amathstudent

The man it was made for tried it with his daughter: http://wadler.blogspot.com/2007/05/oh-no-alligators.html

Thank you!

Perhaps you might enjoy an essay I wrote on this very topic, based on my experiences of learning math on my own for 5 years: https://medium.com/@amathstudent/learning-math-on-your-own-3...

It's hardly 'long-forgotten'...

From Körner's book 'Fourier Analysis' (CUP, 1988):

"[...] Kelvin ... designed and built a ... machine (the harmonic analyser) to perform the task 'which seemed to the Astronomer Royal so complicated and difficult that no machine could master it' of computing the coefficients from the record of the past height [of tides].

Kelvin's harmonic analyser has a good claim to be the grandfather of today's computers not only because he obtained government money to build it but also because it represents the first major victory in the struggle 'to substitute brass for brain' in calculation. It is pleasant to record that Kelvin's instruments were so well adapted to their purpose that it took electronic computers 20 years to replace them.' - p.30-1

and

'We have seen ... how Kelvin invented machines which could compute periodic functions from their Fourier series and conversely obtain the Fourier series of a given periodic function. One such machine was constructed by Michelson to work to a higher accuracy and to involve many more terms that previous models. (Michelson's ability to build and operate equipment to new standards of accuracy was legendary. Of his interferometer which he invented and used in the Michelson Morley experiments it was said that it was a remarkable instrument - provided you had Michelson to operate it. His experiments to measure the diameter of the nearest stars using an interferometer were not reproduced for 30 years.)" - p.62

That was a well written article up until the links to sites behind Harvard University's paywall accessing service.

Of course, the problem with things like this, Huff's book, everything by David Freedman, etc., is that people want to lie with statistics. To put it more prosaically, people have biases, prejudices, socially-created expectations, ulterior motives, and usually statistics is a more-or-less subtle technique for whitewashing those into 'scientific knowledge'. This happens all across the social & biological sciences, in medical research, and in industry.

What a lovely comment!

What choices did you make that make KaTeX faster than MathJax? (i.e. 'how is it done?')

Here's something you might find interesting: http://vserver1.cscs.lsa.umich.edu/~crshalizi/weblog/698.htm...

There have are also loads of replication projects, some currently ongoing, of both experimental and statistical papers, with generally dismal results.

I think that's a very important point.

Indeed, when you try to explain something simply to people, they often won't believe that it's really that simple, since there's all those symbols!

As someone who knows it intimately, I would like to say that this kind of thing is endemic across the social science literature. What is frustrating is that only very few people seem to have the ability to understand why it is not sound.

I tried. I was hoping for something more like: "a field is something you can add, subtract, multiply, & divide in" and less like: "a field is a set that is a commutative group with respect to two different operations (excepting 0), linked by the distributive law".

I need something to hold on to when reading the more formal treatment.

I'm curious - can anyone point me to an overview/exposition of this that is more hand-wavy than the book? I'm interested understanding the ideas in this work, because proofs as objects would be a major step forward, but I don't even know much about the existing systems of foundations (ZFC etc), nevermind type theory...

That's fine, I like theoretical problems too.

I was wondering: I find this topic interesting from a conceptual point of view, but I'm reluctant to learn more about it without having some concrete useful application as motivation. Can anyone give an example like that?

Again a bit of a tangent, but I wrote an essay on learning math on your own based on my experiences: https://medium.com/@amathstudent/learning-math-on-your-own-3... - perhaps it will help you.

Wow, thank you so much! Finally I'll be able to understand what Arnold is on about in his talks! :-)

Thanks for that insightful explanation! I was wondering: could you explain in a nutshell what the KAM theorem is all about? I've heard about it many times, but I still have no idea what 'invariant tori' are...