The great British physicist Ernest Rutherford once said "In science, there is only physics; all the rest is stamp collecting." This is kind of the ultimate example of the arrogance of physicists, given a lovely ironic twist by the fact that when Rutherford won a Nobel Prize, it was in Chemistry. (He won for discovering that radioactive decays lead to transmutation of elements, causing one contemporary to quip that the most remarkable transmutation ever was Rutherford's change from a physicist to a chemist for the Nobel.)
Of course, there's a little truth to the statement-- not the part about the inferiority of other sciences, but the fact that there are very different ways of doing science in different subdivisions of the subject. I had a bit of a Rutherford Moment yesterday, when I ran across Brian Switek's review of The Calculus Diaries, specifically this comment:
There is nothing so ugly as an equation in a scientific paper. As a friend once told me, an equation in a paper looks like a dog turd on the lawn - the only reason you want to look at it is to know how to go around it.
This is almost completely inconceivable to me (at the risk of leaving myself open to the Vizzini joke). In my part of science, a paper without an equation is suspect, and I'm not exactly the world's most mathematically inclined physicist. Physics is so intimately connected to math, and the business of doing physics is so inherently mathematical that its difficult to imagine a scientific paper about physics that doesn't contain at least one equation. A press release or popular article, sure, but to a physicist, the equations aren't some offal to be avoided en route to the science. The equations are the science. Objecting to the presence of an equation in a scientific paper is like objecting to the presence of meat in a steak sandwich.
This is not a knock on Brian, who writes a very good blog, and has a pop-science book of his own that you should check out. It's just a general comment about the different operating modes of different sciences. I'm so immersed in physics at this point in my career that it's always a little surprising to be reminded that there are areas of science where math doesn't play the same central role that it does in physics. That's so counter to the way physics operates, that it's not hard to see how somebody within physics could dismiss less mathematical branches of science as mere stamp collecting.
(Of course, the Nobel in Chemistry isn't the only irony to the Ruthford comment, at least in this context. Rutherford was an experimentalist to the core, and always distrustful of theory (he made an exception for Niels Bohr, because he was a good soccer player), preferring direct measurements to mathematical predictions (as is right and proper). And even the theorists of Rutherford's day were relatively unsophisticated mathematically. Einstein needed ten years to develop General Relativity after he published the papers on Special Relativity in 1905, mostly because he had to learn a whole new branch of mathematics (and almost got scoopd by Hilbert, who knew the math but not how to apply it to physics). Heisenberg expended a great deal of effort working out his formulation of quantum mechanics because he had to independently develop matrix algebra that was already well known to mathematicians, and then had a great deal of trouble getting physicists to accept his theory, because they didn't know matrix math either. Physics became dramatically more mathematically sophisticated after WWII. Prior to that, it was probably closer to the "stamp collecting" sciences of today.)
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Some fields are indeed better off not relying too heavily on mathematics. I'm thinking particularly of economics, and this arXiv paper: WARNING: Physics Envy May Be Hazardous to Your Wealth by Andrew Lo and Mark Mueller.
My own subfield straddles the cultures. Some aspects are highly mathematical, while others are more on the stamp-collecting side of things. There may be a third aspect, namely cartoon drawing (we often draw simplified pictures to represent some of the phenomena we study). I've seen similar struggles to Einstein's and Heisenberg's to first master and then get others to accept new mathematical techniques (e.g., that wavelets rather than Fourier techniques are what you want when you are dealing with non-stationary phenomena, as is often the case in my subfield), while many older scientists are skeptical of these new tools (often for good reason, since there is an aspect of using fancy mathematical tools without demonstrating that the more familiar tools of the field are inadequate for the problem at hand).
Thank you for this comment.
I learned at school biology that was less than 30 years old at the time (DNA, RNA and all that) but the all mathematics in my (very standard) curriculum had at least two centuries on its venerable back; it was presented with no mention of history or possible applications and relations with other disciplines, both in the sciences and in the humanities. I wonder whether that contributes to the fact that so many people, including the unfortunate Brian, find mathematics unattractive.
Unfortunate because they don't know what they miss. I'm sorry for them, and keep hoping one day they'll chance on a copy of Feynman's "The character of Physical Law".
It doesn't surprise me anymore when faculty in the humanities (or even the social sciences) proudly proclaim their ignorance and fear of math. However, it still shocks me when faculty in biology or chemistry express dislike or fear of math. That is surprisingly common.
http://xkcd.com/435/
/obligatory
To be fair to Rutherford, in his time sciences like biology and zoology were much more focussed on cataloging rather than fundamental understanding of processes. They have come a long long way since then even though they are not as intimately entangled with mathematics. Others, like chemistry were and are applied physics.
To clarify my quote, I was not speaking for paleontology or biology as a whole. My comment specifically had to do with my own math-phobia and should not be taken to indicate that paleontologists eschew math whenever possible. In fact, I just downloaded a paleo paper - Helical burrows as a palaeoclimate response: Daimonelix by Palaeocastor - which uses formulas to model the air volume and circulation within the burrows of an extinct beaver. Likewise, paleontologists such as David Raup and Jack Sepkoski relied on statistics to model mass extinctions, and there are various branches of paleontology in which math is frequently used (outside of just measuring old bones). What I wrote has to do with my personal experiences. It is a misinterpretation to say that the quote represents a "two cultures" divide in science. Instead it points out rather a common problem with math education which, I think, spans across many scientific disciplines.
i have alwasys thought since chemistry deals with chemical reactions with electron clouds, and radioactive decay deals with nuclear reactions in the nucleus, Rutherford's Nobel should not have been in chemistry.
stoopid chemists! trying to take the nucleus away from physicists!!1!!1!one!!!1!
On the two cultures, and being immersed in physics:
I was a grad student at Cornell when the Richardson-Lee-Osheroff Nobel Prize was announced. (Richardson and Lee were on the Cornell faculty; the prize was for work done when Osheroff was a student at Cornell.) Everyone filed up to a seminar room for the press conference, which featured Richardson and Lee and the University President. The grad students, at least, chuckled at the questions the reporters asked about the popularized version of the description of the work.
But what really took me aback was when the University President said something to the effect that the prize recognized the "great science" done at Cornell. We didn't do "science"--we did "physics"!
In my bigoted view, the well rounded scientist should be competent at least with calculus, scalpel, and binoculars.
@NoAstronomer, I thought you'd beaten me to it, but no...
http://xkcd.com/793/
Brian's quote above made me cry a little inside.
Having been trained as a theoretical physicist, there are few things that I love more than equations. Being fluent in advanced math is like being fluent in a beautiful language that has unparalleled ability to concisely and precisely capture one's thought process. Sort of how beautiful classical music or literature capture emotions.
If someone think equations are ugly, they're certainly entitled to their opinion. But the idea that someone who thinks equations are ugly would become a "science writer" is an absurdity.
It's like someone of the mind that "There is nothing so ugly as throwing, kicking, or hitting a ball" becoming a sports reporter. Sure, they could cover cycling or sprinting without a problem, but for the majority of their job they're going to be hobbled by the fact that they're repulsed by one of the the central elements of what they're allegedly writing about.
Math does not necessarily have to be expressed only in equations, though. If you have a moderately complicated dynamical system such as the behaviour of a neuron model, the equations really don't tell you much. They don't make the dynamics clear to the reader, and it's the dynamics they'd be interested in.
So a good neuron modeling paper relegates the equations to an appendix (or even a separate publication), and puts the focus on state and phase diagrams where the interesting dynamics are plain, not hidden.
Likewise, too often you see papers that use equations to describe something where a verbal description would have been much simpler and easier to understand, while retaining all the rigour. There's no shortage of extreme cases such as formally defining a set of values 'V' and giving the equation - on its own line, with its own number - for the average of its values, rather than simply say "we take the average of the measurements."
Use equations only when they clarify and illuminate. Skip them when they don't. Rely on diagrams and verbal descriptions when they are clearer, and trust your readers not to confuse the format with rigour.
When I switched from being a physicist to being a science writer, one of my big worries was how I would explain things without equations. As it turns out, it's not nearly as hard as I feared, because a popular story need only motivate the ideas, not provide the complete logical support as a journal article does. But there's still no substitute for equations to be sure that a concept is being precisely described.
@Eric Lund: If what you mean by "not relying too heavily on mathematics" is not ceasing to think about the economic sense of your models then of course what you say is true. Overmathematisation can't rescue bad economics. But it is not less maths that is needed, it is better-applied maths. Suggesting economics should use less maths pushes the discipline in the hopeless direction of model-free reliance on hand waving and conventional wisdom.
The Lo and Mueller paper you refer to doesn't seem to disagree with this. "Blaming quantitative models for the crisis seems particularly perverse, and akin to blaming arithmetic and the real number system for accounting fraud." They end up arguing against "quantitative illiteracy" and for "painstaking debate between idealized quantitative models and harsh empirical realities." That sounds to me like a plea for doing economics properly not for reducing reliance on mathematics.
*cough*cough*Dirac*cough*cough*Jordan*cough*cough*
*cough*cough*Dirac*cough*cough*Jordan*cough*cough*
@7:
The techniques used by Rutherford were those of chemistry, but the important thing was that his discovery overturned centuries of dogma in chemistry about the immutability of an element.