We have friends in other fields---in biology, for instance. We physicists often look at them and say, "You know the reason you fellows are making so little progress?" (Actually I don't know any field where they are making more rapid progress than they are in biology today.) ``You should use more mathematics, like we do." They could answer us---but they're polite, so I'll answer for them: "What you should do in order
for us to make more rapid progress is to make the electron microscope 100 times better."
...It is very easy to answer many of these fundamental biological questions; you just look at the thing! You will see the order of bases in the chain; you will see the structure of the microsome. Unfortunately, the present microscope sees at a scale which is just a bit too crude. Make the microscope one hundred times more powerful, and many problems of biology would be made very much easier. I exaggerate, of course, but the biologists would surely be very thankful to you---and they would prefer that to the criticism that they should use more mathematics.
There's some truth to this: advances in biology have frequently been driven more by technology than ideas about biology. For long time, many (not all, but many) answers to biological questions have been obvious once we have the technology to "just look at the thing."
As a result, you have generations of biologists with little training in math, who approach their work primarily by intuitive reasoning about their system of interest. And of course you have some very clever, amazing technologies (developed by biologists as well as physicists).
Many of the fundamental questions that can be solved by just looking at things have been solved; as a result, a lot of biological research isn't about fundamental questions - it's about details, about how something works in a different cell type or a different organism, or at a different stage of embryonic development.
The result is that there is a growing recognition that there are important, remaining fundamental questions that can be solved by getting quantitative - by having more formal, mathematical ideas about biology. We can generate mountains of data, and we can do unbelievable, nano-scale experimental manipulations that Feynman would have loved, but do we know how to think about biology instead of technology?
Some of these important questions include how the structure of regulatory networks gives rise to the network dynamics: how do regulatory networks control gene expression in space and time? How do you get irreversible transitions in cell division or development? What types of structural features produce robust biological oscillators? How do regulatory pathways evolve - either adaptively or neutrally? How can we formally describe information transduction or processing inside of a cell in a way that leads to useful insights?
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