Present-day computers are remarkably fast…a garden-variety laptop can do over a billion basic operations (additions, multiplications, etc) every second. The machine on which you are reading this can do more calculating, if you ask it nicely, than the entire population of the United States. And supercomputers are available which are much faster.
Yet there are important problems for which all this computational capacity is completely inadequate. In their book Natural Computing, Dennis Shasha and Cathy Lazere describe the calculations necessary for the analysis of protein folding…which is important in biological research and particularly in drug design. Time must be divided into very short intervals of around one femtosecond, which is a million billionth of a second, and for each interval, the interactions of all the atoms involved in the process must be calculated. Then do it again for the next femtosecond, and the next, and the next…
To perform this calculation for one millisecond of real time (which is apparently a biologically-interesting interval) would require 100,000 years on a conventional computer.
Under the sponsorship of David Shaw (of the investment and technology firm D E Shaw & Co), a specialized supercomputer has been built to address the protein-folding problem. Named Anton (after Anton van Leeuwenhoek, the inventor of the microscope), this machine can simulate 10 microseconds of protein-folding activity in only one day of real time…implying that the important 1-millisecond period can be simulated in only 100 days.
An alternative approach to the problem has been taken by the project Folding@Home, in which individuals contribute their unused computer time (PCs, game machines such as the Playstation 3, etc) to a vast distributed-computing network, which now has something like 400,000 participating machines.
It is sobering to think about what vast computational resources are necessary to even begin to simulate what tiny bits of nature do all the time.
And note that the protein-folding problem is a deterministic physical problem, without the complexities of human behavior which are involved in economic modeling.