Will this be useful?

[Judith Rosen <***>]

> "NEW MATH MODELS TO PICK UP WHERE COMPUTERS FAIL" ...

> (Jack Park was kind enough to forward on to me the link for the story, copied partly in below... ) The last line of the story makes me wonder if they will be able to put all that time, money, and work to good use... or will it just be another colossal waste of time and resources? The line is:
> "With success, they said, someday the problems may be simplified enough that a supercomputer can handle them."
>
> This is very frustrating! Among the subjects Robert Rosen discussed at length was the fact that mathematics is a complex system which cannot be reduced entirely to syntax without losing most of mathematics in the process (and causing the genesis of outrageous paradoxes as a side effect). I could save OSU a whole lot of time and tell them that if their goal is to simplify the problem so that the supercomputers can handle it... they can do that anytime! We know how to do that already! But to do so causes a whole set of new problems... because they won't be solving the same problem they were trying to solve. So, they will still have the original problem, plus all the new, interactive/interacting side effects from remediation attempts based on an oversimplified model.
>
> This is not an issue that can ever be addressed by more powerful/faster/better digital super-computing. Water moving through soil? Soil isn't an element! What kind of soil? At what temperature? At what altitude? With what sort of ecosystem? During what part of Earth's orbital status (including the moon's orbit around US)? Secondly: Water has properties that make it as different, based on context, as if it were not the same material "stuff". In addition, there is the effect of scale on water. For example, the surface tension of pure water has an entirely different impact on interaction in micro and macro scales. If the water has dissolved additives in it or if it interacts with soil ecologies, then the resulting surface tensions will be different from information derived from pure water.  Worse: In the environment, there are going to be multiple scales (multiple "contexts") interacting with one another all at the same time. The effects of that sort of interaction can never be predicted by any amount of modeling of any single scale on its own. Similarly, the effects will never be predictable even if a model including various interactions between scales can be built. Every interaction is relational, which means that the effects will be entirely context dependent. The context-dependent nature of the situation is what cannot be digitized-- the variations are clearly infinite. 
>
> How depressing!
>
> Judith
>
> Taken from: http://www.sciencedaily.com/releases/2005/11/051125105520.htm: 
-- Excerpt:

> For all the advances in computer power of recent years, many real-world processes are still so complex that they defy the capability of even the most advanced supercomputers to describe them - and to address such problems, mathematicians are being called for help.
>
> As part of that effort, Oregon State University recently received a $647,000 grant from the U.S. Department of Energy. It's one project in a national, $20-million initiative to have advanced mathematics pick up where sheer computing power is inadequate.
>
> In this project, OSU mathematicians will be trying to model the flow of fluid through a porous medium, such as water through soil. It may sound simple, but in practice this can be so extraordinarily complex that there are still more questions than answers.
>
> "The use of models that are suitable for laboratory experiments to describe processes on the scale of a watershed will bring any computer to its knees," said Ralph Showalter, professor and
>
> head of the OSU Department of Mathematics. "We're trying to connect information at the microscale to the big picture, and for that we need new mathematical systems that at least give the computers a chance."
>
> This federal initiative will cover many topics, ranging from the production of energy to pollution cleanup, manufacturing smaller computer chips and making new "nanomaterials." OSU is one of 17 universities and eight Department of Energy participating laboratories, which include many of the most prestigious research and technology institutions in the country.
>
> The program tackles problems of "multi-scale mathematics" - questions that span time scales from fractions of a second to years, and the atomic level to whole watersheds. The problems are so vast they cannot easily be broken down into simpler questions that could be solved using traditional mathematical techniques and models.
>
> OSU's role will be to better describe fluid flow, which might relate to many topics, such as groundwater movement, blood flow through tissue or injection molding processes used in industry.
>
> Even in the study of something as basic as water moving through soil, what you see depends on what window you look through, Showalter said.
>
> "You look through a microscope at a liquid moving for a few moments between soil particles and you observe a certain behavior," he said. "Study the same process at the scale of a bucket or barrel, and longer time scales, and the picture is incredibly different. And for our purposes, we might need to effectively model this process on the scale of a reservoir or a polluted field of groundwater over a period of decades."
>
> Showalter said that conceptually, it's similar to trying to describe the path of a butterfly on a long migration, rather than the up-and-down motion of its body with each cycle of its wings. Existing mathematics is able to do this averaging or "upscaling" in many cases, he said, but not yet in the more complex problems the DOE initiative plans to address.
>
> Primary investigators on the OSU research are Showalter and Malgorzata Peszynska, an assistant professor of mathematics. They will try to create new mathematical models that are able to tackle these topics, and then do analysis and simulation to study their accuracy.
>
> With success, they said, someday the problems may be simplified enough that a supercomputer can handle them.
>
> -- End Excerpt.