The latest Cosmic Log column on msnbc.com concerns Lawrence Krauss’s new book Hiding in the Mirror and the author asked Krauss a question I’m expecting that physicists will be hearing more and more often as time goes on: “Why is string theory science but intelligent design isn’t?”
Krauss gives a response that isn’t completely convincing. He says that “the difference is that Ed Witten and the other good string theorists will, if an experiment comes along that demonstrates that supersymmetry isn’t discovered in a definitive way, be the first to say the theory is wrong.” This isn’t really true. Since the scale of supersymmetry breaking is unknown, one can’t hope to experimentally definitively show supersymmetry is not there. And the question at issue is string theory, not supersymmetry. Will string theorists abandon the theory when supersymmetry is not found at the LHC? We’ll see in a few years, but I already see them hedging their bets and many undoubtedly will not see the lack of supersymmetry at LHC energies as proving string theory wrong.
The behavior of string theorists that Krauss identifies as most like religion is the argument that “the theory is so beautiful it must be true.” I actually don’t hear many string theorists making this argument these days. If the theory actually were beautiful in the sense of providing some impressive new understanding of physics in terms of some simple, compelling mathematical or physical idea, that actually would be a good reason for believing in it, although not a completely conclusive one. All attempts so far to connect the theory to real physics lead to hideously complicated and ugly constructions. Some string theorists such as Susskind, argue that one should believe in string theory anyway, and it is this argument which seems to me to be more like religion than science. It’s my impression that Susskind and others are believing something for sociological and psychological reasons, something for which they have no rational, scientific argument. This behavior is not distinguishable from that of many of the intelligent designers, and if it becomes more widespread it ultimately threatens to do real damage to the public perception of science in general and theoretical physics in particular.
Krauss gets closer to the real difference between string theorists and intelligent designers when he says that string theorists “are trying to come up with predictions that actually do something”. More sensible string theorists are well aware that what they are doing isn’t going to be part of science until they figure out a way to use it to make real predictions that can be tested. In general, given a new speculative idea, it will not be obvious how to figure out all of its implications and see whether it can lead to real predictions. It can take years of work for this to become clear, and this sort of work is definitely science. On the other hand, if after a lot of work, there still is no indication that an idea can produce predictions, the continued pursuit of it at some point stops becoming science and starts becoming something more like religion. Susskind and other anthropic landscapeologists have already gone past this point: they have no plausible idea about how to ever get real predictions out of their framework. String theorists who argue that the theory is still too poorly understood, that more work is needed to understand whether there is some way around the radical non-predictivity implied by the landscape, are nominally still doing science. But at some point, as years pass without any progress in this direction, and evidence mounts that hopes for ways to get predictions aren’t working out, this activity stops being science and it too starts being a non-scientific activity pursued for sociological and psychological reasons. We’re close to that point, if not already past it.
Update: There’s a defense of string theory against the charge that it’s like intelligent design over at Kasper Olsen’s blog. I don’t find it very convincing, since it doesn’t address at all the question of how string theory is ever going to do what a real science is supposed to do: make falsifiable predictions. Much of Olsen’s list actually strikes me as a recitation of a catechism of supposed reasons why string theory is so wonderful, rather than a serious scientific argument. Some of these are also highly dubious (e.g. “the Standard Model can be reproduced in a very simple way”), they’re things that one has to be a true believer to say, since they really don’t accord with reality.
One commenter (Gavin), gave a very good reason for distinguishing string theory from intelligent design: “the former is trying to explain something that is already explained, while string theory is trying to solve a mystery” and he correctly notes that while string theory’s scientific credentials may be weak, the problem is that there aren’t really good alternatives (LQGers may argue with this…). John Baez’s comment about the relationship of math and physics was also quite nice.
“A non-scientific activity pursued for sociological and psychological reasons” seems an overly broad characterization, if it encompasses both religion and — as most people would characterize non-empirical string theory — abstract mathematics. Do you really want to be arguing that non-physics mathematics (which string theory may prove to be) is equivalent to religion? Even totally absent “predictions that actually do something,” string theory as mathematics would still be a very different type of activity from religion, and would deserve a very different treatment in our schools (were a high school ever to attempt to teach totally abstract math).
“Why is string theory science but intelligent design isn’t?â€?
Even if string theory is not physics, it is mathematics. Depending on your point of view, mathematics is the handmaiden or the queen of sciences.
Now that it has been mentioned, one cannot deny that if “beauty” is the justification to do string theory then the same can be invoked for Intelligent Design (ID) also. The supporters of ID claim that it is more elegant than evolution, stressing that it is the messiness of probabilites that they are trying to banish.
If some people are doing string theory because of its mathematics, then perhaps it should be done in the Math Departments. There is no question that falsifiability should remain the primary criterion of any physical theory.
Well, it could be worse. At least the ID people propose an alternative to evolution, however crazy. They don’t just tell us, year in, year out, that evolution is not science, that evolutionists are pursuing the theory for purely sociological reasons, etc etc etc, without ever proposing anything that even looks like an alternative.
Arun said:
“Even if string theory is not physics, it is mathematics. Depending on your point of view, mathematics is the handmaiden or the queen of sciences.”
I am sorry. Mathematics is not science. Mathematics is just a language, a language that is suitable to be used to describe science. But it is not itself a science. Mathematics do not make predictions and do not experiment with nature. So mathematics is NOT science. You can easily figure out how to calculate the surface area of a sphere in a hypothetical 26 dimentional space, using pure math, but such math constructs have nothing to do with nature, which is certainly not 26 dimentions.
Quantoken
playing devil’s advocate, SST/m-T does predict SUSY & 11-D which *could* be falsible.
also, one contact SST does make is reproducing the BH entropy
I agree and disagree with Quantoken. Yes, mathematics is not a science. No, mathematics is not just a language to describe science.
Modern mathematics, the way I look at it, is a creative endeavor in which we study abstract well-defined objects that we find intriguing, in a certain language (set theory, category theory, …) that’s internal to mathematics. In particular, a priori, there’s no connection of mathematics with any language that describes how the world works. That mathematics itself happens to be the best language to “do” science in, is co-incidental and a consequence of the fact that (historically) SOME PARTS (calculus, say) of mathematics were invented to solve problems external to mathematics, and SOME PARTS (representation theory, say) of modern mathematics, besides being of great interest within mathematics, simply HAPPEN to describe the real world spectacularly well. — it’s a gross generalisation to say that all of mathematics is just a language to describe the real world. And yes, mathematics is not a science since, as defined above, it serves its own ends and does not attempt to describe how the “real world” works .
One may conclude from the above that, as BD does with Peter’s post, that I believe mathematics is “equivalent” to religion. This seriously depends on the definition of equivalence. If two subjects become equivalent simply because they both arise from psychological motivations, then yes — mathematics and religion are equivalent. In this case, however, I think your definition of equivalence needs rethinking. After all, physics and biology (or even economics) arise from similar motivations — they both try to describe a certain aspect of the real world. Does this make them “equivalent”? I think not.
I disagree with the notion that math is not science. Mathematics relates to properties of objects in a formal system (that may or may not correspond with a physical system) together with rules of association amongst those objects. Since such formal systems are a product of our mind, mathematical truths are of fundamental importance and they may be viewed as extensions of logic. Obviously claims in a formal system are falsifiable excepting in cases where the system of axioms is not rich enough for one to prove or disprove an assertion.
Jack, I am really hoping your being sarcastic, for you have attributed to stringers what ID proponents have been doing since 1987 when Pandas and People was first published. Please go check out Pandas Thumb or Pharyngula if you need a refresher course on the sadness that is the Intelligent Design movement.
I believe Peter has made this analogy before, and I cannot help but wince. String theory has numerous problems, especially with regards to experimental testing. Intelligent Design is a socio-religious movement that wishes to repackage old school creationist trash in a form that will squeeze by the establishment clause. I doubt stringers have hired their own international PR firm, and are attempting to teach Gauge theory to fourteen year olds.
If there was any “religious quality” about string theorists it reminds me more of New Agers, whose theories while holistic, are absolutely worthless. I find Planck’s original derivation of his radiation law beautiful due to its ingenuity, but its wonderful agreement with experimental evidence is just as aesthetically pleasing as the mathematics he used.
ID is far more dangerous and near term, for its proponents have sold their souls and intellectual integrity to promote a defunct faith and the bastardization of the scientific method.
What I wrote was intended in the following spirit:
“Mathematics is the Queen of Science, and Arithmetic the Queen of Mathematics. – C. F. Gauss”
“The Handmaiden of the Sciences. Eric Temple Bell (1883-1960), [Book by that title.] ”
“Mathematics serves as a handmaiden for the explanation of the quantitative situations in other subjects, such as economics, physics, navigation, finance, biology and even the arts.” – H. F. Fehr
Intelligent Design and “is mathematics science?” make for sterile arguments.
The problem with the claim mathematics is what distinguishes religion from science is that it runs into trouble when you consider numerology or pythagoreanism. There’s been a lot of mathematical mysticism from the early days of Pythagoras on up to even the present. Go down to that goofy isle in Barnes and Noble that sells “metaphysical” books and you’re bound to find at least one book that is complete silly gibberish but very mathematically.
The relationship between math and religion is quite old. Remember that Plato saw geometry as one of the best illustrations of his rather odd notion of an immortal soul and remembering. Since we weren’t creating the geometric proof we have to be “perceiving” them in some sense or remembering them.
Complete balderdash, of course, but hugely significant. This rebirth of mathematics as religion can even be found in fairly prominent scientists. Read some of the discussions of Newton as a hermeticist to see this.
Anyway, I don’t have much to say vis a vis ID or string theory. I reject ID and have my doubts about strings, as interesting as they are. But I didn’t go far enough down that line of physics to be able to say much of worth to the science.
Subhash:
Has it been falsified, or not falsified, in mathematics, the statement that two parallel lines shall never cross? You’ve got to know neither case is right or wrong.
There is no empirical truth in mathematics. All math are logical derivations from a few fundamental rules which we probably took for granted, but which do not need to be taken for granted as truth, like the parallel line hypothesis. As such, all you could ever say is certain statement is either consistent, or inconsistent, with the set of hypothesises that your math is based on. There is no absolute truth.
Another example, you may take it for granted that 1+1 surely equals 2. But there is a hidden presumption here that you discuss the problem within the arithmatics rules built on the set of natural numbers. You could well establish an arithmatics system which is self consistent, for example one where the only numbers exist are 1 and 0. In that case, 1 + 1 gives 0, and 2 doesn’t exist.
You might think an arithmatic system with only 0 and 1 and no other number may sound silly. But remember, for a long time, our math of geometry only dealt with 3 dimentional space, not anything more than 3-D, and certainly not infinite dimentionality. And it is still difficult for our limited mind to comprehend higher dimentionality than 3. What is true in a 3D world may not be true in other dimentionality.
So, there is no absolutely truth in math. All you can ever show is some statement are consistent or inconsistent with other statements.
Quantoken
Thanks for all the interesting comments.
I’ve said this many times before, but I should be more precise about what aspects of string theory I’m criticizing as unscientific. What I have in mind is specifically the idea that one can unify the standard model and gravity using a 10/11-d string/M-theory. Things like AdS/CFT, where strings are used to construct a dual to a strongly coupled gauge theory, are certainly physics. Things like topological strings and their relations to Gromov-Witten invariants and much else are definitely mathematics. But the 10d superstring compactified on a Calabi-Yau is a very complicated mathematical structure, one that doesn’t seem to have any special deep significance. Studying aspects of this complicated structure can lead to a lot of interesting mathematical work, but the full structure itself is not mathematically compelling, a good reason to believe it isn’t going to be a successful TOE.
As for the mathematics/religion comparison, well they’re quite different pursuits, although I’m sure one can find some relations between them. The mathematics/physics relationship is a very deep question, and I don’t think we know enough about either subject to yet know precisely what the relation is. My own inclinations are kind of hyper-Platonist, thinking that ultimately we will see that the deepest mathematical structures and the deepest physical structures are very closely related.
Through a strange coincidence I received the following quote from Aldous Huxley in the mail yesterday:
Where beauty is worshipped for beauty’s sake as a goddess, independent of and superior to morality and philosophy, the most horrible putrefaction is apt to set in. The lives of the aesthetes are the far from edifying commentary on the religion of beauty.
Peter writes:
The mathematics/physics relationship is a very deep question, and I don’t think we know enough about either subject to yet know precisely what the relation is. My own inclinations are kind of hyper-Platonist, thinking that ultimately we will see that the deepest mathematical structures and the deepest physical structures are very closely related.
It’s interesting how your post about Lawrence Krauss’ book provoked this almost totally irrelevant discussion about whether mathematics is a science, etcetera. I think there’s a lot of what the economists would call “pent-up demand” for better understanding the relationship between mathematics and science – it bursts out at inappropriate moments, like just now.
The problem of course is that in the standard modern picture, science is empirical, based on induction, and tends to favor a materialistic ontology, while mathematics is non-empirical, based on deduction, and tends to favor a Platonist/Pythagorean ontology… yet somehow they need each other!
So, mathematics is not only the queen and handmaiden of the sciences – it’s the secret mistress as well, a source of romantic fascination but also some embarrassment.
The hard-nosed physicist is supposed to treat mathematics as a mere “language”, but finds himself becoming fascinated by its “beauty”. He finds that the pursuit of beauty can lead to practical results that a merely pragmatic approach would never obtain – the “unreasonable effectiveness” of mathematics.
This is already puzzling enough, but the full story is even trickier: beauty – or at least our possibly mistaken notion of beauty – can seduce us and lead us astray! Is string theory beautiful and correct, beautiful and false, or actually ugly but pretending to be beautiful, like Cinderella’s elder sister, struggling to fit the glass slipper on her oversized foot?
It’s all so confusing. 🙂
A shorter answer: String theorists are sincerely interested in extending known and tested science. Intelligent design “theorists” are interested in undermining the public’s faith in known and tested science.
Natural supersymmetry has already been ruled out by experiment, AFAIU. If no sparticles are found at the LHC, slightly unnatural SUSY will be ruled out as well, leaving very unnatural (split or supersplit) SUSY as the only possibility.
SUSY has long been invoked as a solution to the hierarchy problem, i.e. why the weak scale 100 GeV is so small in units of the Planck mass. Although SUSY reduces this problem, recent experiments (in particular limits on the Higgs mass and permanent dipole moments) rule out the possibility that SUSY will solve it completely. This is usually expressed by the phrase “SUSY requires fine-tuning at the percent level”.
Let me add that this does not make me happy because I dislike SUSY. Rather, it’s the other way around: I dislike SUSY because it seems very much to disagree with experiments.
“A shorter answer: String theorists are sincerely interested in extending known and tested science”
tell that to one of lubos motl’s critics!
Well it seems to me that yes ST is religion, but its 11th century religion, not Baptist fundies.
-drl
If we were to take an Hegellian approach and consider the theory of evolution, the thesis, and the intelligent design theory, the antithesis, then perhaps we need to seek a synthesis of the two. If we turn to physics, we find that the atom, indeed, any atom, is almost a perfect vacuum, closer to perfect than outer space. All objects in our physical universe are made up from molecules, which are in turn consist of atoms. As atoms are vacuums, then molecules would be vacuums, then so too is the substance of our universe. So our physical universe is almost a perfect vacuum, an absence of matter. There is next to nothing there. Of course, I am not suggesting that the physical universe is an illusion, but rather that our perception of it is illusionary. The universe is one big Disneyland! And it is simply the coarseness of our senses, that makes us believe that the physical universe is substantial.
Our eyes respond to visible light, which is electro-magnetic radiation with wavelengths very much larger than the diameter of an atom and at the same time the frequency of these radiations is very much lower than the frequency of electron orbits forming the shell of the atom. This means that visible light will bounce off an atom rather than pass through it. Sound and touch involve much much larger wavelengths than visible light, so they too would tend to find a physical object impenetrable. On the otherhand, cosmic rays have a wavelength much smaller than the diameter of an atom, and scientists going down into deep mines have found that cosmic rays can penetrate thousands of metres into the Earth.
It is one’s minds which interprets his senses and passes it on to him, the inner self. The conscious, intelligent part of us. Oh dear! It would seem I’m making a case for intelligent design. Oops!
“Why is string theory science but intelligent design isn’t?� its not really the question, the question is “Why is standard model (hot Big Bang cosmology, etc) science but intelligent design isn’t?�
All these questions refer to metaphysical foundations of sciences and are actually the core of the so called demarcation problem (of Popper). There is no good answer to that. One can presumably DEFINE science so that the standard model is science and intelligent design is not, though it is not trivial at all (for example by using Popperian conjectures and refutations program). One can also presumably DEFINE science so that the string theory is science and intelligent design is still not. One can also try to device a demarcation line between sciences and religion, for example by assuming that there is no transcendental knowledge, see what is left and call it science. One can also take the Spinozian pantheistic stand, and assume that the physical universe is just god (I am simplifying things here, of course), and then intelligent design is nonsense, logically.
Of course, intelligent design is just fiddling with judeo-christian-muslim image of god: an old man who treats the physical universe as his playground. If you accept this I can hardly see how you could do science at all since causality does not work any more (or at least there are uncontrollable exceptions).
But whatever you do, this is a metaphysical exercise, and not a scientific one (ie. one cannot define science from within the science itself.) So the question “Why is string theory science but intelligent design isn’t?� is basically not even wrong
It is notoriously difficult to draw the Popperian demarcation line, but surely there is a fundamental difference between string theory and intelligent design. When embarking on a scientific research program, it is not always possible to tell from the start what falsifiable predictions or practical applications might emerge, and theoretical scientists have to go on well-formulated hunches and search for ways to corroborate their hypotheses; nonetheless, their efforts can still be called science. Intelligent design, however, is not science– not because it cannot be falsified, but because it cannot, even in principle, be corroborated either. How can an ID proponent move forward with his “research programâ€?? All he can do is attempt to expose places where evolution supposedly fails as an explanation… but this is not how science works. A scientist who spends his time trying to reveal gaps in loop quantum gravity is not doing string theory by default. Science doesn’t work in the negative—you have to try to corroborate claims of your own hypothesis, not simply attack the claims of others. And clearly ID has no means of corroborating their “hypothesisâ€? in a self-contained, positive manner. Of course, it may prove to be impossible to test string theory’s hypotheses directly, but actually this is where mathematics can step in and render string theory legit science. The power of mathematics is that it can reveal equivalences among physical statements that are in no way evident in science alone – and that’s because ‘science alone’ consists of physical interpretations we impose upon mathematical structures. These interpretations are limited by imagination and physical intuitions, but mathematics is not. AdS-CFT is a prime example, and if string theory’s structure can be shown to be equivalent to something we can better understand physically, and therefore test, its proponents’ efforts will not have been in vain. Surely there are many mathematically equivalent physical theories all expressing the same basic truths about nature, so it can’t hurt to pursue multiple lines and hope some clever scientists (or mathematicians) unveil their hidden relationships. On that note, I’m really curious to know if there have been any interesting developments in the search for a dS/CFT?
Prof. Motl’s review of the book on amazon.com says that superstring predicts fermions.
To me that is stretching the meaning of prediction to an extreme, but your mileage may vary.
One important distinction between intelligent design and string theory is that the former is trying to explain something that is already explained, while string theory is trying to solve a mystery. Intelligent design is useless because evolution is the right explanation for the origin of species. However, we don’t have a theory of quantum gravity. String theory may be wrong, or even untestable, but I think that we should have a lot of freedom to speculate when we are trying to solve an open problem.
The biggest threat to string theory isn’t experiment, it is somebody coming up with a straight forward way to quantize gravity without all of the extra dimensions, branes, etc. of string theory. The draw of string theory isn’t its strong scientific credentials, it is the weakness of any competition.
Gavin
A couple of replies
Woit
I think that you are almost right in your personal valuation. Almost all of string theorists have spent much time on string theory research. But this is not the true problem; the problem has been the premature publicly in mass media. String theory was presented as ‘fundamental’, as ‘the last theory’. This has generated a lot of hype around it. For example, it is usually thought by arrogant people that any guy working in string theory is a genius and any outsider is a ‘mo – – n’, etc. It is usually thought that any other theory is derived from string theory as a special case, etc. Of course, nothing of this is true.
I am rather sure that string theory community can be splinted into three parts:
– Workers. E.g. graduate students doing PhD because they did not find other area of research due to pressure of string physicists on research programs.
– Leaders. People who is a fanatic of the theory. For example Kaku, who has no problem in claiming, “Absence of aliens in the universe is a sign of that string theory may be correctâ€?. The basis for such one bizarre idea is that they used string theory for travelling, via a hidden dimension, to other universe!
– Rest.
I think that only ‘leaders’ will continue to work in the theory even if they is experimentally proved to be incorrect. In fact, there is a very good basis for this thinking: the own history of the field. String theory was always refuted by experiment, and each new experiment or internal contradiction did that string theorists developed a new version or reparameterised previous one –curiously are always called ‘string theory’-. There is a joke circulating in the Internet saying that if string theory is shown to be experimentally false like a theory of everything, the ‘leaders’ will explain that is due that string theory is really a theory of more than everything.
For anyone who do not know the history of the field, the joke is based in that when string theory failed in the nuclear regime and was substituted by QCD, string theorists as Schwartz claimed that the problem was that string theory was more that a theory of strong force and included also gravity and then began a new -more general- formulation. Curiously, that more general theory has not still explained the strong force like QCD has done during decades…
Regarding beautiful arguments, I simply want to say that beauty always was a subjective feature. I personally find all string theory research an ugly subject, with lot of irrelevant math and wrong physical stuff.
At least, some string theorists openly state that his belief on string theory is only that. James Gates recognizes “the analogy to a religion has been noted by a number of people. In a sense that’s right; it is kind of a church to which I belong. We have our own popes and House of Cardinals.�
Arun
It is not true that string theory was mathematics.
People working in string theory is doing mathematical research because some parts of string theory need of mathematics still do not developed. That is VERY different from claiming that string theory ‘is’ mathematics:
Mathematics is Calabi-Yau manifolds and G2s, topology, K-theory, etc.
Chemists and mathematicians working in molecular structure have developed some useful techniques on graph theory, but chemistry is not math not graph theory a branch of chemistry.
John Baez
I respect you opinion but I follow Newtonian philosophy. Math is an idealized construct for the description of the physical word. Feynman explaining between geometrical lines and light ‘lines’ was brilliant.
Your claim about that “mathematics is non-empirical� is being debated by own mathematicians. Have you heard about experimental mathematics?
Will be math sufficient? Any reply will be speculative. However, I begin to believe that for a ‘real’ understanding of world, math alone will be not sufficient. In my opinion, there is not a kind of marriage between math and physical world in the end. Math is a beautiful kind of simple intermediate language that contains many features of that we call physical world…
Probably the great failure of string theory is directly related that its main practitioners are people with mathematical-oriented minds… and therefore unable to really understand physical word. One only need the many paper on the subject.
We need is not another Witten in physics, we need a new Feynman 🙂
Juan R.
Center for CANONICAL |SCIENCE)
John wrote
“It’s interesting how your post about Lawrence Krauss’ book provoked this almost totally irrelevant discussion about whether mathematics is a science, etcetera. I think there’s a lot of what the economists would call “pent-up demandâ€? for better understanding the relationship between mathematics and science – it bursts out at inappropriate moments, like just now.
”
I guees this partly has to do with a somewhat naive application of Popper’s falsification method. Remember Popper wanted to distinguish between science and pseudo-science. Now we obvioulsy don’t want maths to be on the wrong side of the line, but a naive application of Popper runs precisely that risk. Has anyone checked what the great philosopher himself wrote about this? He was a clear thinker!
Commenting on John Baez comment:
Funny on how a science/religion argument closes in on the math/physics question, indeed! A recent paper by Hut, Alford and Tegmark dives fully into this puddle curiously without touching string theory! The target happens to be Penrose himself a thorough critic of String Theory along Peter’s lines, seems to me. What strikes me is the tone of the discussion which is entirely set in religious terms advocating a plurality of “mind sets” rather than any self-critical departure. How postmodern!
Something for your one of your “This Week’s” entries, John? I would be curious to know your opinion on this gem…
-Joao
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Peter, you say “topological strings and their relations to Gromov-Witten invariants and much else are definitely mathematics”, “dual to a strongly coupled gauge theory, are certainly physics” which is fine. Then you claim “But the 10d superstring compactified on a Calabi-Yau is a very complicated mathematical structure, one that doesn’t seem to have any special deep significance”.
This seems a contradiction to me, since all is the same.
GW invariants of topological strings are most interesting on CY, they do describe 4d strongly coupled gauge theory and in reverse most of the well studied 4d strongly coupled gauge theories are dual to (GW on) CY. Topological string on CY is nothing but a low energy sector of superstring on the same CY. So how can the same subject be relevant mathematics and physics and without significance at the same time.
Hi Ygorff,
There’s no question that you can get some interesting mathematics or physics to study by looking at certain limits or subsectors of superstring theory. The examples I gave are what seem to me the most interesting ones for mathematics and physics. But just because something has a very interesting low-energy limit doesn’t mean it is necessarily especially interesting itself. By now there’s a huge variety of different things that people have looked into motivated by superstring theory. They’re not “all the same”, even if they have the same motivation. People need to carefully see which things have led to good mathematics and physics, pursue those, and abandon those parts of superstring theory that haven’t led to good math or physics.
If you want to promote the idea of working on superstring theory because it has a topological subsector that gives interesting invariants of certain complex three-folds, or because it might give a useful string dual to QCD, that’s fine. But that’s not what people promoting this research are doing; they keep pushing the failed idea that the full 10d superstring theory will give a unified TOE. It is this idea that not only doesn’t work, but leads to ugliness like the landscape, not to anything particularly mathematically deep.
an interested observer said
…..That mathematics itself happens to be the best language to “doâ€? science in, is co-incidental and a consequence of the fact that (historically) SOME PARTS (calculus, say) of mathematics were invented to solve problems external to mathematics, and SOME PARTS (representation theory, say) of modern mathematics, besides being of great interest within mathematics, simply HAPPEN to describe the real world spectacularly well. — it’s a gross generalisation to say that all of mathematics is just a language to describe the real world. And yes, mathematics is not a science since, as defined above, it serves its own ends and does not attempt to describe how the “real worldâ€? works ….
The above statement is an absolutely ridiculous idea. Math CANNOT be invented, it can only be discovered. New math was always a result of a need for explanation of observable fenomena in reality.
Calculus was NOT “invented” by Newton, he actually disovered that Euclidian geometry was not adequate to describe his physical observations. That process continue to happen now too, whenever physics is not able to describe an observable phenomena with available mathematical tools, we are going to see attempts to find new, adequate tools.
To think the opposite one would have to admit that there is no difference between math and fiction writhing. The only reason that math is the best language for science is that math indeed describes the real world because mathematical descriptions of reality are representing real physical qualities of matter.
Try to use your “invention” process and create a new math to describe any already settled physical theory, lets say, Carnot cycle, and tell me what you come up with. If you say that math is “invention”, you should not have any difficulties to do so.
Peter, the point was, that if you compactify 10d string theory on 6d CY, you get a strongly coupled 4d gauge theory (very similar to QCD) and the internal part of the superstring in addition gives you the non-perturbative action, which you could hardly get from field theory.
A field theorist, who indeed would be strong enough to get the action from scratch, would necessarily reconstruct 6 extra dimensions in the form of a CY, whether she likes 10d strings or not. Even if she refuses to take these dimensions as physical, she would find that dynamical questions in the gauge theory have a mathematical structure that describes certain dynamics of strings on the internal 6d dimensions.
Whether or not you take the internal space and these strings on it as physical, this structure of 4d x 6d CY emerging from gauge theory is rather simple and efficient and this seems at odds with attributes like “complicated” and “without deep significance”, at least for me.
As for coupling to gravity, the very same argument also gives you the coupling of gravity to this field theory, by considering contributions from GW at higher genus. So the internal part of the 10d superstring is worth of a lot of interesting physics and mathematics.
Not too many string theorists would seriously claim that string theory as it is today is already the TOE of THIS universe, but most of them would agree on that unifying gauge theory and gravity is one of the main motiviations to study strings. The above example shows that the (pretty sketchy) ansatz of 10d superstrings on CY does already a surprisingly good job, a better job then any other known ansatz. A lot of work and ideas will be necessary to apply strings to this universe, but there is no reason whatever to worry about anything else but the reach of human brain power. So far things work surprisingly well and I don’t see why you say the idea is “failed” or “doesn’t work”.
I think it is a reasonably well-defined question mathematically to ask what a quantum theory of extended objects would look like, and a reasonably well-defined mathematical answer is it would look like string theory. Hence string theory is at least mathematics.
Does such a theory have any physical relevance is the question, and the answer is, yes, it does, except perhaps not as much as the most rabid hypemeisters of theory proclaim.
Ygorff,
Sure, you can try and study various strongly coupled supersymmetric 4-d gauge theories by constructing string duals using 10d superstrings compactified on a CY. But this is a complicated business and in general these are complicated constructions of unclear mathematical signficance. The physical significance is that you’d like to solve QCD this way. This hasn’t yet happened. Maybe this will ultimately be the path to finding a string dual of QCD, maybe some very different idea using neither 10d superstrings nor CYs will be required.
Sorry, but to describe the current situation of attempts to unify the standard model and gravity using superstrings as “so far things work surprisingly well” is just absurd. We’re at 21 years of work by thousands of smart people and counting, without a single prediction of any kind, and the best guess as to where this all leads is the landscape framework which is horrifically ugly and can’t predict anything. By any reasonable accounting, this is an idea that has failed and doesn’t work.
Arun,
String theory is of course mathematics in the sense that it is a collection of mathematical formulas.
As for its physical relevance, it’s not just “rabid hypemeisters” who are claiming you can unify gravity and the standard model this way. If most string theorists have actually given up on this idea, I think they should say so.
God said to Abraham: Kill me a son
Abe said man: you must be puttin’ me on
Has theological debate progressed any more than has science?
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Excuse the typos on my earlier comment. (It was late at night) Anyway, a few more comments on this very interesting discussion.
John Baez The problem of course is that in the standard modern picture, science is empirical, based on induction, and tends to favor a materialistic ontology, while mathematics is non-empirical, based on deduction, and tends to favor a Platonist/Pythagorean ontology… yet somehow they need each other!
Is mathematical platonism still dominant? I know that the quasi-realism of folks like Putnam has intrigued a lot of people. But I thought that the logicists and the constructivists were now dominant. Of course that might be more among the philosophically well read. So I couldn’t even guess in the typical math department let alone physics department.
Woit My own inclinations are kind of hyper-Platonist, thinking that ultimately we will see that the deepest mathematical structures and the deepest physical structures are very closely related.
Doesn’t that verge upon being more of a religious belief? (Not that there is anything wrong with that – so long as it isn’t taught as science the way ID tries to portray itself) I just bring it up since it seems, as John Baez seems to suggest, that at this level where we’re so far removed from empiricism many things more religious or aesthetic seem to dominate. I think that’s true of ID and perhaps is an influence in some thinking about string theory.
“Blue Fog” The above statement is an absolutely ridiculous idea. Math CANNOT be invented, it can only be discovered.
That’s true only in some formulations of mathematics. Other formulations say it is all invented/constructed. To say that math can’t be invented is akin to saying a nuclear reactor can’t be invented, only discovered. Unless one is clear about how to distinguish invention from discovery in an unambiguous fashion, I’m not sure this approach is useful.
Hi Clark,
I don’t think that my views on math or physics have much to do with religion, although they do have something to do with aesthetics. That deep mathematics and deep ideas about physics are sometimes closely related is an empirical fact about the history of physics and math. My belief that there is more along these lines is just a working hypothesis about where to look for promising ideas. It is based both on extrapolating from past history and some very specific conjectures about the relation of math and physics that look compelling to me, although much work needs to be done to see if they really make sense.
Peter,
Certainly string theory is more than just a collection of mathematical formulas. It has led to one if not two Fields medals.
-Arun
Hi Peter,
Thought I’d contribute a “manual trackback entry” (since my blog software doesn’t support trackbacks):
http://www.scottaaronson.com/blog/2005/10/insert-string-pun-here.html
[…] In short, if the ID’ers are armed squatters in the apartment building of science, openly scorning the materialistic concept of rent, then the string theorists are model tenants who often drop by the landlord’s office to say good afternoon, and by the way, that check from 20 years ago should clear any day. (In their defense, the other tenants’ checks haven’t cleared either.) To me, this raises an interesting question: does science need a notion of “resource-bounded falsifiability,” which is to Popper’s original notion as complexity is to computability?
Hi Scott,
Thanks. I just saw your blog posting and was about to link to it from here but you beat me to it. I love your analogy of science as apartment building and scientific predictions as rent.
Interesting to hear that Frederik Denef has been consulting with you on Landscape/computational complexity issues.
Blue fog said:
“Try to use your “inventionâ€? process and create a new math to describe any already settled physical theory, lets say, Carnot cycle, and tell me what you come up with. If you say that math is “inventionâ€?, you should not have any difficulties to do so. ”
Hey you make invention sound so easy and trivial. Let me ask you have you ever patented anything at all during your lifetime? I bet you have not applied patent for even one damn little silly invention, all your intelligence notwithstanding.
Mathematics is a language, invented and developed over thousands of years by the whole of human intelligence. It is a great invention so please do NOT trivialize it by challenge any individual to come up with an invention that is in par. We saw great civilizations in human history that built great palaces and cultivated plantations, but failed to develope modern science because they have not invented the necessary language to describe science.
Peter wonders how mathematics and physics are so close in describing nature. Maybe you should also wonder why English and French, two completely different language, happen to describe exactly the same thing in the reality world? The languages, whether it is English or mathematics, are invented to describe the world we observe. So they have got to be closedly related to nature.
Besides, mathematicians who study fields that more or less has some association with the reality world have a better chance of getting support and being able to forward the study, versus stuff that sounds totally silly and totally detached from reality. I predict that all the mathematics tools that folks developed in super string theory research will pretty soon be completely forgotten, once it’s been shown it has no resemblance to the reality world.
Quantoken
ARUN: Yeah, but none of those Fields Medals have been related to the way string theory uses Calabi-Yau manifolds. CY manifolds are nice spaces, but they don’t seem to be of fundamental significance in mathematics. It doesn’t bother me that the Standard Model makes use of an object as random as SU(3)xSU(2)xU(1), but string theory purports to be fundamental. It’s aesthetically disappointing it seems to require an arbitrary choice of Calabi-Yau manifold.
ygorff’s point is very strong, and I might add, some people are strong enough to get the internal dimensions and their geometry from purely field theoretical considerations. Namely, Seiberg and Witten have shown that in their exact solution of d=4, N=2 SQCD a rather mysterious curve appeared, the period matrix of which described the effective couplings of the gauge theory. Soon it was realized that this curve is precisely the internal manifold on which you need to compactify string theory if you want to realize this SQCD theory on branes.
I’m kind of surprised Peter doesn’t understand this point. So far I thought he was a hard boiled skeptic of the relevance of string theory to nature, but distinguished from pure crackpots by his realization that string theory does lead to highly non-trivial and useful results for a lot of semi- or non-realistic models — such as N=2 SQCD. Now it seems that Peter has given up his last piece of wisdom. I will not go as far as Lubos who labels him an “empty head”, but…
The comments on this post haven’t said all that much about Intelligent Design, despite its mention in the post’s title. I thought I would add this modest contribution (with thanks to William Saletan of Slate, and Monty Python).
Dan,
I think I’ve written that string theory is useful for studying supersymmetric gauge theories and and is a promising approach to understanding QCD several times already in this posting and somewhere between 10^2 and 10^3 times on this weblog.
There’s some sort of weird and very specific disease that afflicts string theorists who read the words I write. Anything critical I write about string theory they interpret as meaning that I am not aware of the achievements of string theory methods in dealing with 4d supersymmetric gauge theories. This is really tedious. They also especially like to do this from behind the cover of anonymity.
Your notion that I used to understand this, but don’t anymore, at least has the charm of novelty.
John Baez:The problem of course is that in the standard modern picture, science is empirical, based on induction, and tends to favor a materialistic ontology, while mathematics is non-empirical, based on deduction, and tends to favor a Platonist/Pythagorean ontology… yet somehow they need each other!
This is a very interesting comment to me. No, not because of my name :), but because it really defines the process, doesn’t it?
Putting ID aside, isn’t this what would make string theory suitable?
If such inductive and deductive processes are indeed followed, as in any other model that you chose to use, furthers insight and development are indicative of advancement, in physics and mathematics?
I think this has already been pointed out, that modest gains may have some value in string theory as a model.
Hi Peter,
I’m afraid you don’t get off the hook so easily. You said:
“Sure, you can try and study various strongly coupled supersymmetric 4-d gauge theories by constructing string duals using 10d superstrings compactified on a CY. But this is a complicated business and in general these are complicated constructions of unclear mathematical signficance. The physical significance is that you’d like to solve QCD this way.”
This is plain wrong in the case of N>=2 SUSY. In particular, the meaning of the Calabi-Yau is *physically* clear from the *field theory* perspective. Your lip service that you understand the significance of string theory to gauge theories is contradicted by your own statements. It’s not a matter how many times you claim you understood…
John Baez said:
I am not sure if you agree with this “modern picture”, but here is a quote from the book Complex Manifolds and Deformation of Complex Structures by Kunihiko Kodaira that I find interesting in relation to the “induction/deduction” issue:
I have the feeling that this was not an isolated incidence in the history of mathematics, but that inductive/experimental approaches in mathematics are alive and well. I also remember reading strongly worded statements by V. I. Arnold on this issue (which I can try to dig up).