[HN Gopher] The joy of sets
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The joy of sets
Author : drdee
Score : 51 points
Date : 2023-01-15 05:18 UTC (17 hours ago)
(HTM) web link (www.prospectmagazine.co.uk)
(TXT) w3m dump (www.prospectmagazine.co.uk)
| NoboruWataya wrote:
| Who are the "knee-jerk literary math-haters" the article is
| aiming at? I'm not aware of any and I certainly don't think the
| public or the establishment, in general, "hate maths". There is a
| weird tribalism in this article.
| adastra22 wrote:
| I think there is context you are lacking. This is an opinion
| piece within a British magazine. The UK prime minister, a
| member of the Conservative Party, has just proposed that the
| standard curriculum for high/secondary school extend the
| requirement to take math through age 18 / grade 12. Apparently
| right now it is only required that math be studied through age
| 16 / grade 10.
|
| Because this is a suggestion coming from the Tories, there has
| been in the last month or so a whole slew of opinion pieces
| ridiculing the suggestion that non-STEM students should be
| required to take maths past age 16. It's been called an
| elitist, out-of-touch policy change, requiring students to
| learn useless math they will never use, etc. etc.
|
| By and large these were all very politically-driven opinions. I
| can't help but think that the same people making these
| arguments might have been arguing the exact opposite--in favor
| of more maths education--if it had been their turn in power, or
| if the Conservative position was different.
|
| So yes, this opinion piece is rather tribal. But I think it is
| because he is responding to an intensely political issue and
| trying to talk some sense into people who are already forming
| opinions on a purely tribal basis.
| greenbit wrote:
| There's a weird tribalism baked into academia, isn't there?
| Thankfully it's not of an adversarial nature, more like garden
| variety dichotomy.
|
| Terminology aside, it didn't seem that the article was trying
| to drive wedges, but in fact attempting to build bridges.
| mananaysiempre wrote:
| "Haters" might be too strong a word, but of ugh-ers there are
| plenty, and humanities education does not seem to help--neither
| with the ugh-ing, nor with the social approval of said ugh-ing.
| And that is substantially harmful up to and including societal
| scales[1].
|
| Not that the ugh-ers are entirely at fault! In society where
| nobody actually teaches anything deserving to be called
| "maths"[2], certainly nothing that would give any clue as to
| why people would actually want to do this thing[3], there's
| little they could do to do better. Except maybe, as adults,
| wonder why there is this strange cluster of people who
| appreciate this apparently repulsive thing and investigate the
| reason for themselves.
|
| (Not that this appreciation is universal even among
| experimental physicists, for example.)
|
| [1] https://twitter.com/TeaKayB/status/1596485647115554817
|
| [2]
| https://www.maa.org/external_archive/devlin/devlin_03_08.htm...
|
| [3] https://physicstoday.scitation.org/doi/10.1063/1.2810679
| KrugerDunnings wrote:
| Sets are probably one of the most dull objects in maths, or at
| least overused as the become dull. Everything is a set, a circle
| is the set of points with a distance r from the center c, and so
| on.
|
| There are a lot more interesting things to write about than yet
| another article about Russels paradox. Maybe next time do the
| Erlanger program on why everything is a reflection.
| rumblerob wrote:
| I think the headline is a mild pun on the book The Joy of Sex:
| https://en.wikipedia.org/wiki/The_Joy_of_Sex
|
| Sets really only get mentioned once in passing; the article is
| more a general defense of the beauty of mathematics.
| alan-crowe wrote:
| Perhaps continuing the riff that Steven Strogatz started with
| his book: The Joy of x.
|
| https://www.stevenstrogatz.com/books/the-joy-of-x
| adastra22 wrote:
| This article isn't about sets.
| edgyquant wrote:
| I clicked into the comments hoping to find a bunch of
| discussion on set theory only to be let down.
| pklausler wrote:
| When non-mathematicians ask me to tell them something
| interesting about math, I show them the lambda calculus. It's
| straightforward and there's a kind of narrative involved when
| talking about reduction. Then it's fun to blow their minds with
| how this simple rewriting process can be used to implement
| anything that a computer can do.
| sureglymop wrote:
| I think they are used everywhere because you can describe
| everything with them easily. I mean i still prefer a set of
| points over a newly introduced definition of a "circle" just to
| be able to express a problem in mathematical language. It's
| kind of the same for functions too, they're used to describe so
| many things sometimes in a weird context too. I think the best
| abstraction is that which creates as little mental overhead as
| possible. Sets and relations are pretty basic and simple in
| that regard.
| c54 wrote:
| Fitting username for someone who didn't read even the beginning
| of the article
| KrugerDunnings wrote:
| Yea, this is HN for you
| 082349872349872 wrote:
| I found it more an article about Snow, about the short 20th
| century (do we have a better name for it yet?), about
| admissible plays in Glass Bead Games, than merely about
| Russell, who was but the hors d'oeuvre.
|
| (and, far from being dry --or at least, if you _are_ having dry
| sets, you might consider paying more attention to your
| interlocutor before introducing connectives--, Comfort has as
| much as Sunak to do with this article)
| greenbit wrote:
| The linked article isn't about sets as such. The item could
| just as easily have been titled _The Plight of the Primes_ or
| _The Anguish of Undecidability_
|
| There's a bit more going on there than just what's your
| favorite kind of math.
| greenbit wrote:
| During my undergrad education in engineering, we were required to
| include a significant number of 'humanities' courses. In
| hindsight this was clearly beneficial but even at the time one
| could see the sense in that. But it struck many of my classmates
| and me that it was a bit odd that the converse requirement did
| not exist. The "arts and humanities" majors were not required to
| take more than a couple of "math and science" courses. Maybe one
| of each? While we were taking full on regular 1st, 2nd, even 3rd
| year courses from their world, there were watered down math and
| science courses on offer for them.
|
| The asymmetry was baffling. We were told this would make us "well
| rounded", but it seemed that those outside the math-science-
| engineering world were considered Just Fine without even a 3rd
| semester of calculus, and were allowed to indulge a greater
| portion of their time at university in matters more directly
| aligned to their interests. This definitely put a division into
| the academic atmosphere, though not an acrimonious one; the two
| camps peaceably coexisted and as undergrads we all just did what
| we had to do.
|
| That was a while ago now, maybe things have changed somewhat. But
| from the article, it sounds like maybe not so much.
| 082349872349872 wrote:
| How will Morlocks ever be able to enjoy _filet of Eloi with
| garlic on its hot stone_ if the latter were to be encouraged to
| sample the former 's courses?
| [deleted]
| mncharity wrote:
| Selection pressure on science courses is largely around
| fulfilling prerequisites for the following course or exam. With
| a few university programs also polling recent graduates about
| what they have/haven't found useful. The connection between
| these, and transferable understanding of the physical world, is
| ... problematic.
|
| A pre-K science educator once suggested children have a human
| right to make sense of their world, "now" rather than several
| lifetimes later. Perhaps they imagined adapting existing K-12
| content to pre-K.
|
| But consider "color", widely taught around K. First-tier
| physical-sciences graduate students often reply to "What color
| is the Sun?" with answers like "it doesn't have a color" and
| "it's rainbow colored", reflecting foundational
| misunderstandings of color. Suggesting the challenge here isn't
| adapting working content to a younger audience, it's a lack of
| working content. And not just for "that falls through the
| gaping cracks" topics. At a first-tier university, asked what
| students entering intro-genetics from intro-bio most lacked, a
| noted professor replied "a firm grasp of central dogma". Which
| is foundational, and _is_ taught, repeatedly - repeatedly
| unsuccessfully.
|
| Consider someone suggesting liberal arts majors should study
| "science" ... as an old-school whole-class call-and-response
| exercise in mindless memorize-and-regurgitate. One might wonder
| if that would largely be a waste of their time. Not because
| their lives couldn't be enriched by understanding _science_ ,
| but because there's so little connection between this form of
| _science education_ and that potential enrichment.
|
| Science for non-majors is sort of a science education research
| area. But how much better are we set up to support it, than a
| call-and-response culture would be?
|
| As for making sense of the physical world, for pre-K, liberal
| arts, or first-tier physical-sciences graduate students? What's
| that phrase ... Big Hairy Audacious Goal.
| lordleft wrote:
| There was once a time when mathematics was considered central
| to humanistic and philosophical development. It is said that at
| the entrance of Plato's Academy, there was the following
| prohibition: "Let no man ignorant of geometry enter here."
| BiteCode_dev wrote:
| Well, most people in math and science majors can pass an arts
| and humanities major. The opposite is not necessarily true.
|
| Anecdotally, I can easily engage in talks about literature,
| politics and art with my friends coming from a biology or
| physics background. I can hardly do so with my friends with a
| major in French or Sociology. When we mix them together, the
| debate is always animated when we talk about philosophy, a
| specific author or book, and even painting. If we speak about
| GPT3 or the CERN, suddenly the table is divided in two.
| adastra22 wrote:
| To be fair though, at least in the USA an engineering degree
| requires significantly more coursework than a humanities
| degree. At my institution it basically added up to an extra
| year of courses, and was approximately equal to the added
| "general education" (non-engineering) requirements. And the
| general-ed requirements for engineers were less demanding than
| for the arts. So it's not like we were getting short-changed in
| a way that they were not.
|
| But that said, I agree with your main point. Humanities majors
| should be required to do a more in-depth survey of math,
| science, and engineering comparable (at the very least) to the
| introduction engineers are required to have of their fields. If
| that means they need to have a 5-year degree as well, so be it.
| _a_a_a_ wrote:
| "Why won't our artistic-literary establishment recognise that
| there's mystery, beauty and humanity in maths?"
|
| I have a maths background and I see none of mystery or beauty in
| it. Dunno what 'humanity' means here.
|
| I've noticed those in humanities are terrible at debating. They
| can't focus, slide off the subject and tend towards handwaving
| arguments with little rigour. Their soft subjects are important
| but they neglect 'our' side of the fence.
|
| > Who dares call maths dry?
|
| Me. But it's useful.
| lostmsu wrote:
| There's quite a bit of beauty in math (see Escher's works, and
| Permutation City; some things are enchanting on their own like
| fractals and strange loops). I think it is just not explored by
| artists enough, potentially due to unfamiliarity.
| bradrn wrote:
| This article reminds me very strongly of Lockhart's Lament [0],
| which at this point I think should be required reading for every
| mathematician and teacher. The essential message is the same:
| maths _is_ itself intrinsically fascinating as the exploration of
| foundational logical reasoning, so teach that instead of the
| boring stuff taught in maths classes now! (Lockhart writes in a
| specifically American context, but the general philosophy seems
| much more widely applicable to me.)
|
| [0]
| https://web.archive.org/web/20221201000000*/https://www.maa....
| edgyquant wrote:
| This has been my thinking for so long. Why teach a bunch of
| courses students say is boring? Can't we instead teach basic
| logic and philosophy in early years and then start students on
| basic set theory (or some equivalent) in their second or third
| year and have them slowly derive mathematics themselves?
| zzedd wrote:
| see https://en.wikipedia.org/wiki/New_Math
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