
From:  Michel Lavaud 
Subject:  Re: [Axiomdeveloper] Re: AMS Notices: Open Source Mathematical Software 
Date:  Tue, 27 Nov 2007 11:47:20 +0100 
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If the plane I'm flying is built based on simulations with commercial mathematical software tools, whose accuracy is guaranteed in the usual way, i.e. no guarantee at all except refund for the price of the software whatever consequences and it is forbidden to get the source code to check if it is correct  then I will for sure take the next plane, if it has been built with free Open Source software :)If the plane I'm flying is built based on simulations with commercial mathematical software tools, I surely want them to be the best.
One ought not to forget that some big catastrophes were the direct consequences of minute software errors, several in rocket launchers (including crash of ArianeV), a complete oil research platform that sunk into the sea, etc. and probably many others that were not detected because they used commercial (closed source) software so that nobody was able to detect a posteriori the origin of the catastrophe ("Pas vu, pas pris"  not seen, not caught)
I think that those who accept the use of commercial software in scientific work, are bringing science 200 years backward, at the time when mathematicians were not too fond of rigorous proofs, and where Fermat (for example) could present an intuition of a result as a "theorem". If computers had existed at that time, we would have had maybe a "Fermat Software Corporation" that would have sold a software implementing instances of Fermat theorem, and all the research in connected fields that has been done to prove Fermat's theorem in the last 200 years would never have been done and no more results discovered, because a real, complete proof would not be considered as a new result : indeed, if one accepts commercial software in scientific work, the logical answer to the submission of a complete proof of the underlying theorem is that "the result is already known since it is included in the Fermat software", and thus the complete, rogorous proof cannot be published in a scientific journal as a research result, since it is not considered as a new one. The same kind of argument coul be extended to the 4 color conjecture, the Poincare conjecture, etc. In the latter case, instead of providing a Fields medal to Perelman for the definitive proof, he would have get the answer " Hey you stupid, it's already known for 100 years !"
Suppose a scientist sends to a referee a theorem with no proof for a lemma ; if the referee asks for the proof and the scientist answers "well no, I will not give you the proof and if you try to find it, I will sue you because somebody could steal my result that is worth one million of dollars" then what ought to be the answer of the referee ? "Sorry sir, no proof, no publication" ? Or "Oh, yes you are right, if it is worth so many bucks, I cannot decently ask you to unveil your proof and compromise the selling of your result to a software corporation, and maybe endanger employments in it". ?
Personnally, I think the only valid, scientific way is the first one : any work proposed for publication that uses commercial software ought to be rejected by the referee, unless it says explicitly and honestly that it used commercial, nonprovable software, so that another researcher can then improve on the article later, and publish another article using a completely Open Source software and provide a complete, rigorous, verifiable proof..
In my opinion, the real and only problem with funding Open Source software like Axiom (and Maxima, Lyx, TeXmacs etc. and all other OS software useful for scientific work) lies in the scientific community itself : many scientists are not willing to accept the preceding argument (reject articles that use commercial software except if explicitly saying so), because either they are unaware of the problem, or more often they blind themselves with the argument "I am not a computer scientist, it's not my job, so I just ask money to buy the software I need and I use the result", forgetting voluntarily that the cure to their incompetence in the subject is trivial : ask the collaboration of a computer scientist whose it is the job. The reason for this selfblinding lies (in my opinion) in the pressure for publishing the most possible (to increase fundings), that replaces more and more often the usual pressure for publishing the most rigorous results possible that used to be the norm in the refereeing system, and which is de facto loosening more and more by the acceptance of unproved results originating from commercial software. In short : if you publish with only your name, your publication index is higher than if you publish in collaboration with a computer scientist.
This trend is especially common among experimental scientists, for two reasons : first, they have lot of money so they can buy very expensive software, and second, there is an inherent uncertainty in experimental results, so they translate their tolerance to errors in experimental results toward tolerance to possible errors in commercial software, without realizing (or wanting to realize) that errors in experiment and software are of a complete different nature : error in an experimental measure is unavoidable and inherent to experimental work, while error in a software is completely avoidable since it is pure mathematics, expressed in a computer language instead of plain English.
The fact that the scientific community itself is responsible for the globally decreasing rigor in scientific articles, related to the use of commercial software, is well illustrated by remarks of somebody on this list (was it William Stein ?) who explained that NSF do not fund software that could compete with commercial software. The reviewers of NSF, who decide this policy, are scientists like us, but they are either blinded or bound by the ideology propagated by Friedmanian economists, that tells us that scientists must go closer and closer to enterprises to help them make more money. I think that, instead of listening to Milton Friedman (whose theories have proved to be excellent for wealthy people but catastrophic for others), they ought to go back to Adam Smith. One of his most famous phrases is that "it is not from the benevolence of the butcher, the brewer or the baker that we expect our dinner, but from their regard to their own interest". So, by applying this principle to the subset of scientists and entrepreneurs, we get : "it is not from the benevolence of the scientists that the entrepreneurs ought to expect their dinner, but from their regard to their own interest". In other terms, the best way, according to Adam Smith, for entrepreneurs to create new products is not to force scientists to imagine new products of a type predefined by the entrepreneur, but to let them do what interests them, and then look among the whole set of results obtained and pick those that can most readily be used to create new products.
And for products that incorporate software or use software to produce them (like planes :) the Adam Smith point of view is that the most profitable way for entrepreneurs to build planes is to let scientists study them  and in particular make software  in their own way. And their own way for software is Open Source as explained above, except if one prefers to jump backward 200 years..
Best wishes, Michel
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