Lubos Motl asked me to comment on this majestic post by a computational biologist at Stanford. This paragraph is worth quoting:
I will enumerate three main points, all of which represent both a challenge and an opportunity. The first will deal with a scientific challenge of a theoretical orientation, namely the lack of a theory for biology. The second with the sociological organization of biologists and biology departments at the leading research institutions. And the third will be part science, part sociology, having to do with the focus of current experimental methods and programs on biomedical research as opposed to basic biological research. The challenges are listed according to my own judgment of their importance.
Here it is an important quote from my exchange with theoretical evolutionary biologist David Haig in regards to theory & biology:
Question: Do you believe most biologists, even evolutionary biologists, appreciate formal theory?
Answer: Most biologists do not appreciate formal theory. Theory is more respected by evolutionary biologists as a group.
Historians do not respect theory because it hasn't led anywhere, Spengler and Toynbee are interesting, but their aim to construct general systems outran the reality of details. In contrast, biology does have a theory, evolution. But evolution is a theory like gravitation, of vast power and scope in aggregates, but weak in its proximate relevance to systems of importance like the processes and mechanisms of a 4-chambered heart. Where is the Strong Force and Weak Force of biology? Its Electromagnetism? The vision of consilience as a whole is not new, and its attainment even within biology is a long term prospect. But, I would like to emphasize Haig's point by way of a comment on Lobus' blog:
I just can say that it is hard to explain differential, including nonlinear chaotic ones, (and partial diferential) equations, markov process, maybe statistical inference, game theory, numerical methods and so on to people who although intellligent, have decided that it is a good idea to begin reviewing derivatives and basic integration.
[edited for clarity]
1) Many biologists are mathematically averse. I once took an upper division ecology course where the instructor threw some basic algebra, calculus and baby statistics up on the board and stated baldy that anyone with problems should leave the course. You know, what is the integral of (2/5)x2, I shit you not. 1/3 of the class never showed up again.
2) The mathematically capable biologists, who are comfortable and skilled with powerful formalisms, are unfortunately rare wizards. Formal, quantitative, thinking is the domain of specialists with whom one collaborates with, it is not the oxygen that biologists breath. This is not totally due to sociological factors, after all, many molecular genetic "models" are still at a very qualitative stage of elucidation
3) So ultimately one must have faith, and keep the fire alive
- Log in to post comments
I didn't read the entire post from which Razib quoted, so take my comments with a grain of salt (as if you wouldn't otherwise). But the lack of some formal theory outside evolutionary genetics has absolutely nothing to say about the future of biology. Biologists with physics envy should see a shrink.
Dear Razib,
Thank you for the kind post. I certainly agree with your analogy of evolution and gravity. That is exactly the problem. Unfortunately, finding biology's equivalent of electromagnetism doesn't appear to be all that easy ;-)
All the best.
Just like what happened to the stock market, eventually biologists too will find something to throw heavy mathematics at.
PS: You misspelled Lubos
As a mathematically inclined biologist (but not a "mathematical biologist" or "computational biologist") I'd make a couple of comments here. I went to a school where ODEs was required of all students, regardless of major. When I went to grad school, most of my fellow students and the scientists in the department were marginally mathophobic. Very few enjoyed or valued math as a part of the process of research in biology. I think the reason for this is crucial to understand. MANY PARTS OF BASIC BIOLOGY RESEARCH INVOLVE LITTLE TO NO MATH. Of course, it is impossible to make reagents or plan reactions without facility at arithmetic. It is helpful if you have a decent grasp on simple equations like the logistic growth equation. In my recent work, I was able to utilize a method for measuring bacterial numbers based on their growth patterns in subsequent inocula. It was helpful that I knew the math behind it (some pretty simple stuff), but really not essential. Now that I run a lab with students, most of whom are deeply mathphobic, I find it frustrating, but in the end, it isn't a very big deal. Running molecular biology experiments, picking mutants, sequencing DNA, etc requires a minimal math investment.
To summarize, then, it is fine for people to be interested in mathematical models in biology. Some of these models and theories are fascinating in and of themselves, but the basic questions of biology are being answered at a wet bench, by people who can plan good careful experiments and carry them out. Most of the time, the mathematical investment in these is quite low.
That said, there are some great realms of biology where facility with data analysis tools such as statistics packages (software) are incredibly valuable. Microarray analysis, proteomics, and other "high-throughput" science is performed using some pretty sophisticated math. However, most of the time the end user can remain fairly ignorant.
Sorry, I know this is a bit of a mess. I'm a bit ambivalent about the issue, because I personally really enjoy math at many levels, and I want to use it more in my research approaches, but it just doesn't fit in with the bulk of the "high yield" approaches.
Paul Orwin's comment is probably modal, even among "mathematically inclined biologist[s]". Working with large datasets in my own research, I appreciate having a facility with math (but mostly canned stats and good-enough scripting), but even this is not truly common yet.
one could make an argument for a comfort and facility with math being important in the way having some liberal arts background can be important: some nice lubricating oil in the cognitive machinery.
I disagree with your analogy regarding evolutionary theory and the theory of gravity. Whereas all theories of gravity allow one to predict the trajectory of a stone thrown into the air (a nice parabola) and although some of them may fail at more complicated problems, I know of no evolutionary theory which predicts consistently anything in a biological system (i.e. more than one outcome is allowed by the theory).
analogies always break part in some manner, otherwise they wouldn't be analogies but identities :) you have shown where the analogy has no correspondence, but my point was to suggest that just as gravity is a theory whose utility is apparently at large scales, so is evolution in regards to numbers and time.
A related problem is those who know math that isn't used in biology -- I learned plenty of "math" for linguistics, but it rarely involved concrete numbers, and it was all discrete. Order-preserving vs order-reversing functions, curried functions & lambda calculus, proofs by induction -- crap like that, which I have yet to encounter in biology. I think I'd make a better transition to computer science, but then that's pretty boring.
Still, I think I'm better off than someone who aced their first two semesters of calculus but did no modeling or proofs (as I understand, those have fallen by the wayside in many calculus courses). Put another way, I'd be less embarrassed to ask a technical wiz to compute some unwieldy integral that I'd proposed as a model for X, than if I were a technical wiz but had no "modeling imagination" (for lack of a better word). Ideally you want to be both, of course, like Fisher or Hamilton, but Darwin was pretty unsophisticated mathematically (both in how much learned math he'd mastered and in how much he used math in his work), but he had good general reasoning & observational skills.
There's actually a worse case than the not-so-creative technical wiz: the technical wiz who doesn't know anything, and so proposes an insane model (and not as in, "it's crazy enough to work"). The recent "rebuttal" letter on Lahn's work which used computational smoke & mirrors to argue for demographic causes rather than selection accounting for Lahn's data -- until you learned that (as Greg Cochran pointed out in the comments at the GNXP post) the effective population size would've been so small (~10) that they would've went extinct by now. There are evo psych arguments that you don't need to see the sophisticated model for to know that they're BS (e.g., treating schizophrenia as the outcome of frequency dependent selection during times of Shamanistic practices).
So I guess the boring conclusion is that it always pays to know more math, and to be more imaginative & have a better bullshit-detector.
Let's not gloss over this point:
"Current experimental work, and biology as a whole, suffer from a serious problem--the perception that their existence is only justified as a tool for medicine."