Re: Wolfram, meet Stefan and Boltzmann
- To: mathgroup at smc.vnet.net
- Subject: [mg117338] Re: Wolfram, meet Stefan and Boltzmann
- From: Roman <rschmied at gmail.com>
- Date: Tue, 15 Mar 2011 06:07:03 -0500 (EST)
- References: <ili6f5$kk2$1@smc.vnet.net> <ilksdj$6b2$1@smc.vnet.net>
AES,
mine is taking 18 seconds as well, and I have a MacBook as well. Maybe
a Mac hardware thing?
Model Name: MacBook
Model Identifier: MacBook5,1
Processor Name: Intel Core 2 Duo
Processor Speed: 2.4 GHz
Number Of Processors: 1
Total Number Of Cores: 2
L2 Cache: 3 MB
Memory: 4 GB
Bus Speed: 1.07 GHz
Boot ROM Version: MB51.007D.B03
SMC Version (system): 1.32f8
$Version: "7.0 for Mac OS X x86 (64-bit) (November 11, 2008)"
Roman
On Mar 14, 11:58 am, AES <sieg... at stanford.edu> wrote:
> Responses to all:
>
> Many of you will recognize that the integral in question
>
> Integrate[x^3/(Exp[x] - 1), {x, 0, Infinity}]
>
> arises in the derivation of the Stefan-Boltzmann constant.
>
> I was reviewing this derivation in Wikipedia. Wikipedia's analytical
> evaluation of the integral itself, given in an Appendix to the
> Stefan-Boltzmann article, takes a couple of screens of text and a dozen
> intermediate formulas, with excursions into contour integration and
> infinite series expansions.
>
> I became curious as to whether Mathematica could "just do" this integral
> so I opened Mathematica, typed in the line above, and evaluated it. I
> was surprised at how long it took the first time, although reevaluation
> of the same cell was essentially instantaneous.
>
> So I shut down Mathematica; re-Opened it; and repeated the evaluation
> using Timing[-]. Did this several times, and found that from a "cold
> start", that is, when I Quit and then re-Open Mathematica, it always
> takes 18 or 19 seconds to do the first evaluation.
>
> My Mac is a 2007 or 2007 vintage MacBook with hardware overview given
> below, running Snow Leopard in a generally vanilla setup (only about 60
> GB occupied on the 160 GB HD).
>
> So, I'm still a bit curious: What's Mathematica doing all that time? -=
-
> loading a lot of other stuff? actually going through some lengthy
> algorithm to evaluate the integral? ???
>
> Hardware Overview:
>
> Model Name: MacBook
> Model Identifier: MacBook2,1
> Processor Name: Intel Core 2 Duo
> Processor Speed: 2.16 GHz
> Number Of Processors: 1
> Total Number Of Cores: 2
> L2 Cache: 4 MB
> Memory: 1 GB
> Bus Speed: 667 MHz
> Boot ROM Version: MB21.00A5.B07
> SMC Version (system): 1.17f0