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I have very mixed feelings about this blog post, let me tell you why (a thread) 1/ https://twitter.com/maanow/status/1291354617780076546
To start, @profkeithdevlin is a very talented math communicator. One thing he does really well is call hard things hard, easy things easy, complicated things complicated. 2/
The blog post does a nice job of illustrating that 2+2=4 is more complicated than it appears and also a nice job of illustrating why it appears easy. 3/
Mixed feeling 1: Devlin acknowledges that the bulk of work on 2+2 and culture has been in primary education, but promptly sets that aside. On the one hand, that's fine, it's not his field. 4/
On the other hand, the context in primary education is actually really important for understanding why the controversy really matters, and why it's definitely *not* a controversy about axiomatization. 5/
Related, mixed feeling 2: I really sympathize with Devlin's impulse to set aside the ignorant straw-man-spouting trolls (to paraphrase the intro), but if your takeaway is "oh, it's about axioms rather than bad-faith trolls" then you've really missed the point. 6/
It would be great of @profkeithdevlin took this opportunity when the expertise of primary educators is under attack from reactionary trolls to stand up for these colleagues rather than dismiss the attacks and set primary educators aside. Maybe a future post? 7/
The cultural politics of primary math education (and the devaluing of culturally-aware instruction) are a huge part of the culture-ness of 2+2 and also a huge part of the background to the attacks on twitter and elsewhere. 8/
Mixed feeling 3: If you're going to make this about axiomatisation, I love the example of Russell and Whitehead's really long and complicated proof of 1+1=2. But Devlin misses some key points about the history that make the example even more relevant and illuminating. 9/
Before elaborating, let me add this link to @benjamindickman 's very on-the-nose point about the "idea" idea in this section, which links to mixed feelings 1 and 2 https://twitter.com/benjamindickman/status/1289950590311649280 10/
The missing historical context is that Russell and Whitehead's project emerged precisely out of major philosophical questions about the relation between mathematical formalisms, ideas, and reality, and the worry that obvious facts weren't backed by underlying truth. 11/
The other key historical aspect, in my view, is that Russell and Whitehead's proof of 1+1=2 was basically illegible and riddled with errors, and has stuck around as a cultural curiosity more than as a contribution to math/axiomatics. 12/
This tends to reinforce Devlin's claim that apparently mathematical discussions of axioms are actually about who has power in math (though "power" is conspicuously absent), so my mixed feeling is mainly about missed opportunity 13/
Mixed feeling 4: the turn to "if you count things in the world" which drops the whole key point Devlin just made about people and power in math. Who gets to be the universal "you" who "counts things"? The stakes of this are huge in primary education, which KD has set aside 14/
This relates to mixed feeling 5: whoa watch out for the tacit racism!
"anthropological studies of remote societies" gets a cheeky parenthetical, but from the 1860s *all the way up to the present* the anthropology of 2+2 has been deeply connected to racism and imperialism 15/
"anthropological studies of remote societies" gets a cheeky parenthetical, but from the 1860s *all the way up to the present* the anthropology of 2+2 has been deeply connected to racism and imperialism 15/
As it happens, I've published some articles on this:
* http://www.newscientist.com/article/mg21028081.500-one-two-many-the-prehistory-of-counting.html
* http://mbarany.com/SavageNumbersBJHS-FirstView.pdf 16/
* http://www.newscientist.com/article/mg21028081.500-one-two-many-the-prehistory-of-counting.html
* http://mbarany.com/SavageNumbersBJHS-FirstView.pdf 16/
Devlin pretty explicitly takes consensus about 2+2=4 as a universal among civilized cultures, and if that doesn't feel racist/imperialist to you in Devlin's article you should compare to how folks talked about 2+2 among the "savages" of Africa and Australia since the 1860s. 17/
Mixed feeling 6: Devlin walks all the way up to the absolutely essential point about how cultures naturalize their ways of seeing the world....
and then blows the point on some dodgy evopsych neurobabble. 18/
and then blows the point on some dodgy evopsych neurobabble. 18/
Let's take a moment to appreciate the key thing Devlin gets right here: as he says, mathematicians are deeply enculturated to see their work in terms of abstract eternal truths ... 19/
To my mind, the best evidence of this enculturation is that mathematicians are perfectly familiar with all the sociological phenomena that make their work contingent and context-bound and they *still* generally say at the end of the day they're doing universal abstractions 20/
So why then say "An answer is to be found" in "how the human brain evolved"? YOU'VE JUST GIVEN A PERFECTLY SENSIBLE NON-NEURAL/EVOLUTIONARY ANSWER WHY RUIN IT WITH THIS SPECULATIVE NONSENSE ABOUT "INEVITABLE" PERCEPTION? 21/
Speaking of which, Devlin just also acknowledged there are anthropological exceptions to his generalization about "universal" arithmetic, does he see how racist it is to then double down on their supposedly universal neural foundations? 22/
My feelings are not very mixed about the link between 0.999... and 1 + 2 + 3 + ....
That's some quality #scicomm
So let's take a moment to amplify @Sneffleupagus (h/t @MarissaKawehi ) on an earlier point: https://twitter.com/Sneffleupagus/status/1291373161028648961 23/
That's some quality #scicomm
So let's take a moment to amplify @Sneffleupagus (h/t @MarissaKawehi ) on an earlier point: https://twitter.com/Sneffleupagus/status/1291373161028648961 23/
Mixed feeling 7: I will leave it to @rmathematicus to dunk on the specious invocation of Galileo, and just add that the rest of that "built on Fibonacci who built on al-Khwarizmi who built on Brahmagupta" is comparably mythological and unhelpful. 24/
It's related to the myth that math is central to "modern western society" *because of* "its heavy dependence on technology" which is a common misunderstanding of the history of math's ubiquity. See https://blogs.scientificamerican.com/guest-blog/mathematicians-are-overselling-the-idea-that-math-is-everywhere/ 25/
This point from @rmathematicus belongs in the main thread: https://twitter.com/rmathematicus/status/1291380440906051584 26/
But the bottom line for mixed feeling 7 is it's good to recognize not all mainstream math is "Western" but it's probably counterproductive to talk about how "many cultures can lay claim to helping advance" math, which undercuts the key points about culture and power. 27/
Mixed feeling 8: it's really good that Devlin eventually gives a shout out to the existence of research on math and culture in K-12 ed! Lots of mathematicians weighing in miss that step. It would be better to promote specific work more recent than 1988. 28/
As Devlin surely recognizes, his endorsement carries a lot of weight for both mathematicians and non-mathematicians. Kind of a waste to use it on an (albeit perceptive and influential) article by a white man from back when Fermat's Last Theorem was still a conjecture. 29/
And on that specific "all modern human societies" point that Devlin extracts from Bishop, see mixed feeling 5. Especially when paired with the evopsych neurobabble (see mixed feeling 6). 30/
Decent list of questions in the conclusion; mixed feeling 9 is about whose perspective Devlin centers with these. He's clearly reaching beyond his own perspective to extend empathy,... who gets to be part of this exercise? 31/
Finally, mixed feeling 10: Devlin has *massively* buried the lede with this bracketed postscript "aside" about his military contract work. I allude to this toward the end of the "Everywhere" essay https://blogs.scientificamerican.com/guest-blog/mathematicians-are-overselling-the-idea-that-math-is-everywhere/ 32/
So, major kudos to Devlin for recognizing that his complicity with the surveillance state and military-industrial-academic complex are part of the story. It may be up to the rest of us to spell out what this means for math, culture, power, and society. 33/33
