1) Fortunately, exceptional mathematical fluency is required in only a few disciplines, such as particle physics, astrophysics and information theory. Far more important throughout the rest of science is the ability to form concepts, during which the researcher conjures images and processes by intuition.
2) In the late 1970s, I sat down with the mathematical theorist George Oster to work out the principles of caste and the division of labor in the social insects. I supplied the details of what had been discovered in nature and the lab, and he used theorems and hypotheses from his tool kit to capture these phenomena. Without such information, Mr. Oster might have developed a general theory, but he would not have had any way to deduce which of the possible permutations actually exist on earth.
Over the years, I have co-written many papers with mathematicians and statisticians, so I can offer the following principle with confidence. Call it Wilson's Principle No. 1: It is far easier for scientists to acquire needed collaboration from mathematicians and statisticians than it is for mathematicians and statisticians to find scientists able to make use of their equations.
3) If your level of mathematical competence is low, plan to raise it, but meanwhile, know that you can do outstanding scientific work with what you have. Think twice, though, about specializing in fields that require a close alternation of experiment and quantitative analysis. These include most of physics and chemistry, as well as a few specialties in molecular biology.
Decani: If you try to do general relativity or quantum mechanics without getting the maths, sorry, you ain't getting it.
OmieWise: and you don't need to be able to read music to be a great musician. But if you can't, you almost certainly aren't.
Really? You know about the strong tradition of blind musicians, right?
mhoye: Call it Wilson's Principle No. 1: It is far easier for scientists to acquire needed collaboration from mathematicians and statisticians than it is for mathematicians and statisticians to find scientists able to make use of their equations.
That seems a bit specious. He doesn't need to know the math, because he can easily find somebody to do the work for him?
Seems to me that the fault often lies with empiricists who stick with their intuitions come hell or high water, and who actively resist the discipline that mathematics imposes on their groundless daydreaming. Intuition is great–as long as it’s only a starting point, and as long as you’re prepared to give it up when it’s proven wrong, even if there’s no better intuition to replace it with. Unfortunately, that’s really hard to do.
Yes; it's not specious at all. I've been hired for just that reason, in the past. It's simply collaboration; it's analogous to a musician hiring a brass player,
I tend to find the idea that scientists should be able to be great at more than one field kind of absurd. It's like telling an athlete that to be a 'whole athlete', they have to be both an amazing marathon runner and baseball pitcher, or some other combination.
You formulate hypotheses by thinking about what the world (or whatever chunk of it is relevant) would be like if your theory were true. In some circumstances you can use mathematics to make very precise hypotheses, but imprecise ones aren't unscientific. Just imprecise.
I understand what you are saying, but it's still true that someone who splits their effort between multiple things can't spend as much time on any of them individually as someone who focuses on one. Having basic mathematical literacy is good; it's a basic component of any graduate biology degree. However, taking the time necessary to be a great statistician would cripple you as a biologist.
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