Taking as his starting point my “rant” about the impenetrability of scientific papers in mathematics, Jason Rosenhouse has written a nice essay on what it’s like to be a mathematician who has to try to make sense of the papers of other mathematicians. It turns out that those papers are often as impenetrable to math professors as to us biologists:
Of course, jargon is an affliction common to just about every academic discipline, and not just in the sciences. I would say, though, that math is probably among the worst offenders. The abstract of a typical research paper in mathematics is opaque not just to non-mathematicians, but to all mathematicians who are not specialists in the particular research area being addressed. And when I say opaque, I mean opaque. As in, you won’t make it past the first sentence.
Biology certainly is not as bad. In evolutionary biology I am definitely an amateur, but I find that I can often understand the introduction and discussion sections of a typical paper well enough to explain the gist to someone else. In math, it is usually impossible even to explain the problem to a non-mathematician. . . .
. . . Simply put, it is an awful, almost physically unpleasant experience to read a research paper in mathematics, at least if you want anything more than a superficial understanding of what was done. That is why it takes so damn long to get a paper through peer review. It’s because every time the referee glances over at the paper sitting on top of the filing cabinet, he thinks of something else he’d rather be doing. If you learn the fate of your paper within six months you’ve beaten the odds, but it’s even money that your paper will just disappear into the ether.
Jason goes on to fault math teaching in general, as well as math textbooks, which, by and large, he sees as “simply horrible.” But he also finds hope in the increasing emphasis on expository writing. The piece is worth a read, if for no other reason than to hear the travails of people in another branch of science.
I assume mathematicians don’t go for the “If you can’t explain it to a non-expert in ordinary language then you don’t really understand it yourself” philosophy.
I knew a bloke whose field was the philosophy of mathematics, I have no idea what that entails but I would hazard a guess that the papers would be completely unintelligable to non-initiates.
there is a hierarchy in the body of knowledge
the higher order concepts require a certain integrity of knowledge at a lower level
if the integrity of knowledge is not properlyaddressed during formative years a person will find it very hard to progress from intuitive to highly abstract
even simple arithmetics is not that simple
there are studies that show that only concepts of “one”, “two” and “many” are most intuitive and easily understood by children easily
the simple step to counting, addition and subtraction requires concepts of “quantity” whioch is already highly abstract and cannot be explained merely in words (try to teach a child to cound without physically counting discrete objects 🙂
“I assume mathematicians don’t go for the “If you can’t explain it to a non-expert in ordinary language then you don’t really understand it yourself” philosophy. ”
It isn’t quite that simple. For example, if given enough time, I might be able to explain what a “compact space” is to a reasonably educated person. But that takes quite a bit of time and effort and, to be frank, my result wouldn’t be of any interest to someone who didn’t already know what a “compact space” was.
Hence such terms don’t get explained in papers.
the current socio-economic system does not need “smart” people; it only needs biomass of “consumers” and “salary slaves”
this is why we are bound to witness the further degradation of education for public with the math being the first victim among hard sciences
the elites will always have their private schools from which they will draw “future leaders”
sad but inevitable
I admit that my research record is modest but here is how I see it: you write a paper. The referee tells you to take out some details, so you do.
Then the paper becomes even more unreadable, but you have another publication.
This works a bit like a zip file; the author is forced to compress the paper, and the reader is expected to decompress it.
And yes, I’ve had to wait for up to 18 months to learn the fate of my paper; that happens.
I mentioned this in the last WEIT post about impenetrable math papers. I think the priority to save space in journals has led to a damnably unpleasant condensing of papers to the point where they can be nearly too dense to read comfortably. It has also led to the elimination of many figures that used to be most helpful in illustrating the work. There is a bit of a bright side of late, tho, in the tendency of some online organs to provide those figures…
If you want to really see some imaginative interpretation of mathematical results then have a look at Josh Rosenaus new piece where he examines Elaine Howard Ecklunds new paper on spiritual scientists!
http://scienceblogs.com/tfk/2011/05/scientists_and_spirituality.php
I can’t take much more of this nonsense.
At least you, David M., and Cuttlefish put up some good responses.
In psychology, this is known as psychobabble.
Would comparable situations in other disciplines then be mathmababble, biobabble, and chemobabble?
I don’t think Jason is talking about your post being a “rant” – the only time he uses the word is in the title of his post. After that he goes off on one about maths jargon. I think “rant” is a self-effacing term for his complaint, which, as you point out, joins ours.
As a mathematician (with a hard-on for evolutionary biology) I can say that the old proverb of explaining things to 9 year olds or grandmothers or whatever simply can’t hold. Part of it is math education, for sure (check out Lockhart’s Lament, below). However, calculus is 300 years old, and a lot of students at the university level don’t even need to take it! I am confident, though, that somehting like calculus can be understood as soon as you can solve something like 4x+7 = 17… in fact, it is arguably easier to transition into heavy algebra after a little calculus rather than the other way around. I tell my students that algebra is the hard part of calculus all the time.
http://www.maa.org/devlin/LockhartsLament.pdf
I am hopelessly mathematically challenged. Which is heartbreaking for me as it has blocked me from pursuing any science education/career. I was tested throughout grade school – they thought I could have a form of autism. I could understand high-school level science and reading in 3rd grade – but seriously couldn’t add 2+1 without a lot of confusion. I didn’t learn how to read a clock until 9th grade but was happily reading anything on cosmology I could get my hands on. I really don’t think I have a learning disability – I think that I just never found the right approach to math, it never “clicked”. I never had an “a-ha” moment. It was always painful and always felt as if I were trying to think through liquid cement – when most other things came much easier and clearer to me. I never understood WHY these certain rules were in place nor WHY they worked – without understanding that, the rest of it is just ethereal and slippery. I wish we could start earlier, with grade school children – finding individual programs for their unique learning needs – but I know it will never happen.
I think being good at maths is like learning a foreign language. There are some abstractions and concepts you need to have mastered before a certain age, or else your brain is too hardened to deal with it later (neoplasticity not withstanding).
I wasn’t too bad at math until after 7th grade, which is when my father told me it was a waste of time to be good at math if you were a girl.
I stayed pretty bad at math until I wanted to understand money.
Marta – I’m sorry you were subjected to such pointless sexism. I had support, just not the right kind. The most frustrating thing to me is that my appreciation of sciences will always be incomplete due to my lack of mathematical skills.
“The most frustrating thing to me is that my appreciation of sciences will always be incomplete due to my lack of mathematical skills.
Me, too.
I have an undergraduate degree in math, and I suspect that the math textbooks only turn terrible once you get into grad school. There’s a slim book on Real Analysis that’s usually used for a two-semester sequence! On the other hand, there seem to be any number of good abstract algebra books — largely because that subject lends itself readily to nice pictures and such.
Undergrad abstract algebra, that is.
Maybe they just turn terribler in grad school. The impression I’ve gotten from elementary through undergrad math courses is that math is a conceptual subject that is taught as a series of memorizable rules and formulae. The nod to comprehension is “showing your work”, which of course means indicating the sequence of memorized rules that were followed to obtain a result rather than just the result (IMO, this amounts to a requirement for methodological orthodoxy rather than comprehension). Where these rules come from or why they are as they are is still left as a rather baffling exercise for the reader.
Obviously, you’ve never had a child stuck with “Chicago Math.”
http://www.math.jmu.edu/~rosenhjd/Research.html
I don’t consider myself completely mathematically obtuse (I would still rather derive the equation for FC conversion than remember it. But then as a grad student in biochemistry, physical chemistry was required. I wanted to take the regular P-chem offered essentially next door to the lab, but was advised to take a watered-down version, which crossing to the other campus across the river. The professor was a rigid sort who would get red in the face if I asked if he could put an equation into words to help me understand it.
I note that Jason Rosenhouse implicitly assume that mathematics reviewers are male.
I have a set of calculus books which are the best I’d ever seen. The first english editions appeared before I was born and it annoys me that most universities use vastly inferior books instead. It seems everyone has their own book to push and few care about quality.
How often “improved” texts aren’t!
Of course, there is a rather famous short essay by Jared Diamond, bemoaning the same trend in biology papers. He gives a couple more reasons why all science should go to considerably longer lengths to be understood by non-experts. Highly recommended!
I did four years of university mathematics. In my third year I learnt the gap between the standard level mathematics course (designed for teachers or scientists and engineers with other specialisations) and the honours level course designed for professional mathematicians: “an honours-level student should be able to sit an exam for a standard level course by glancing over the curriculum the night before”
That was from a lecturer who saw me sitting in a pass level course (the honours level curriculum was a mix of pass and honours level options) and told me not to bother turning up to the classes and being bored by a term of what would be covered in an hour at the higher level.
In my final year, the only time I ever saw numbers other than 0, 1 or 2 were as page numbers.