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

From: William Stein
Subject: Re: [Axiom-developer] Re: AMS Notices: Open Source Mathematical Software
Date: Mon, 26 Nov 2007 12:14:47 -0800

On Nov 26, 2007 10:01 AM, root <address@hidden> wrote:
> ==> Ed Borasky writes:

> >> There is nothing particularly special about mathematics software that
> >> makes it winning in a similar sense impossible, as much as Wolfram
> >> would argue that (as he often used to do in interviews I've read online).
> >
> >I disagree. Mathematics software is the most difficult software to
> >write, and it's market is very limited. And *symbolic* mathematics
> >software / theorem proving are more difficult to write than numeric
> >software. I've never used Mathematica, and only briefly used Maple, so I
> >can't really compare either of them with Axiom in the same sense as I
> >compared OpenOffice with Microsoft Office, Firefox with Internet
> >Explorer, or the Linux desktop with the Windows desktop in the context
> >of a corporate workstation. But again, I'm guessing that people who can
> >cost-justify Mathematica or Maple will keep them in business and "winning."

Mathematical software is indeed difficult to write.  You're right --
what I hope to
accomplish with the Sage project is impossible.  I don't care; I'm going to do
it anyways.

> Clearly you've not studied your "Art of War" by Sun Tsu. :-)

Actually I have.   Evidently my interpretation of it is much different
than yours.

> A frontal attack against a strongly held point never wins.  You are
> trying a direct head-to-head competition against a well financed,
> heavily backed position. As Ed points out, even if you *could* match
> the 3Ms point for point in the usual checklist feature game there are
> still forces which make it difficult, if not impossible, for people to
> use your software. You plan to march onto the field of battle,
> confront the enemy strength-to-strengh, and win by force of arms.
> That's not strategic thinking, and clearly not a successful strategy.
> You let the enemy define your tactics.  That is, if MMA develops a new
> parallel matrix multiply (opening a new wing of the battle), you must
> turn to confront this and apply effort to develop a similar checklist
> point. Since they are larger, faster, and better financed it is
> unlikely that you can match them continuously on every point. Linux
> plays this game, and loses, on the desktop. That's not strategic
> thinking, and clearly not a successful strategy.
> You train recruits for your enemy. Because you fight the same battle
> on the same turf with the same tactics, the people you lose to industry
> are perfectly trained to compete against you. Thus the person who
> writes the great new prototype harmonic analysis software for his
> thesis (giving you a new checklist point nobody competes with), then
> this same person is perfect for the 3Ms to hire. In fact, the best use
> of his talent would be to develop a better version of his thesis work
> and add it as a new, better checklist feature point. Thus, you trained
> and financed your enemy. That's not strategic thinking, and clearly
> not a successful strategy.
> You give away your material freely to your enemy. Because you work in
> open source and you encourage publication of your work the enemy can
> see everything. But the publications are tiny (5 pages) and the thesis
> work is obscure so it will take much time to convert this into a
> useful "product". The 3Ms have the idea, the time, and the money.  You
> gave it all to them because you published the idea, trained the
> people, and bought 3M's software "for the department". That's not
> strategic thinking, and clearly not a successful strategy.
> You let the enemy use your own strength against you. What's to stop
> the 3Ms from becoming useable with the Sage front end?

Nothing.  In fact, one of the main features of the Sage front end
already is that it
can be used with the 4Ms (don't dismiss Magma, which belongs in
there -- it's very good quality commercial software).

>  How hard would
> it be for them to define "plug-ins" that either use the MMA workbook
> browser or the full Maple engine?

Trivial, since we already do that.

> If mathml allows one to transfer
> (content-free) equations from one system to another, cannot one of
> those systems be one of the 3Ms?


> Thus they gut your whole system.

No they don't.  Sage is GPL'd.  Any improvements or changes they make to Sage
must be given back.

> They can make the claim that they "work with Sage" which allows them
> to sell licenses to locations where you've "won". That's not strategic
> thinking, and clearly not a successful strategy.
> I don't know why you've chosen to benefit the enemy
> but I can't prevent it.

True, you can't.    But honestly I really don't see the 4M's as the
enemy.  They are four high quality
valuable tools for mathematical computation.  I love mathematics and
doing computation
in the context of mathematics, and at some level I really like using
any mathematical
software.  With Sage I want to provide a viable free open source
alternative, not put the
4M's out of business.  Software is not a zero sum game.    Especially
in research that
relies on computation -- trying to find the right conjecture -- it can
be quite valuable to compare
output produced by several different programs.

> I also would like to replace these commercial systems with open
> systems.  (Actually, I'd like to replace commerce with science.)
> However, my plan is to change the war so that the 3Ms cannot compete
> and their field of battle, which they strongly hold, is irrelevant. By
> redefining what the "best of breed" systems mean, and by defining them
> so that commercial systems cannot compete, the battle is won without a
> fight.
> Commercial systems cannot compete against a fully documented, literate
> system. They cannot compete in proving their software is correct if they
> cannot show the software. They cannot compete if there are standards
> that every system must meet in order to ensure that ANY system can be
> used that fulfills the standard.
> Clearly, systems that are fully documented, literate, proven, and
> standards-conforming are "best of breed". And they also happened to
> be "open" but that's just a required fact, not a feature.

Whether or not a system can compete is determined by what actual real
people really want and can afford when teaching or doing research.
It's not at all clear to me that actual research mathematicians, teachers
and engineers  want what you're describing above more than the
other options they will have available.  In fact, I think it highly unlikely.

> A frontal attack against a strongly held point never wins. But I don't
> plan to attack. I have redefined the fight so they can't compete.
> You let the enemy define your tactics. But I don't care about their
> tactics. I can't prevent short term wins. But battles do not decide
> the outcome of wars.
> You train recruits for your enemy. Training people to write fully
> literate papers that just drag-and-drop means that they are trained
> to publish everything which is a skill that the 3Ms can't use. By
> training them to use, modify, and enhance each other's work and build
> on prior science the 3Ms have to worry about huge legal issues whereas
> you can just ask me for permission to use (or collaborate with me) on
> a new "release" of my literate paper and algorithm.
> You give away your material freely to your enemy. But of what use is
> conforming to a standard that allows any system to replace any other?
> This cannot benefit the 3Ms. And what use is a proof since they cannot
> SHOW the code necessary to support the proof? And what use is a thesis
> that can be "drag-and-dropped" onto an open system? It already works
> and can be quickly enhanced whereas the 3Ms need to rewrite it.
> You let the enemy use your own strength against you. The Axiom front
> end is the same as the Axiom back end. It's all "of a piece" so that
> viewing the documentation and the code are all a single thing. When
> you read the documentation like a book (ala Knuth or Queinnec) you
> learn the whole system. The 3Ms cannot do this. And Axiom equations
> need to carry the type because that's where the meaning is. Thus
> mathml isn't a reasonable transfer mechanism and cannot be trojaned.
> I could go on but Tsu's book is small, cheap, and widely available.
> The 30 year horizon seems like an impossible dream goal. Read Sun Tsu.
> It is clear that the fight with the 3Ms will last at least 30 years no
> matter what strategy is used. But the strategy you've chosen actually
> works for them and against you. My strategy makes the 3Ms useless toys.

You're right, the strategy I'm using may benefit the 4M's.  That doesn't
bother me at all, since my first allegiance is to mathematics and mathematical
research, and I think having more options and more support for mathematical
software tools is a plus for mathematics, even if some of them are commercial.
I'm just going to try to make sure at least one of the tools is
simultaneous open
and free, and can do what everyday people need.   For way too long
it's been an embarrassment to "pure" mathematics that we don't have such
software yet.    Also, it is bad for mathematics that it is difficult
for the 4M's
plus other systems like Axiom to work together -- one of the three main goals
for Sage is to make such cooperation much easier, because that benefits
mathematics as a whole.

 -- William

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