply degenerate cases of pure mathematical
problems."
[Just found in a signature on one of the Haskell mailing lists.]
--
http://blog.orphi.me.uk/
http://www.zazzle.com/MathematicalOrchid*
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On Fri, 30 May 2008 12:03:49 +0100, Invisible <voi### [at] dev null> wrote:
>"Real-world problems are simply degenerate cases of pure mathematical
>problems."
>
>[Just found in a signature on one of the Haskell mailing lists.]
Obviously not an engineer. :)
--
Regards
Stephen
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Stephen wrote:
> Obviously not an engineer. :)
Hmm... so is "software engineer" not an engineer then? ;-)
--
http://blog.orphi.me.uk/
http://www.zazzle.com/MathematicalOrchid*
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>> "Real-world problems are simply degenerate cases of pure mathematical
>> problems."
>
> Obviously not an engineer. :)
"Hey look buddy, I'm an engineer, and that means I solve problems. Not
problems like 'what is beauty?' - because that would fall within the
preview of your connundrums of philosphy. I solve PRACTICAL problems.
For example: How am I gonna stop some big bean mutha hubba from tearing
me a new, structurally superflous behind? The answer: Use a gun. And if
they don't work: Use MORE gun. Like this little old tripod-mounted
number right here, designed... by ME... built... by ME... and you'd
better HOPE....... NOT POINTED AT YOU!"
[Not that I've watched the trailer obsessively and memorised every line
of it or ANYTHING like that, you understnad.]
--
http://blog.orphi.me.uk/
http://www.zazzle.com/MathematicalOrchid*
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On Fri, 30 May 2008 13:09:21 +0100, Invisible <voi### [at] devnull> wrote:
>Stephen wrote:
>
>> Obviously not an engineer. :)
>
>Hmm... so is "software engineer" not an engineer then? ;-)
Not if s/he thinks that s/he is a mathematician.
--
Regards
Stephen
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On Fri, 30 May 2008 14:24:02 +0100, Invisible <voi### [at] devnull> wrote:
>
>[Not that I've watched the trailer obsessively and memorised every line
>of it or ANYTHING like that, you understnad.]
Of course not!
Would someone tell me what that rant is about?
On second thoughts, don't :)
--
Regards
Stephen
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Stephen wrote:
> Would someone tell me what that rant is about?
> On second thoughts, don't :)
As you may or may not know, Valve recently greated a computer game known
only as Team Fortress 2. In this game, you can play as one of 9
different characters - all with different weapons and abilities, and all
heavily characitured.
One such character is the Engineer. We wears a yellow construction
helmet and talks in a sterotypical Texus accent. Walks around carrying a
wrench and yelling that "I need some God-darn'd help here!" and "plant
yourself on the point, mister!"
His most notable ability is building sentry guns. These, as the name
suggests, shoot anybody on the enemy team who walks within range. Maps
are won or lost based on how many sentry gens a team has built, how
cleaverly placed they are, and how effectively their team of engineers
can keep them repaired.
Valve also released a series of videos entitled "Meet the team". One of
them was "Meet the Engineer". In this, we see the engineer sitting on a
rock beside his camp fire softly playing an accoustic guitar and
describing what he does for a living. At the end of the video, the
camera pulls out, and we discover that the camp fire has 4 sentry guns
round it, and while the Engineer calmly sits playing his guitar, an
entire army of enemy personnel are attempting to attack him, and being
mowed to the ground by the sentry guns.
"and you'd better HOPE....... NOT POINTED AT YOU!"
*insane battlefield shot with Engineer calmly sitting in the middle,
guarded by his sentries*
*TF2 themetune and credits*
--
http://blog.orphi.me.uk/
http://www.zazzle.com/MathematicalOrchid*
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On Fri, 30 May 2008 15:02:41 +0100, Invisible <voi### [at] devnull> wrote:
>Stephen wrote:
>
>> Would someone tell me what that rant is about?
>> On second thoughts, don't :)
>
>As you may or may not know, Valve recently greated a computer game known
>only as Team Fortress 2. In this game, you can play as one of 9
>different characters - all with different weapons and abilities, and all
>heavily characitured.
[snip]
>*TF2 themetune and credits*
What part of "don't" do you not understand, Andrew? ;)
We've met, did I look like "an interested in games" type of person?
On second thoughts, don't answer that :)
--
Regards
Stephen
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Invisible wrote:
> "Real-world problems are simply degenerate cases of pure mathematical
> problems."
I recently attended a talk given by Arthur Jaffe, a (co)founder of the
Clay institute and professor at Harvard (forgot if he's in the math or
physics dept). His work is mathematical physics.
I don't know his stance, but he knows many top physicists and perhaps
mathematicians as well who'd disagree. Essentially, the (very boring)
talk was about this very issue: Are mathematics and physics consistent
with each other?
A lot of the calculations in physics as currently performed are
actually mathematically invalid. He gave this startling example. You see
the g_s in the equation on this page?
http://en.wikipedia.org/wiki/Magnetic_moment#Magnetic_moment_of_electrons
It has now been measured to around 12 significant figures - perhaps the
most precise measurement ever made. Those 12 figures agree with theory.
And that theory is simply mathematically invalid (at least with the
current state of mathematics).
You just have to "think" differently to do serious theoretical physics.
From what little I've studied, I seriously think mathematics is a bit
easier. At least in math, you're bound by certain rules - everything has
to be logical and provable. In physics, I see them do wild things (i.e.
mathematically questionable) fairly frequently and get good results. I
just can't think that "freely" and ignore the fact that my infinities
can be neglected, or something.
--
Why is the person who invests all your money called a broker?
/\ /\ /\ /
/ \/ \ u e e n / \/ a w a z
>>>>>>mue### [at] nawazorg<<<<<<
anl
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"Invisible" <voi### [at] devnull> wrote in message
news:483fee71@news.povray.org...
> Stephen wrote:
> > Obviously not an engineer. :)
> Hmm... so is "software engineer" not an engineer then? ;-)
True, programmers often pretend to be engineers, scientists and architects.
Thankfully, "software doctor" is not a term that has yet caught on..
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Stephen wrote:
> What part of "don't" do you not understand, Andrew? ;)
Um... the abbreviated part? :-}
> We've met, did I look like "an interested in games" type of person?
> On second thoughts, don't answer that :)
Well gee, I don't know. I mean I got the impression... oh wait, you said
DON'T answer that? ;-)
Heh. well screw the game. I just find the idea of a guy casually having
a beer and a sing-song in the middle of a warzone kinda humurous...
--
http://blog.orphi.me.uk/
http://www.zazzle.com/MathematicalOrchid*
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Invisible wrote:
> For example: How am I gonna stop some big bean mutha hubba from tearing
> me a new, structurally superflous behind? The answer: Use a gun. And if
> they don't work: Use MORE gun.
Reminds me of an old #xml channel topic. "XML is like violence. If it
doesn't solve the problem, use more."
(I don't agree with it)
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On Fri, 30 May 2008 16:08:46 +0100, Invisible <voi### [at] devnull> wrote:
>
>Heh. well screw the game. I just find the idea of a guy casually having
>a beer and a sing-song in the middle of a warzone kinda humurous...
Yeah, I would not have thought that war zones were the best place for
a boozy sing song. Unless it was
Spam, spam, spam, spam, spam, spam, baked beans, spam, spam, spam and
spam
Spam, sausage, spam, spam, spam, bacon, spam, tomato and spam
--
Regards
Stephen
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Nicolas Alvarez wrote:
> Reminds me of an old #xml channel topic. "XML is like violence. If it
> doesn't solve the problem, use more."
>
> (I don't agree with it)
"Sometimes, you have a problem, and you think 'hey, I could solve this
using Perl!' And then you have TWO problems..." ;-)
--
http://blog.orphi.me.uk/
http://www.zazzle.com/MathematicalOrchid*
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Invisible <voi### [at] devnull> wrote:
> "Real-world problems are simply degenerate cases of pure mathematical
> problems."
Not related, but saw this today:
"Any sufficiently advanced magic is indistinguishable from technology"
-- Larry Niven's corollary to Clarke's Third Law.
--
- Warp
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Mueen Nawaz wrote:
> And that theory is simply mathematically invalid (at least with the
> current state of mathematics).
I gave up when I learned what "spin 2" particles actually means. :-)
--
Darren New / San Diego, CA, USA (PST)
"That's pretty. Where's that?"
"It's the Age of Channelwood."
"We should go there on vacation some time."
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On 30 May 2008 11:34:54 -0400, Warp <war### [at] tagpovrayorg> wrote:
>Invisible <voi### [at] devnull> wrote:
>> "Real-world problems are simply degenerate cases of pure mathematical
>> problems."
>
> Not related, but saw this today:
>
>"Any sufficiently advanced magic is indistinguishable from technology"
> -- Larry Niven's corollary to Clarke's Third Law.
That brought a smile to my face.
--
Regards
Stephen
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Invisible wrote:
> Stephen wrote:
>
>> Obviously not an engineer. :)
>
> Hmm... so is "software engineer" not an engineer then? ;-)
>
definitely not. Engineer is (at least here in the Netherlands and the
US) a protected title. You are not allowed to call yourself an engineer
unless you have passed a final exam in one of the certified engineering
courses. It is therefor not hard to prove that nearly all software
engineers are breaking the law. I know the IEEE (of which I am an
associate member, because I am not an engineer) finds the software
engineers a treat to the perception of engineers by laymen. IIRC the
practice is so wide spread that they think it has become impossible to
enforce the law in these cases. That does not stop them from being annoyed.
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Warp wrote:
> "Any sufficiently advanced magic is indistinguishable from technology"
> -- Larry Niven's corollary to Clarke's Third Law.
How true it is... ;-)
[...for example, I am speakin to a person I've never met, who is
currently in a country I've never visited. Cavemen would be astounded!]
In our lab, some joker put the following on the wall:
"Statinger's Law: It works better if you plug it in."
"Horner's Five Thumb Postulate: Experience varies directly with
equipment ruined."
"Snells Rule: Whatever we did, that was what we planned to do."
--
http://blog.orphi.me.uk/
http://www.zazzle.com/MathematicalOrchid*
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Warp wrote:
> Invisible <voi### [at] devnull> wrote:
>> "Real-world problems are simply degenerate cases of pure mathematical
>> problems."
>
> Not related, but saw this today:
>
> "Any sufficiently advanced magic is indistinguishable from technology"
> -- Larry Niven's corollary to Clarke's Third Law.
>
Hmm apparently a cookie thread. let's add another one:
I got this fortune cookie less than 24 hours ago:
"Our government has kept us in a perpetual state of fear -- kept us in
a continuous stampede of patriotic fervor -- with the cry of grave
national emergency... Always there has been some terrible evil to
gobble us up if we did not blindly rally behind it by furnishing the
exorbitant sums demanded. Yet, in retrospect, these disasters seem
never to have happened, seem never to have been quite real."
-- General Douglas MacArthur, 1957
(Possibly one of the offensive cookies)
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Orchid XP v8 wrote:
> Warp wrote:
>
>> "Any sufficiently advanced magic is indistinguishable from technology"
>> -- Larry Niven's corollary to Clarke's Third Law.
>
> How true it is... ;-)
>
> [...for example, I am speakin to a person I've never met, who is
> currently in a country I've never visited. Cavemen would be astounded!]
I think that one is covered by the original Third Law of Arthur C Clarke
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Warp wrote:
> Invisible <voi### [at] devnull> wrote:
>> "Real-world problems are simply degenerate cases of pure mathematical
>> problems."
>
> Not related, but saw this today:
>
> "Any sufficiently advanced magic is indistinguishable from technology"
> -- Larry Niven's corollary to Clarke's Third Law.
Any technology distinguishable from magic is insufficiently advanced.
-- some other corollary to the 3rd Law.
--
Tim Cook
http://empyrean.digitalartsuk.com
-----BEGIN GEEK CODE BLOCK-----
Version: 3.12
GFA dpu- s: a?-- C++(++++) U P? L E--- W++(+++)>$
N++ o? K- w(+) O? M-(--) V? PS+(+++) PE(--) Y(--)
PGP-(--) t* 5++>+++++ X+ R* tv+ b++(+++) DI
D++(---) G(++) e*>++ h+ !r--- !y--
------END GEEK CODE BLOCK------
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On Fri, 30 May 2008 16:16:48 -0400, Tim Cook <z99### [at] gmailcom>
wrote:
>
>Any technology distinguishable from magic is insufficiently advanced.
> -- some other corollary to the 3rd Law.
Cook's corollary to the 3rd Law? :)
--
Regards
Stephen
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Stephen wrote:
> Cook's corollary to the 3rd Law? :)
Nah, I found it somewhere on the web.
--
Tim Cook
http://empyrean.digitalartsuk.com
-----BEGIN GEEK CODE BLOCK-----
Version: 3.12
GFA dpu- s: a?-- C++(++++) U P? L E--- W++(+++)>$
N++ o? K- w(+) O? M-(--) V? PS+(+++) PE(--) Y(--)
PGP-(--) t* 5++>+++++ X+ R* tv+ b++(+++) DI
D++(---) G(++) e*>++ h+ !r--- !y--
------END GEEK CODE BLOCK------
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andrel wrote:
> "Our government has kept us in a perpetual state of fear -- kept us in
> a continuous stampede of patriotic fervor -- with the cry of grave
> national emergency... Always there has been some terrible evil to
> gobble us up if we did not blindly rally behind it by furnishing the
> exorbitant sums demanded. Yet, in retrospect, these disasters seem
> never to have happened, seem never to have been quite real."
> -- General Douglas MacArthur, 1957
>
> (Possibly one of the offensive cookies)
I've got a great book on Harry S Truman. You should see what he said
about MacArthur.
Unfortunately, I'm too lazy to dig it out :( Suffice it to say, he
called the guy an idiot.
...Chambers
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On Sat, 31 May 2008 15:36:22 -0700, Chambers wrote:
> andrel wrote:
>> "Our government has kept us in a perpetual state of fear -- kept us in
>> a continuous stampede of patriotic fervor -- with the cry of grave
>> national emergency... Always there has been some terrible evil to
>> gobble us up if we did not blindly rally behind it by furnishing the
>> exorbitant sums demanded. Yet, in retrospect, these disasters seem
>> never to have happened, seem never to have been quite real."
>> -- General Douglas MacArthur, 1957
>>
>> (Possibly one of the offensive cookies)
>
> I've got a great book on Harry S Truman. You should see what he said
> about MacArthur.
Is the book "The Fifties" by David Halberstam? The quote that's listed
on wikiquote from there is about MacArthur's "Old soldiers never die"
speech - "Nothing but a d*mn bunch of BS" (paraphrased).
Jim
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Mueen Nawaz wrote:
> Invisible wrote:
>> "Real-world problems are simply degenerate cases of pure mathematical
>> problems."
>
> I recently attended a talk given by Arthur Jaffe, a (co)founder of
> the Clay institute and professor at Harvard (forgot if he's in the math
> or physics dept). His work is mathematical physics.
>
> I don't know his stance, but he knows many top physicists and
> perhaps mathematicians as well who'd disagree. Essentially, the (very
> boring) talk was about this very issue: Are mathematics and physics
> consistent with each other?
>
> A lot of the calculations in physics as currently performed are
> actually mathematically invalid. He gave this startling example. You see
> the g_s in the equation on this page?
>
> http://en.wikipedia.org/wiki/Magnetic_moment#Magnetic_moment_of_electrons
>
> It has now been measured to around 12 significant figures - perhaps
> the most precise measurement ever made. Those 12 figures agree with theory.
>
> And that theory is simply mathematically invalid (at least with the
> current state of mathematics).
I'm not sure that "mathematically invalid" means anything here. It
would be more precise to say that the model described by the mathematics
in question does not apply to the phenomena described.
Is .5c + .5c = 1c mathematically valid? Well, yes. If two observers,
moving at .5c relative to one observer, in opposing directions, observe
each other, do their observations of each others' motion equal 1.0c? We
now know that they will observe a lesser value (.75c, IIRC). .5c + .5c
=1.0c is still mathematically valid, but the math describes a model of
motion that does not apply to real-world motion (although the error is
important only at velocities that are significant fractions of c).
So it isn't a case of the math being wrong, it's a case of the math
being irrelevant, which is the reason for this famous physics quote by
Wolfgang Pauli: "This isn't right. This isn't even wrong."
Regards,
John
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John VanSickle <evi### [at] hotmailcom> wrote:
> Is .5c + .5c = 1c mathematically valid? Well, yes.
The problem with that equation is that it lacks the proper context,
more precisely the topology used.
In a linear cartesian space that equation is correct. However, the
context of the equation is not a linear cartesian space. Thus, in context,
it makes it invalid.
I would say that mathematics can always be used to represent reality
when put in the proper context.
--
- Warp
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Chambers wrote:
> andrel wrote:
>> "Our government has kept us in a perpetual state of fear -- kept us in
>> a continuous stampede of patriotic fervor -- with the cry of grave
>> national emergency... Always there has been some terrible evil to
>> gobble us up if we did not blindly rally behind it by furnishing the
>> exorbitant sums demanded. Yet, in retrospect, these disasters seem
>> never to have happened, seem never to have been quite real."
>> -- General Douglas MacArthur, 1957
>>
>> (Possibly one of the offensive cookies)
>
> I've got a great book on Harry S Truman. You should see what he said
> about MacArthur.
>
> Unfortunately, I'm too lazy to dig it out :( Suffice it to say, he
> called the guy an idiot.
>
A couple of remarks:
- According to that most reliable source of wikipedia, it was Truman
that fired MacArthur for disagreeing with him. So I would be surprised
if he did not try to portrait him as an idiot. That is irrespective of
whether he was right or wrong. Simply the case that a president fires a
famous general dictates that the president should convince the public
that he was much better equipped than the general.
- The reason I found this quote interesting is that when you start
reading it you expect some left wing attack on president Bush for his
Iraq invasion. An then it isn't. Even if it had been a 50 year old quote
from a true idiot it would still be interesting.
- He is not the only general to show insights into the political process
after their active duty in a way that makes you wonder why they did not
resign themselves earlier. In fact that seems to hold also for
presidential spokesmen and the like.
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Warp wrote:
> I would say that mathematics can always be used to represent reality
> when put in the proper context.
The fascinating thing to wonder about is ... why is this so?
Most people are so used to it that it's hard to even imagine a world
where this isn't true. Even the religious types try to come up with
"laws" that would govern the supernatural.
Of course, maybe that's just anthropogenic. If the universe didn't work
consistently, I'd (wild-ass) guess that it's likely that life capable of
wondering about it wouldn't have evolved.
And the thing about QED is there doesn't seem to be math at the bottom
level - it's random on an event-by-event basis. (Maybe there's a math
for that? I don't know of any. Statistics only deals with multiple events.)
--
Darren New / San Diego, CA, USA (PST)
"That's pretty. Where's that?"
"It's the Age of Channelwood."
"We should go there on vacation some time."
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Darren New <dne### [at] sanrrcom> wrote:
> Of course, maybe that's just anthropogenic. If the universe didn't work
> consistently, I'd (wild-ass) guess that it's likely that life capable of
> wondering about it wouldn't have evolved.
I'm sure if you asked a physicist specialized in quantum mechanics he
would say that life would probably not be possible without the wild
uncertainties of quantum phenomena (such as particles physically being
at multiple locations at the same time).
Yet, even the counter-intuitive quantum phenomena can be subject to
mathematical formulation.
--
- Warp
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Darren New wrote:
> And the thing about QED is there doesn't seem to be math at the bottom
> level - it's random on an event-by-event basis.
My personal theory is that it *isn't* random - we just can't see it well
enough to find a pattern. (As in, it's not possible to make the actual
measurements that would reveal a pattern.) But hey, what do I know?
--
http://blog.orphi.me.uk/
http://www.zazzle.com/MathematicalOrchid*
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Warp wrote:
> Yet, even the counter-intuitive quantum phenomena can be subject to
> mathematical formulation.
A closed set can also be an open set.
It is possible to construct a 2D set of points such that each point
simultaneously touches three other connected sets.
A propper class is a collection of things larger than any possible set.
Mathematics is *littered* with utterly counter-intuitive things. ;-)
[And people wonder why mathematicians are so pedantic about everything.
If YOU worked with something so unpredictable, you'd be cautious too...]
--
http://blog.orphi.me.uk/
http://www.zazzle.com/MathematicalOrchid*
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andrel wrote:
> A couple of remarks:
> - According to that most reliable source of wikipedia, it was Truman
> that fired MacArthur for disagreeing with him. So I would be surprised
> if he did not try to portrait him as an idiot. That is irrespective of
> whether he was right or wrong. Simply the case that a president fires a
> famous general dictates that the president should convince the public
> that he was much better equipped than the general.
Basically, it all came down to the fact that MacArthur wanted to go out,
fight, and win WWIII.
Truman did everything in his power to avoid an actual war - he thought
two World Wars were more than enough, and would rather see the conflict
played out on a smaller scale. The Korean War (and, eventually, the
Vietnam War) were direct results of his policies in that respect, as was
the Cold War in general.
People blame our leadership for those confrontations, but fail to
realize that the alternative was all out war on a scale similar to, if
not larger than, WWII.
...Chambers
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Orchid XP v8 wrote:
> My personal theory is that it *isn't* random - we just can't see it well
> enough to find a pattern. (As in, it's not possible to make the actual
> measurements that would reveal a pattern.) But hey, what do I know?
No, you can actually measure that isn't the case. Look up "Bell's
Inequality."
Basically, if you measure A, you get W or X. If you measure B, you get Y
or Z. If there was some variable C that told you which you got, you'd
get a distribution of W,X,Y,Z when you measured some As and some Bs
that's different from what you really get. Hence, there's no actual
"hidden variable", not even one that you theoretically can't measure.
It's complex and ugly, but if you actually find a decent tutorial, it
makes sense.
--
Darren New / San Diego, CA, USA (PST)
"That's pretty. Where's that?"
"It's the Age of Channelwood."
"We should go there on vacation some time."
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Warp wrote:
> I'm sure if you asked a physicist specialized in quantum mechanics he
> would say that life would probably not be possible without the wild
> uncertainties of quantum phenomena (such as particles physically being
> at multiple locations at the same time).
I imagine that life based on DNA and chemistry and such wouldn't work
the same way. I was talking more about if (say) the universe worked the
way you thought it should, or there really were demons and spirits that
could make fundamental changes to how the world works, etc.
(BTW, you don't get particles being physically present at multiple
locations. If you actually measure where they are, they're only in one
place.)
> Yet, even the counter-intuitive quantum phenomena can be subject to
> mathematical formulation.
Only statistically speaking, tho. Nobody has figured out what causes it
to have the properties they have, even tho (surprisingly enough) it's
the only way you can get a mathematically consistent treatment. In a bit
more detail, QED is based on probabilities. The only probabilities that
work are 1-dimensional probabilities (i.e., real numbers, and =
multiply, or = add), and 2-dimensional probabilities (i.e., complex
numbers as probabilities). I believe it's been mathematically proven
that you can't have something with the properties of "probability" that
has more than 2 dimensions. QED has two-dimensional probabilities for
events, and when you average enough of them you get one-dimensional
probabilities for events.
--
Darren New / San Diego, CA, USA (PST)
"That's pretty. Where's that?"
"It's the Age of Channelwood."
"We should go there on vacation some time."
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andrel wrote:
> exorbitant sums demanded. Yet, in retrospect, these disasters seem
> never to have happened, seem never to have been quite real."
> -- General Douglas MacArthur, 1957
That doesn't really sound like a MacArthur quote. More like something
Truman said to MacArthur. :-)
--
Darren New / San Diego, CA, USA (PST)
"That's pretty. Where's that?"
"It's the Age of Channelwood."
"We should go there on vacation some time."
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"Darren New" <dne### [at] sanrrcom> wrote
> Warp wrote:
> > I would say that mathematics can always be used to represent reality
> > when put in the proper context.
> The fascinating thing to wonder about is ... why is this so?
Easy. Mathematics can represent *anything*, since you get to make up your
own axioms.
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Orchid XP v8 <voi### [at] devnull> wrote:
> Mathematics is *littered* with utterly counter-intuitive things. ;-)
Ever heard of the Banach-Tarski paradox? A solid ball in 3-dimensional
space can be split into several non-overlapping pieces, which can then be
put back together in a different way to yield two identical copies of
the original ball.
--
- Warp
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Darren New <dne### [at] sanrrcom> wrote:
> (BTW, you don't get particles being physically present at multiple
> locations. If you actually measure where they are, they're only in one
> place.)
But their simultaneous location in more than one place can be inferred
by other side-effects. For example a single electron can pass through two
slits at the same time, interfering with itself after doing so.
--
- Warp
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Chambers wrote:
> andrel wrote:
>> A couple of remarks:
>> - According to that most reliable source of wikipedia, it was Truman
>> that fired MacArthur for disagreeing with him. So I would be surprised
>> if he did not try to portrait him as an idiot. That is irrespective of
>> whether he was right or wrong. Simply the case that a president fires
>> a famous general dictates that the president should convince the
>> public that he was much better equipped than the general.
>
> Basically, it all came down to the fact that MacArthur wanted to go out,
> fight, and win WWIII.
>
> Truman did everything in his power to avoid an actual war - he thought
> two World Wars were more than enough, and would rather see the conflict
> played out on a smaller scale.
Indeed, just what Truman would say ;)
> The Korean War (and, eventually, the
> Vietnam War) were direct results of his policies in that respect, as was
> the Cold War in general.
>
> People blame our leadership for those confrontations, but fail to
> realize that the alternative was all out war on a scale similar to, if
> not larger than, WWII.
>
> ...Chambers
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> Ever heard of the Banach-Tarski paradox? A solid ball in 3-dimensional
> space can be split into several non-overlapping pieces, which can then be
> put back together in a different way to yield two identical copies of
> the original ball.
I hadn't heard of that one, but it makes perfect sense in a topology
context.
In that context "split" really means a 1:2 mapping of spaces.
Cut the ball in half, then in the two hemispheres the new equator plane
is a curve from the lip that follows a 0.5*y scaled sphere, from there
just map the curved planes back to flat to get two spheres.
Since we're talking about a mapping, not a real object, there's no
conservation of volume, a sphere is a sphere, no matter what the size.
The paradox is that the more mathematicians learn,
the less they are able to explain clearly.
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On Sun, 1 Jun 2008 13:34:22 -0600, "somebody" <x### [at] ycom> wrote:
>"Darren New" <dne### [at] sanrrcom> wrote
>> Warp wrote:
>
>> > I would say that mathematics can always be used to represent reality
>> > when put in the proper context.
>
>> The fascinating thing to wonder about is ... why is this so?
>
>Easy. Mathematics can represent *anything*, since you get to make up your
>own axioms.
>
Oh! You let the secret our :)
--
Regards
Stephen
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Darren New wrote:
> Warp wrote:
>> I'm sure if you asked a physicist specialized in quantum mechanics he
>> would say that life would probably not be possible without the wild
>> uncertainties of quantum phenomena (such as particles physically being
>> at multiple locations at the same time).
>
> I imagine that life based on DNA and chemistry and such wouldn't work
> the same way.
It wouldn't work at all. Let's put it this way: if the Universe was as
complicated as the most inventive physicist can image, it would still
not be complex enough for life to develop. Hmm, there might be a good
sig in that for this physicist.
--
Physics is incompatible with life.
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somebody wrote:
> Easy. Mathematics can represent *anything*, since you get to make up your
> own axioms.
Now try inventing a *consistent* set of axioms. ;-)
--
http://blog.orphi.me.uk/
http://www.zazzle.com/MathematicalOrchid*
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Tim Attwood <tim### [at] comcastnet> wrote:
> I hadn't heard of that one, but it makes perfect sense in a topology
> context.
> In that context "split" really means a 1:2 mapping of spaces.
> Cut the ball in half, then in the two hemispheres the new equator plane
> is a curve from the lip that follows a 0.5*y scaled sphere, from there
> just map the curved planes back to flat to get two spheres.
> Since we're talking about a mapping, not a real object, there's no
> conservation of volume, a sphere is a sphere, no matter what the size.
That doesn't work. The volume of the sphere cannot be modified by a
simple change in topology. You cannot simply change the topology and
then calculate the volume as if you hadn't. You have to calculate the
volume using the *new* topology, not the old one.
Besides, if what you say was true, the same trick would work with a
2-dimensional circle, but it has been proven that it doesn't.
And besides, the original setup happens in regular cartesian coordinates,
without any change in topology.
> The paradox is that the more mathematicians learn,
> the less they are able to explain clearly.
You clearly haven't understood the theorem.
--
- Warp
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Warp wrote:
> Ever heard of the Banach-Tarski paradox?
There's another cool one, I don't remember what it's called, that proves
you can chop up a filled-in circle (I.e., a 2D slice thru a ball,
whatever you call that) and then put it back together again as a perfect
square, with no overlaps and no gaps.
Personally, I can't imagine how that can be possible, but you can
apparently do it with sufficiently many cuts.
--
Darren New / San Diego, CA, USA (PST)
"That's pretty. Where's that?"
"It's the Age of Channelwood."
"We should go there on vacation some time."
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Warp wrote:
> But their simultaneous location in more than one place can be inferred
> by other side-effects.
Nope. When you actually measure it, it's only going thru one slit.
> For example a single electron can pass through two
> slits at the same time, interfering with itself after doing so.
Not as such. Yes, you get interference patterns. No, as far as I know,
there's no evidence to suggest it goes through both slits. Nobody is
quite sure how it works, but there's no measurement that when you say
"where is the thing" it ever gives you more than one answer.
That's the funky part. It *isn't* intuitive.
Indeed, there are all kinds of experiments (like closing one slit too
close to the photon for it to know that the slit was closed, or
something like that) that indicate that you can't treat the situation
like the photon or electron goes through both slits at once.
--
Darren New / San Diego, CA, USA (PST)
"That's pretty. Where's that?"
"It's the Age of Channelwood."
"We should go there on vacation some time."
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somebody wrote:
> Easy. Mathematics can represent *anything*, since you get to make up your
> own axioms.
Except for two things: all the equations are actually pretty simple,
none of them seem to change.
It's not really the case you can represent *anything* with mathematics.
You cannot represent God (pretty much by definition of God), and you
cannot represent a partially-inconsistent system (one that is
inconsistent sometimes but not other times, or in some places but not
other places). Just as a couple of offhand examples.
--
Darren New / San Diego, CA, USA (PST)
"That's pretty. Where's that?"
"It's the Age of Channelwood."
"We should go there on vacation some time."
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"Darren New" <dne### [at] sanrrcom> wrote
> somebody wrote:
> > Easy. Mathematics can represent *anything*, since you get to make up
your
> > own axioms.
> Except for two things: all the equations are actually pretty simple,
> none of them seem to change.
Simplicity is in the eye of the beholder.
> It's not really the case you can represent *anything* with mathematics.
> You cannot represent God (pretty much by definition of God), and you
That's because "god(s)" are not anythings. When one shows that
they/he/she/it is, there's no reason why you won't be able to model
they/he/she/it.
> cannot represent a partially-inconsistent system (one that is
> inconsistent sometimes but not other times,
Then you incorporate time into your equations/model.
> or in some places but not
> other places).
Then you incorporate places into your equations/model.
> Just as a couple of offhand examples.
Isotropy/homegeneity of space/time has nothing to do with whether
representation is possible. Since observation can be thought of as a
representation, anything observable automatically has one representation at
least. Whether that model can be simplified, and can have predictive powers
or not is the question, and if it has redundancy, it can. A reality that can
not be expressed with a simplified model, would, in essence, be random in
*all* aspects (again, redundancy leads to prediction). I cannot imagine how
intelligence of any sort can arise in such a reality.
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