Saturday, October 25, 2008
So many String Theories, so Little Time
Why 10 to the 500th power is a small number.
NOTE - what follows is a very restricted argument about one aspect of one point made versus String Theory, the size of the possibilities it admits: 10 to the 500th power. I'm not competent to wander from that restricted topic here; although I include references to statements from those who are. My point may be so minor that everyone in effect assumes it, never bothering to state it, but the frequency and vigor with which the number 10500 pops up appears to belie this.
Suppose you are a prosecuting attorney. You believe you have the criminal. Unfortunately you need evidence, and so far the admissible evidence, including a blood type only restricts the perpetrator to one of 10 to the 500th power DNA combinations, isn't anything like sufficient. 10 to the 500th people is obviously greater than the earth's population, for starts. Even if only a few hundred million people are actually walking around with the right blood type, it would seem that you haven't made much progress on your case. If you need to go to court tomorrow, of course you ought to dismiss the case.
But let's say you can count on more than a year before this case shows up on the calendar. That's lots of time to get new evidence, and if even a little DNA shows up, then that will narrow the possibilities instantly, and at least logarithmically. There are so many DNA combinations that almost any substantive DNA result will be more unlikely than "merely" 10 to the 500th power. So, sure, right now, your evidence is consistent with too many possibilities. But one DNA discovery will blow nearly all, or all, of those possibilities away. Additionally, suppose you find 10 pieces of more ordinary evidence that are compatible with only one in a thousand of the suspects that haven't yet been ruled out by blood type. Barring codependent variables, that's 10,000 of your 500 zeros gone into the ether... in other words, this sort of evidence will eliminate possibilities logarithmically, also. In other words, for investigators contemplating possibilities, 10 to the 500th just isn't as large a number as it is for, say, the average price-sensitive shopper.
Just then your assistant says, "Hey, our LHC - the Large Heuristic Collator is supposed to start up this year! It data mines way more than our current databases. Just one or two discoveries there, could knock out nearly all of those other supposed suspects - or all of them, if we've got the wrong guy." Now things don't look so hopeless.
The Large Hadron Collider might do something similar to, or for, String Theorists; knocking out all but one of their models, or all of their models. According to Woit, just one unexpected new particle within the energy range of the LHC and String Theorists will be mighty short of zeros in that exponent, very quickly, since none of their possible theories will be compatible with such a particle. Still, it's not logically impossible (actually some sever critics say the theory is already inconsistent, I believe) that other LHC results, will narrow the window and do so in a way that remains consistent with M-theory and 10 to the 500th will be history, replaced by 1000, 100, or 1 (or zero). Woit demurs, at least in part, saying that in the case of the search for superpartners that they've already hedged their bets with the anthropic principle, and have an explanation at hand for every result.
Woit's claim of hedging brings up the real worry, it seems to me: which is whether 10 to the 500th in fact represents the last kludge, or the last epicycle. Is 10 to the 500th in truth just the tiniest tip of the iceberg of what malleable multi-dimensional math can be patched up to provide (pardon the aglomeration of alliteration, there), once string theorists are more motivated to expand their horizons?
If the latter, then what string theorists have been developing is "merely" a language in which some future theory could be expressed. Woit would then be correct to say that it's no more a theory than calculus, by itself, is a physical theory. Now, such research is not necessarily useless, by any means (although its application might turn out to be far removed from particle physics.) Developing a language in advance of need is, however, surely no reason to crimp anybody else's funding, much less everybody else's funding - particularly anybody trying to develop an actual theory, you know, with predictions and stuff. If Woit is right about the irrelevance of the LHC for string theorists (so long as the standard theory isn't equally embarrassed, I take it), then given the expense involved in creating collisions that are orders of power more energetic, perhaps a moratorium on spending in "language development" for at least a few decades is in order.
From my uninformed viewpoint, string theory might still be a winner. Someone knowing calculus before Liebnitz or Newton might have a hunch that it could describe planetary orbits and reasonably start groping around for a relationship or constant to plug in that might pop out some elliptical orbits. This may even be roughly what Newton and Hooke did, in fact. (According to Hooke) when a particular possibility for the attraction between masses (inverse square of distance) was mentioned to Newton by Hooke (who may have already proved the consistency of an inverse square law with circular orbits), Newton had in hand the mathematical language to prove that that specific relationship fit the elliptical evidence Kepler and Tycho had previously provided. Newton also claimed at the time that he had already previously proved this result for ellipses and an inverse square law: but his papers did not contain such a work or any notes concerning it, whereas a discussion between Christopher Wren, Robert Hooke and Edmond Halley about whether the inverse square law would produce elliptical orbits took place in 1684, two years before Newton published the Principia. The interesting possibility is that, whether or not he had anticipated Hooke, Newton's preeminence today may be a direct result of his spending considerable time researching the language with which future theories might be expressed, rather than trying to charge ahead to next discovery with the mathematical tools already developed, or pressing ahead with experiments not much different than those already published. If string theorists have done the same, that may not be all bad. Given the cost of each new generation of cyclotron, it may even be inevitable. During the nineteen twenties, Russian filmakers had no film. Year after year, they could only sit around and discuss what future films might be like, and the techniques they could employ - in other words, all that they could do was to invent the next language of film. As "Battleship Potemkin" showed, they succeeded wonderfully in this, and turned out not to be "useless eaters" [if the reader will pardon that Nazi-era phrase] after all.
Other places to peruse re this topic:
http://backreaction.blogspot.com/2006/08/lee-smolins-trouble-with-physics.html
'Theory of everything' tying researchers up in knots
Keay Davidson, Chronicle Science Writer
Monday, March 14, 2005
http://www.sfgate.com/cgi-bin/article.cgi?f=/c/a/2005/03/14/MNGRMBOURE1.DTL
Woit's blog:
http://www.math.columbia.edu/~woit/wordpress/
NOTE - what follows is a very restricted argument about one aspect of one point made versus String Theory, the size of the possibilities it admits: 10 to the 500th power. I'm not competent to wander from that restricted topic here; although I include references to statements from those who are. My point may be so minor that everyone in effect assumes it, never bothering to state it, but the frequency and vigor with which the number 10500 pops up appears to belie this.
Suppose you are a prosecuting attorney. You believe you have the criminal. Unfortunately you need evidence, and so far the admissible evidence, including a blood type only restricts the perpetrator to one of 10 to the 500th power DNA combinations, isn't anything like sufficient. 10 to the 500th people is obviously greater than the earth's population, for starts. Even if only a few hundred million people are actually walking around with the right blood type, it would seem that you haven't made much progress on your case. If you need to go to court tomorrow, of course you ought to dismiss the case.
But let's say you can count on more than a year before this case shows up on the calendar. That's lots of time to get new evidence, and if even a little DNA shows up, then that will narrow the possibilities instantly, and at least logarithmically. There are so many DNA combinations that almost any substantive DNA result will be more unlikely than "merely" 10 to the 500th power. So, sure, right now, your evidence is consistent with too many possibilities. But one DNA discovery will blow nearly all, or all, of those possibilities away. Additionally, suppose you find 10 pieces of more ordinary evidence that are compatible with only one in a thousand of the suspects that haven't yet been ruled out by blood type. Barring codependent variables, that's 10,000 of your 500 zeros gone into the ether... in other words, this sort of evidence will eliminate possibilities logarithmically, also. In other words, for investigators contemplating possibilities, 10 to the 500th just isn't as large a number as it is for, say, the average price-sensitive shopper.
Just then your assistant says, "Hey, our LHC - the Large Heuristic Collator is supposed to start up this year! It data mines way more than our current databases. Just one or two discoveries there, could knock out nearly all of those other supposed suspects - or all of them, if we've got the wrong guy." Now things don't look so hopeless.
The Large Hadron Collider might do something similar to, or for, String Theorists; knocking out all but one of their models, or all of their models. According to Woit, just one unexpected new particle within the energy range of the LHC and String Theorists will be mighty short of zeros in that exponent, very quickly, since none of their possible theories will be compatible with such a particle. Still, it's not logically impossible (actually some sever critics say the theory is already inconsistent, I believe) that other LHC results, will narrow the window and do so in a way that remains consistent with M-theory and 10 to the 500th will be history, replaced by 1000, 100, or 1 (or zero). Woit demurs, at least in part, saying that in the case of the search for superpartners that they've already hedged their bets with the anthropic principle, and have an explanation at hand for every result.
Woit's claim of hedging brings up the real worry, it seems to me: which is whether 10 to the 500th in fact represents the last kludge, or the last epicycle. Is 10 to the 500th in truth just the tiniest tip of the iceberg of what malleable multi-dimensional math can be patched up to provide (pardon the aglomeration of alliteration, there), once string theorists are more motivated to expand their horizons?
If the latter, then what string theorists have been developing is "merely" a language in which some future theory could be expressed. Woit would then be correct to say that it's no more a theory than calculus, by itself, is a physical theory. Now, such research is not necessarily useless, by any means (although its application might turn out to be far removed from particle physics.) Developing a language in advance of need is, however, surely no reason to crimp anybody else's funding, much less everybody else's funding - particularly anybody trying to develop an actual theory, you know, with predictions and stuff. If Woit is right about the irrelevance of the LHC for string theorists (so long as the standard theory isn't equally embarrassed, I take it), then given the expense involved in creating collisions that are orders of power more energetic, perhaps a moratorium on spending in "language development" for at least a few decades is in order.
From my uninformed viewpoint, string theory might still be a winner. Someone knowing calculus before Liebnitz or Newton might have a hunch that it could describe planetary orbits and reasonably start groping around for a relationship or constant to plug in that might pop out some elliptical orbits. This may even be roughly what Newton and Hooke did, in fact. (According to Hooke) when a particular possibility for the attraction between masses (inverse square of distance) was mentioned to Newton by Hooke (who may have already proved the consistency of an inverse square law with circular orbits), Newton had in hand the mathematical language to prove that that specific relationship fit the elliptical evidence Kepler and Tycho had previously provided. Newton also claimed at the time that he had already previously proved this result for ellipses and an inverse square law: but his papers did not contain such a work or any notes concerning it, whereas a discussion between Christopher Wren, Robert Hooke and Edmond Halley about whether the inverse square law would produce elliptical orbits took place in 1684, two years before Newton published the Principia. The interesting possibility is that, whether or not he had anticipated Hooke, Newton's preeminence today may be a direct result of his spending considerable time researching the language with which future theories might be expressed, rather than trying to charge ahead to next discovery with the mathematical tools already developed, or pressing ahead with experiments not much different than those already published. If string theorists have done the same, that may not be all bad. Given the cost of each new generation of cyclotron, it may even be inevitable. During the nineteen twenties, Russian filmakers had no film. Year after year, they could only sit around and discuss what future films might be like, and the techniques they could employ - in other words, all that they could do was to invent the next language of film. As "Battleship Potemkin" showed, they succeeded wonderfully in this, and turned out not to be "useless eaters" [if the reader will pardon that Nazi-era phrase] after all.
Other places to peruse re this topic:
http://backreaction.blogspot.com/2006/08/lee-smolins-trouble-with-physics.html
'Theory of everything' tying researchers up in knots
Keay Davidson, Chronicle Science Writer
Monday, March 14, 2005
http://www.sfgate.com/cgi-bin/article.cgi?f=/c/a/2005/03/14/MNGRMBOURE1.DTL
Woit's blog:
http://www.math.columbia.edu/~woit/wordpress/
