The joy of sets
prospectmagazine.co.uk
prospectmagazine.co.uk
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.
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.
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.
I have a feeling many technically minded people would struggle to read and write an essay about Heidegger or Habermas. In fact, I doubt most people are even aware of that type of philosophy due to not having actually delved into it very deeply, and yet as outsiders to such fields they feel confident in making claims that those fields are "easier." (And usually there is also an implication that this being "easier" is an indication of those fields being less serious or worthwhile.)
However, it's not the case.
I also find more stem people reading entry level materials in philosophy around me (like Moral letters to Lucilius), that I will find non stem people ready entry level materials in science (like A brief history of time).
The ratio is hugely disproportionate, and while I understand this is all anecdotal, I have a large and very diverse social circle to observe, spanning on wide areas of age, social backgrounds, political preferences, sexual orientation and jobs.
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.
[0] https://web.archive.org/web/20221201000000*/https://www.maa....
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.
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
Terminology aside, it didn't seem that the article was trying to drive wedges, but in fact attempting to build bridges.
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.
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.
(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)
Sets really only get mentioned once in passing; the article is more a general defense of the beauty of mathematics.
There's a bit more going on there than just what's your favorite kind of math.