To Whom It May Concern:
As the result of the publication of my article in CS&E on the need for verifiable computing, I have been contacted by William Walster. Dr. Walster has brought me up-to-date on his efforts to introduce some innovative and potentially very important technology to the computer industry.
I have reviewed Dr. Walster's research work through his web site posting, and found it eye-opening. I had no idea interval arithmetic--and verifiable computing in general--had come so far. This kind of thing is like the difference between chemistry and alchemistry. With respect to the largest government procurements like those for the ASCI program, this technology should be mandatory. The ASCI participants HAVE to do it if they want to make credible pronouncements about nuclear weapon stewardship. There will still be people who say not all the relevant physics is in the models, but that's still a much smaller criticism than not being able to establish firm results for the physics that _is_ being modeled.
I used to work in the marketing department when I was at FPS. Like many computer companies, FPS had a somewhat adversarial relationship between its engineering visionaries and its marketing executives. I say this because I had a foot in both camps, and I understand how an engineering-driven idea like "interval arithmetic" seems radical when the marketing department sees that almost no one is presently selling computers because they have this feature. Before FPS fell into financial disarray, we had stumbled on the work on interval arithmetic publicized by Miranker and Kulisch, and we were in the process of developing a hardware product for verifiable computing that could have saved the company by giving it a unique product that a certain part of the marketplace would insist on owning... once they realized it were technically possible: A computer for simulation that can guarantee its answers.
I believe that interval arithmetic could do as much for scientific computing as the graphical user interface has done for personal computing. It is that different. It is that revolutionary. Like the graphical user interface, it was a technology that had existed for many years in a research setting but had been ignored by industry. All it took was one major vendor willing to make the leap, and after the usual reluctance and "paradigm shift" inertia, everyone followed suit. That's exactly what could happen with interval arithmetic.
I am in contact with Dr. Gil Weigand, who is in charge of the ASCI program. Years ago, upon learning of the program, I asked him, "Have you ever heard of interval arithmetic?" He had not; he belonged to the school of thought that you make computer simulations more accurate by getting more and more FLOPS in the design until it seems like it's enough. Since then, I understand Dr. Walster has approached Weigand and found him more educated and more receptive to the idea that interval arithmetic, in hardware and software, might be crucial to the primary mission of ASCI: to simulate something without the possibility of confirmation by physical experiments.
It does not take a lot of imagination to see what might happen if the next major ASCI procurement rests heavily on interval arithmetic and verifiable computing techniques. Companies that use structural analysis (possibly the largest consumer of floating-point arithmetic cycles) would soon insist that the buildings, bridges, machine parts, etc. that they design be tested using only verifiable methods. Financial modelers would demand to know the range of uncertainty in their predictions. Weather and climate prediction, another source of large federal computer procurements, would be able to state a firm interval instead of the guesses. This does not even touch on the advances in _optimization_ that Walster has made... the ability to guarantee where the solution of an optimization problem does and does not exist in a computer program with a vast number of variables.
In short, the people who presently buy computers to predict physical behavior will in many cases take certainty over peak speed if the choice is offered to them. When the technology of interval arithmetic (and Walster's approach in particular) becomes commercially available, I'll be among those lining up to purchase it.
Dr. John L. Gustafson
Ames Laboratory - USDOE
If you have a question related to validated computing, interval analysis, or related matters, I recommend