February 2012 - mathfun@mailman.xmission.com

[math-fun] My intro/bio
by Spiked Math 13 Feb '12

13 Feb '12

Hi all, I recently joined this list (yesterday) and it was suggested I introduce myself. My name is Mike and I am currently a postdoc in Calgary. My interests range from combinatorics, graph theory, matrix theory/linear algebra, Markov chains, optimization, recreational mathematics, applications in chemistry, biology, geoscience, etc. One of my hobbies is publishing a (slightly lame) math comic, called Spiked Math, hence my email address. A few people seem entertained by it, so I try to update regularly. I'm always open for suggestions and ideas if you happen to have any (and I glady give credit where credit is due)! All the best, Mike

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Re: [math-fun] Black, Scholes, and why the "Nobel prize in Economics" is a bad idea
by Steve Witham 13 Feb '12

13 Feb '12

>From: Warren Smith <warren.wds(a)gmail.com> > >Now normally, a scientific theory that is often off by a factor of >10^10000 would not be considered >ultra good and worthy of a Nobel prize. But this is economics, where >the scientific standards >are a little different. Huh, I was just reading about that... "On the one hand the still recent establishment of the Nobel Memorial Prize in Economic Science marks a significant step in the process by which, in the opinion of the general public, economics has been conceded some of the dignity and prestige of the physical sciences. On the other hand, the economists are at this moment called upon to say how to extricate the free world from the serious threat of accelerating inflation which, it must be admitted, has been brought about by policies which the majority of economists recommended and even urged governments to pursue. We have indeed at the moment little cause for pride: as a profession we have made a mess of things." ... "But the effects on policy of the more ambitious constructions have not been very fortunate and I confess that I prefer true but imperfect knowledge, even if it leaves much indetermined and unpredictable, to a pretence of exact knowledge that is likely to be false. " ... "Yet the confidence in the unlimited power of science is only too often based on a false belief that the scientific method consists in the application of a ready-made technique, or in imitating the form rather than the substance of scientific procedure, as if one needed only to follow some cooking recipes to solve all social problems. It sometimes almost seems as if the techniques of science were more easily learnt than the thinking that shows us what the problems are and how to approach them." "The Pretence of Knowledge," Fredrick Hayek's 1974 Nobel Prize Lecture http://www.nobelprize.org/nobel_prizes/economics/laureates/1974/hayek-lectu… As in many fields, not all of economics, only 95%, is crap. --Steve

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Re: [math-fun] software eutrophication [was: math-fun] about pdf readers
by Bill Gosper 13 Feb '12

13 Feb '12

es> So, Bill, have you had any better luck with Macsyma, or some other symbolic software? -- Gene I'm *constantly* pasting back and forth between virtual XP Macsyma and Mma. (My PeeSee with Derive and an ancient Maple has died.) PC Macsyma 2.4 was compiled in NT on an i286 in another century. Besides microcephaly, the underlying Lisp has a storage leak. And there are other serious bugs and deficiencies. Howard Cannon has fixed some of these in 2.5, which he is not allowed to give me. Mathematica, apart from the Sum braindamage, has amassed awesome functionality and capacity. E.g., factoring that EDS[314] polynomial of degree 6163 with 1090 digit coefficients. An unreleased version with even greater numeric capacity has smashed the pi continued fraction record. WRI clearly still has things under control. I can only hope they will soon recognize the Sum situation as untenable. --rwg

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[math-fun] software eutrophication [was: math-fun] about pdf readers
by Bill Gosper 13 Feb '12

13 Feb '12

RobM> The reason we lose more performance than Moore's law gives back is because there are so many programmers (undeserving of the title "software engineers") who would rather use some huge, unoptimal software package or library than spending days, weeks or even years learning how to do it efficiently. (Market forces play a role too :-) Something like this describes Mathematica's misbegotten and hopelessly overloaded Sum facility, which grows slower with each version. It just took 9 minutes to do absolutely nothing with one of those Lambert identities I sent. Trying a trivial simplification like shift or rename the summation index takes many more minutes. Julian, Corey and I wasted most of yesterday trying to work around this, which is pretty much of a showstopper for porting my path invariance stuff to Mma. We tried hiding HoldForms everywhere, inserting undefined functions, faked summation operators,... but nothing was much good for actually manipulating Sums Just now I made a function which, if wrapped around a transformation of a Sum, reduces the time from many minutes to many seconds. But it happens inside the Sum, and doesn't help you extract summand factors which are independent of the index, e.g. Of all the insane things Mma must be trying in those 9 minutes, why not this actually useful one? Hillclimbing for performance workarounds is made difficult by Sum attempting to ameliorate the delays by caching results. Which ClearSystemCache doesn't clear! The whole design of Sum appears based on the assumption that the very last thing in the world I want from typing Sum is a sum. I would *much* rather have several screenloads of HypergeometricPFQRegularizeds, or just give up and get $Aborted. Sum even offers 6*22 strategy X method combinations with which to destroy my sum. Unfortunately, the default is Automatic, and there is no Method->None ! (And if there were, it would ruin the typesetting.) This too is neither math nor fun. --rwg Perhaps the problem is ossified project leadership.

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[math-fun] triangle dissection puzzle
by Bill Gosper 13 Feb '12

13 Feb '12

In how many ways can a right isosceles triangle be dissected into seven acute isosceles triangles? And eight? --rwg

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Re: [math-fun] yet another triangle dissection puzzle
by Dan Asimov 13 Feb '12

13 Feb '12

Veit -- Can the word "just" be omitted without changing the meaning here, or is it in some way limiting the number of mirror-symmetric pieces that such a triangle can be dissected into? Thanks, Dan Veit asked: << Which triangles can be dissected into just two mirror-symmetric pieces? ________________________________________________________________________________________ It goes without saying that .

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[math-fun] Black, Scholes, and why the "Nobel prize in Economics" is a bad idea
by Warren Smith 12 Feb '12

12 Feb '12

The main problem with Black & Scholes was that, in the case of Long Term Capital Management, they assumed the probabilities of failure of Russian investment A, was independent of any other B. But actually, every Russian investment in the universe got simultaneously affected by one common reason. Oops. So even an unlikelihood 10^(-10000) was of course actually quite likely. (And nonGaussianity also can matter, but not as much.) Now normally, a scientific theory that is often off by a factor of 10^10000 would not be considered ultra good and worthy of a Nobel prize. But this is economics, where the scientific standards are a little different. You might defend Black & Scholes by saying their theory did not need to assume Gaussianity or anything, it can be defined in a wholy general probabilistic setting. However, Myron Scholes was a major player in and paid a gazillion dollars by LTCM to be their brain trust so everybody could know that LTCM was a great company that had Nobel laureates working for them devising their plans. So evidently the independence assumption was endorsed by them. So then LTCM failed and got a huge bailout paid for by you and me, while Black & Scholes got off scot free with Nobel prizes in hand, and all the main LTCM players walked off with gazillions in your money. The whole system was of course not reformed at all. Now of course, you might normally think that after one of the most gigantic failures in history -- translated from money into lives this was equivalent to murdering thousands of people -- that Myron Scholes' name would be mud. But no: this is economics, so he's actually greatly lauded. Nobel himself, who had nothing whatever to do with and did not want there to be a "Nobel prize in economics," must be spinning in his grave. Now I contend that the direct cause of this disaster was the Nobel Prize. Had the so-called Nobel prize in economics been abolished, this disaster would have been averted. This prize has by a long shot caused far more damage to the world than good. Generally speaking what happens is, some idiot is awarded the Nobel, and then every word he utters is believed like the Word Of God from then on often by immensely powerful and wealthy entities. Actually said "idiot" might be pretty good in some ways, but in many other ways he is utterly unqualified and nevertheless the "word of God" effect ensues in all areas, including the ones he is unqualified in. This in turn causes entire areas of economics to be pretty much destroyed for no good reason. And basically, many of the Nobel prizes in economics were awarded for what, in other areas, would not be considered very impressive work. For example work by computer scientists on cryptographic money & voting protocols are far more impressive than anything that has ever won a Nobel in economics, but this work, even though economical, will never win an economics Nobel because its authors are not in the right clubs. -- Warren D. Smith http://RangeVoting.org <-- add your endorsement (by clicking "endorse" as 1st step)

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Re: [math-fun] Ian Stewart: The mathematical equation ...
by Axel Vogt 12 Feb '12

12 Feb '12

> Date: Sun, 12 Feb 2012 12:47:29 -0800 (GMT-08:00) > From: Dan Asimov<dasimov(a)earthlink.net> > Subject: Re: [math-fun] Ian Stewart: The mathematical equation ... > > I worked in high finance '87-'91 as a mathematician/analyst/programmer. > ...<snipped>... > > So it's hard for me to believe that Black-Scholes is responsible > for the recent recession/depression. > > My guess is that the repeal of Glass-Steagall in 1999 introduced > market instability that played a large role. One buzz word is CDS, credit default swaps. And their relatives, bundled.

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Re: [math-fun] Black, Scholes, and why the "Nobel prize in Economics" is a bad idea
by Dan Asimov 12 Feb '12

12 Feb '12

Regardless of one's opinion of the Nobel Peace Prize, this is illogical reasoning. (Maybe the intended word is hypocrisy rather than oxymoron?) In any case, Nobel invented dynamite, which is a lot less likely to explode accidentally than nitroglycerin, which is what killed his brother and motivated his invention. But my main point is that whatever led up to the creation of the Nobel Peace Prize is a separate issue from the merits of the prize itself. --Dan << . . . the Economics Nobel hasn't become the oxymoron that the "Nobel Peace Prize" has (Nobel invented weapons grade nitroglycerin). >> ________________________________________________________________________________________ It goes without saying that .

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Re: [math-fun] Ian Stewart: The mathematical equation ...
by Dan Asimov 12 Feb '12

12 Feb '12

I worked in high finance '87-'91 as a mathematician/analyst/programmer. Already by then it was widely known in the financial community that it was far superior to use distributions (of interest rates and volatility) estimated from actual data, rather than presuming they conformed to some specific parametric family of distributions, as does the original version of Black-Scholes. In those days, doing this right was extremely compute-intensive. But in this millennium it would be a piece of cake. So it's hard for me to believe that Black-Scholes is responsible for the recent recession/depression. My guess is that the repeal of Glass-Steagall in 1999 introduced market instability that played a large role. --Dan ________________________________________________________________________________________ It goes without saying that .

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