Mathematicians and scientists have vague folk theories of what math and science are that both are blurred ancestral memories of pre-WWII logical positivism.
These theories are totally wrong, but do little *direct* harm because they are mainly ignored in practice.
-
Show this thread
-
Comfortable folk theories of technical work do harm by filling the space where a better understanding could go, making its absence invisible. “Yes of course we know how to do science! We are scientists!” But clearly you didn’t, because you go so much of it wrong.
2 replies 3 retweets 36 likesShow this thread -
Some sciences are upgrading their understanding, which I am optimistic will lead to better science.https://meaningness.com/metablog/upgrade-your-cargo-cult …
2 replies 2 retweets 30 likesShow this thread -
Does the folk theory of mathematics also cause trouble? Here I am less confident, because math rarely has replication crises. However, this paper suggests to me that more and better math might get done if it were upgraded: https://personalpages.manchester.ac.uk/staff/hung.bui/ideal.pdf …pic.twitter.com/XSbDWXhDpz
4 replies 3 retweets 33 likesShow this thread -
"Of course we know how to do mathematics! We are mathematicians!" But there's good evidence you don't, and so you can't teach it clearly, and you can't reflect on whether you are doing it well or badly. https://personalpages.manchester.ac.uk/staff/hung.bui/ideal.pdf …pic.twitter.com/YsL16YdGVe
9 replies 4 retweets 41 likesShow this thread -
Replying to @Meaningness
yeah, I suspect that for many students who find they're "no good at" a subject (even when they're good at other similarly difficult subjects), it's because they can't catch on to the pattern of which things that discipline includes in its models and which are "irrelevant details"
2 replies 3 retweets 15 likes -
Replying to @s_r_constantin @Meaningness
My copy of that Ideal Mathematician essay has this Wittgenstein story at the start. "If a child does not respond to the suggestive gesture, it is separated from the others and treated as a lunatic."pic.twitter.com/lFMVTXqAux
1 reply 0 retweets 5 likes -
(the book is Tymoczko's 'New Directions in the Philosophy of Mathematics: An Anthology')
1 reply 0 retweets 2 likes -
Replying to @drossbucket @s_r_constantin
Would you recommend it? ("This provocative book goes beyond foundationalist questions to offer what has been called a “postmodern” assessment of the philosophy of mathematics — one that addresses issues of theoretical importance in terms of mathematical experience.") —blurb
1 reply 0 retweets 0 likes -
Replying to @Meaningness @s_r_constantin
Yeah I would, though you've already read the best bits - The Ideal Mathematician and Thurston's Proof and Progress. There's also some of Lakatos Proofs and Refutations, and I liked Judith Grabiner on 18th c mathematical culture - emailed you notes on that a while back.
2 replies 0 retweets 1 like
I re-read your notes on Grabiner. Good stuff! Maybe you could post publicly? With minimal polishing if that seems necessary.
-
-
Replying to @Meaningness @s_r_constantin
I'd completely forgotten what I'd written! Reading back, yeah that does look possible but probably want to polish a little bit, will take a proper look later
0 replies 0 retweets 2 likesThanks. Twitter will use this to make your timeline better. UndoUndo
-
-
-
Thanks. Twitter will use this to make your timeline better. UndoUndo
-
Loading seems to be taking a while.
Twitter may be over capacity or experiencing a momentary hiccup. Try again or visit Twitter Status for more information.