An early career scientist's thoughts on mathematics.

Sayres wrote: Blindly trusting in a mathematician’s computations is just as foolish as a mathematician unquestioningly accepting the results of a biological experiment.

If you think critically, and find collaborators who are good at mathematics and statistics, you can be a successful scientist

Oh, and one more criteria:

3. The nerd must always keep in mind that no matter how beautiful mathematical equations are, they have to be TESTABLE by experiment!

For truly on countless occasions throughout my life I have had this experience: persons for a time talk pleasantly with me because of my work among the sick, in which they think me very well trained, but when they learn later on that I am also trained in mathematics, they avoid me for the most part and are no longer at all glad to be with me.

Calculus isn't just for kidney stones.

Glen Davidson

I minored in mathematics in college. (Major was computer science.)

My personal belief — inherently nonreplicable, not statistically significant, etc. — is that math-aversion is as much pedagogy-aversion as subject-aversion. In short, we teach math so badly that we drive people away from it both in terms of competence and in terms of interest.

Math is the only "language" for which American pedagogy insists that one must master an entire part-of-speech-and-person vocabulary before moving on to another part of speech... or even any understanding of what that part of speech is. Just imagine trying to learn conversational German while waiting to introduce the formal Sie until the third year of study... or discovering the difference between the past perfect and the pluperfect as a prerequisite to studying modal verbs in any tense, even though the formal grammar of the modal verbs is closely related to that of the pluperfect. And then there's the umlaut!

Of course, it doesn't help that so many teachers in early classrooms are not, themselves, all that happy with math, and betray that unhappiness to their students!

An early career scientist’s thoughts on mathematics

When I studied public administration, we were required to take a course in computer programming. And a lot of the students asked why, since they never expected to do any programming.

The instructor (a colonel in the Air Force) basically said: You aren't expected to become wizard programmers. But when some geek comes into your office and dumps a big heavy printout on your desk and says "We just modeled the air war over Europe in WWIII, and it says we need 37 more jets" you have enough knowledge of programming to understand that it's a crock.

I think the same works for math. You don't have to be a mathematician, but you do need enough familiarity with math to know what it can do and what it can't, to know that calculations are based on assumptions, etc. At the very least, so that you won't read Dembski's books, bristling with nasty-looking equations and Greek symbols, and get snowed.

Thanks, Glen :)

diogeneslamp0. I am simplifying, but I didn't say that Wilson said to trust blindly. That is my conclusion alone. And, in fact, the second quote you have, is from my charitable interpretation of Wilson's statement (not from Wilson's statement directly). If you read his article, nowhere in there does he state that you should be critical of your mathematical collaborator's work. To be fair, he also doesn't say to trust blindly, but he does give examples where the biologist works on the biology and the mathematician works on the math.

I am sure there are many good scientists who are not good at math, but I argue that it can only help them to try to learn a little of the math that is related to their question. Yes, we need collaborators who are experts, but we should also be unafraid to learn a bit of the fields of our collaborators so that we have a deeper understanding of our own work. Wilson does not advocate for this. Instead he seems to advocate for division of labor. I think there is some division of labor, but there should also be a general understanding of all aspects of the question.

cepetit.myopenid.com said: My personal belief — inherently nonreplicable, not statistically significant, etc. — is that math-aversion is as much pedagogy-aversion as subject-aversion. In short, we teach math so badly that we drive people away from it both in terms of competence and in terms of interest.

Flint said: ...you have enough knowledge of programming to understand that it's a crock. I think the same works for math. You don't have to be a mathematician, but you do need enough familiarity with math to know what it can do and what it can't, to know that calculations are based on assumptions, etc.

I remember reading Martin Gardner's original article on hexaflexagons in Scientific American in 1956 when I was in high school - I read his Mathematical Games column for decades. That's what turned me on to math.

As an undergraduate, I took math in order to keep up with the math in my physics courses. I liked math somewhat, but I kept taking math out of an anxiety that I was too mathematically stupid and didn’t know enough math to get through physics. At some point, someone informed me that if I took two more math courses, I would also have a major in math; so I did. With some of those same anxieties, I continued taking math courses all the way through my PhD in physics; the result was that I ended up with as many applied math courses as I did physics courses.

But my real interest was in experiment; I loved working in the lab designing, building, and doing experiments. Nevertheless, I have found myself in positions of having to do theoretical work as well as having to come up with algorithms and computer programs in order to do my work in physics; so all that math actually turned out to be useful in the long run. My anxieties about math turned out to be irrational leftovers from somewhere back in my youth. Now I love math.

There were many changes taking place in the way math was taught while I was going through all this. Math is taught much better these days than it was back in the 1940s and 50s. Looking back, I might not have had so much anxiety about math if it had been taught as it is today. Kids getting math today are much farther ahead going into college than we were.

On a related side note; one of the physics professors in high energy experimental physics at the University of Michigan had a way of sorting out grad students he would accept as PhD candidates under his mentorship. After an interview in his office, he would feign an afterthought and ask the prospective candidate to help him get a large, long table out of his office and into the hallway (or in the other direction if the table was already in the hallway). He played dumb and let the student do all the guiding. If the student jockeyed the table through all the obstacles and around corners and through the doorway successfully on the first try, the professor took him on as a candidate.

diogeneslamp0 said: Melissa, I think you're oversimplifying and misrepresenting Wilson's point.

Sayres wrote: Blindly trusting in a mathematician’s computations is just as foolish as a mathematician unquestioningly accepting the results of a biological experiment.

Wilson wrote: Wilson didn't say "Blindly trusting in a mathematician’s computations". He said:

If you think critically, and find collaborators who are good at mathematics and statistics, you can be a successful scientist

This is not the same as "blind trust." If you collaborate with someone who is mathematically skilled, AND if you have strong physical intuition, then your nerd-collaborator can go to your whiteboard and sketch out the math for you and you better understand it. Then your nerd-collaborator can write it up as software, and make a graph of the results. Even if a scientist is not mathematically skilled, if he has strong physical intuition, he can understand and interpret the plots. Thus a mathematically skilled scientist [read: nerd] must be good at plotting and visual representation. Let's be clear that Darwin's Origin of Species has no math, nor did Descent of Man. As far as we can tell, Darwin SUCKED at math but had strong physical intuition. If Mendel's genetics had been widely known in Darwin's time, and if Darwin had had mathematical collaborators at the level of the neo-synthesis guys of the 1930's, evolutionary theory would have had a HUGE jump start. Darwin's suckage at math did not prevent him from advancing a testable hypothesis, because he: 1. Had EXTRAORDINARY physical intuition, and 2. Was constantly, constantly, asking himself: "How can I TEST this theory?" With these two rare properties, Darwin could triumph. However, it would have been better if he been able to correspond with Haldane, Sewall Wright, Kimura, Tomoko Ohta et al. And now, I will describe my personal experience, if you may tolerate for a moment such self-centeredness. My Ph.D. is in a highly mathematical branch of science. So I was not the bad-math guy, I was the nerd that bad-math guys went to consult with. I point this out not as self-flattery, but in order to rebut any accusation that I am biased against math. If anything I'd be biased FOR math. I have known scientists who had BOTH strong physical intuition AND great math skills. But I've also know scientists who had strong physical intuition and NO great math skills. I learned to have a lot of respect for this second category of person. They would come to me and ask me how to solve such-and-such equation. I would go off, solve it, and sketch it out on their white-board. Sometimes they would say to me, "Whoa! Too complicated!" and then do their own thing. Other times they would learn what they needed to learn to address the particular problem they cared about. My conclusion is that such collaborations, between nerd and non-nerd, can be fruitful on these conditions: The non-nerd must satisy these criteria: 1. The non-nerd has EXTRAORDINARY physical intution, and 2. The non-nerd constantly, constantly, asking himself: "How can I TEST this theory?" The nerd must satisy these criteria: 1. The nerd can communicate his mathematical results visually e.g. with plots or analogies, 2. The nerd can instruct the non-nerd in just enough math so he can do what he needs to do.

Melissa,

When trolls like Byers show up they have only one goal, to disrupt the thread with off topic nonsense. They are incapable of learning, even if given the opportunity. It is customary to dump their posts to the bathroom wall, where a more "spirited" exchange of "ideas" is appropriate. I would recommend this course of action. Failure to do so invariably results in degradation for the thread and all participants. The trolls quickly learn which threads are unmoderated and then a feeding frenzy usually commences. I can provide you with a list of known trolls and associated riff raff if you so desire.

Thank you.

Thanks, DS. I'll try it out today. I'm just unsure of whether I'm going to have the time to constantly babysit the comments.

I work in the geosciences. We run numerical models of the atmosphere and the ocean. A model domain typically has 1000x1000 grid points, with 20 vertical levels, for a total of 20 million cells. At each of those grid cells we solve the basic equations of state/motion on every time step, typically 10-60 seconds. Hurricane models run for a simulated week or two while the system is approaching landfall.

That's a lot of math! Fortunately we have digital computers that run in parallel (~64 processors) to complete all those calculations in a reasonable amount of time, and deliver the forecast before the hurricane actually hits a populated area. A timely forecast can save lives and property, as people make preparations and evacuate from risk-prone coastal areas.

Math saves lives.

DS said: Melissa, When trolls like Byers show up they have only one goal, to disrupt the thread with off topic nonsense. They are incapable of learning, even if given the opportunity. It is customary to dump their posts to the bathroom wall, where a more "spirited" exchange of "ideas" is appropriate. I would recommend this course of action. Failure to do so invariably results in degradation for the thread and all participants. The trolls quickly learn which threads are unmoderated and then a feeding frenzy usually commences. I can provide you with a list of known trolls and associated riff raff if you so desire. Thank you.