Ooh, I’d forgotten about that test, and how the beer version was much easier—that would be another good one to read up on.
Not a full answer, but I would expect most of this kind of debate to be in more informal channels rather than journals (as in LiorSuchoy’s answer).Einstein, for example, was a prolific letter writer, and corresponded with many of the great physicists and mathematicians of the day, e.g. Born, Cartan and Schrödinger (from a quick google it looks like the Schrödinger letters are still not published as a collection, so I haven’t linked them).I read the Cartan letters, some time ago. I don’t have access to a copy now, but IIRC they get much more into picking at disagreements/clearing up confusions than anything you’d find in journals. For example, I opened up the Google Books preview, and immediately found the following from Einstein (on page 13):
I am sending to you my articles on the subject, published so far by the Academy. The second, on the approximate field equations, suffers, however, from the drawback that, with the choice made there for the Hamiltonian, a spherically symmetric electric field is impossible...
Then as well as letters, there’d be conversations at conferences, gossip over lunch and in department common rooms, question sessions after lectures. This stuff is mostly lost, though, whereas the letters can still be read now, so that’s where I’d look. All of this still goes on between researchers now, of course, and that’s still how news travels in individual research areas. If you want to know what’s wrong with published papers you’re much better off talking people in that field than trying to find retractions in the published literature. But academia was so much smaller then that informal networks of correspondence might plausibly cover large areas of science rather than a small research speciality.
Strangely, it can sometimes also go the other way!
One of my most eye-opening teaching experiences occurred when I was helping a six-year-old who was struggling with basic addition – or so it appeared. She was trying to work through a book that helped her to the concept of addition via various examples such as “If Nellie has three apples and is then given two more, how many apples does she have?” The poor little girl didn’t have a clue.
However, after spending a short time with her I discovered that she could do 3+2 with no problem whatsoever. In fact, she had no trouble with addition. She just couldn’t get her head around all these wretched apples, cakes, monkeys etc that were being used to “explain” the concept of addition to her. She needed to work through the book almost “backwards” – I had to help her understand that adding up apples was just an example of an abstract addition she could do perfectly well! Her problem was that all the books for six-year-olds went the other way round.
I think this is unusual though.
Ah yeah, I meant to make this bit clearer and forgot.
I’m not really sure what to make of that statement you put in italics. The jump in success rate could be down to better trained intuition. It could also be due to better access to formal methods. I don’t really see it as good evidence for my guess either way.
If I get more time later I’ll edit the post.
Thanks for the explanation!
This is the most compelling argument I’ve been able to think of too when I’ve tried before. Feynman has a nice analogue of it within physics in The Character of Physical Law:
… it would have been no use if Newton had simply said, ‘I now understand the planets’, and for later men to try to compare it with the earth’s pull on the moon, and for later men to say ‘Maybe what holds the galaxies together is gravitation’. We must try that. You could say ‘When you get to the size of the galaxies, since you know nothing about it, anything can happen’. I know, but there is no science in accepting this type of limitation.
I don’t think it goes through well in this case, for the reasons ricraz outlines in their reply. Group B already has plenty of energy to move forward, from taking our current qualitative understanding and trying to build more compelling explanatory models and find new experimental tests. It’s Group A that seems rather mired in equations that don’t easily connect.
Edit: I see I wrote about something similar before, in a rather rambling way.
Thanks for writing this, it’s a very concise summary of the parts of LW I’ve never been able to make sense of, and I’d love to have a better understanding of what makes the ideas in your bullet-pointed list appealing to those who tend towards ‘rationality realism’. (It’s sort of a background assumption in most LW stuff, so it’s hard to find places where it’s explicitly justified.)
What CFAR calls “purple”.
Is there any online reference explaining this?
Side note, but I really appreciated the bolded sentences marking the start and end of the ‘tiring symbolic reasoning’ section.
I normally give up on posts on this sort of topic precisely because I can see that I’m getting into an unknown amount of unpleasant mental effort holding all the “he said she said she said”s in my head at once. This time I could quickly gauge how much of that stuff there was, and it looked manageable, so I persevered.
I’m happy to answer questions, as I always like rambling about boring implementation details! I mentioned that I fancied trying this on Twitter and got a few takers. Right now I’m going for a pretty low tech approach where I just email it out—I write each one in a Google Doc and then paste it into Gmail and hope the formatting doesn’t mess up too much. I could definitely improve this!
I have another Google Doc going throughout the month where I make brief notes on what I’ve been reading or thinking about, any useful links, etc, so that I have something to work with once I start writing. This is actually really valuable on its own.
I’m not trying for any particular length but seem to be writing a fair bit—the last one was about 5000 words split over three or four topics. Generally one section of it is talking about whatever physics topic I’m currently interested in, and the rest is more of a mixed bag based on what I’ve thought about that month.
Update: I’ve done four of these now and have really enjoyed it. It works brilliantly for motivating me to keep a record of what I’m doing, and I’ve had some great followup conversations too. Thanks very much for introducing me to the idea!
my name is Dross,
and wen i see
the shiyning text
leap out at me,
i look at wot
it tels my hed -
i read the rules.
i like the red.
No, I also definitely wouldn’t lump mathematical analysis in with algebra… I’ve edited the post now as that was confusing, also see this reply.
Your ‘how much we know about the objects’ distinction is a good one and I’ll think about it.
I just start gnawing on the corn cob somewhere at random, like the horrible physicist I am :) But the ‘analysis’ style makes more sense to me of the two, it had never even occurred to me that you could eat corn in the ‘algebra’ style.
I also think about linear algebra in a very visual way. I’m missing that for a lot of group theory, which was presented to us in a very ‘memorise this random pile of definitions’ way. Some time I want to go back and fix this… when I can get it to the top of the very large pile of things I want to learn.
Ah, that probably needs clarifying… I was using ‘analysis’ in the sense of ‘opposed to synthesis’ as one of the dichotomies, rather than the mathematical sense of ‘analysis’. I.e. ‘breaking into parts’ as opposed to ‘building up’. That’s pretty confusing when one of the other dichotomies is algebra/geometry!
I agree that algebra and (mathematical) analysis are pretty different and I wouldn’t particularly lump them together. I’d personally probably lump it with geometry over algebra if I had to pick, but that’s likely to be a feature of how I learn and really it’s pretty different to either.
Thanks for writing this up! I was interested last time you mentioned it somewhere, and this time you’ve motivated me enough that I’m going to try it for a couple of months.
I also identify more with the elephant, which I (probably unhelpfully) think of as the one that ‘actually does maths and physics’, in the sense of gaining insights into problems and building intuitive understanding.
I (also probably unhelpfully) think of the rider as a more of a sort of dull bean counter who verifies the steps in my reasoning are correct afterwards, and ruins my fun for some of my wilder flights of fancy.
I’m slowly learning to like the rider more—it’s doing more than I give it credit for.
Probably some of the issue is trying to fit everything into these two categories. I think Sarah Constantin has convinced me that there are at least three things in the world—flow states, formal step-by-step reasoning and insight. I’ve been unthinkingly lumping flow state in with insight as the good stuff, and leaving the rider with just formal verification. Someone else might lump insight differently.
I like this and agree that this thing deserves its own name. In my own head (you may not agree) this view often also includes ideas like ‘explicit formal metrics often get Goodhart-ed into useless cargo cults, top-down rational plans often erase illegible local wisdom’, etc. The kind of cluster people seem to get from Seeing Like A State, The Great Transformation, etc. (I’ve never read either of those myself though.)
To my mind this cluster is something like ‘pomo ideas grafted on analytic rootstock’, rather than the normal continental rootstock. And I think the main influence it misses because of this is phenomenology (gworley I think may be pointing somewhere similar). Thinking seriously about subjective internal experience often pulls people towards a more thoroughgoing rejection of modernism than the ‘skeptical modernism’ one.
I don’t understand any of this well myself, though, and I’d struggle to unpack any of this into a compelling argument for someone who didn’t basically already agree with me.
I would also be interested in this! I saw a use for it within about an hour of reading the post, when I did something stupid and easily fixable with a bit of thought. I just wrote the problem into a gmail draft, but if doing this turns out to be useful I’ll try something more structured.