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(Discover)   Twenty things you didn't know about math. I was told there would be no list of things I didn't know about math   (discovermagazine.com) divider line 44
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7417 clicks; posted to Geek » on 05 May 2012 at 1:59 AM (2 years ago)   |  Favorite    |   share:  Share on Twitter share via Email Share on Facebook   more»



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2012-05-05 12:33:42 AM
aka, 20 titles of Big Bang Theory episodes.
 
2012-05-05 12:33:45 AM
Kurt Gödel suffered periods of mental instability and illness. He had an obsessive fear of being poisoned; he would eat only food that his wife, Adele, prepared for him. Late in 1977, Adele was hospitalized for six months and could no longer prepare Gödel's food. In her absence, he refused to eat, eventually starving to death.

Not really about math, but this is Sheldon Cooper level behavior.
 
2012-05-05 12:48:51 AM
If math was real, it wouldn't have so many "problems"

As it is, it's an artificial system created by humans. It's an idealized thing. A Jessica Rabbit.

It's useful, infinitely useful even, but you'll never find a real object that is actually math. A "perfect circle" made of a special iridium alloy and kept as close to absolute zero as possible would still actually be a collection of charges hovering in empty space and moving slowly relative to one another. At best, it would be a handful of nigh static points arranged so that most of the time they could be superimposed on a circle and match up 99 of the time.

But at human temperatures? Everything you see is a chaotic little dance of a trillion trillions of invisible object blasting around every which way but loose. Even if you could model it correctly, you'd need a dozen super computers just predict what would happen if you farted into a hollow sphere at sea level.
 
2012-05-05 02:21:37 AM
Navier-Stokes equations are vexers because they are built from datum, they aren't proper mathematician ideas. Even then they only provide an approximation of results. Navier-Stokes equations don't agree 100% with FEA solutions or practical experience.

/BSME
//Wish I gone BSCS so I could program worth a damn
///But I can build physical objects
 
2012-05-05 02:32:38 AM
21) I got to see my math instructor nude
 
2012-05-05 02:42:46 AM

wild9: 21) I got to see my math instructor nude


Isn't that something you do know about math, though? Or are you claiming to have unknowingly watched math porn?
 
2012-05-05 02:44:49 AM

Araltaln: wild9: 21) I got to see my math instructor nude

Isn't that something you do know about math, though? Or are you claiming to have unknowingly watched math porn?


Could go either way

content.shooshtime.com
 
2012-05-05 02:49:27 AM
That was a list of 19 things I did know about maths, and a bit of trivia about median SAT scores.

(maths is plural, math ith a roman catholic servith)
 
2012-05-05 02:52:56 AM
I knew every one of these.

wildcardjack: Navier-Stokes equations are vexers because they are built from datum, they aren't proper mathematician ideas. Even then they only provide an approximation of results. Navier-Stokes equations don't agree 100% with FEA solutions or practical experience.


Pretty much everything you wrote is wrong. The Navier-Stokes equations have a theoretical basis (and it's actually pretty simple to explain each term if you know the underlying fluid mechanics). They are approximations in the same way that pretty much all physical equations are approximations, i.e., they make some assumptions and don't account for measurement. And FEA is not a set of equations, it's a method of solving equations. It's nonsensical to ask whether NS or FEA is better. In fact, Navier-Stokes can be solved using FEA methods, though I don't know how often this is done. As for the results not agreeing with practical experience, that's utterly ridiculous. NS is used to design aircraft parts and shapes all the time. Results don't exactly match wind tunnel tests, but it's not because the equations are wrong. It's because it's so damn expensive to solve the equations that they have to use simplifications (such as turbulence models) just to finish the solution in a human's lifetime.
 
2012-05-05 03:06:23 AM
The Dantzig one (that, like many on the list, is spread over more than one item) isn't actually true.
 
2012-05-05 03:14:08 AM
And more than one of Hilbert's 23 haven't been solved.
Galois started something that came to be known as group theory, which does prove that quintic equations don't have a general closed-form solution, but Galois himself didn't prove that, nor did he call it group theory.
In the Fermat's last theorem [sic - it ought to be Wiles' theorem now] item, it's rather important that they numbers are integers.

Discover, I thought you were better than this.
 
2012-05-05 03:23:48 AM
" If math is a queen [according to Gauss], she's the White Queen from Alice in Wonderland, who bragged that she believed "as many as six impossible things before breakfast." (No surprise that Lewis Carroll also wrote about plane algebraic geometry.)"

Wait, really? They tossed this out there without explaining that Alice was basically a long metaphor-laden critique of Gauss's ideas about non-Euclidean geometry?
 
2012-05-05 03:31:44 AM

LazarusLong42: " If math is a queen [according to Gauss], she's the White Queen from Alice in Wonderland, who bragged that she believed "as many as six impossible things before breakfast." (No surprise that Lewis Carroll also wrote about plane algebraic geometry.)"

Wait, really? They tossed this out there without explaining that Alice was basically a long metaphor-laden critique of Gauss's ideas about non-Euclidean geometry?


Well, since Charles Dodgson wasn't particularly known for "plane algebraic geometry", it's about par for this article.

Of course, as a queen of the sciences, math is much like the queen of Canada, being German.

(And yes, I realize that the Dantzig story is more or less true, but the version in this article has the usual exaggerations.)
 
2012-05-05 03:56:32 AM
Quaternions, which can describe the
rotation of 3-D objects, were discovered in
1843. They were considered beautiful but
useless until 1985, when computer scientists
applied them to rendering digital animation.
`
/sometimes it takes a while for IRL to catch-up with knowledge.
 
2012-05-05 04:14:29 AM

wildcardjack: Navier-Stokes equations are vexers because they are built from datum, they aren't proper mathematician ideas. Even then they only provide an approximation of results. Navier-Stokes equations don't agree 100% with FEA solutions or practical experience.

/BSME
//Wish I gone BSCS so I could program worth a damn
///But I can build physical objects


What part of the NS equations do you mean "aren't proper mathematician ideas?" Conserved transport laws, including the conservative terms in fluid flow, sit on a foundation that's as solid as special relativity.

The validity of the continuum approximation, and of averaging the velocity parts of the Boltzmann equation away, and of inserting our models for the viscosity tensor... that makes a mess of things. But not knowing the full non-ideal system to solve doesn't mean the idealized system is lacking in mathematical beauty. If anything, it's all the beautiful symmetries that the NS equations respect that make them unable to capture everything we see, because the real world isn't beautiful like that.
 
2012-05-05 04:31:11 AM
nerdapproved.com

Fermaaaaaaaaaaaaaat!
 
2012-05-05 06:07:50 AM
21) who is Gregory Perelman hairdresser
 
2012-05-05 06:34:55 AM

Boatmech: Quaternions, which can describe the
rotation of 3-D objects, were discovered in
1843. They were considered beautiful but
useless until 1985, when computer scientists
applied them to rendering digital animation.
`
/sometimes it takes a while for IRL to catch-up with knowledge.


Except this one is wrong too, quaternions have been used in inertial navigation since Von Braun in the 30s.
 
2012-05-05 06:38:57 AM
21) Counting to 20 is hard, so we're going to pad this out by spreading some facts across two items, and tossing in a few things that are pretty well known and rounding out with some things that have barely anything to do with math.
 
2012-05-05 07:17:49 AM
The one time I watched big bang theory they show someone in front of a blackboard that that "eigervalues" written on it. Geek cred = 0.
 
2012-05-05 07:45:56 AM
Galois didn't rove that no quintic equation could be solved by any means. He proved that there is no "quadratic formula" analog for quintics.
 
2012-05-05 08:45:29 AM

Schubert'sCell: Galois didn't rove that no quintic equation could be solved by any means. He proved that there is no "quadratic formula" analog for quintics.


Relax. TFA was written by some staffer at Discover MAGAZINE. One should not presume magazine writers know what they're talking about, or even understand the question. After all, they majored in English or "communications"...not math.

/oh, and I knew of all but the last two...
 
2012-05-05 09:18:08 AM

assjuice: The one time I watched big bang theory they show someone in front of a blackboard that that "eigervalues" written on it. Geek cred = 0.


I once tried to climb up Mount Eigen and down the other side, but it turns out you can't cross a vector with a scaler.
 
2012-05-05 09:29:35 AM
Huh. Never knew that about the NS equations. I learned them in a university level physics class and the prof just sorta said "here, use these for fiuid dynamics and yeah, they're sorta weird."
 
2012-05-05 09:56:33 AM
I met George Dantzig when I was about six, so I'm getting a kick out of this thread.

The unsolvable problem thing is true. The article even gave a fairly accurate version of it (arrived late, copied two unproved theorems, worked out proofs - as opposed to "answers" - and ended up getting them published).

/my mum had worked with him at IIASA in Vienna, he showed us around Stanford University
 
2012-05-05 10:14:20 AM

Invincible: Boatmech: Quaternions, which can describe the
rotation of 3-D objects, were discovered in
1843. They were considered beautiful but
useless until 1985, when computer scientists
applied them to rendering digital animation.
`
/sometimes it takes a while for IRL to catch-up with knowledge.

Except this one is wrong too, quaternions have been used in inertial navigation since Von Braun in the 30s.


Yes, Werhner and NASA etc. knew the math AND had to computational power to make practical use of it. Until the 80's and desktop computing pretty much no one else could actually do anything practical with them.
 
2012-05-05 10:17:42 AM

gwowen: That was a list of 19 things I did know about maths, and a bit of trivia about median SAT scores.

(maths is plural, math ith a roman catholic servith)


What he said.
 
2012-05-05 10:26:27 AM

Boatmech: Quaternions, which can describe the rotation of 3-D objects, were discovered in 1843. They were considered beautiful but useless until 1985, when computer scientists applied them to rendering digital animation.


Actually, quaternions were competitors to 3D vectors (and preceded the modern understanding of vector algebra), but vectors eventually won out after 1900.
 
2012-05-05 10:40:07 AM

Schubert'sCell: Galois didn't rove that no quintic equation could be solved by any means. He proved that there is no "quadratic formula" analog for quintics.


That and Galois didn't prove it. It was first proven by Abel in 1823 or 1824, after Galois died. (Ruffini had a really long, slightly erroneous, "proof" in 1799, so his name is often added to Abel's - one hears of "Abel's impossibility theorem" or the "Abel-Ruffini theorem") The Galois theory proof is more elegant (and much shorter) than Abel's original and is more-or-less the one you usually see in graduate algebra courses, but it came about 60 years later.
 
2012-05-05 10:45:27 AM

Ambitwistor: Boatmech: Quaternions, which can describe the rotation of 3-D objects, were discovered in 1843. They were considered beautiful but useless until 1985, when computer scientists applied them to rendering digital animation.

Actually, quaternions were competitors to 3D vectors (and preceded the modern understanding of vector algebra), but vectors eventually won out after 1900.


No way in hell am I going to get into vectors on a Saturday morning.
 
2012-05-05 11:44:50 AM

wildcardjack: Navier-Stokes equations are vexers because they are built from datum, they aren't proper mathematician ideas. Even then they only provide an approximation of results. Navier-Stokes equations don't agree 100% with FEA solutions or practical experience.


maybe you should have taken a physics course too. it wouldn't have guaranteed that you wouldn't write something quite this idiotic, but it might have reduced the probability of that happening. of course, you may not grasp the notion of probability either. hope to not drive over any bridges you build....
 
2012-05-05 12:04:16 PM

proteus_b: wildcardjack: Navier-Stokes equations are vexers because they are built from datum, they aren't proper mathematician ideas. Even then they only provide an approximation of results. Navier-Stokes equations don't agree 100% with FEA solutions or practical experience.

maybe you should have taken a physics course too. it wouldn't have guaranteed that you wouldn't write something quite this idiotic, but it might have reduced the probability of that happening. of course, you may not grasp the notion of probability either. hope to not drive over any bridges you build....


95% is all anyone needs.
 
2012-05-05 12:49:35 PM
Pretty neat.
 
2012-05-05 01:55:43 PM
Graduate student George Dantzig...

i769.photobucket.com

It's Danzig motherfarker...
 
2012-05-05 03:20:49 PM
Pretty much everything you have written about the Navier-Stokes/conservation of momentum equations is wrong! It is derived from first principles with the background of Newtonian mechanics. it's limitations are exposed with non-Newtonian fluids (for which there are correction terms - modified NS equations) and in situations where the continuum assumption is invalid.

The complete NS equations are solved for in DNS (direct numerical simulation), but since this is very computationally expensive for practical problems, further simplifying assumptions are used, particularly to model turbulence with finite volume, finite difference or finite element techniques. An intermediate approach to turbulence modeling (between capturing turbulent structures at all scales as in DNS or fine spectral methods and much coarser techniques like the k-epsilon/k-omega/Reynolds Stress models) is to use large eddy simulation techniques by filtering out the smaller scales.

For most engineering/practical flows encountered, the NS equations have proved almost as bulletproof as the Special Theory of Relativity.

/Chemical engineer.

wildcardjack: Navier-Stokes equations are vexers because they are built from datum, they aren't proper mathematician ideas. Even then they only provide an approximation of results. Navier-Stokes equations don't agree 100% with FEA solutions or practical experience.

/BSME
//Wish I gone BSCS so I could program worth a damn
///But I can build physical objects

 
2012-05-05 03:31:07 PM
What makes the NS equations such a headache when you attempt to use any analytical techniques on it is the highly non-linear nature of that system of equations at high Reynolds numbers, particularly the inertial (convective acceleration) term.
 
2012-05-05 05:10:16 PM
The first being that it has an 's' at the end of it.

I don't know - we give you the English language and the first thing you people do is break it!
 
2012-05-05 07:04:45 PM
Ok will someone please explain the (UK-only?) fascination with spelling it as "maths" rather than "math". Since we are going to go through the trouble of shortening the word "mathematics" and finding an abbreviation, why in the hell would anyone want to lengthen up the abbreviation by adding the s back on to it and making sound awkward and stupid at the end. Might as well have never bothered shortening "mathematics" in the first place.
 
2012-05-05 07:11:56 PM
FTFA: 6 Some math problems are designed to be confounding, like British philosopher Bertrand Russell's paradoxical "set of all sets that are not members of themselves." If Russell's set is not a member of itself, then by definition it is a member of itself.

For some reason, my eyelids turned inside-out when I finished reading this one.
 
2012-05-05 09:07:40 PM

Fark Me To Tears: FTFA: 6 Some math problems are designed to be confounding, like British philosopher Bertrand Russell's paradoxical "set of all sets that are not members of themselves." If Russell's set is not a member of itself, then by definition it is a member of itself.

For some reason, my eyelids turned inside-out when I finished reading this one.


It's one of the best, because it's so simple to state yet so devastating in effect. What Russell demonstrated with this paradox is that our intuitive sense of what constitutes a "set" is hopelessly broken. And that's rather unfortunate because he and his fellow mathematicians had been in the middle of trying to put arithmetic itself on a formal (rather than intuitive) foundation using set theory. So Russell broke arithmetic.

Fortunately, a fix was found -- essentially, a rigorous definition of what can constitute a set -- that was subsequently shown to be related to the wonderfully-named Von Neumann Universe, which by coincidence is also either the title of my science fiction novel-in-progress or the name of my next band.
 
2012-05-06 03:30:18 AM

assjuice: The one time I watched big bang theory they show someone in front of a blackboard that that "eigervalues" written on it. Geek cred = 0.


Yeah, but they have a photo of the Whirlpool Galaxy taped to their 'fridge, so it all evens out.
 
2012-05-06 05:03:25 AM
erik-k, beelzebubba76, proteus_b

Nice to see I wasn't the only one correcting the slander that was uttered against the Navier-Stokes equations.
 
2012-05-07 03:42:35 PM

wildcardjack: Navier-Stokes equations are vexers because they are built from datum, they aren't proper mathematician ideas. Even then they only provide an approximation of results. Navier-Stokes equations don't agree 100% with FEA solutions or practical experience.

/BSME
//Wish I gone BSCS so I could program worth a damn
///But I can build physical objects


I don't have anything to add about Navier-Stokes, other than that it is nothing more than conservation of momentum expressed in the Eulerian reference frame, with stress being a linear function of strain rate.

I will, however, say that if you think FEA solutions are gospel, then you have no business using finite elements. As far as numeric techniques go, they've got lots of advantages, but no numeric technique is perfect. Like any other approximation method, finite element analysis is only as good as what you put into it (equations + data).

/been doing research in continuum mechanics and numerical techniques for the last seven years
//ohpleasedeargodcanigraduatealready??
 
2012-05-07 10:05:36 PM

DrPainMD: assjuice: The one time I watched big bang theory they show someone in front of a blackboard that that "eigervalues" written on it. Geek cred = 0.

Yeah, but they have a photo of the Whirlpool Galaxy taped to their 'fridge, so it all evens out.


The were getting ready to eigen the Eiger.

/nerd pun
 
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