[HN Gopher] The two cultures of mathematics and biology (2014)
___________________________________________________________________
The two cultures of mathematics and biology (2014)
Author : xingyzt
Score : 54 points
Date : 2024-01-07 23:28 UTC (1 days ago)
(HTM) web link (liorpachter.wordpress.com)
(TXT) w3m dump (liorpachter.wordpress.com)
| vaidhy wrote:
| This article was written in 2014 and I do not know if the
| specifics are still true. However, I think mathematicians and
| biologists work in two different levels of abstraction.
|
| One is a lawful good with occasional venture into chaotic good,
| only to reform the chaos. The other is a true neutral with lot of
| expeditions into chaotic evil just for fun.
| dekhn wrote:
| Well, it's 2024, I'm a biologist, I read the thing about
| schemes, and I still don't understand what they are or how they
| would help me understand biology any better.
| irchans wrote:
| I'm an applied mathematician (Ph.D. in math but never a
| professor) and I did not want to try to understand the
| description of schemes in the obituary. I thought that the
| obituary was too technical for me. On the other hand, if I
| thought that schemes were useful for my work, then I would
| dig into them and try to understand them.
| dang wrote:
| Discussed at the time:
|
| _The two cultures of mathematics and biology_ -
| https://news.ycombinator.com/item?id=8819811 - Dec 2014 (69
| comments)
| dsign wrote:
| There are currently 251131639 sequenced proteins in UniProt[^1],
| so, that's a very lower bound on the number of things a modern
| biologist has to amuse themselves with. Many still consider
| biology as the study of each individual biological organism,
| system, or protein. But since there are so many of those, I argue
| that biology must become a science of methods of understanding,
| and not a science of bare understanding. It's the difference
| between a company that produces mining machinery and a company
| that sends miners with pick and shovel underground. And that
| transformation is going to require for biologists to become
| system scientists and engineers, steeped to the brim in math,
| biochemistry and computer sciences.
|
| [^1]: https://www.ebi.ac.uk/uniprot/TrEMBLstats
| RandomLensman wrote:
| There is an element to this, but at the same time things tend
| to get incredibly messy at the level of whole complex
| organisms. (Btw., that also holds for mining/geology: you can
| do a lot of complex measurements from the surface, drill some
| holes and still be wrong about what you encounter underground).
| DrScientist wrote:
| Why is there any science at all above pure maths? Why isn't
| physics, chemistry, geology etc etc just maths?
|
| That's because choosing the right level of abstraction is
| really important for making practical progress.
|
| For example penicillin was discovered and used to save millions
| of lives without any rigorous mathematical understanding of how
| the drug interacts with it's target.
|
| I'm not saying maths isn't incredibly useful and increasingly
| important in the study of biology, I'm just saying that
| approaches that don't need maths ( beyond simple counting et al
| ) are also very important as well - biology is so complex, it's
| too easy to get bogged down in the detail.
|
| Also I do wonder sometimes whether mathematicians don't
| actually _understand_ some of the maths they work on - they can
| follow the mathematical logic but can 't "see it". ie then find
| their way through the logic maze by following a logical thread
| in the darkness - better than stumbling around randomly - but
| it doesn't mean you understand the maze - and because they
| don't understand it beyond the 'following the logical thread'
| they can't communicate it to others.
|
| Perhaps the latter is unfair - I'm not a mathematician - I'd be
| interested to hear other views on that.
| chongli wrote:
| _Also I do wonder sometimes whether mathematicians don 't
| actually understand some of the maths they work on_
|
| We don't. One of the first steps to mathematical maturity is
| learning to let go of the need to understand, the need to
| visualize. Much of mathematics is a formal affair of making
| arguments to satisfy necessary and sufficient conditions.
| Trying to understand infinite-dimensional spaces or highly
| abstract sets and objects is too much, and unnecessary.
|
| _"Young man, in mathematics you don 't understand things.
| You just get used to them."_
|
| -- John von Neumann
| viknesh wrote:
| I would disagree. Mathematicians certainly don't need to
| visualize everything but "intuition" is a commonly used
| phrase which is a notion of understanding.
|
| Although math merely requires proving some statement, often
| having an intuition / understanding of how concepts
| interact with each other helps figure out which things are
| likely to be true.
| nyssos wrote:
| > Much of mathematics is a formal affair of making
| arguments to satisfy necessary and sufficient conditions.
|
| Some areas have a formalist culture like this (descriptive
| set theory seems to, for instance, though that might just
| be what it looks like from the outside), but it's far from
| universal. At the other end of the spectrum I find it hard
| to imagine anyone getting far with algebraic geometry
| without building intuition. And then of course in
| mathematical physics the intuition-frontier is always
| decades ahead of the formal one.
| jvvw wrote:
| I never felt I properly understood a proof unless I
| understood it both intuitively and formally. The formalism
| is to make sure your intuitions are water-tight. But there
| are proofs you can accept are formally correct without
| intuitively understanding them - I would accept the truth
| of such proof but not feel like I understood them.
| miguelmurca wrote:
| While I agree that it's very questionable that Nature would
| invite someone to write an obituary (or what have you) and then
| reject it, I fail to see what's so controversial about the text
| being overly technical. I work in Physics, and "[...] locus of
| solutions of sets of polynomial equations by combining the
| algebraic properties of the rings of polynomials with the
| geometric properties of this locus, known as a variety" is still
| an incredibly tough sentence to parse on the first pass. I cannot
| imagine how it would read for someone who is either unfamiliar
| (or only passingly familiar) with, for example, the concept of a
| ring; "algebraic properties of a ring of polynomials"? This just
| seems like a case of https://xkcd.com/2501/ , with a hint of
| arrogance in thinking everyone working in STEM must be as
| comfortable with abstract concepts of mathematics as
| mathematicians are.
| dullcrisp wrote:
| Just curious if you removed the words "rings of" would you have
| the same objections?
| melagonster wrote:
| this is unfortunately, author keep talk about this is useful in
| phylogeny, but biologists who work on phylogeny is not popular
| in the group of biologists who frequently publishing articles
| on Nature.
| jp57 wrote:
| The estrangement he observes aren't that surprising, in either
| direction. Many universities have both Math and Applied Math
| departments. Why have both unless the mathematicians in the Math
| department don't want to work on applications? I have spoken with
| people who say if you're working on an application, "it's not
| really math."
|
| In biology, there is almost certainly a self-selection effect in
| which the field attracts people who want to study science but are
| not comfortable with math, or just people who have a particular
| interest in plants or animals, which is uncorrelated with math
| skills.
|
| I suspect there is a self-selection effect in the other direction
| too. I was always good at math, but I never wanted to major in it
| or go to grad school in it. I got a PhD in AI and machine
| learning, which was quite mathematical enough, and yet I can't
| recall ever interacting with anyone from the math department. As
| far as I knew, they wanted to do "pure math" and weren't
| interested in applications. So the people who want to do
| practical things select them selves into other majors like
| physics, engineering, and computer science.
| jltsiren wrote:
| Each field has its own culture and its own way of thinking.
| People are often socialized to a particular culture in the
| university or even earlier, and it sticks. You can learn other
| fields on your own, but it's hard to adopt the culture without
| socialization.
|
| I did theoretical computer science in the university, leaning
| towards more applied stuff by the end of my PhD. I'm still a
| computer scientist at heart. I can follow some topics in
| research mathematics, but I don't think like a mathematician
| and I'm not interested in the same things. I work in
| bioinformatics these days, but I often zone out when people
| start talking about the stuff that goes in the results section
| of a paper. I'm not a bioinformatician, and I'm not interested
| in the same things. I've seen a similar culture gap between
| bioinformatics and "proper" biology, but I don't have first-
| hand experience with that.
| nyssos wrote:
| > Many universities have both Math and Applied Math
| departments. Why have both unless the mathematicians in the
| Math department don't want to work on applications?
|
| "Applied Mathematics" as a field is not literally "mathematics
| applied to something"; it's a fuzzy group of related topics
| (things like numerical analysis, PDEs, or computational linear
| algebra) that's grown large and culturally distinct enough to
| have its own department, much like theoretical CS or
| statistics. There are plenty of "applied" mathematicians who
| don't work on applications, and some "pure" mathematicians who
| do.
| Aromasin wrote:
| Applied Mathematics certainly has the intention of using Math
| to solve problems from other fields though. I studied
| Robotics, and shared several classes with people from the
| Applied Mathematics course; * Transportation Modelling (using
| math to model transport on roads, rail, and shipping, and
| solve optimisation problems) * Computer Vision (using math to
| recognise patterns in images) * Biomechanics (using math to
| model the movement and formation of all things biology; we
| did everything from a sperm cell locomotion to an Achilles
| tendon spring strength)
|
| There were others, but all of them had a very practical
| purpose, and most of the people I spent time with on the
| Applied Mathematics course were actively pursuing a career in
| engineering of some sort, while the Mathematics course was
| made up of either Pure Math people looking to go into
| academia, or people destined for finance.
| fritzo wrote:
| While Pachter enumerates differences in culture and breakdowns in
| collaboration, I feel the root cause is individual social
| attitude. The two cultures differ because their self-selected
| members differ in personality. What drew me to study math was the
| department's attitude of anarchy and irreverence. Status didn't
| matter, funding didn't matter, appearance didn't matter,
| prerequisites didn't matter, you just needed two people and two
| pieces of chalk and a blackboard and an afternoon. By contrast
| biologists I've worked with have been acutely attuned to
| hierarchy and funding strategy and marketing and credit
| attribution - social maneuvering that would fall as flat in math
| departments[1] as "third cohomology group" falls flat on Nature's
| reviewers.
|
| [1] in my limited experience of two math departments
| tbitrust wrote:
| > Status didn't matter
|
| Allow me to doubt that mathematics departments are immune to
| status competition.
| fritzo wrote:
| Sure a segment of the population aims for department head,
| but another segment is happy just being left alone to do
| their thing and pay via teaching. It was this less ambitious
| more self-motivated group who attracted me.
| nextos wrote:
| I think you are super right. As someone with extensive Math
| and pure CS training, this has been my experience working
| in Biology vs Math departments.
| klyrs wrote:
| In my limited experience...
|
| Status matters. Politics are nasty. Every subfield has its own
| culture, its own royalty. Better funded professors get more and
| higher status students. Bigotry is common, and so are "quirky
| personalities" -- and due to the tolerance of weirdos, bigotry
| is assumed to not exist. Mathematicians are not without their
| people problems. Just like every other slice of humanity, they
| lie to themselves.
| Herring wrote:
| These kinds of articles are not helpful. "Why isn't A talking to
| B? Isn't that so sad?".
|
| People are busy (on both sides). If Mathematicians want to want
| to get Biologists' attention, they should do something like
| Deepmind's AlphaFold - tackle a long-standing extremely difficult
| problem in biology using mathematical approaches.
| waterheater wrote:
| For a ten year old article, it holds up remarkably well. Grant
| writing and academic research are typically divergent skill sets.
| Since research grants (the vast majority from DHHS, NSF, and DoD)
| have become a major source of revenue for universities, the most
| valuable faculty to a university are those who acquire grants,
| leading universities to hire faculty who will likely acquire many
| grants. These faculty select for similar students, and the cycle
| continues. Because pure mathematics research is intrinsically
| resource-minimal, the same paradigm doesn't work over there.
|
| In a possible reflection of that reality, I have a strong feeling
| that, on average, university biology departments are housed in
| much newer and nicer buildings than university mathematics
| departments.
| anthk wrote:
| Read The Computational Beauty of Nature. Also, compile the
| samples from the GitHub repo. If the samples panic X or your
| window manager, use DieHard.
| tech_ken wrote:
| > ... what mathematicians can deliver to genomics that is special
| and unique, is the ability to not only generalize, but to do so
| "correctly".
|
| I think this isn't really special or unique to mathematics.
| Certainly it's something that some mathematicians work hard to be
| good at, but many great mathematicians never play this game. Look
| at like Terry Tao, the man is undoubtedly one of the (if not the)
| greatest living mathematician, but IMO his best work tends to be
| these crazy mind-bending proofs or developments within specific
| areas of math. He's not a Grothendieck or a Hilbert who
| reorganizes concepts in elucidating ways or creates powerful
| generalizations. This isn't a knock on Tao, it's just pointing
| out that research fields are broad and require different
| skillsets. In terms of hard science it's IMO kind of the
| difference between a brilliant theorist and a brilliant
| experimentalist.
|
| Taking that comparison one step further, biology also has its
| theoreticians and its experimentalists. Being a skilled
| theoretician, understanding how to organize abstract concepts to
| the right level of generality, is definitely something that math
| can help you improve at, but it in no way is limited to
| mathematics. For example, Stephen Jay Gould was IMO brilliant at
| operating abstractly, but he had no formal mathematical training
| I'm aware of. Critical thought belongs to every field, even ones
| outside of research science (ex. Law, Philosophy).
|
| > But wouldn't it be better if mathematicians proved they are
| serious about biology and biologists truly experimented with
| mathematics?
|
| For the reasons above, this isn't clear to me. Does a first-year
| Ecology PhD really need to think critically about Hilbert spaces?
| They might find it to be a fun exercise, and I could see how they
| could get benefits from it, but they could get similar benefits
| from like any advanced philosophy course, IMO. I'm all for
| collaboration when it benefits both fields, but collaboration for
| collaboration's sake seems like a time sink without an obvious
| impact.
|
| caveat: this is all said 10 years after the post was written, I
| do think the cultural divide the author talks about has closed
| somewhat since writing, so maybe this arrangement is now just
| more palatable to me.
___________________________________________________________________
(page generated 2024-01-09 23:02 UTC)