There’s a lovely picture on the cover of the Proceedings of the National Academy of Sciences this week:
And a description of what it depicts, which is intriguing:
Cover image: Pictured is a modern version of the Borromean rings, a topological arrangement of three interlocked symmetric rings that owes its name to the Borromeo family of Italy on whose coat of arms the rings appear. Although the three rings cannot be pulled apart, no two of them are linked—a fact that becomes apparent when one of the rings is hidden from view. Jim Conant, Rob Schneiderman, and Peter Teichner derived this particular realization of the link from their theory of Whitney towers, where it represents the Jacobi identity, or IHX-relation. See the article by Conant et al. on pages 8131–8138, which is part of the Special Feature on Low Dimensional Geometry and Topology. Image courtesy of Jim Conant, Rob Schneiderman, and Peter Teichner.
But when you go to the paper, you’ll see that its abstract is so opaque to a non-mathematician that it might as well be written in Martian:
We show how to measure the failure of the Whitney move in dimension 4 by constructing higher-order intersection invariants of Whitney towers built from iterated Whitney disks on immersed surfaces in 4-manifolds. For Whitney towers on immersed disks in the 4-ball, we identify some of these new invariants with previously known link invariants such as Milnor, Sato-Levine, and Arf invariants. We also define higher-order Sato-Levine and Arf invariants and show that these invariants detect the obstructions to framing a twisted Whitney tower. Together with Milnor invariants, these higher-order invariants are shown to classify the existence of (twisted) Whitney towers of increasing order in the 4-ball. A conjecture regarding the nontriviality of the higher-order Arf invariants is formulated, and related implications for filtrations of string links and 3-dimensional homology cylinders are described.
(Presumably “Arf invariants” don’t refer to the unchanging vocalizations of a dog. )
This shows how far removed mathematics is from even other scientists. Or are our own biology abstracts just as opaque to mathematicians?
Conant, J., R. Schneiderman, and P. Teichner. 2011. Higher order dimensions in low level topology. Proc. Nat. Acad. Sci. USA 108:8131-8138.
h/t: Matthew Cobb
54 thoughts on “Math argot”
I would say: pretty much. Just a random pick here:
B cell-specific coactivator OCA-B, together with Oct-1/2, binds to octamer sites in promoters and enhancers to activate transcription of immunoglobulin (Ig) genes, although the mechanisms underlying their roles in enhancer-promoter communication are unknown. Here, we demonstrate a direct interaction of OCA-B with transcription factor TFII-I, which binds to DICE elements in Igh promoters, that affects transcription at two levels. First, OCA-B relieves HDAC3-mediated Igh promoter repression by competing with HDAC3 for binding to promoter-bound TFII-I. Second, and most importantly, Igh 3′ enhancer-bound OCA-B and promoter-bound TFII-I mediate promoter-enhancer interactions, in both cis and trans, that are important for Igh transcription. These and other results reveal an important function for OCA-B in Igh 3′ enhancer function in vivo and strongly favor an enhancer mechanism involving looping and facilitated factor recruitment rather than a tracking mechanism.
This abstract sounds appropriate for a specialist’s conference, but should not appear in a journal like PNAS.
Context and audience-appropriateness is everything.
I went to graduate school in mathematics, and yet I understand this biology abstract at least as well as the math one.
Come on! Enhancers and silencers do exactly what they say to promoters which initiate or promote transcription. Transcription is a high school term. Cis and trans and in vivo are Latin.
I’m sure most people, if they actually tried, could fake their way through most of this bio-med stuff.
4-Balls are also exactly what they say. 😉
Oh well, i don’t know… i studied both maths and biology and, while i can undestand, at least, what you’re writing about (even if i don’t know what OCA-B and TFII-I are), the mathematical abstract is martian, for me 🙂
OCA-B: Bone marrow-cell (backronym!) specific transcription coactivator.
These things are only abbreviations.
That math abstract is already opaque to many mathematicians.
The math abstract would certainly appear opaque to anyone who has not taken graduate-level courses in differential topology and knot theory. I have taken both and it’s not entirely transparent to me either.
I feel like maybe one or two sentences in most of my abstracts might be incomprehensible to someone with no knowledge of biology whatsoever. But, I think there’s an obligation to make most of it (at the very least the first few introductory sentences) clear to any educated reader, especially for such a widely-read journal as PNAS. These guys dive right into Sokal-level jargon in the first sentence and never look back. I don’t know what a single sentence in that abstract means.
I do wish more scientific papers would trumpet cool visuals. And have more cool visuals.
…And pay for more cool visuals. I gotta eat.
Which caused me to check out your website. Nice!
You might consider joining the Guild of Natursl Science Illustrators – http://www.gnsi.org/
Sorry to Jerry – just realizing how trolly that came off. And thanks Diane and Leslie – I’m a fan of the GNSI already though not a member.
My intention wasn’t to troll for hits, but just to agree that cool visuals can enhance understanding and enthusiasm in science. And right now, there are more and more science-related artists and image-makers doing tremendously cool stuff. I maintain the ScienceArtists Feed for scienceblogging.org, and there’s awesomeness there daily.
Any field of research within mathematics is likely to be unintelligible to many people from other fields of math. Topics like the Borromean Rings come up in the mathematics of topology and manifolds and would likely be incomprehensible to, say, a statistician. I’m sure you can take a paper from some field of biology and show it to a person in another field and find that they don’t understand much at all.
Yeah, gone are the days when someone like Euler could be at the cutting edge of many different fields at the same time. I’ve gotten used to it over the course of my PhD; now I don’t expect to understand any paper or seminar unless it’s closely related to my work.
I’m sure there was an xkcd comic about this recently…
“Arf invariant” sounds like it could be the name of a Frank Zappa song.
I envisioned an “Arf invariant” as the state of Evelyn, who was only able to go “Arf” while pondering the significance of short person behavior, in pedal-depressed and other highly ambient domains.
Except, the above sentence actually makes more sense than the math article, especially if you have experience stepping on a piano’s sustain pedal while making all kinds of noise above the strings.
(pedal-depressed, pan-chromatic, and other highly ambient domains… excuse me)
Flip side of “Poodle Lecture”
By Pure Maths standards the paper is extremely readable.
This shows how far removed mathematics is from even other scientists. Or are our own biology abstracts just as opaque to mathematicians?
Wow. No. Here, let me google that for you: http://lmgtfy.com/?q=topoisomerase+milnor+invariant
What’s worse, Andy Rooney scooped you by over two decades:
haha I loved it! and I am going to use that lmgtfy.com all the time now.
“Arf” is actually a proper name (of a Turkish mathematician) who discovered this algebraic object; to understand it you need a rigorous course in linear algebra.
The paper you talked about is about 4-dimensional topology; mathematicians who are non-specialists (even other topologists) would have difficulty understanding the statement of the abstract.
If you want to understand it, I’d suggest treating Shmel Weinburger to lunch; he is one of the world’s best topologists and he is at your university. He doesn’t know me, but I’ve seen him give invited lectures several times.
And yes, biology papers are, from my point of view, filled with technical language. I fully understand why; when you and your colleagues write papers, you are communicating to experts. You can’t start from scratch every time. 🙂
Speaking of the Borromean Rings, I might recommend this reference? 🙂
I work in social networks analysis, which has its own highly specialized set of jargon. It’s pretty abysmal, actually.
I work more on the practical applications side of it, but it gets really opaque the more you get towards the theoretical, modeling end of it.
“If there is evidence of Markov (and social circuit) dependence in y we may rule out “long-range” dependencies in the data generating process. The action
of removing an actor i does however induce dependencies among the tie-variables that are not of the type, Markov (and social circuit) dependence, that were assumed for y. Loosely speaking, the MD approach is able to pick out interdependencies between tie variables, that should be conditionally independent according to a model defined on the induced subgraph, as stemming from unobserved potential ties, the AC approach is unable to cope with this since it does assume that there are no unobserved tie
from: “Extreme Actors – Outliers and Influential Observations in exponential random graph (p-star)
I’m in the field, and that takes me too long to figure out what has been said, if I’m able to figure it out at all.
Indeed biological abstracts are opaque to mathematicians. Having a degree in mathematics and working in a biological lab for the last few years, I can attest that most mathematicians are absolutely unable to follow any biological text. However, it should be said that the mathematical abstract cited here is also not understood by most mathematicians. Currently mathematical disciplines such as topology and, say, statistics are so removed from each other that people working in one field have no possibility of exchanging even the abstract description of their results… How is it between biologists? Is it imaginable for a biologist to not understand a PNAS from a different sub-discipline of biology?
The answer to your question is “yes”.
I just came from a conference where all the talk was about SMADs and MIRs (miRNA) and HIF1-alpha, and all the rest.
Every priesthood needs its language.
I see several commenters noted already how specialist this math is, and how inappropriate for PNAS.
Unfortunately this is the type of abstract that got a strong push when knot theory became important for the latest fad in theoretical physics, string theory. IIRC Whitney moves tells you how to classify and unravel knots with respect to their topology.
I assume obstructions to moves tells you which knots persist. And I had to google filtrations: apparently they connect the topology to geometry, which takes you even further towards some nebulous use in theoretical physics.
I think you’re thinking of Reidemeister moves. “Whitney moves” here refers to what’s also called the “Whitney trick”, a way of getting rid of (self-)intersections of lower-dimensional manifolds inside higher ones. It only works when the dimension is high enough, and the fact that it fails in dimension 4 is (so I’m told by people who know this stuff much better than I do) connected with the fact that lots of topological things are easy in dimensions 5 and up or 4 and up, but go wrong in dimension 3 or 4 or thereabouts.
Talk of “measuring the obstructions” usually means that there’s some mathematical object that somehow classifies the ways in which something fails. It often seems to have something to do with cohomology. That appears to be the case here, but I regret that I don’t understand nearly enough of the paper to say anything more coherent.
Yes. I am very familiar with the Reidemeister moves, and the above is about the trick of removing self-intersections.
Dimension 5 and up are easier because we have the h-coboardism theorem, knots make stuff in dimension 3 hard, and 4 is just plain weird for a whole host of reasons.
Learn something new every day here! And there seems no subject to remote to not at least attract two or three experts 😉
the fact that lots of topological things are easy in dimensions 5 and up or 4 and up, but go wrong in dimension 3 or 4 or thereabouts
Is the key the understanding the Pointcare conjecture.
Which essentially deals with how can you tell if something looks like the surface of a four dimensional ball.
Every simply connected, closed 3-manifold is homeomorphic to the 3-sphere.
The problem was solved for all dimensions except four and finally solved after a hundred or so years of work just a couple of years ago.
I know that by “closed” you mean “compact, without boundary” but that should be emphasized.
“Whitney trick”, a way of getting rid of (self-) intersections of lower-dimensional manifolds inside higher ones
In other words Whitney came up with a trick to “Hide the decline” in dimensions. These scientists can not be trusted.
How much of a problem is caused by journals’ pressure to save space? There’s technical language, and then there’s dense technical language…
Engineers do it too . . .
I’m taking cytology right now at university, and some parts of my textbook might as well be written in Klingon. Tough class. Class average on 1st 2 midterms was below 55%.
You might enjoy the High Energy Physics paper generator:
We’ve actually played the game
and it’s not always easy even for an experienced theorist to tell which is the snarkticle.
That is a hoot! I only got 50%, which is of course chance.
As commented by many other people, math is an extreme case of specialization. Differential geometry/topology/knot theory doubly so. However, maybe it is worthy of nothing that there are still subfields of math that are accessible to normal people. Before I switched to biology, I was a math major. I used to walk past the office of one of the world’s leading experts in combinatorics. Every time the professor became impatient in solving some problem, he posted a note on his office door, promising a certain amount of monetary reward. The problems that he worked on tend to be explainable in less a page. Interestingly, some of those problems were solved by random people who walked by. The professor was very passionate about engaging lay person into solving original math problems.
I barely comprehend math beyond fairly basic algebra, but I LIVE the graphic. I soooooooooo want to create an embroidery piece using that graphic…
Argh – LOVE, not live. Damn fat fingers on the iPhone…
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!
You’re right, that is wonderful! Thanks for the link!
As an author of the paper, just let me comment that we tried to make the introduction readable and understandable to non-specialists and non-mathematicians, but we followed the standard mathematical convention of having the abstract describe the contents of the paper in technical detail. Seeing as how this was perceived, I now feel we should have also made the abstract less technical. Pure math papers in PNAS are a relative rarity, so we are treading on unexplored ground. We learn from our mistakes, and in I hope to see many more pure math papers appear in PNAS in the future.
It’s always nice when the subject of a post shows up for the conversation!
Much as I would love to be able to understand everything in every journal (HA!), there simply have to be subjects with specialized vocab so arcane as to seem like a second language. Which means some papers will indeed be opaque to most unless one footnotes every discipline-specific term with a lengthy, reader-friendly definition. I’m sure that would go over well. :rolls eyes:
BTW, we’re happy everyone liked the cover graphic. For me, it conveys the spirit of our discipline (low-dimensional topology) more effectively than words anyway.