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The relationship between mathematics and biology 
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#1
Aug407, 08:14 AM

P: 12

Hello,
I have been interested in the relationship between Mathematics and Biology for a while. I recently read Richard Feynman's "The character of physical law", which features a segment about this relationship: "In biology, for example, the action of a virus on a bacterium is unmathematical. If you watch it under a microscope, a jiggling little virus finds some spot on the odd shaped bacterium  they are all different shapes  and maybe it pushes its DNA in and maybe it does not. Yet if we do the experiment with millions and millions of bacteria and viruses, then we can learn a great deal about the viruses by taking averages. We can use mathematics in the averaging, to see whether the viruses develop in the bacteria, what new strands and what percentage; and so we can study the genetics, the mutations and so forth." I have some questions about this; any input is much appreciated! 1. Feynman says that the action of one virus is not mathematical. Is this to say that the behavior of the individual virus is chaotic, or could it be understood by other, nonmathematical principles? 2. Feynman says that mathematics is important in understanding genetics and mutations. Would it be correct to say that these fields have been reduced to information sciences best described by computers crunching numbers (I guess Ray Kurzweil would hold that view) or are they too complex to be described by computational models? Thank you! Peace Andy. 


#2
Aug407, 04:32 PM

P: 282




#3
Aug807, 08:33 PM

P: 235

To respond to your first question:
Feynman's point should be taken along the lines that: individual situations have an immense amount of variation and as such individual behavior and observed activity does not generate enough data to form a model for virus behavior; however, over a large enough span of time enough instances occur that statistical methods can be used to create a model of generalized behavior in biology. It isn't that virus behavior is chaotic, it is that there are too many variations to deal with each virus's individual behavior mathematically. It is much akin to saying we could in principle attempt to determine something about the behavior of an ideal gas by computing all of the forces and motions of all of the atoms in a mole of gas, or we could treat the gas as an ideal gas and be done with it. 


#4
Aug1307, 12:18 PM

P: 12

The relationship between mathematics and biology
The relationships may be found on various levels.
So, I guess that to say that the virus' actions could be better described by other nonmathematical principles is a bit far fetched. Unless by description we mean just a general, well, description. The situation changes (?) when we move to higher organisms, where the language of purpose, planning and eventually thinking seems to be much better that attempts at mathematizations. As a result it is not that genetics has been reduced to information sciences. On the contrary: information sciences in XXI Century will benefit from our progress in understanding biological processes. Eventually, yes, mathematics will play a crucial role, but my guess is that we shall discover similar surprises of complexity and beauty as were found when people first `discovered' fractals. (BTW: did fractals exist before people tried to run their little computers to see Mandelbrot set or Julia Set?) At the lowest level: there are quite interesting theories (I do not say I believe them all, but who knows), which state that at the basic level all Universe is `computational' The most widely known example is the New Kind of Science of Wolfram, where he postulates that all we find in the world is somewhere a cellular automaton. Far below quarks and Planck scale. I do not believe it, but if this would be true that all the world would be mathematical to the core. See me on http://countryofblindfolded.blogspot.com/ exphysicist 


#5
Aug1307, 09:42 PM

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#6
Aug1407, 02:24 AM

P: 12

Of course one can construct simpler equations, for statistical description of processes or for simplified description of some biological processes (famous example: equations describing propagation of electric spikes in neurons). But these simplified equations are, as I said, CONSTRUCTED: one picks some properties and tries to describe them mathematically. And thanks to enormous wealth of mathematics and its tools (differential equations, PDE, integral equations, Markov processess, well... too many to think of) some sort of `fitting' would be found. But as to whether a particular virus behaviour versus particular cell can be PREDICTED by mathematical tools  deducing subsequent steps from the initial state, this would require not only knowing this state with arbitrary precision but also knowing how to solve QM equations for a `dirty, hot and wet system'. best regards, see me on http://countryofblindfolded.blogspot.com/ 


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