by PhilipJ on 1 June 2006
More from The Character of Physical Law, this time from the second lecture on the relation between physics and mathematics:
In thinking out the applications of mathematics and physics, it is perfectly natural that the mathematics will be useful when large numbers are involved in complex situations. 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 strains and what percentage; and so we can study the genetics, the mutations and so forth.
Much has changed since 1964 when Feynman gave this set of lectures at Cornell, and I think he would be excited about the “mathematisation” of biology. We now can study the physics of viruses using optical tweezers and fluorescent techniques. In particular the beautiful work by the Bustamante lab on the φ29 packaging motor, showing the viral genome being packaged in its protein capsid (subscription required) and the microscopy studies on viral entry into cells by the Zhuang lab (click here to watch a cool movie). So while it might have been true in 1964, it is no longer true that biology is unmathematical at any scale.