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The Accidental Astrophysicists

Posted by kdawson on from the all-math-to-me dept.

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."

37 of 97 comments (clear)

  1. Suprise! by cobaltnova · · Score: 5, Funny

    Mathematics results are physically relevant. News at 11.

    1. Re:Suprise! by CorSci81 · · Score: 3, Insightful

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

    2. Re:Suprise! by Jason+Levine · · Score: 4, Insightful

      Of course they are. They're the purist of the scientific fields.

      --
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    3. Re:Suprise! by Secret+Rabbit · · Score: 2, Insightful

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

    4. Re:Suprise! by Secret+Rabbit · · Score: 4, Insightful

      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.

    5. Re:Suprise! by NoobixCube · · Score: 4, Interesting

      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.

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    6. Re:Suprise! by Anonymous Coward · · Score: 5, Funny

      No way. Mathematics is merely applied logic.

    7. Re:Suprise! by Mr.+Beatdown · · Score: 5, Funny

      Logic is merely applied reality.

      --
      My fellow Americans, let's restore the death penalty for child rapists. Let's do it . . . for the children.
    8. Re:Suprise! by CorSci81 · · Score: 2, Interesting

      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.

    9. Re:Suprise! by RiotingPacifist · · Score: 2, Insightful

      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

      --
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    10. Re:Suprise! by rossifer · · Score: 4, Insightful

      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.

    11. Re:Suprise! by kandela · · Score: 3, Insightful

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

      --
      Conservation of angular momentum makes the world go round.
    12. Re:Suprise! by nategoose · · Score: 2, Funny

      Mathematics is merely applied magic.

    13. Re:Suprise! by Secret+Rabbit · · Score: 2, Insightful

      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.

    14. Re:Suprise! by Secret+Rabbit · · Score: 2, Interesting

      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...

  2. animation depicting gravitational lensing by Anonymous Coward · · Score: 5, Informative

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

  3. Re:Accidental My Ass by Manfre · · Score: 2, Funny

    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.

  4. To update Clarke by xactuary · · Score: 2, Funny

    OMFG! It's full of stars!

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  5. Re:Perhaps I am missing something... by CorSci81 · · Score: 2, Informative

    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.

  6. Re:Perhaps I am missing something... by Anonymous Coward · · Score: 2, Insightful

    Clearly n is the fudge factor.

  7. Further proof ... by three333 · · Score: 4, Funny

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

    --
    Three is my favourite number
    1. Re:Further proof ... by TerranFury · · Score: 4, Interesting

      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.

    2. Re:Further proof ... by Peow · · Score: 3, Insightful

      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.

    3. Re:Further proof ... by east+coast · · Score: 3, Interesting

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

      --
      Dedicated Cthulhu Cultist since 4523 BC.
    4. Re:Further proof ... by someone300 · · Score: 2, Interesting

      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).

    5. Re:Further proof ... by forkazoo · · Score: 4, Insightful

      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.
    6. Re:Further proof ... by AstrumPreliator · · Score: 4, Interesting

      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.

    7. Re:Further proof ... by swillden · · Score: 4, Informative

      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.

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    8. Re:Further proof ... by aproposofwhat · · Score: 5, Insightful

      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.

      --
      One swallow does not a fellatrix make
    9. Re:Further proof ... by kmac06 · · Score: 2, Interesting

      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.

    10. Re:Further proof ... by MindStalker · · Score: 2, Interesting

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

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

  8. Re:Perhaps I am missing something... by techno-vampire · · Score: 2, Interesting

    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?

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  9. Re:Perhaps I am missing something... by Anonymous Coward · · Score: 3, Informative

    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.

  10. Re:Can one of you mathematicians explain by coliverhb · · Score: 2, Informative

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

  11. Re:Can one of you mathematicians explain by tirerim · · Score: 4, Informative

    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.

  12. Re:Perhaps I am missing something... by kevinatilusa · · Score: 3, Informative

    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.
  13. Re:Perhaps I am missing something... by aproposofwhat · · Score: 2, Informative
    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?

    --
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