Computation and Reality

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.

9 thoughts on “Computation and Reality”

  1. The deeper you drill into biology, the more complex you find the structures. In the days before the realization that DNA was the location of the genetic code, protein was believed to be the site. Now, we are finding that more primitive objects that seem to possess the qualities of life, at least enough of them to cause trouble, do not have DNA or RNA. They must have a protein genetic structure. Prions are an example.

  2. The real killer in simulation is non-linear feedback. Biology is stuffed with it as is all subsets of biology such as economics. Non-linear feedback makes it almost impossible to get the same answer twice and make trivial error, even minor variation in hardware bring down the entire simulation.

    Non-linear feedback distorts simulations because it amplifies tiny fluctuations into to system wide changes. Feedback happens when A feeds into B which feeds into C which feedback to A: A–>B–>C–>A. If the effect is linear i.e. one unit of A produces one unit of B which produces one unit of C, then minor variation in A has little effect.

    However, if one A–B^2–C^2–>A^2, then a one unit of increase in A produces a 16 fold increase in C and a 32 fold increase in the volume of A in the next iteration. In just a few iterations a one unit change in A can trigger a magnitude change in C of billions and trillions.

    Biological system are nothing but a vast series (hundreds of thousands) of chemical positive and negative feedback loops. That is why there are so many poisons. A chemical only has to disrupt one feedback loop to damage or kill. It’s also why sometimes, apparently healthy people just drop dead.

    Protein folding is so hard to model because of there are numerous feedback loops for every atom in the simulation.

    It is also what makes economics at best an immature science. Not only can we not make stable models of economic behavior but we can’t collect precise enough data in real time to feed into the models if we had them. Incredibly minor inputs hit a feedback loop and before you know it the model has shot out all over the place.

    I’ve looked at the math of economic modeling and I don’t think the economy will ever be predictable and that we will never be ever to really know what result our actions will have.

  3. “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 all the sillier it makes those people sound who would have us think that all of this is merely a coincidentally perfect falling into place of a virtually infinte number of variables from a big bang.

  4. Shannon..”Non-linear feedback distorts simulations because it amplifies tiny fluctuations into to system wide changes”

    The way in which chaos theory was developed offers an interesting example of this. Circa 1961, a researcher was running weather-prediction models on what was (even by the standard of the time) a very slow computer. He wanted to re-run the model with the same data for some reason, and to save time, he didn’t start it again from the beginning but manually entered data from a printout that had been taken halfway through the original run. But the results were completely different from what they had been the first time around.

    Turned out that the printing process rounded to 3 digits, while the internal machine representation of the numbers was 6 digits. People would have expected slight differences like .125 instead of .125432 to have resulted in similarly slight differences in results, but instead the differences in results were huge.

    An intuitive way of understanding this is that if you place a marble on top of a hemisphere, a very tiny difference in where you put the marble initially can result in a very big difference in where it will be a couple of seconds later.

  5. Human nature expects linearity. However, we keep learning about important events (World War 1, stock-market crashes, etc.) that happen non-linearly. But because we expect linearity, we tend to rationalize away the non-linear characteristics of such events, and learn the wrong lessons from them.

  6. David, the marble experiment is now being run on the entire country, by people who think themselves competent to improve the outcome by closely controlling every detail.

  7. Interesting example of a small change having a big impact, here. The subject is Collateralized Debt Obligations:

    “Suppose that we misspecified the underlying probability of mortgage default and we later discover the true probability is not .05 but .06. In terms of our original mortgages the true default rate is 20 percent higher than we thought–not good but not deadly either. However, with this small error, the probability of default in the 10 tranche jumps from p=.0282 to p=.0775, a 175% increase. Moreover, the probability of default of the CDO jumps from p=.0005 to p=.247, a 45,000% increase!

    The dark magic of structured finance conjured many low-risk securities out of many risky securities. Like all dark magic, however, the conjuring came at a price because if you didn’t get the spell exactly correct it was easy to create something much more risky and dangerous than you were likely to have ever imagined.”

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