The term “from months to days” is a favorite slogan of mine and I have relied on it religiously for over two decades to illustrate the fundamental benefit of symbolic computation. Whether it’s the efficient development of complex physical models using MapleSim, or exploration of parametric design surface equations (my dissertation) using good old fashioned Maple V Release 2, the punch that symbolic computation provided was to automate the algebraic mechanics of equation development. Countless generations of grad students have developed equations for complex models, produced impressive results, and got to the finish line faster because of the algebraic boost of symbolic computation. I’m thrilled to see this fundamental dimension carry through to our latest generation of products anchored by MapleSim. The context is much more focused today and the stakes seem to be much higher but when all is said and done, everything is about saving massive amounts of time and effort.

I have to thank my friend and colleague Dr. Stephen Watt (of Maple and Axiom fame), for posting a link on Facebook to a recent post  in MIT’s Technology Review physics blog. It discusses the work of Christoph Koutschan and Doron Zeilberger as they analyze the efforts of 1950’s physicist Chaim Pekeris of the Weizmann Institute of Technology in Israel. Pekeris was one of the first to apply computing techniques to solve problems in quantum physics (e.g. the Schrödinger equation).  Koutschan and Zeilberger are modern researchers in the field of computer algebra (intimately related to symbolic computation).

A highlight of the article were the anecdotes of Pekeris’ Herculean efforts to both procure and use a computer of the 1950’s. I was particularly intrigued by his comment that it was John Von Neumann who had to twist Albert Einstein’s arm (both served on the Institute’s technical committee at the Weizmann) to approve the building of the Institute's first computer (sorry, no Best Buy during those days). The silly side of my brain, tucked neatly behind my right brain, immediately began musing about the possible dialog between these two giants of modern science ...

Von Neumann:  I think we need a computer.
Einstein: What for? Computers are nothing but nuts and bolts. What we need to do is be smarter and more imaginative!
Von Neumann: You know Al, one day, you’ll be able to get recipes through your computer...
Einstein: ... I think we need a computer ...

In the end, of course, Pekeris did get his computer and did manage to break miraculous new scientific ground merging physics with the then nascent field of computer science.

Fast forward to today, Koutschan and Zeilberger’s work retraced Pekeris’ mathematical and computational steps and accessed what the effort would have been. The findings were not surprising in some ways but surprising in others. First, as expected, in terms of shear numerical processing power, your average desktop today is orders of magnitude more capable than their original WEIZAC machine. As the article states, “WEIZAC was an asynchronous computer operating on 40-bit words. Instructions consisted of 20-bits: an 8-bit instruction code and 12-bits for addressing. For a memory it had a magnetic drum that could store 1,024 words. Today you'd get more processing power out of a washing machine.” The net result was really from days to fractions of seconds.

The WEIZAC computer currently on display [image from Wikipedia]

The surprising part was on the equation development side. The first step in any exercise in modeling is, of course, the equation derivation. For this Koutschan and Zeilberger managed to successfully replicate Pekeris’ recipe, and using modern algebraic tools like Maple, managed to speed up this part of the task from the original 20 days to about 2 days – i.e. one order of magnitude.

So one part of me cheers … my claim of  “from months to days” has been validated by some pretty heavy-duty scientists. Twenty to 2 days is essentially the same single order of magnitude speed up as months to days. There is, however, the flip side of this coin … is this about the best we can do? Could there be a natural and fairly restrictive limit to a “Moores-type” Law for algebraic manipulation for modeling? As the article comments, the issue is “wetware”. The human factor. As long as humans are included in the modeling loop, there will be a natural floor to how quickly a complex task can be done.

Being an eternal optimist, however, the end-conclusion I developed was that although there will always be wetware bottlenecks, you can still achieve a heck of a lot by continually automating out more and more human volatility from the workflow. In many ways, I believe this is what MapleSim is doing and indeed, what Maple has always done in a broader context. Take care of more and more algebraic tedium and clutter to reduce sources of error and speed up sub tasks one “20 to 2 days” at a time. With complex modern systems like cars and space vehicles, there are an awful lot of subsystems and these time saving add up pretty quickly. I’ll take that extra 18 days any day.

Links

The original article from the MIT Technology Review blog

Homepage of Doron Zeilberger

Homepage of Christoph Koutschan