# Biology is unmathematical?

## 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.

Isn’t the Feynman quote an argument that the behavior they could observe at the time isn’t mathematical but that it is statistical?

Statistical isn’t mathematical?

Is “unmathematical” a real word? I’m not sure that it’s one of Feynman’s more eloquent moments :)

You make a good point though, which is that biology is no longer considered “soft science”. When I was in high school, the attitude was that biology was for people who lacked the mathematical and computational skills to do a “hard science” like physics. We were taught that biology was fuzzy, messy and illogical and that there were no rules – in short, that it wasn’t really like science at all.

This was nonsense of course – when you view cells as complexes of molecular machines there clearly are rules – otherwise things like cell division and embryonic development could never occur in an orderly, repeatable fashion.

So it’s great that we now live in the age of bioinformatics and computational biology. This provides us with a logical, conceptual framework for biological research. It also allows for true cross-disciplinary science – to succeed in research, biologists have to use elements from physics, engineering, mathematics, statistics and computer science. Really, biology is becoming a branch of information science and that’s a good thing.

Well, I don’t know that I agree with biology becoming a branch of information science (unless I’m secretly good at information science while not even really knowing what it is!), as at least from the experimental biophysics side of things, I don’t run into bioinformatics at all. It is most certainly becoming an important aspect of biology research though!

I also find that the quantification of biology isn’t coming from the traditional biologists.. it seems to me far more of a one-way street in that all the other sciences are becoming aware of the interesting problems to solve in biology, and not biologists embracing quantitative techniques. Though I’d be thrilled if I was in fact wrong about this. It seems far more people in physics are excited by biology than people in biology excited by sophisticated physical techniques, no matter the kinds of exciting information you can get. In the end it won’t matter, but it is an interesting aside all the same.

And you’re right, that isn’t one of Feynman’s more quotable quotes. Hopefully he’s got something a little more memorable in another lecture. :)

Niel, part of it is also that, stigmas and old fogeys aside, it’s a lot easier to see the overlap when mathematics is successfully applied in biology and physics in the previous century has incorporated just as much of the non-deterministic messiness imprecated by said fuddy duddies.

PhilipJ, how many statisticians do you see in math departments? Heck, many “pure” maths people don’t even want “applied” math around, since it’s only a dim shadow of their real live we-don’t-do-arithmetic-we-do-algebra type topics (keeping in mind that this is the algebra and such from the advanced level books, the ones that scare you because they start using expressions like “Introduction to …” in a way that represents pain, bondage, and the dark arcana of epsilon-delta proofs). No, in history and in practice mathematics and statistics, at an academic level, are very different fields who borrow each others’ tools and pick each others’ brains when they find it useful (and when the benefits justify the mathematicians sullying their purity with something as banal as working with numbers).

Mistaking a mathematician for a statistician is often only one step further removed from summary evisceration than is incorrectly attributing a Latino’s nation of origin—you just don’t want to go there.

Heh, it is very true that statisticians and mathematicians are usually not even in the same department, but Feynman was a physicist, and we care far less about those distinctions than the mathematicians do.

More importantly, I think Feynman’s statement was also ignoring the distinction. He says that a single virus infection event is unmathematical – that there’s no quantitative measurement people can do with any reliability, it is only when looking at large N events that any “mathematisation” of the process can occur, even if it is statistical. My argument is that this isn’t true anymore.

Can biology lead to new theorems?

See the recent article

http://math.berkeley.edu/~bernd/ClayBiology.pdf

and the book “Algebraic Statistics for Computational Biology” by Lior Pachter and Bernd Sturmfels

http://www.amazon.com/gp/product/0521857007/103-8980959-1731045