Imagine retiring and making a living reviewing mathematics and science videos on YouTube. Could a computer do this job? *This Weeks Finds in Mathematical Physics VDO’s*. Seems to have a suitable i-gener dopey ring to it.

Well, if AI ever can respond emotionally to VDO content then perhaps there is no long term future in such an occupation, but for now I’d feel secure in such a retirement occupation if there were donations from readers. Not sure if I would be adding much value with such a service, but sometimes I daydream about some kind of semi-ideal existence. The problem with the idea is that you cannot truly be passionately involved in science or mathematics — to a level that would really add terrific value as a reviewer — unless you are also of the mind that gets captivated by puzzles and wants to explore them.

Because once you start launching an extension of an investigation suggested by a cool lecture or seminar, then you have a time sink. That’s ok though, you would probably simply add your investigations to the VDO review blog.

As for the need …? It would be a conceit to imagine anyone would be interested in a review article. Why not just click on the link that was recommended? Perhaps you have to read a bit of the blog of the person doing the recommendations, just so you feel they have a worthwhile opinion, so you don’t waste your time waiting for the ads and intro of a YouTube clip to get going only to find it is rubbish. But beyond this, I think there is a minor need for good VDO reviews. Maybe not quite yet, but perhaps soon there will be enough awesome science content on the Web that simply using a Google search will not get all the best videos onto the front hits page. So a reputable website with a reliably good quality list would be nice.

A few such lists already proliferate. So maybe my retirement plan is flawed. But there is still the hope that some creative insights could be added to the review, making them worth someone’s time to browse. Then after a few years at this your lists get long and so extended they become unreadable and useless, a list is needed for your list. The tyranny of obsession. When one is truly obsessed it becomes ironically impossible to interest others in your obsession. Then frustrated in not gaining converts, and ever increasingly being convinced of the virtues of one’s obsession, one finds it ever implausible that other people cannot be interested, one eventually then grows mad from the cognitive dissonance, and transcends into existence as an xkcd comic frame.

What I really want is for such brilliant quality science videos that it makes me forget about eating, and feeds my brain through sheer emotional charge. I’ve watched perhaps less than a half dozen such videos in my life so far, perhaps fewer. I will say that apart from Mr Feynman, there is a very nerdy but lunch-forgetting, series of lectures recorded at the Perimeter Institute by guest lecturer Carl Bender (PIRSA:C11025 – 11/12 PSI – Mathematical Physics ).

Actually those lectures gave me such an intellectual hard-on it had the reverse effect. I started making tuna and avocado salad grand sandwiches on whole grain with two quadruple shot latté’s accompanied by dark Whittaker’s dark chocolate and roasted cashew nuts, as my mid-morning brunch endangering my keyboard as I watched Bender gives his lecture’s in the privacy of my study. Tickets were free for this entertainment. Brilliant!

Mr Bender might be a superior educator to Mr Feynman. Feynman wins on entertainment value perhaps, but Bender gets ahead in terms of practical use.

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All that is a bit of a long introduction to a plug for one particular video find. “Douglas Hofstadter — Feuerbach’s Theorem: A Beautiful Theorem Deserves a Beautiful Proof” (www.youtube.com/watch?v=4Up22XOEVKc) It’s not viral or mind-blowing. It’s just a simple pleasure to find one like this to watch while eating lunch.

I wish Doug Hofstadter had a personal secretary who went around everywhere he speaks and videotaped the talks and lectures. Imagine all the university lectures he has given that have been lost for posterity because he lived in an era before ubiquitous video production. Oh yeah, sure, there will be more Hofstadter’s and Feynman’s in the future. One day even an Isaac Newton level dude or dude-ess will appear and all their talks will be recorded, maybe even their “brain waves” (you know what I mean).

(Is “dude” genderless???)

I was one of the rare theoretical physics, or mathematics major, students in my generation who actually took a course on Euclidean geometry. Most people (who are inclined to think about it) probably think Euclidean geometry was a bit of elementary mathematics in high school, mostly done as part of trigonometry. It’s sad if that’s true. For one thing, it is really cool to get immersed in Euclidean geometry and then slowly realise that when the lessons catch up to the 19th century math we begin to feel like something is uneasy, then we get Lobachevsky and Bolyai and then Gauss and Riemann and when General Relativity finally emerges it is like entering an Alice in Wonderland world.

This “astonishment and wonder” effect actually occurs even when you already know about Einstein’s spacetime and general relativity. There is just something special about studying a good well-paced course of Euclidean geometry with a good historical flavour in addition to the philosophical rigour.

I forget the lecturer’s name for the course I took at Victoria University of Wellington, New Zealand. All I recall was the weird association that struck me as bizarre, that the guy was a philosophy professor. The mathematics department at the time seemed too elite to bother with Euclidean geometry. Mathematics would start only with differential geometry and topology. Euclid was beneath them. (That may no longer be true, or it may be worse, but whatever the case, I am thankful to the VUW Philosophy department.)

So what’s so great about Hofstadter’s Feuerbach theorem lecture?

Just go see for yourself. It’s cool.

Hofstadter has his MacBook desktop exposed, with Geometer’s SketchPad showing some interactive demo’s of basic Euclidean geometry proofs. There are many little highlights: “good theorems deserve good names”; the remote triangle π sum theorems and variants, the “Andrew Wiles called out by a high school kid” anecdote. Another is the proof of the Isosceles Triangle Theorem — the philosophy dude who taught the VUW geometry course did not mention this one, so it was actually new and fresh for me.

That’s pretty awesome isn’t it? That you can find something very elementary and yet new and fresh and brilliant in such a well known century old subject. It’s a great lesson for educators. No subject need ever get stale. There are always creative new ways to present old knowledge. When the good educator finds new wyas to present old topics they are actually adding value and in some sense presenting a new thing, an original new idea, meta to the old idea perhaps, but still new. In my mind this is one reason why GOFAI will never replace a great teacher.

The point is, I think you can add to human experiences by teaching old topics that anyone can just find on Wikipedia or elsewhere, by adding new angles, new ways to express the same ideas. Furthermore, I see this as a useful and creative endeavour. It is a great service to investigate prior knowledge but present it in new crisper or more artistic fashion. Most importantly, I want the school teachers who teach my children, and your children, to understand this, and to not get bogged down by any existing curriculum or style of teaching.

In act one should go further, and teach the teachers to down-right ignore the pre-existing curricula. There is little value in syllabus’ and curricula , or standardized education models. At least when compared to the power of fresh approaches and creative or never-before-seen experiences in learning, compared to such innovations traditional school instruction is perhaps less than valuable, it might even be value-subtracting, if that’s possible! Why might it be “value subtracting”? One reason is that what already is available on the Internet is at most children’s fingertips, at least in the tech-enabled regions of the planet. And whatever is already at one’s fingertips is largely a waste of time trying to re-learn or learn through some inefficient school teacher’s bumbling lessons interrupted by the classroom distractions of other kids.

So teachers! Hear me! In your classroom forget about all the received knowledge and dry textbooks. Teach something new and fascinating or do not teach at all! Give them a book of puzzles rather than a textbook. If you have nothing creative to add then give your students an Internet connection and refer them to Wikipedia. That’s the least you can do for them, and it will at least not harm them.

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Well gosh, I know I had some other things to write about this little VDO of Hofstadter’s, but I seem to have forgotten my original point.

(BTW, Geometer’s Sketchpad is Non-Free software, so I’m not giving you the link! Try Geogebra instead.)

### Life advice for Today from OneOverEpsilon

Watch math lectures for lunch, not LOL Cats or Hollywood movies.

There are enough great sciency-math lectures out there now for great entertainment for many years worth of lunchtimes.

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(https://creativecommons.org/licenses/by-nc-sa/4.0/legalcode)