Facility with calculus, specifically integration and differentiation, is mandatory for just about any technical discipline. Slog the first is setting up the problem, Slog the second is hacking through whatever differential equations and/or integrals present themselves. For those of us of a certain age, getting to calculus in high school was a badge of honor and being able to evaluate difficult integrals through clever substitutions and grit a point of pride.
Time has passed and the standards have gone up. Way way up. The kids these days are learning more, learning it earlier, and are scaling peaks we didn’t know existed. The mathematics subculture on the Internet is fueling this fire and a particular segment of Youtube is devoted to these calculations both for fun and for education. MIT has even held an “Integration Bee” for many years where students go head-to-head under time pressure.
Leading this pack is Jens Fehlau, an early twenty-something bro from Germany whose skills and presentation style make us glad we aren’t in a class where he’s ruining the curve. His Flammable (formerly Fappable) Maths channel has a strong following with early videos in German and more recent ones in excellent English with calming sounds of chalk on a chalkboard. Fehlau also reminds me of a college classmate of mine who did exactly that and is now an eminent professor of chemistry.
Here’s one of his playlists. Fair warning – the language can get salty at times.
I’ve studied Schubert’s Op.90 E-flat Major Impromptu off and on for years, long before I was ready for it. In fact, I’m still not. With expert teaching, even novices can use the great repertoire to learn and develop technique as a complement to scales, pedagogical exercises, and short pieces. Up and coming pianist Martin James Bartlett has, at the age of 22, a mantelful of awards and a promising career ahead of him. This Impromptu is no challenge for his considerable technique. Nevertheless, Knight Commander András Schiff gently guides him towards bringing out the orchestral colors hidden in the piece, to bow a percussive instrument like a viol, and frees Bartlett’s voice without imposing his own will on the young musician. Schiff’s legendary dry wit never oversteps into unkindness, except of course to the very late Carl Czerny who often takes it in the shorts in Schiff’s Guardian Lectures on the Beethoven Sonatas. It is gratifying to see that the steps to improvement at ones own level often recapitulates those of experts. This is education at its finest.
Without much further comment, here’s a very deep look into an industrial gas turbine engine. The CAD/CAM work is terrific and one wonders at the design and manufacturing effort put into just this one product.
[Edited 3 September 2018: Original video was taken down by the Youtube poster. Replaced with another link]
[Edited 6 January 2019: No longer available on the backup site, either. Takedowns suspected]
[Edited 13 March 2019: Aaand it is back. For now]
Eric Betzig‘s lab at the Janelia Research Campus has just released a jaw-dropping high-definition 3D movie of cellular machinery in motion. Words are not sufficient to describe the beauty of the data and the impact of the method which will soon be made available to researchers interested in using or developing it.
I met the man a few times during my postdoctoral life at Bell Laboratories where he was a research scientist. An acknowledged star in a building full of brilliant people, his Near-Field Scanning Optical Microscope was considered Nobel worthy. The Labs went down the tubes a few years later when the MBA visigoths took over. Betzig left, reinvented himself a couple of times, and came back with even more pathbreaking ideas in microscopy that overcame what he felt were insurmountable limitations of his first breakthrough. He went to Stockholm in 2014 for the newer inventions and the doors they opened. The Prize has not slowed him down.
Observing the cell in its native state: Imaging subcellular dynamics in multicellular organisms
T. Liu et.al.
Science 360, eaaq1392 (2018). DOI: 10.1126/science.aaq1392
The Abstract is also available through PubMed
The Internet overall is hastening the demise of what’s left of civilization. That’s hard for an early adopter to say but even harder to refute. The availability of online courses is a refuge of sweet in a tsunami of bitter. These series by Prof. Venkataraman Balakrishnan of IIT Madras explain subjects I thought I knew and give me an incentive to understand topics I never thought I would. One man, one chalkboard – utterly engrossing.
The sequence: Classical physics, Selected Topics in Mathematical Physics, Topics in Nonlinear Dynamics
LIGO took a lot of heat for twenty years. Too speculative, too expensive, real soon now, when already? Once it got over the hump… Damn! Two LIGOs and VIRGO pointed the way. Perhaps they should be rechristened Bonnie, Anita, and Ruth.