Not quite knitting, but close - you may like this piece by Sarah Perry explaining a spinning metaphor of Wittgenstein's:
And we extend our concept of number as in spinning a thread we twist fibre on fibre. And the strength of the thread does not reside in the fact that some one fibre runs through its whole length, but in the overlapping of many fibres.
Just curious, are you planning to migrate blog comments too? I didn't know about Netlify, but it looks very promising for what I want - a mostly static site with some support for storing form submissions - so I'm going to investigate it a bit now.
There was a Durham University study running from 2010 to 2013 where they asked the public to record their earworms (I contributed a few).They suggest a few features that go into a particularly persistent earworm. A couple that stood out to me:- Simple exposure. Songs that are currently popular tend to predominate. (There is a lot of Lady Gaga in their corpus.)- A melody in the 'sweet spot' where it's generic enough to be easy to remember and sing but also has some kind of distinctive 'hook' like an unusual interval.The popularity feature definitely fits Baby Shark. I think the melodic-sweet-spot feature does too: it's overall an extremely generic and repetitive tune, but also has the distinctive, painfully memorable 'doo doo do doo doo' bit.The paper they published is here (pdf link). From a quick skim I'm not convinced that the stats are going to be all that great, but you'll have to read it more closely to judge for yourself. At the least it might give you some useful hints on other references and some terminology to google.(And if you find anything interesting, let us know! I'm extremely prone to getting songs stuck in my head and would also like to know more about earworms.)
Oops, I fixed that in my blog version and then accidentally posted the old draft here. Edited now, thank you!
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.