Hi Tim and Aaron,
One of the most distinguished living biologists, geneticist Richard Lewontin of Harvard, profoundly disagrees that mathematics or mathematical physics is capable of accurately representing the natural world; that is, the specifically biological part of the natural world. In last month's issue of New York Review of Books, Lewontin reviews MIT professor E work, , and flatly states that the biological world is simply too "messy" to be represented according to any mathematical model, Newtonian or post-Newtonian. In a letter to the current edition of New York Review of Books, Lewontin reaffirms his position and states that he considers that even future attempts to make neat systemic mathematical models of biology will "inevitably" fail.
What science might be able to produce is a very "messy" (ie inaccurate and unreliable) model of the biosphere that simply does not do the job the way Newton's model does for the planets, the moons, the comets, and the stars. Newton's model was worked on by LaPlace, Euler, Gauss, Henri Ponicare and other giants of mathematical intelligence before it become the polished, reliable instrument it is today. According to Lewontin, when it comes to biology there isn't any mathematical model to work on and there probably cannot be (he charitably refrains from commenting on whether there are any Newtons, Gausses, LaPlaces, Eulers, or Ponicares around to develop such a model).
There are physicists and mathematicians who believe that, even for non-biological phenomena, the usual way of expaining reality by mathematical models has come to the end of its tether. The most famous of these is Stephen Wolfram, multi-millonaire developer of Mathematica software. Wolfram took his PhD in physics from Cal Tech at the tender age of 21 or 22, and while he was making his fortune by day in the software industry, by night he was pursuing his dream of explaining the physical world by cellular automata rather than conventional mathematics. The fruit of his persistent moonlighting appeared last year: a lavishly illustrated 1200-page book, "A New Kind of Science." Wolfram maintains that the physical world is more akin to a computer program than it is to a mathematical formula. The program for the world is composed of simple steps (cellular automata), which in combination and permutation manage to produce the welter of booming, buzzing complexity and confusion that we see around us. Wolfram, in other words, believes that complexity proceeds from simplicity, not from arcane and involved mathematical formulas. Complexity eludes explanation by mathematics. One of his most vivid illustrations is that of a steam of water breaking up into drops as it hits an obstacle (say a rock) and then fluidly reassembling itself into a silver flow on the other side. What mathematical formula could represent such a division and reunion, such a departure from form and instant return to form? (Similar questions were asked by D'Arcy Wentworth Thompson, a more elegant writer and thinker decades ago in his book, "On Growth and Form" ).
The response of most physicists and mathematicians to Wolfram's theory has been less than enthusiastic. Freeman Dyson of the Princeton Institute for Advanced Studies (the old stomping ground of Einstein and Kurt Godel) dismissed Wolfram's book as "worthless," and others suggested that Wolfram wrote the book for publicity (he is making his rounds on lecture circuits) to advance the sales of his software. My favorite review of the book (and the theory) is by Ray Kurzwiel, the ingenious inventor who developed computer software that can read printed text to the blind and also developed the superb Kurzweil keyboard synthesizer, a favorite of musicians everywhere. (For the complete review go to google.com and search for "Kurzweil review of A New Kind of Science.")
Kutzweil, a good applied mathematician and one of the sharpest inventors around today, finds a fatal flaw in Wolfram's simple computer model of the universe: "One could run these automata for trillions or even trillions of trillions of iterations and the image would remain at the same limited level of complexity. They do not evolve into, say, insects or humans or Chopin preludes or anything else that we might consider of a higher order of complexity than the streaks and intermingled triangles that we see in these images."
I would add that Wolfram's model does not evolve into bacteria, fungi, multicellular plants, tropical rain forests, or natural gardens either. It does not explain plant guilds, coevolution, ocean plankton, or photosynthesis. It is just an interesting grouping of "streaks and intermingled triangles" that does not come alive. So if mathematical models and computer cellular automata models do not do justice to evolving biological forms, is there anything else? Rather than ending this discussion on a note of despair, I would suggest that the recent attention of chemists and physicists to "self-assembly" in nature might be a helpful approach. Oxford chemist Philip Ball has written a lucid summary of how the physical world assembles itself into complex patterns. His book, a popularization highly respected by top workers in the field, is "The Self-Made Tapestry: Pattern Formatin in Nature." But Ball seems much more comfortable describing self-assembly in the inanimate world than in the animate, which brings us right back to Lewontin's notion that biology is intrisically messy and just does not line up for inspection when the sargent (mathematican, scientist) barks out the orders to "fall in."
Bob Monie, southeast Louisiana
Tim Peters <psr@...
..." Mathematics can describe with accuracy the natural world, if the
mathematician spends enough effort in perfecting the equation. It's like
absolutely true from what I have seen. ...it is all quite calcuable.
...like the weather. ...it is the myriad of details that can throw you for
not calculating them in.
Yahoo! Groups Sponsor
To unsubscribe from this group, send an email to:
Your use of Yahoo! Groups is subject to the Yahoo! Terms of Service.
Do you Yahoo!?
Free online calendar with sync to Outlook(TM).
[Non-text portions of this message have been removed]