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(Scientific American)   The ultimate ultimate theory of physics. It's not BS, it's just that you're not smart enough to understand it   (blogs.scientificamerican.com) divider line 43
    More: Unlikely, string theory, strong forces, medical practices, supersymmetry, classical physics, square roots, Emperor Palpatine, real numbers  
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4683 clicks; posted to Geek » on 04 Apr 2012 at 10:02 AM (3 years ago)   |  Favorite    |   share:  Share on Twitter share via Email Share on Facebook   more»



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2012-04-04 10:08:04 AM  
They call me Mister Dunning Kruger at the university!

/Talking physics to smart chicks will get you laid, son.
 
2012-04-04 10:08:41 AM  
"The universe is not only stranger than we imagine, it is stranger than we can imagine."
 
2012-04-04 10:09:07 AM  
24.media.tumblr.com
 
2012-04-04 10:09:42 AM  
I'm more of an advocate of the Supertheory of Supereverything (new window)
 
2012-04-04 10:10:08 AM  
FTA:
It actually goes back to the 1990s and the ferment within string theory back then, although it languished until fairly recently. The unnerving thing about the theory is that physicists think it exists even though they've never written it down and are not even sure they can. In this, the Emperor resembles that other creation of the mid-1990s: M-theory, a theory whose existence seems to be implicit in string theory, even though physicists hem and haw when you ask what exactly it is. Both M-theory and the Emperor theory are physics versions of an inchoate feeling you struggle to verbalize.

Oblig xkcd reference.
 
2012-04-04 10:11:43 AM  
...a quantum dimension, whose coordinates are not ordinary real numbers but a whole new class of number that can be thought of as the square roots of zero. (Yes, that's allowed. This is quantum physics, after all.)

Since when was the square root of zero not allowed? I'm not surprised this theory is incomprehensible to someone lacking such a basic grasp of simple math.
 
2012-04-04 10:25:47 AM  
I'm pretty sure the "square roots of zero" they're referring to are just nilpotent elements of some ring:

Nilpotent

The thing is these "numbers" are not equal to zero yet some power of them is.

As a math student working near mathematical physics, I've come to the conclusion that the vast majority of theoretical physicists at this level (not named Witten) don't actually understand mathematics well enough to make any sense to mathematicians. To the physicists the theories seem mysterious since there is so much left to figure out but they have potential to work, and to the mathematicians they seem mysterious since they don't make any rigorous sense and/or use a completely different (and less rigorous) language. It drives me crazy trying to read their research papers, so if I sound bitter it's because I am.
 
2012-04-04 10:27:55 AM  
Apparently, from TFA, neither are the physicists.
 
2012-04-04 10:28:17 AM  
If they can't explain it then I don't even have a chance to not understand it.
 
2012-04-04 10:29:00 AM  
ENTER: DEEP THOUGHT

/wouldn't it be hilarious if the number 42 factored into this Emperor theory of supersymmetry...
 
2012-04-04 10:31:15 AM  

Baryogenesis: If they can't explain it then I don't even have a chance to not understand it.


Basically, one of the biggest problems with string theory at the moment is creating a theory that has space and time being results of the theory, rather than the setting for the theory. Basically, they're trying to come up with rules that create themselves. There's a few candidates floating around ATM to try to address it, but it's incredibly insane.
 
2012-04-04 10:31:33 AM  

TheUltimateFunctor: I'm pretty sure the "square roots of zero" they're referring to are just nilpotent elements of some ring:

Nilpotent

The thing is these "numbers" are not equal to zero yet some power of them is.

As a math student working near mathematical physics, I've come to the conclusion that the vast majority of theoretical physicists at this level (not named Witten) don't actually understand mathematics well enough to make any sense to mathematicians. To the physicists the theories seem mysterious since there is so much left to figure out but they have potential to work, and to the mathematicians they seem mysterious since they don't make any rigorous sense and/or use a completely different (and less rigorous) language. It drives me crazy trying to read their research papers, so if I sound bitter it's because I am.


Ha- been there, done that.

I got into computer science. It's been a blast.
 
2012-04-04 10:33:57 AM  
Physicists should simply NOT try to practice philosophy. For starters, they tend to dismiss the logical underpinnings - the Laws of Rationality - claiming that the universe and thought itself tolerates contradictions - while relying on those very laws for the math parts (afterall, an equation can't describe a world which isn't what it is describing, right? They demand rational consistency for some parts, ignore it entirely for other parts of their worldviews).

These guys plethora of theories are just ridiculous philosophical interpretations of the data, they sound no more plausible or mature than Berkeley's exciting "discovery" that the world is immaterial, that extension etc is illusory. It's nonsensical accounts of "how the world really is". Screw that. We just need a good mathematical model that is consistent with what we see. We don't need to waste time and money on fancy ideas about the actual nature of the universe. This shiat, it's dime store philosophy at best. Professional philosophers can deal with this kind of thing, professional physicists should focus on something else, something of serious pragmatic consequence, theories that can eventually be proven true or false and applied accordingly in the real world.
 
2012-04-04 10:39:27 AM  

sprawl15: Baryogenesis: If they can't explain it then I don't even have a chance to not understand it.

Basically, one of the biggest problems with string theory at the moment is creating a theory that has space and time being results of the theory, rather than the setting for the theory. Basically, they're trying to come up with rules that create themselves. There's a few candidates floating around ATM to try to address it, but it's incredibly insane.


Why is that a problem? I'd say that's a pretty big question that deserves an answer. Are space and time fundamental properties or do they come about as a result of some other more basic property of the universe?

Doesn't it seem like physics has been moving that direction anyway? Our human intuition about absolute space and absolute time being the backdrop for physical events has been overthrown by Einstein and quantum physics. We can't separate space and time from the events that take place "in" them so maybe they're just high level manifestations of a more basic property.
 
2012-04-04 10:40:54 AM  

Fubini: TheUltimateFunctor: I'm pretty sure the "square roots of zero" they're referring to are just nilpotent elements of some ring:

Nilpotent

The thing is these "numbers" are not equal to zero yet some power of them is.

As a math student working near mathematical physics, I've come to the conclusion that the vast majority of theoretical physicists at this level (not named Witten) don't actually understand mathematics well enough to make any sense to mathematicians. To the physicists the theories seem mysterious since there is so much left to figure out but they have potential to work, and to the mathematicians they seem mysterious since they don't make any rigorous sense and/or use a completely different (and less rigorous) language. It drives me crazy trying to read their research papers, so if I sound bitter it's because I am.

Ha- been there, done that.

I got into computer science. It's been a blast.


Haha awesome. Nice name btw! :)
 
2012-04-04 10:44:00 AM  

Fubini: TheUltimateFunctor: I'm pretty sure the "square roots of zero" they're referring to are just nilpotent elements of some ring:

Nilpotent

The thing is these "numbers" are not equal to zero yet some power of them is.

As a math student working near mathematical physics, I've come to the conclusion that the vast majority of theoretical physicists at this level (not named Witten) don't actually understand mathematics well enough to make any sense to mathematicians. To the physicists the theories seem mysterious since there is so much left to figure out but they have potential to work, and to the mathematicians they seem mysterious since they don't make any rigorous sense and/or use a completely different (and less rigorous) language. It drives me crazy trying to read their research papers, so if I sound bitter it's because I am.

Ha- been there, done that.

I got into computer science. It's been a blast.


As a Computer Science student, I've taken a few classes where my entire take-away was "I know what I'm NOT doing when I get out of school." The theory courses were two of those courses. My brain just doesn't work when you start talking about infinity. (It didn't help that the teacher was one of those utterly brilliant people who could not explain his concepts to us mere mortals. Got a 57%, which got curved to a B+).

/Also, the 2nd half of Databases. 1st half was really useful SQL/use of/some underlying math theory. 2nd half was "How to write the underlying database, and make it minimize disk use on queries", and it was this giant mess of buffer pools, and indexes, and gah. Only class where I got below a B.
 
2012-04-04 10:50:07 AM  

TheUltimateFunctor: As a math student working near mathematical physics, I've come to the conclusion that the vast majority of theoretical physicists at this level (not named Witten) don't actually understand mathematics well enough to make any sense to mathematicians. To the physicists the theories seem mysterious since there is so much left to figure out but they have potential to work, and to the mathematicians they seem mysterious since they don't make any rigorous sense and/or use a completely different (and less rigorous) language. It drives me crazy trying to read their research papers, so if I sound bitter it's because I am.


XKCD is the new Simpsons Did It
 
2012-04-04 10:55:45 AM  

meyerkev: Fubini: TheUltimateFunctor: I'm pretty sure the "square roots of zero" they're referring to are just nilpotent elements of some ring:

Nilpotent

The thing is these "numbers" are not equal to zero yet some power of them is.

As a math student working near mathematical physics, I've come to the conclusion that the vast majority of theoretical physicists at this level (not named Witten) don't actually understand mathematics well enough to make any sense to mathematicians. To the physicists the theories seem mysterious since there is so much left to figure out but they have potential to work, and to the mathematicians they seem mysterious since they don't make any rigorous sense and/or use a completely different (and less rigorous) language. It drives me crazy trying to read their research papers, so if I sound bitter it's because I am.

Ha- been there, done that.

I got into computer science. It's been a blast.

As a Computer Science student, I've taken a few classes where my entire take-away was "I know what I'm NOT doing when I get out of school." The theory courses were two of those courses. My brain just doesn't work when you start talking about infinity. (It didn't help that the teacher was one of those utterly brilliant people who could not explain his concepts to us mere mortals. Got a 57%, which got curved to a B+).

/Also, the 2nd half of Databases. 1st half was really useful SQL/use of/some underlying math theory. 2nd half was "How to write the underlying database, and make it minimize disk use on queries", and it was this giant mess of buffer pools, and indexes, and gah. Only class where I got below a B.


So...you're saying "I'm a bad student b-b-but THIS STUFF SUCKS so therefore IT'S OK THAT I'M A BAD STUDENT" ?
 
2012-04-04 10:58:56 AM  
A 3 dimensional projection of a 5 dimensional reality?

Wow, my brane hurts.
 
2012-04-04 11:13:07 AM  
The unnerving thing about the theory is that physicists think it exists even though they've never written it down and are not even sure they can.

Right, so we're back to "the universe runs on magic."

Awesome.

/No, seriously, that's kind of awesome.
 
2012-04-04 11:23:32 AM  
Sigh.....Another case of "I understand the words but the sentences confuse me".

Put Steven Hawking on the case. He's probably bored with whatever theoretical physics hobby he's working on at the moment anyway.

And we're certain they aren't just making this stuff up, right?
 
2012-04-04 11:26:23 AM  

Baryogenesis: Why is that a problem? I'd say that's a pretty big question that deserves an answer. Are space and time fundamental properties or do they come about as a result of some other more basic property of the universe?


They've pretty much decided that they are not fundamental properties, the problem lies in defining a system that can generate space and time as interactions between entities. It's about 20 years of college and a half pound of Brain Serum beyond me how they're even going to attempt to approach the problems.
 
2012-04-04 11:36:04 AM  

torusXL: So...you're saying "I'm a bad student b-b-but THIS STUFF SUCKS so therefore IT'S OK THAT I'M A BAD STUDENT" ?


Put it split evenly between

1) Yes, except that it's not OK that I'm a bad student, but I can't pull all-nighters anymore. With databases, I was taking 4 CS classes at once, which is pretty much the definition of "reach exceeds his grasp", and that class got screwed, because I cared less about that class, and just didn't have time between the other 3 classes (and ever since that semester where I averaged 3 all-nighters a week, and once was up for 5 days straight, my body just can't do it).

2) One of the nice things about CS is that there's about 33 different things you can do that are "Computer Science". So I know that I don't want to write a DBMS application that runs a database (not the same as using SQL or similar to call into a database BTW), and that I suck at the higher-level math because my brain doesn't work that way. So what? There's still 31 other things that I can do (of which I'm probably "good, if not great" at about 10 - 15, which means that I'm 9 - 14 potential careers ahead of my parents).

3) See the bit about where my 57% got curved to a B+. That meant that (somehow?) I was in the top 15-20% of the class. So yeah, I sucked, but so did everyone else.

/And in continuing #3, I did actually ask the GSI why everyone was failing. He basically said that with the theory stuff, 1 exceptional guy gets more done than 10,000 mediocre guys, so they make the class so that 2 people actually get it, and the other 198 people in the class just get a massive curve.
//When the class average on the true/false section is less than 50%, someone(s) somewhere screwed up big.
 
2012-04-04 11:56:55 AM  

Zombalupagus: A 3 dimensional projection of a 5 dimensional reality?

Wow, my brane hurts.


I heard Sagan use the analogy of what it would be like to be a two-dimensional being trying to describe the third dimension. That's what this reminds me of.

Photons, for example, exhibiatcharacteristics of both waves and particles... This seems like an interesting tack for an explanation.
 
2012-04-04 12:04:45 PM  
The universe is a series of quantum tubes.
 
2012-04-04 12:06:19 PM  
Can someone dumb any of this down enough so that a business BA can understand it? If not, I will go back to my sandbox...
 
2012-04-04 12:49:39 PM  
meyerkev//When the class average on the true/false section is less than 50%, someone(s) somewhere screwed up big.

Hey, I gotta CSB. I was TA'ing a class on "critical thinking" where the class average was about 33% for the first couple of short-answer tests (where the textbook carefully bolded the right answers for student convenience), and ~40% for the multiple-choice questions. We managed to pull the class up by writing blatantly easy True/False tests and then graded on a curve. I think the problem was that the students were expecting a creative writing class or something.

Mind you, in another class (introduction to logic) I had to give this guy a 7/10 for a conceptual analysis question because he decided to stop at 7 out of the ten steps required to tell the prof and I his considered opinion on conceptual analysis and where we could shove it. Which was unfortunate because it meant that he got less than 100% on the entire thing and I wasn't allowed to write "I agree! :)" on his test.

I wish I'd taken math...
 
2012-04-04 12:55:41 PM  
this is the sort of stuff where if you understand the question you pass the test. No time limit, yes you can research.
 
2012-04-04 01:19:40 PM  

xkillyourfacex: Physicists should simply NOT try to practice philosophy. For starters, they tend to dismiss the logical underpinnings - the Laws of Rationality - claiming that the universe and thought itself tolerates contradictions - while relying on those very laws for the math parts (afterall, an equation can't describe a world which isn't what it is describing, right? They demand rational consistency for some parts, ignore it entirely for other parts of their worldviews).

These guys plethora of theories are just ridiculous philosophical interpretations of the data, they sound no more plausible or mature than Berkeley's exciting "discovery" that the world is immaterial, that extension etc is illusory. It's nonsensical accounts of "how the world really is". Screw that. We just need a good mathematical model that is consistent with what we see. We don't need to waste time and money on fancy ideas about the actual nature of the universe. This shiat, it's dime store philosophy at best. Professional philosophers can deal with this kind of thing, professional physicists should focus on something else, something of serious pragmatic consequence, theories that can eventually be proven true or false and applied accordingly in the real world.


Know how I know your concept of physics includes nothing more technical than Scientific American?

The people working on the edges of field theory aren't philosophizing; they're trying to develop the mathematical framework necessary to express new practical theories. They know some properties that a successful theory must have, and some that it probably should have, but they're still working out how to build a foundation that could possibly support a functional theory.

It's the hack science journalists (and the odd attention-whoring physicist <cough>Greene</cough>) who are trying to claim that half-baked speculation and larval hypotheses are telling us things about "how the world really is." Where there is actual progress, some philosophy occurs as an accidental byproduct (much to the dismay of the professional masturbphilosophers), but the great majority of theorists are humble enough to admit that no cause yet exists to claim new, irrefutable insights into the fundamental workings of nature.
 
2012-04-04 01:40:06 PM  

Crunch61: Zombalupagus: A 3 dimensional projection of a 5 dimensional reality?

Wow, my brane hurts.

I heard Sagan use the analogy of what it would be like to be a two-dimensional being trying to describe the third dimension. That's what this reminds me of.

Photons, for example, exhibiatcharacteristics of both waves and particles... This seems like an interesting tack for an explanation.


My basic theory is that assuming 1) our reality is just a spot on a probability curve and 2) there are 10 dimensions (string theory) but we can only see 3 and the others are just wrapped up on themselves then: from another reality we would look like one of those wrapped up dimensions.

There's more to it but it make my head a splode.

/should have posted "Get a brane, morans!" instead
 
2012-04-04 03:12:57 PM  
I always thought probably, a rotating object would explain things well. Particularly if you chained them together.

I've been trying to come up with a name for these objects. 'Gyros' is the only thing popping into my head.
 
2012-04-04 05:15:22 PM  

TheUltimateFunctor: As a math student working near mathematical physics, I've come to the conclusion that the vast majority of theoretical physicists at this level (not named Witten) don't actually understand mathematics well enough to make any sense to mathematicians. To the physicists the theories seem mysterious since there is so much left to figure out but they have potential to work, and to the mathematicians they seem mysterious since they don't make any rigorous sense and/or use a completely different (and less rigorous) language. It drives me crazy trying to read their research papers, so if I sound bitter it's because I am.


Hmm, what has pure math ever predicted about reality? That's right, nothing.

What has physics ever predicted about reality? That's right, everything that we actually (even partially) understand.


But it's the physicists who don't know what they are doing ...
 
2012-04-04 06:28:35 PM  

Professor Science: The people working on the edges of field theory aren't philosophizing; they're trying to develop the mathematical framework necessary to express new practical theories. They know some properties that a successful theory must have, and some that it probably should have, but they're still working out how to build a foundation that could possibly support a functional theory.


If I could +1 this paragraph, I would.

sprawl15: They've pretty much decided that they are not fundamental properties, the problem lies in defining a system that can generate space and time as interactions between entities. It's about 20 years of college and a half pound of Brain Serum beyond me how they're even going to attempt to approach the problems


It boggles my mind. How you you generate space and time without using space or time? How can you represent that as a manifold?
 
2012-04-04 06:58:22 PM  

DarwiOdrade: ...a quantum dimension, whose coordinates are not ordinary real numbers but a whole new class of number that can be thought of as the square roots of zero. (Yes, that's allowed. This is quantum physics, after all.)

Since when was the square root of zero not allowed? I'm not surprised this theory is incomprehensible to someone lacking such a basic grasp of simple math.


From the sentence context it may just be that the author screwed up with "square roots of zero" when what people actually said was "square roots of -1"

The quaterions and octonians have three such values - i, j, k.

And as this google search shows, people do use such numbers in Yang-Mills theory.
 
2012-04-04 07:11:38 PM  

idsfa: Hmm, what has pure math ever predicted about reality? That's right, nothing.

What has physics ever predicted about reality? That's right, everything that we actually (even partially) understand.


But it's the physicists who don't know what they are doing ...


If you mean when has mathematics, in complete isolation, come up with an description of a physical observable, that is setting the bar quite high. It requires some physical context. If you mean: when have previously undiscovered physical realities appeared out of mathematics of a physical theory? The the examples are too numerous to list. Dirac's discovery of antimatter being a familiar example.
 
2012-04-04 08:19:01 PM  

Crunch61: Photons, for example, exhibiatcharacteristics of both waves and particles... This seems like an interesting tack for an explanation.


LOL...filterpawned! ;^)

roc6783: Can someone dumb any of this down enough so that a business BA can understand it? If not, I will go back to my sandbox...


Would you like to borrow my grandson's Tonka truck?
 
2012-04-04 08:20:07 PM  

HairBolus: DarwiOdrade: ...a quantum dimension, whose coordinates are not ordinary real numbers but a whole new class of number that can be thought of as the square roots of zero. (Yes, that's allowed. This is quantum physics, after all.)

Since when was the square root of zero not allowed? I'm not surprised this theory is incomprehensible to someone lacking such a basic grasp of simple math.

From the sentence context it may just be that the author screwed up with "square roots of zero" when what people actually said was "square roots of -1"

The quaterions and octonians have three such values - i, j, k.

And as this google search shows, people do use such numbers in Yang-Mills theory.


I'm pretty sure that Functor was right and they are talking about nilpotent elements. I feel a bit silly actually - I had no idea what the article writer was on about even though I am a fan of algebra. I guess I should spend more time learning the standard analogies/explanations to confuse people with instead of just being confusingly confusing by trying to explain things on the spot.

Are they really thinking that the coordinates of this quantum dimension don't even form an integral domain? That's pretty cool to think about.
 
2012-04-04 08:44:55 PM  
I am not science smrt. Could someone who is science smrt translate that article into MBA-level language?

Thanks.
 
2012-04-04 10:50:41 PM  

Graeme Garden: idsfa: Hmm, what has pure math ever predicted about reality? That's right, nothing.

What has physics ever predicted about reality? That's right, everything that we actually (even partially) understand.


But it's the physicists who don't know what they are doing ...

If you mean when has mathematics, in complete isolation, come up with an description of a physical observable, that is setting the bar quite high. It requires some physical context. If you mean: when have previously undiscovered physical realities appeared out of mathematics of a physical theory? The the examples are too numerous to list. Dirac's discovery of antimatter being a familiar example.


Can I add statistics to the realm of "pure math"? We've found the normal distribution (derived using pure math) again and again in nature in situations where the theory predicted it (i.e. situations involving i.i.d. or something reasonably close to it).

/You can't do physics without statistics. Without statistics, you're just taking the measurement that is closest to your theory and hoping it means your theory reflects reality.
 
2012-04-04 11:12:30 PM  
The key phrase...
"The theory does have the disadvantage that it does not and cannot describe the real world"

OK, let me say this.
I specialize in this topic...while not a pro, I still work on it on the side. (there's no money in it for FT)
But I've had pros hear/see my stuff...and it's moving forward, not quite finished yet.

I hate that Physicists punt in this way.

If you are going to attempt to describe the "ultimate" theory,
then you HAVE TO include, HERE, NOW...all points inbetween and all scales.

You cannot say, Oh they shrank away in the past. Hooonk, irrelevant.
You cannot say, Oh they are moving away faster than the speed of light. Buuzzz, irrelevant.
You cannot say, Oh it works at this scale, but not in real life which we live in. Bang, still irrelevant.

Why do the "better" scientists waste their time on it?
It might be nice, as a math game...or a sci-fi story with some basis in the truth,
but unless you are actually describing true reality...don't come up with a silly reasoning.
It's science, it needs to be testable...for what we live in.

I don't object to the multiple dimensions.
Perhaps you haven't figured out what they are yet? That's legit.

If so, then propose one. That's cool. Prove it.
And it doesn't have to be friggin' spatial. (hint)
Time: hey, not space, it's a dimension too...Duh.

Don't just come up with ideas just for the sake of proving a point.
Don't just play with the numbers, use them as a tool.
But PLEASE have it be something that exists for US.

/idiots
 
2012-04-05 12:22:59 AM  

idsfa: TheUltimateFunctor: As a math student working near mathematical physics, I've come to the conclusion that the vast majority of theoretical physicists at this level (not named Witten) don't actually understand mathematics well enough to make any sense to mathematicians. To the physicists the theories seem mysterious since there is so much left to figure out but they have potential to work, and to the mathematicians they seem mysterious since they don't make any rigorous sense and/or use a completely different (and less rigorous) language. It drives me crazy trying to read their research papers, so if I sound bitter it's because I am.

Hmm, what has pure math ever predicted about reality? That's right, nothing.

What has physics ever predicted about reality? That's right, everything that we actually (even partially) understand.


But it's the physicists who don't know what they are doing ...


1. The physicists I'm talking about are string theorists, and yes, even they will tell you that they don't know what they're doing. Their theories are largely impossible to test empirically and thus their entire existence is in the language of pure mathematics. The problem is they went to school for physics and to properly understand the mathematical objects their working with (beyond their definitions, but even just learning those could be out of reach, see Stacks) requires years of study in pure math. The vast majority need to be working closely with mathematicians just in order to properly formulate any ideas they have.

2. All of physics is just applying pure math? Without Hilbert spaces and functional analysis we have no quantum mechanics. Without differential geometry and topology we have no general relativity, electrodynamics, and gauge theories. Without symplectic geometry we have no classical mechanics. Without calculus we have nothing. Without algebraic geometry, higher category theory, homological algebra, everything else mentioned before and more, there is no string theory.
 
2012-04-05 12:51:37 AM  

Nanny Statesman: HairBolus: DarwiOdrade: ...a quantum dimension, whose coordinates are not ordinary real numbers but a whole new class of number that can be thought of as the square roots of zero. (Yes, that's allowed. This is quantum physics, after all.)

Since when was the square root of zero not allowed? I'm not surprised this theory is incomprehensible to someone lacking such a basic grasp of simple math.

From the sentence context it may just be that the author screwed up with "square roots of zero" when what people actually said was "square roots of -1"

The quaterions and octonians have three such values - i, j, k.

And as this google search shows, people do use such numbers in Yang-Mills theory.

I'm pretty sure that Functor was right and they are talking about nilpotent elements. I feel a bit silly actually - I had no idea what the article writer was on about even though I am a fan of algebra. I guess I should spend more time learning the standard analogies/explanations to confuse people with instead of just being confusingly confusing by trying to explain things on the spot.

Are they really thinking that the coordinates of this quantum dimension don't even form an integral domain? That's pretty cool to think about.


The idea of having nonzero functions f on a space in which some finite power f^n = 0 goes way back to my main man Grothendieck. His introduction of Schemes was revolutionary. The idea is totally awesome - from any commutative ring you essentially get some geometric object. You can study its geometry from the properties of you original ring. Then you can glue all of these together (like making a Manifold but purely algebraically). You can even construct algebraic analogues of calculus, quotients, intersections (this part is VERY HARD) among other things. When you specialize to the case of say schemes defined over complex numbers, you get essentially the same geometric data that you would if you considered this object geometrically in the usual way. (ex: the scheme corresponding to x = 0 in C^2 is still just a plane topologically (C = R^2))

One of the good arguments for including nilpotents is to remember multiplicities of intersections. You could consider the ring R[x,y]/(x) (which is just R[y]) as polynomial functions in x and y modulo ones vanishing on x=0 (the y-axis). So we can consider this as the polynomial functions on the y-axis (since we modded out by the ones that restrict to zero). So the geometric "scheme" we get is the vertical line. But what if our ring was R[x,y]/(x^2)? Now we have a function x that evaluates to zero along the whole y-axis but is not the zero function. Its square is, however. We want to be able to distinguish these two schemes, so we retain the knowledge of these nilpotent functions. This is required to make rigorous the fact that say y = x^2 and y = 0 intersect at the origin to an order of two. The scheme you will get is R[x,y] / (y, y-x^2) = R[x]/(x^2), again retaining some nonzero function. (This is a 2 dim vector space, and it is no coincidence that 2 also is the multiplicity of the intersection!)
 
2012-04-05 07:15:03 AM  

xkillyourfacex: Physicists should simply NOT try to practice philosophy. For starters, they tend to dismiss the logical underpinnings - the Laws of Rationality - claiming that the universe and thought itself tolerates contradictions - while relying on those very laws for the math parts (afterall, an equation can't describe a world which isn't what it is describing, right? They demand rational consistency for some parts, ignore it entirely for other parts of their worldviews).

These guys plethora of theories are just ridiculous philosophical interpretations of the data, they sound no more plausible or mature than Berkeley's exciting "discovery" that the world is immaterial, that extension etc is illusory. It's nonsensical accounts of "how the world really is". Screw that. We just need a good mathematical model that is consistent with what we see. We don't need to waste time and money on fancy ideas about the actual nature of the universe. This shiat, it's dime store philosophy at best. Professional philosophers can deal with this kind of thing, professional physicists should focus on something else, something of serious pragmatic consequence, theories that can eventually be proven true or false and applied accordingly in the real world.


So a physicist, a mathematician, and a bitter farker walk into a fast-food place. And the Professional Philosopher (????) takes their orders.
 
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