Re: [Axiom-developer] Re: AMS Notices: Open Source Mathematical Software

[Michel Lavaud]

> If the plane I'm flying is built based on simulations with commercial
> mathematical software tools, I surely want them to be the best.
>   
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 :-)

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, non-provable 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 self-blinding 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 pre-defined 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