In 1958, Chaim Pekeris completed a landmark project in computer science. As a physicist at the Weizmann Institute of Technology in Israel, he grow to be fascinated with the comparatively new science of quantum mechanics and its possible to explain from 1st principles the behaviour of atoms.
There was a dilemma however. The equation developed by Schrodinger that could do the job was too complex for mere mortals to manage. Making use of it to establish the electronic energy levels of a even a lowly helium atom was seemingly impossible.
Chaim had an notion, even so: why not exploit the incipient field of laptop or computer science to do the job.
Nowadays, Christoph Koutschan and Doron Zeilberger analyse the work he carried out over many years and compare it to the approach that they would take to the difficulty nowadays. It makes for interesting reading.
Chaim’s task was monumental. He first had to persuade the Wiezmann Institute and a technical committee such as Einstein and Von Neumann, to develop a computer. Einstein proved difficult to persuade but was ultimately won over by Von Neumann.
WEIZAC, Israel’s very first electronic laptop or computer was built between 1954 and 1954. According to Wikipedia, 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.
These days you’d get much more processing power out of a washing machine.
Prior to the pc could get involved, Pekeris had to function out how to describe the two atoms and nucleus of a helium atom utilizing the kind of recurring partial differential equations that a laptop or computer could deal with. The result was a remarkable 33-term equation which he derived by hand, a single calculation that Koutschan and Zeilberger estimate need to have taken 20 person hours.
The laptop or computer than had to be programmed-in machine code. That means writing it entirely in 0s and 1s, for which he recruited aid from an early self taught programmer referred to as Yigal Accad.
This program then kept WEIZAC busy for months, eventually producing a set of tables describing the energy levels of a helium atom, the first time this had been done accurately..
So how has Moore’s Law affected this process, ask Koutschan and Zeilberger.
They repeated Pekeris’ project using the modern tools of computer science to see how they compare.
They say that the numeric computation-the function done by WEIZAC-can be completed in a fraction of a second on any laptop such as Pavilion dv9000(Hp dv9000 battery) and Hp PB991A.
They also point out that the programming is much easier too, thanks to the numerous high level programming languages available right now. Couple of people these days have to mess around with machine code, thankfully.
But perhaps the most surprising thing is that the algebra for working out the differential equations can also be accomplished a lot faster right now using computer algebra programs such as Mathematica and Maple.
Koutschan and Zeilberger say they were able to condense this component of the project, which took Pekeris at least 20-hours, into a 2-hour session.
That’s a fascinating study and counterintuitive in some approaches too. While it is straightforward to see the several orders of magnitude improvement that has improved hardware, it is clear from this work that the speed up from software program is more limited.
In particular, an order of magnitude improvement-from 20 hours to 2 hours-in the time it takes to do the algebra for this issue is a surprisingly little improvement over a 50 year period.
But given the nature of the problem, it’s challenging to imagine how further order of magnitude improvements can be achievable. What type of personal computer algebra software could allow a human to program it work out these kind of differential equations in minutes or seconds.
Of course the limiting factor here is not the software program but the ‘wetware’. Which means that the next generation of improvements will either have to focus on enhancing the wetware or taking it out of the loop entirely.