Lubos Motl
Sep24-04, 03:29 PM
<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no, location=no,scrollbars=yes,resizable=yes,status=no ,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>On Fri, 24 Sep 2004 rof@maths.tcd.ie wrote:\n\n> Quite right. In fact, there\'s a quantitative way to see how good a theory\n> is. Take the amount of information (measured in bits, or digits if you\n> prefer) required to specify the theory (and any auxiliary parameters,\n> for example, a point in the landscape) and compare this to the\n> amount of information correctly predicted by the theory. If the\n> former is not smaller than the latter, then the theory has failed\n> to compress the observed data, and should be discarded.\n\nIncidentally, I agree that this counting or a very related one - including\nthe bits, to make it quantitative - is a good criterion to judge the\npredictive success of a theory! Of course, a good theory predicts\neverything in the Standard Model, which are terabytes of information\n(results) recorded not only at Tevatron. ;-) We must refine your criterion\nin such a way that we are not multiply-counting the same or very related\nsuccessful predictions, which is of course subtle. This decision requires\nus to know which experiments are just minor copies of some previous\nexperiments, and which ones have the potential to give completely new\ndata. We need to be smart in order to make such decisions, and these\ndecisions will still depend on our models.\n\nIf we really exclude all theories that have no chance to describe these\nterabytes - for example loop quantum gravity - then I agree with your\ncounting, assuming that an appropriate compression of the information is\nmade.\n\nIf something reproduces the Standard Model, it only has 19 parameters\n(plus 10 for neutrino masses), and we only want to count the information\nabout these parameters as the "output" of your theory. Incidentally, if\nyou measure the 29 parameters of the nu-Standard Model with precision of\n11 digits per each parameter, then you get over 300 decimal digits of\ninformation from the experiment - which means that even among 10^{300} of\ndiscrete vacua, it is unlikely that one of the will work exactly, and if\nit would, it would be a highly impressive, unlikely prediction. (And I\nhave not included the extra bits that describe the "discrete" properties\nof the Standard Model, like the number of generations and the gauge\ngroups and representations.)\n\nWhat I want to emphasize is that in theories with potentially infinite\naccuracy, a discrete choice of the vacua - even if it is one vacuum from a\nfamily of 10^{320} sibblings - is still much much smaller fine-tuning than\nthe fine-tuning of new continuous parameters, especially if the number of\nsuch continuous parameters is infinite (like in nonrenormalizable\ntheories or loop quantum gravity coupled to general matter). When the\ntheory of everything is found, time will be playing for us - the\nquantitative predictive power will increase as the accuracy of the\nexperiments gets better.\n\nOn the other hand, I agree that this is not a dogma - that discrete\nchoices are always more acceptable - and the border that decides whether\ndiscrete or continuous parameters are more acceptable in a predictive\ntheory is determined by the accuracy of the predictions that a given\ntheory can offer. If the accuracy is rough and bad, there is not much\ndifference between continuous parameters and discrete choices from a large\nensemble. As the accuracy increases, the new continuous parameters become\nmuch worse for predictivity.\n\nI am still nearly sure that in this counting, string theory is the most\npredictive theory of fundamental physics we have.\n___________________________________________ ___________________________________\nE-mail: lumo@matfyz.cz fax: +1-617/496-0110 Web: http://lumo.matfyz.cz/\neFax: +1-801/454-1858 work: +1-617/384-9488 home: +1-617/868-4487 (call)\n^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^\n\n\n\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form"> View this Usenet post in original ASCII form </a></div><P></jabberwocky>On Fri, 24 Sep 2004 rof@maths.tcd.ie wrote:
> Quite right. In fact, there's a quantitative way to see how good a theory
> is. Take the amount of information (measured in bits, or digits if you
> prefer) required to specify the theory (and any auxiliary parameters,
> for example, a point in the landscape) and compare this to the
> amount of information correctly predicted by the theory. If the
> former is not smaller than the latter, then the theory has failed
> to compress the observed data, and should be discarded.
Incidentally, I agree that this counting or a very related one - including
the bits, to make it quantitative - is a good criterion to judge the
predictive success of a theory! Of course, a good theory predicts
everything in the Standard Model, which are terabytes of information
(results) recorded not only at Tevatron. ;-) We must refine your criterion
in such a way that we are not multiply-counting the same or very related
successful predictions, which is of course subtle. This decision requires
us to know which experiments are just minor copies of some previous
experiments, and which ones have the potential to give completely new
data. We need to be smart in order to make such decisions, and these
decisions will still depend on our models.
If we really exclude all theories that have no chance to describe these
terabytes - for example loop quantum gravity - then I agree with your
counting, assuming that an appropriate compression of the information is
made.
If something reproduces the Standard Model, it only has 19 parameters
(plus 10 for neutrino masses), and we only want to count the information
about these parameters as the "output" of your theory. Incidentally, if
you measure the 29 parameters of the \nu-Standard Model with precision of
11 digits per each parameter, then you get over 300 decimal digits of
information from the experiment - which means that even among 10^{300} of
discrete vacua, it is unlikely that one of the will work exactly, and if
it would, it would be a highly impressive, unlikely prediction. (And I
have not included the extra bits that describe the "discrete" properties
of the Standard Model, like the number of generations and the gauge
groups and representations.)
What I want to emphasize is that in theories with potentially infinite
accuracy, a discrete choice of the vacua - even if it is one vacuum from a
family of 10^{320} sibblings - is still much much smaller fine-tuning than
the fine-tuning of new continuous parameters, especially if the number of
such continuous parameters is infinite (like in nonrenormalizable
theories or loop quantum gravity coupled to general matter). When the
theory of everything is found, time will be playing for us - the
quantitative predictive power will increase as the accuracy of the
experiments gets better.
On the other hand, I agree that this is not a dogma - that discrete
choices are always more acceptable - and the border that decides whether
discrete or continuous parameters are more acceptable in a predictive
theory is determined by the accuracy of the predictions that a given
theory can offer. If the accuracy is rough and bad, there is not much
difference between continuous parameters and discrete choices from a large
ensemble. As the accuracy increases, the new continuous parameters become
much worse for predictivity.
I am still nearly sure that in this counting, string theory is the most
predictive theory of fundamental physics we have.
__{_______________________________________________ _____________________________}
E-mail: lumo@matfyz.cz fax: +1-617/496-0110 Web: http://lumo.matfyz.cz/
eFax: +1-801/454-1858 work: +1-617/384-9488 home: +1-617/868-4487 (call)
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ ^^^^^^^^^^^^^^^^^^^^^^^^^^^^
> Quite right. In fact, there's a quantitative way to see how good a theory
> is. Take the amount of information (measured in bits, or digits if you
> prefer) required to specify the theory (and any auxiliary parameters,
> for example, a point in the landscape) and compare this to the
> amount of information correctly predicted by the theory. If the
> former is not smaller than the latter, then the theory has failed
> to compress the observed data, and should be discarded.
Incidentally, I agree that this counting or a very related one - including
the bits, to make it quantitative - is a good criterion to judge the
predictive success of a theory! Of course, a good theory predicts
everything in the Standard Model, which are terabytes of information
(results) recorded not only at Tevatron. ;-) We must refine your criterion
in such a way that we are not multiply-counting the same or very related
successful predictions, which is of course subtle. This decision requires
us to know which experiments are just minor copies of some previous
experiments, and which ones have the potential to give completely new
data. We need to be smart in order to make such decisions, and these
decisions will still depend on our models.
If we really exclude all theories that have no chance to describe these
terabytes - for example loop quantum gravity - then I agree with your
counting, assuming that an appropriate compression of the information is
made.
If something reproduces the Standard Model, it only has 19 parameters
(plus 10 for neutrino masses), and we only want to count the information
about these parameters as the "output" of your theory. Incidentally, if
you measure the 29 parameters of the \nu-Standard Model with precision of
11 digits per each parameter, then you get over 300 decimal digits of
information from the experiment - which means that even among 10^{300} of
discrete vacua, it is unlikely that one of the will work exactly, and if
it would, it would be a highly impressive, unlikely prediction. (And I
have not included the extra bits that describe the "discrete" properties
of the Standard Model, like the number of generations and the gauge
groups and representations.)
What I want to emphasize is that in theories with potentially infinite
accuracy, a discrete choice of the vacua - even if it is one vacuum from a
family of 10^{320} sibblings - is still much much smaller fine-tuning than
the fine-tuning of new continuous parameters, especially if the number of
such continuous parameters is infinite (like in nonrenormalizable
theories or loop quantum gravity coupled to general matter). When the
theory of everything is found, time will be playing for us - the
quantitative predictive power will increase as the accuracy of the
experiments gets better.
On the other hand, I agree that this is not a dogma - that discrete
choices are always more acceptable - and the border that decides whether
discrete or continuous parameters are more acceptable in a predictive
theory is determined by the accuracy of the predictions that a given
theory can offer. If the accuracy is rough and bad, there is not much
difference between continuous parameters and discrete choices from a large
ensemble. As the accuracy increases, the new continuous parameters become
much worse for predictivity.
I am still nearly sure that in this counting, string theory is the most
predictive theory of fundamental physics we have.
__{_______________________________________________ _____________________________}
E-mail: lumo@matfyz.cz fax: +1-617/496-0110 Web: http://lumo.matfyz.cz/
eFax: +1-801/454-1858 work: +1-617/384-9488 home: +1-617/868-4487 (call)
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ ^^^^^^^^^^^^^^^^^^^^^^^^^^^^