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The Accidental Astrophysicists

kdawson posted more than 6 years ago | from the all-math-to-me dept.

Math 97

An anonymous reader recommends a ScienceNews story that begins: "Dmitry Khavinson and Genevra Neumann didn't know anything about astrophysics. They were just doing mathematics, like they always do, following their curiosity. But five days after they posted one of their results on a preprint server, they got an email that said 'Congratulations! You've proven Sun Hong Rhie's astrophysics conjecture on gravitational lensing!'... Turns out that when gravity causes light rays to bend, it can make one star look like many. But until Khavinson and Nuemann's work, astrophysicists weren't sure just how many. Their proof in mathematics settled the question."

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Suprise! (5, Funny)

cobaltnova (1188515) | more than 6 years ago | (#23818107)

Mathematics results are physically relevant. News at 11.

Re:Suprise! (3, Insightful)

CorSci81 (1007499) | more than 6 years ago | (#23818173)

Sometimes it takes decades to find the relevant uses for the math though. For example the beta function [wikipedia.org] and string theory [wikipedia.org]

Re:Suprise! (4, Insightful)

Secret Rabbit (914973) | more than 6 years ago | (#23818383)

You're assuming that String theory is useful. It isn't even a theory. You see, to be a theory it has to do what it says it does to at least a large degree. Point of fact, there is exactly ZERO experimental evidence that it is physically correct to /any/ degree. String "Theory" is a bloody joke that has plagued Physics for decades and is now (far to late IMO) coming under significant fire for its lack of experimental evidence. Thankfully, that fire also comes in the form of much less funding so that other *far* more promising fields can get some research done.

Re:Suprise! (4, Interesting)

NoobixCube (1133473) | more than 6 years ago | (#23818573)

I agree that String Theory is hardly a theory. I call it String Musing, since all it is is thought experiments and possibilities. However, if we ignore it entirely, then there will never be any experimental evidence of it. Right now it's nothing but a mathematical curiosity, but there is no way of telling, from today's perspective based on today's knowledge, what may come of this mathematical curiosity in the future. I'm not a supporter of String Theory (not that my support would matter anyway, since my knowledge of physics is everything from highschool plus whatever I'm curious about at the time), but more research is required before we can dismiss it outright.

Re:Suprise! (1)

Secret Rabbit (914973) | more than 6 years ago | (#23829779)

More than the, what about, 40 years its already had?

Re:Suprise! (1)

iamacat (583406) | more than 6 years ago | (#23835643)

but more research is required before we can dismiss it outright.
More research than needed into Christianity, Islam or Buddhism? Why, because it has those complicated-looking mathematical equations that require physics beyond high school level to comprehend? It's amazing how much scientists, especially astrophysicists neglect the same scientific method that they ridicule the general population for ignoring. We don't really know what happens inside black holes or if they actually exist as described in textbooks. We can scarcely comprehend the conditions that exists in the core of our own Sun, much less seconds after the Big Bang. Most of the current universe is comprised of so called "dark matter", which is another way to say that we don't understand most of the physics happening on cosmological scale.

I would hope for some textbooks that present proven facts about cosmology separately from the most popular current non-scientific theory. The later belongs to a philosophy course along with intelligent design.

Re:Suprise! (0)

Anonymous Coward | more than 6 years ago | (#23819245)

You're funny! You speak as if you actually know what you are talking about.

Re:Suprise! (2, Interesting)

CorSci81 (1007499) | more than 6 years ago | (#23819293)

I'm not really debating the usefulness of string theory, I'm just pointing out the lag time between "curiousity" math being done and a use being found. Whether or not string theory is useful is something only time will tell. Plenty of other physics theories hung around for decades before some evidence one way or another was established. I'm content to give it time and just enough funding to find out if it's just mathematical masturbation or something with real legs.

Re:Suprise! (2, Insightful)

Secret Rabbit (914973) | more than 6 years ago | (#23829891)

The problem with that is that:

1) It's already had about 40 years, and

2) It's very fundamental basis is problematic when considering it for force unification. You see, it's based on particle physics which is frame dependant, where as GR is frame independent. There are other *far* more likely theories, e.g. quantum loop gravity, that are frame independent as well.

So, even if there is even just a hint of reality to string "theory", it'll prove *very* problematic in the long run for other very *very* necessary things. You know, like consistency.

Re:Suprise! (4, Insightful)

rossifer (581396) | more than 6 years ago | (#23819429)

String Theory is more correctly a descriptive language of physical theories. Within the mathematical framework of String Theory it is possible to describe just about any configuration of the universe. In that way, it's more similar to applied math than anything else.

What String Theorists have been doing is building descriptive models of actual theories. It's a valuable exercise, but they shouldn't feel that String Theory is going to provide anything other than another modeling and analysis tool. Specifically, because String Theory is so expressive, it is impossible to make a falsifiable assertion in pure String Theory. You always need an outside theory, and it's the outside theory that provides the falsifiable assertion.

String Theory can describe just about any system, so it's impossible to prove right, and more importantly for this discussion, impossible to prove wrong. Which means that it is not science. Knowledge of this reality is gradually percolating through the physics establishment. Give it time.

Why bother, though (1)

Moraelin (679338) | more than 6 years ago | (#23820595)

The thing is, though: why bother? We already have simpler maths to describe the same phenomena and theories. Remember Occam's Razor, basically. If the same thing can be described simpler, and without multiplying unneeded entities like strings and branes, then why take the scenic route?

Having one set of equations to rule them all, one set to find them, one set to bring them all and in the darkness bind them... erm... wrong movie ;) Well, it's a noble goal, but not at the expense of making everything more complicated than it already is, without explaining anything new.

It also seems to me to defeat the whole idea of physics. The idea is to simplify the model to whatever is strictly necessary. If you just have to calculate in what time a mag-lev train travelling at 200 mph would go from Peking to Shanghai, you don't even need to know what mass or size the train is. If you want to calculate the engine to reach that speed, mass and shape become very important, but the colour of the train is still useless. The idea is to simplify maths, not make it more complicated.

Re:Why bother, though (1)

paulgrant (592593) | more than 6 years ago | (#23825077)

Depends - if you're looking for a novel effect, then a comprehensive equation is much simpler to solve than several (insufficient) functions coupled together. I don't know String theory (so i can't comment on that), but I can tell you that as a descriptive model, the Standard model is currently insufficient.

Re:Why bother, though (0)

Anonymous Coward | more than 6 years ago | (#23825229)

The thing is, though: why bother? We already have simpler maths to describe the same phenomena and theories.
Because we know the current theories are incomplete (aka wrong). To fix them we might need a new mathematical framework like string theory. We just don't know yet.

Re:Suprise! (0)

Anonymous Coward | more than 6 years ago | (#23824695)

So in a sense String Theory is just like religion or XML.

Re:Suprise! (2, Interesting)

Secret Rabbit (914973) | more than 6 years ago | (#23829993)

See my comment to CorSci81 above.

Also, String "theory" doesn't have something very *very* important in it. Or at least by its nature it isn't in it. That being a "big bang". Quantum Loop Gravity has one of those in it *by the very nature of Quantum Loop Gravity*. /Also/, falsifiability is a REQUIREMENT of any physical theory. If a theory doesn't have the possibility of being falsified, then it isn't a theory.

"""
Knowledge of this reality is gradually percolating through the physics establishment. Give it time.
"""

Wrong. Knowledge of this has been known in the physics establishment for a long *long* time. It's just that the funding, etc isn't done by the physics establishment. But, rather by administrators that are easily swayed by String "theory's" nasty PR campaign. But, the lack of results has lead even that to not hold as much sway any more. Luckly...

Re:Suprise! (1)

aproposofwhat (1019098) | more than 6 years ago | (#23819595)

Let's just call it 'String Conjecture' and then we'll all be happy :o)

I'll raise you one String Conjecture to your Electric Univarse [sic] :P

There's a problem. (1, Insightful)

Anonymous Coward | more than 6 years ago | (#23820375)

It'd be great if we could call this particular Cosmological spade a merely-Conjectured one, because that's what it is and nothing more.

But many of its professional adherents (ie, actual, paid-to-be-Cosmologists Cosmologists) would feel a tad miffed. They often get quite grumpy when the "conjecture" word is waved in front of them. And yet some of them are perfectly okay with it all, because they know as well as anybody that String Conjecture is just a bunch of really fascinating What Iffing.

The big problem is going to be the immense Holy war triggered when the amateur Cosmologists - the lay-astrophysicists-cum-security guards or bookstore clerks who read Omni and New Scientist - hear that their fad-du-jour has been relegated to the scientific cheap seats where it belongs.

Between them and the offended professional Cosmologists, astronomy forums throughout 73h 1n7a4rw3bz will become unbearable.

Well, more unbearable.

There's no Theory in String Conjecture, just as there's no room in Science for faith.

Damn! That last remark just blew away my hopes for a (Score:+5, Insightful). Me and my big mouth... :(

Re:Suprise! (1)

rasputin465 (1032646) | more than 6 years ago | (#23821511)

coming under significant fire for its lack of experimental evidence.
Actually, it's worse than that. String theory hasn't even provided any physical predictions. It's one thing for a theory to be unsupported by observation, it's entirely another thing for it to be untestable.

Re:Suprise! (1)

zehaeva (1136559) | more than 6 years ago | (#23823279)

Hopefully more and more people will finally realize this. It truly irritates me when someone who has no rigorous training in physics comes up to me and rants on about how all this crazy stuff is possible just because they saw a show about it on the discovery channel or read an article in popular mechanics. things like needing to prove the assertion there are more than 3 spacial dimensions completely pass them by and they jump to the end conclusion.

it is nice that the crazy assertions do inspire a curiosity and wonder about the universe, that it just might inspire a few people to walk the path of the physicist. but i still wish we taught our general public enough about the world for them to look at all of this and ask

wait a second here, have you proved any of this? or are you just talking about some math that you wrote on the back of a bar napkin one day that just happens to equal out? cause i can 'prove' that 1 = 2 for sufficiently large values of 1

</rant>

Re:Suprise! (0)

Anonymous Coward | more than 6 years ago | (#23825805)

Because the amount of money to support a year of string theory mathematics is so much greater than the amount of money to maintain an accelerator or other experimental apparatus. The "taking funding from more promising research" thing is a red herring. This is the old war between experimentalists and theorists, nothing more.

Re:Suprise! (1)

bmwm3nut (556681) | more than 6 years ago | (#23826799)

I'm a Chemical Physicist (so I don't work with anything smaller than atoms), but I've been to a number of string theory talks. One thing that always bugs me is that the string theorists cannot design an (unlimited funds) experiment that could prove or disprove their theory. I've asked the question myself "given no technical constraints, give me an experiment to prove what you just said" and I've _NEVER_ gotten a response. Until an experiment (even a thought experiment made famous from Einstein) can be proposed, I don't believe the theory at all.

Re:Suprise! (1)

pugugly (152978) | more than 6 years ago | (#23829521)

No, to be a theory it just has to make predictions that can conceivably be tested.

String theory makes predictions that can be tested - just not at energies that are within easy reach.

Just because this reminds me of it - I had a science teacher that explained it well with the 'faerie theory of gravity' - his pet theory that things were held to the earth by tiny faeries that grabbed on and flitted their wings.

Then he forced us to quit laughing and prove him wrong, based on the predictions of the faerie theory - i.e, that items with more surface area to grab should fall faster than items with less surface area, item in a vacuum shouldn't fall at all, etcetera.

As silly as it sounds, it was a pretty good intro into concepts of science philosophy, making predictions and testing them, the confirmation bias trap, that if the theory says one thing and the data another the theory needs to be altered, etcetera.

Pug

Re:Suprise! (1)

Secret Rabbit (914973) | more than 6 years ago | (#23830229)

"""
String theory makes predictions that can be tested - just not at energies that are within easy reach.
"""

Every one of those so called predictions not only cannot be currently tested, but those experiments that cannot be run also don't have the falsifiability requirement in them. And I've only hear of ONE so called experiment. And I've been paying attention to this nonsense from a while now. So, I'm calling bullshit on this statement.

"""
making predictions and testing them
"""

And String "theory" has done this when? Calling String "theory", String Theory does nothing but show ignorance of what a scientific theory actually is.

http://en.wikipedia.org/wiki/Theory [wikipedia.org]
"In science a theory is a testable model of the manner of interaction of a set of natural phenomena, capable of predicting future occurrences or observations of the same kind, and capable of being tested through experiment or otherwise verified through empirical observation."

String "theory" fails this accepted definition of a scientific theory. It might as well be intelligent design.

Re:Suprise! (1)

pugugly (152978) | more than 6 years ago | (#23832317)

Wow - if only I had a science teacher that had gone into notions of falsifiability, testing, confirmation bias, and so on I might know something about that.

Oh - that's right, I did.

You are correct, in that string theory predictions are not falsifiable *at our current level of technology* - the predictions they make are at higher energies than currently feasible. But it *does* make predictions, and frankly, if you are sitting here claiming it doesn't, and then claiming you've followed this for years, I have some difficulty reconciling the two statements.

I will be the first to concede, there was a point where I was having vague notions that it was going to turn out string theory was homomorphic to all of mathematics or something, but that's been awhile, and seems (to me, as an interested layman) to be adequately addressed by M-theory [wikipedia.org] .

But saying that it's not practical to test the predictions yet, doesn't dismiss it as not being a valid theory. Often theories aren't testable at the time - actually, the ones that come up and are immediately testable that day are the exceptions, not the rule.

Sooo . . .either there are no ways to distinguish quantum theories of gravity until we can build solar structures . . . or, we'll come up with something clever that allows us to distinguish them. Unless you intend to posit that we just shouldn't bother making theories about it until we reach dyson sphere tech, I really don't see the point of trying to scream that "String Theory = Intelligent Design", when they are philosophically different - one can be tested in principle - the other cannot, in principle, be proven wrong.

Fundamental difference.

Pug

Re:Suprise! (2, Insightful)

RiotingPacifist (1228016) | more than 6 years ago | (#23819319)

The longer it is, the better the mathematician is. The 18th century mathematicians like Gauss & Legendre were proud that nobody could find an application to thier work.

I mean Einstein & Born get all the credit but most of the time great physicists are just applying the maths of great mathematicians 50+ years before them

Re:Suprise! (1)

HuguesT (84078) | more than 6 years ago | (#23827279)

I wouldn't say that, really. For instance calculus was invented to solve a series of physics problems, most prominently point dynamics.

The relationship between maths and physics (all of science really) goes both way. If you read the article, you'll see that the original astrophysics conjectures provided an instance of maximal solution that the mathematicians hadn't found.

If you read the history of general relativity, you'll find that Einstein did a lot of significant work with David Hilbert, the leading mathematician of the early 20th century, on tensor theory. However it was Einstein who came up with the correct formulation of the gravity theory thanks to his physical insight (coming from Mach's principle). It's a fascinating story.

Re:Suprise! (1)

sixthousand (676886) | more than 6 years ago | (#23821795)

The only relevant application and marginally meaningful contribution of string theory is that of choreographic inspiration.
Dance: The Elegant Universe [worldsciencefestival.com]

Re:Suprise! (4, Insightful)

Jason Levine (196982) | more than 6 years ago | (#23818239)

Of course they are. They're the purist of the scientific fields. [xkcd.com]

Re:Suprise! (5, Funny)

Anonymous Coward | more than 6 years ago | (#23818747)

No way. Mathematics is merely applied logic.

Re:Suprise! (5, Funny)

Mr. Beatdown (1221940) | more than 6 years ago | (#23819099)

Logic is merely applied reality.

Re:Suprise! (1)

statemachine (840641) | more than 6 years ago | (#23819765)

Reality is merely applied substitution.

Re:Suprise! (1)

DRAGONWEEZEL (125809) | more than 6 years ago | (#23829771)

Substitution is merely the applied associative property.

Re:Suprise! (1)

weirdcrashingnoises (1151951) | more than 6 years ago | (#23819785)

Reality is merely applied sex.

Thus mathematics = sex.

Re:Suprise! (0)

Anonymous Coward | more than 6 years ago | (#23825481)

And as we all know, physics is to math as sex is to masturbation.

Re:Suprise! (3, Insightful)

kandela (835710) | more than 6 years ago | (#23819919)

Logic is an extension of intuition. It does not always serve us well.

Re:Suprise! (1)

smartdreamer (666870) | more than 6 years ago | (#23827733)

Talk for you. Logic serves people with real sense of logic. The only place where you may have trouble is with individuals of opposit sex. Seems like different logics don't mix well.

Re:Suprise! (0)

Anonymous Coward | more than 6 years ago | (#23821407)

And Sociology/Psychology is a study of realities. The circle is complete.

Re:Suprise! (1)

rickatnight11 (818463) | more than 6 years ago | (#23822405)

"Reality" is merely applied robot technology.

Re:Suprise! (1)

kalirion (728907) | more than 6 years ago | (#23822679)

Oh please, since when has logic had anything to do with reality?

Re:Suprise! (2, Funny)

nategoose (1004564) | more than 6 years ago | (#23822957)

Mathematics is merely applied magic.

Re:Suprise! (1)

khallow (566160) | more than 6 years ago | (#23831797)

And logic is applied philosophy. The big question is what is philosophy an application of? I'm thinking applied semantics, maybe applied ontology, or both.

Re:Suprise! (0)

Anonymous Coward | more than 6 years ago | (#23827899)

I'm going to become filthy rich by inventing a device that will apply an electric shock to anyone who posts an XKCD comic.

Re:Suprise! (2, Insightful)

Secret Rabbit (914973) | more than 6 years ago | (#23818327)

Correction: Certain interpretations of Mathematical results can be physically relevant.

Accidental My Ass (-1, Troll)

imstanny (722685) | more than 6 years ago | (#23818113)

Accidental Astrophysicist?! ...that's like saying I accidentally got a bitch pregnant -- She, uhh, jumped, tripped, and landed on my dick.

Re:Accidental My Ass (2, Funny)

Manfre (631065) | more than 6 years ago | (#23818139)

It happens more often than you think. Parents, tell your daughters to watch out for slippery ground. They may be the next one to slip and fall on a penis.

Re:Accidental My Ass (1)

Underfunded (1039600) | more than 6 years ago | (#23822243)

xkcd has a cartoon for that too: http://xkcd.com/417/ [xkcd.com]

animation depicting gravitational lensing (5, Informative)

Anonymous Coward | more than 6 years ago | (#23818135)

The wikipedia article on gravitational lensing [wikipedia.org] has a neat animation [wikimedia.org] produced with a numerical model. I wouldn't make it your desktop background though because it might warp your file icons.

To update Clarke (2, Funny)

xactuary (746078) | more than 6 years ago | (#23818145)

OMFG! It's full of stars!

Perhaps I am missing something... (1)

clonan (64380) | more than 6 years ago | (#23818165)

but I don't see where in the article they describe what "n" is.

I think it relates to the mass creating the lens but since the mass is not an integer I don't see how the math could work.

Does anyone have a link or maybe an explanation?

Re:Perhaps I am missing something... (2, Informative)

CorSci81 (1007499) | more than 6 years ago | (#23818189)

n refers to the number of massive objects causing the lensing as I understand it, but I could be wrong. I'm slightly drunk while posting and my previous existence as an astronomy grad student eludes me.

Re:Perhaps I am missing something... (2, Insightful)

Anonymous Coward | more than 6 years ago | (#23818219)

Clearly n is the fudge factor.

Re:Perhaps I am missing something... (1)

blueg3 (192743) | more than 6 years ago | (#23818301)

n is the number of massive objects (e.g. stars); as per the article, it's 5n-5 for n > 1

Re:Perhaps I am missing something... (2, Interesting)

techno-vampire (666512) | more than 6 years ago | (#23818453)

There's something I don't understand here. If n > 1, the number of images is 5n-5, or 5(n-1). As n must be an integer (You can't have a fraction of a massive object.) that means that the number of images must be a multiple of 5. And yet, there's a picture of a set of 4 images of a quasar in the article. Not only that, somebody links to the Wikipedia article on gravitational lensing, and that shows a picture of an "Einstein Cross:" four images of a quasar surrounding a galaxy between it and us. Four, in both cases, not five. Yes, I realize that in both cases n = 1, but can anybody explain how you end up with four in that case?

Re:Perhaps I am missing something... (3, Informative)

Anonymous Coward | more than 6 years ago | (#23818551)

I think the article says that this equation is used to find the maximum amount of star images that could be created by a massive object, so in the case of one massive object, according to the equation, you could get a maximum of 5 images of the star.

Re:Perhaps I am missing something... (1)

techno-vampire (666512) | more than 6 years ago | (#23819061)

Actually, it says that's true for n > 1. I'm asking if anybody understands the math behind the result for n = 1.

Re:Perhaps I am missing something... (3, Informative)

kevinatilusa (620125) | more than 6 years ago | (#23819365)

There's something I don't understand here. If n > 1, the number of images is 5n-5, or 5(n-1). As n must be an integer (You can't have a fraction of a massive object.) that means that the number of images must be a multiple of 5. And yet, there's a picture of a set of 4 images of a quasar in the article. Not only that, somebody links to the Wikipedia article on gravitational lensing, and that shows a picture of an "Einstein Cross:" four images of a quasar surrounding a galaxy between it and us. Four, in both cases, not five. Yes, I realize that in both cases n = 1, but can anybody explain how you end up with four in that case?
As I understand it, the 5n-5 only describes the maximum number of images that can be seen. It doesn't mean that in general you will always see the full 5n-5, only that in some cases it is possible to see that many.

So the number you see doesn't have to be a multiple of 5 always, even for n>1.

Re:Perhaps I am missing something... (2, Informative)

aproposofwhat (1019098) | more than 6 years ago | (#23819659)

4 images from gravitational lensing, plus 1 image not distorted (straight through the lens) equals, in my book, 5.

There's no guarantee that you can see the 'straight through' image, because the object doing the lensing might be in the way.

And for n objects lensing, the effect is multiplicative.

What's so difficult about that?

Re:Perhaps I am missing something... (1)

techno-vampire (666512) | more than 6 years ago | (#23824631)

4 images from gravitational lensing, plus 1 image not distorted (straight through the lens) equals, in my book, 5.


Thank you! Yes, of course, there would be an image in the center because light coming straight at us won't be displaced. I'd never thought of that. Of course, that image will be blocked by whatever's causing the lensing, but it's going to exist. And, I'd guess, with more than one object, there will me one or more images similarly blocked.

Re:Perhaps I am missing something... (1)

mikael (484) | more than 6 years ago | (#23818523)

I don't understand. If these four massive objects were lined up towards the observer, and each massive object can split the light into two paths, then shouldn't there be (2^n)-1 stars, rather than 5n-5?

If they were side by side, then the maximum would be 2n?

Cross-Disciplines! (1, Interesting)

Anonymous Coward | more than 6 years ago | (#23818195)

Mathematically, this is the first post.

And isn't that wonderful, that our sciences are so wide in breadth that one discipline may hold answers to other disciplines' questions?

And much much better is that someone in another discipline is willing to look across those divisions to see an answer that might have gone unremarked.

Re:Cross-Disciplines! (1)

Hognoxious (631665) | more than 6 years ago | (#23820301)

Mathematically, this is the first post.
We're all C programmers here, so really it's second.

Can one of you mathematicians explain (1)

sweet_petunias_full_ (1091547) | more than 6 years ago | (#23818245)

How many stars will be seen?

TFA says 5n-5, but I don't get it because if n=1, then zero stars would be seen.

Can someone clear this up?

Re:Can one of you mathematicians explain (1)

Lord Crc (151920) | more than 6 years ago | (#23818329)

TFA says 5n-5, but I don't get it because if n=1, then zero stars would be seen.
The relevant part comes after that:

... all they could show was that such a function couldn't have more than 5n-5 solutions, if n was bigger than one.
In other words, their formula simply does not apply for the case when n = 1.

Re:Can one of you mathematicians explain (1)

sweet_petunias_full_ (1091547) | more than 6 years ago | (#23818537)

That solves the n=1 case, but the n=2 case is still as clear as mud.

I'm supposed to see a maximum of 5 stars through gravitational lensing, if there were two original light sources?

Something doesn't make sense here - why should there be discrete output from lensing? I would think it would be possible to output an elongated blob of light from a point light source.

Maybe this will need an astrophysicist to explain it.

Re:Can one of you mathematicians explain (2, Informative)

coliverhb (886806) | more than 6 years ago | (#23818595)

n = # of massive objects in the way, not light sources.

Re:Can one of you mathematicians explain (4, Informative)

tirerim (1108567) | more than 6 years ago | (#23818661)

I'm not actually an astrophysicist, but I may be able to sort of explain. Take a look at the diagram in TFA: it's just in two dimensions, specifically the plane defined by the distant star, the massive object, and the observer. We see two images that are in that plane, because only light rays from the star that are traveling in that plane can be bent by the massive object so that they can reach us; rays traveling in any other plane would be bent to arrive at some other location. And the star is effectively a point source, so we see exactly two point images. With multiple massive objects, there are more planes, but the planes are still discrete, so there are still discrete images. The only exception is when the star, the massive object, and the observer are exactly in line, in which case we see a circle.

Galaxies, on the other hand, are not point sources, which is why when we see gravitationally lensed galaxies they often look stretched out along arcs -- different points in the galaxy line up differently, and thus can look farther apart from each other than they would if we were seeing them without lensing.

Further proof ... (4, Funny)

three333 (453814) | more than 6 years ago | (#23818255)

... that xkcd is right: http://xkcd.com/435/ [xkcd.com]

Re:Further proof ... (4, Interesting)

TerranFury (726743) | more than 6 years ago | (#23818393)

I think the role of math as "leading" is oversold. I get the impression that a heck of a lot of math was inspired by physics. It seems as though the two develop in tandem. In particular, vector calc and E&M come to mind.

It can also be argued that philosophy is more basic than math. Some might say that we need our ontologies and epistemologies before we can do calculations involving them.

Re:Further proof ... (3, Insightful)

Peow (1308839) | more than 6 years ago | (#23818463)

But isn't physics still mathematics? Like, physics is a subcategory of math? along with... everything else... Hell what do I know, I'm only 16.

Re:Further proof ... (1)

jasonmanley (921037) | more than 6 years ago | (#23818601)

16!? Damn you're doing pretty well. When I was 16 I couldn't even spell maeths or psychics

Re:Further proof ... (3, Interesting)

east coast (590680) | more than 6 years ago | (#23818665)

Mathematics is a common language between the sciences. I don't see any need to debate it from there.

Re:Further proof ... (0)

Anonymous Coward | more than 6 years ago | (#23823649)

Mathematics is a language we can share as humans just like French or Italian. The amazing thing about it though is that the universe speaks it surprisingly well. We should listen carefully.

Re:Further proof ... (1)

mikael (484) | more than 6 years ago | (#23825165)

Another amazing thing is that all the symbols of mathematics have been defined since the mid 1800's. You can read a mathematics book written 100 years ago and still understand it as if it were just newly released publication. In many cases the high-school books of then seem to cover topics in greater detail than current publications.

Though it is a strange feeling to think that someone is able to share their knowledge of a subject even though they are no longer here in person; with a modern textbook the authors usually have a webpage forum, if not an E-mail address you can use to contact them.

Re:Further proof ... (2, Interesting)

someone300 (891284) | more than 6 years ago | (#23818679)

I wouldn't say so. Mathematics is a set of rules and axioms, but you need physics to help design the set of rules that is useful for modelling real life. You could design a custom mathematical system to be however you want and still be self-consistent, but be completely non-useful for questions involving reality.

Generally things like propositional logic and the axioms of mathematics are held to be self-evident physically. However, some things were thought to be mathematically self evident until physicists proved that they either weren't always true or that they depend on the universe in some way, Euclidian Geometry for example.

Then as the GP states, some people argue that maths is a subset of philosophy. Indeed, some people argue the other way around too.

My belief is that they are all interrelated fields that when combined can be used to answer questions about reality, but when studied individually can be interesting nevertheless (and sometimes even useful).

Re:Further proof ... (4, Insightful)

forkazoo (138186) | more than 6 years ago | (#23818755)

I wouldn't say so. Mathematics is a set of rules and axioms, but you need physics to help design the set of rules that is useful for modelling real life. You could design a custom mathematical system to be however you want and still be self-consistent, but be completely non-useful for questions involving reality.


I really want to agree with you, but people keep finding ways that obscure, useless little pieces of purely abstract math suddenly explain something interesting about the real world. Sometimes it takes a century or two, sure. But, if you told the first people to work on imaginary numbers how useful their math would be for expressing many engineering things, and how it would be a major tool for engineering students learning to build very real things, well they'd just call you a moron. Likewise, boolean algebra, or any number of other mathematical concepts that make our current world possible and relatively comprehensible.

Re:Further proof ... (2, Interesting)

kmac06 (608921) | more than 6 years ago | (#23819921)

An interesting observation is that imaginary numbers are completely unnecessary (but of course quite useful) for most engineering (e.g., signal processing). It is only in quantum mechanics that imaginary numbers are necessary to describe something physical.

Mathematics can't do experiment (1)

Nowhere.Men (878773) | more than 6 years ago | (#23822199)

One of the big question in cosmologi is the topology of the universe.

Matematics allow you to create an infinity of different topology. I'm sure that one of them will be able to represent the universe.

But The Mathematicien will never be able to say which one is the correct one. For them they are all the same, methematical models.

For the physician which have his experiments and data, only one is the correct one. The rest is just models.

Mathematics is not a science.

 

Re:Further proof ... (0)

Anonymous Coward | more than 6 years ago | (#23818993)

Like most science, physics provides a ( not "the" but "a") reason to develop mathematics. Without scientific questions, the amount of mathematics known would be less I'm sure. However there would still be mathematics known. Mathematics does not require the other sciences to exist, but the other sciences of any importance (yes its a subjective thing to say but really, a lot of science is simply naming things and we could always name these things a different way) do require mathematics.

Re:Further proof ... (4, Informative)

swillden (191260) | more than 6 years ago | (#23819577)

However, some things were thought to be mathematically self evident until physicists proved that they either weren't always true or that they depend on the universe in some way, Euclidian Geometry for example.

The development of non-Euclidean Geometry argues against your point, rather than supporting it.

Non-Euclidean geometry arose out of pure mathematical attempts to correct a "flaw" in Euclidean geometry. Namely, that the parallel postulate was so big and complex that it didn't seem like a proper axiom, not like Euclid's other four axioms.

Lots of mathematicians had tried various ways to prove that the parallel postulate wasn't necessary, that it could be derived from the other four, and many flawed "proofs" were constructed. A few mathematicians, notably Saccheri, decided to take a less constructive route and try to disprove the necessity of the parallel postulate by contradiction.

The idea was: Replace the parallel postulate with something else that means the opposite, and then show that geometry breaks down, that logical contradictions can be shown. Saccheri thought he succeeded because he was able to prove some things that made no sense within the Euclidean framework.

Later mathematicians realized that, in fact, Saccheri had "failed" to find a contradictions, that his results resulted in a geometry that was weird and non-Euclidean, but perfectly consistent, and in fact made perfect sense if you applied it in the context of a hyperbolic surface. Under a different modification of the parallel postulate, you get a geometry that makes perfect sense on the surface of a sphere.

Later still, physicists picked up on these alternative geometries and began applying them to great benefit. Notably, Einstein's notion of spacetime as non-Euclidean.

It goes both ways, of course. Physics often motivates math, and pure math is often adopted and applied by physics. Neither would be as rich without the independent work of the other.

Re:Further proof ... (0)

Anonymous Coward | more than 6 years ago | (#23819819)

quick, get off the internet, before it's too late!

Re:Further proof ... (0)

Anonymous Coward | more than 6 years ago | (#23823755)

Stop being ageist on yourself.

Re:Further proof ... (0, Troll)

TheLink (130905) | more than 6 years ago | (#23818917)

Math is not leading (and I don't think that xkcd strip claims it).

In fact in this case, Rhie found the limit first but just couldn't prove it.

As for proving stuff, Math can help prove some stuff, but not other stuff (it can't normally be used to prove what you had for lunch yesterday).

Re:Further proof ... (0)

blahplusplus (757119) | more than 6 years ago | (#23819125)

"I think the role of math as "leading" is oversold. I get the impression that a heck of a lot of math was inspired by physics. It seems as though the two develop in tandem."

There is a reason why that is, math and physics are part of the the same discipline, whether anyone else has realized it or not one only has to look to geometry to see how they cannot be dis-united. The real physical world is full of geometry (i.e. physics) and you need an abstract representational system to describe that geometry (math). You see a sphere x the real world and need some kind of ABSTRACT REPRESENTATIONAL SYSTEM to describe it... (i.e. 1, 2, 3, etc) therefore math is an abstract descriptive language we need to categorize and describe the world itself.

So math is - the language of the shapes.

Re:Further proof ... (4, Interesting)

AstrumPreliator (708436) | more than 6 years ago | (#23819255)

The way things look to a mathematician are probably different than the way things look to a physicist which are also probably different than the way things look to everyone else. I'm in the first group, so my opinions may be biased here =).

Firstly I don't think there are any absolutes, sometimes math and physics develop in tandem and other times there's a lag time with one or the other leading. I personally think math "leads" the way. Not because it wants to describe the physical world but because it's interesting. Just remember that the math you learn in high school is hundreds of years old, you don't get to the current stuff until grad school. Whereas a physicist uses math as his tool to achieve his goal and will only invent a new tool if his toolbox is insufficient, a mathematician creates new tools just because he wants to understand them. In other words the goal of a mathematician is to make to tools, the goal of a physicist is to apply the tools. That's personally why I think math is "leading" most of the time. I'd rather not get into naming specifics examples as there are millions and I don't believe anyone could win that argument.

As far as math being a subset of philosophy I'll have to disagree; I think they are inexorably linked but neither proper subsets. They share the same grammar, logic, but differ in their dictionaries.

Those are just my thoughts on the matter though.

Re:Further proof ... (0)

Anonymous Coward | more than 6 years ago | (#23844133)

I would argue that most fields of study are born in philosophy and move away from it in to their own realm. It happens over-and-over again, though each field is distinct and unto itself; philosophers are the first ones to think the crazy stuff up and then people specialize from there.

Basic math probably proceeded philosophy but beyond arithmetic I doubt much else did.

Re:Further proof ... (0)

rossifer (581396) | more than 6 years ago | (#23819259)

Math is the language.

Physics is the subject matter.

So yeah, they change together. Different from the normal relationship between language and subject, you've got plenty of math without a known application in the real world, but as long as you're using the same axioms, it all seems to eventually make sense...

Re:Further proof ... (5, Insightful)

aproposofwhat (1019098) | more than 6 years ago | (#23819745)

It can also be argued that philosophy is more basic than math. Some might say that we need our ontologies and epistemologies before we can do calculations involving them.

Some might, but I wouldn't.

Mathematics has its own ontology - namely the axioms that it is based upon.

It has no need for a separate epistemology - it is what it is, and that's that.

Propositional calculus, on which Russell, Frege and Wittgenstein based their mathematical philosophy (which I see as applicable to all rational thought) is itself the root of mathematics - thus mathematics (or logic, however you wish to phrase it) is fundamental to philosophy, rather than philosophy being fundamental to mathematics.

You can't have an ontology without maths - epistemologies are more equal, but essentialy the whole of philosophy is based on the propositional calculus, which is only one of many possible formulations of mathematics.

Too Narrow view of philosophy (1)

Tungbo (183321) | more than 6 years ago | (#23839497)

You've succumb to the shuttered view of Analytic Philosophy which consider the field only about manipulation of languages and symbols.

Get out more. Read some Kierkergaard and Tao Te Ching. Check out existentialism, phenonemology, and sunyata in buddhism....

Re:Further proof ... (1)

Razor Sex (561796) | more than 6 years ago | (#23841697)

It sounds like you're only thinking of the Wittgenstein of the Tractatus - the later Wittgenstein of Philosophical Investigations does not give mathematics primacy in any way. The later Wittgenstein and the whole of the Continental tradition of philosophy deal much more in questions of ontology, of "why are we here?", and so on, without any reference to mathematics.

Re:Further proof ... (2, Interesting)

MindStalker (22827) | more than 6 years ago | (#23822191)

Yep, if you change Sociology to Philosophy you get a complete circle.

Philosophy -> Physiology -> Biology -> Chemistry -> Physics -> Math -> Philosophy ->

Re:Further proof ... (1)

azgard (461476) | more than 6 years ago | (#23825641)

I find it amusing that if Khavison and Neumann would discover the theorem say 10 years earlier (and Rhie would just apply their result), then they wouldn't become astrophysicists, they would be just mathematicians, as usual.

Re:Further proof ... (1)

mikael (484) | more than 6 years ago | (#23825711)

think the role of math as "leading" is oversold. I get the impression that a heck of a lot of math was inspired by physics. It seems as though the two develop in tandem. In particular, vector calc and E&M come to mind.

Many fields of mathematics were created simply to solve the real-world physics problems of the time. Attempts to predict tide levels in the 1800's led to the development of mechanical calculators and signal processing (sum of weighted sine waves).

A Renaissance parlor trick of placing salt on a vibrating table led to the development of the field of harmonics theory (the king offered a reward if someone could provide an explanation).

The need to be able to calculate the refraction of light for eye glasses led to the field of optics theory.

The need to understand electromagnetism led to the development of the theory like Maxwell's equations .

Re:Further proof ... (1)

Peow (1308839) | more than 6 years ago | (#23818435)

Dammit you beat me to it.>.>

hip hip hooray! (-1, Troll)

Anonymous Coward | more than 6 years ago | (#23818589)

actual science instead of star wars faggotry or lemmings going on and on about loving to be fucked in the ass by jobs or linus. slashdot may still have hope yet.

Curiousity Killed the Cat (1)

KGIII (973947) | more than 6 years ago | (#23819005)

But I haven't got four legs nor do I sport a tail.

Some of these theories offer (often long standing as I understand) a financial reward for the person(s) who proved them. I did some looking and I'm not seeing any for this one in particular. My questions (yeah, I ask those a lot here) total just two today. Was there one in this case? If there was then, well, who would get it?

Am I the only one (1, Funny)

PakProtector (115173) | more than 6 years ago | (#23819479)

who thought that this was about Penzias and Wilson?

I mean, C'mon.

I'm thuper thereal, guys!

"totally extraterrestrial" (1)

argent (18001) | more than 6 years ago | (#23824559)

The final quote, "I find the whole experience totally extraterrestrial", wins the Internet.
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