When you see it, you'll shit bricks by 
Ciro Santilli 37 Updated 2025-06-02 +Created 1970-01-01
Ciro Santilli 37 Updated 2025-06-02 +Created 1970-01-01This one might actually be understandable! It is what Richard Feynman starts to explain at: Richard Feynman Quantum Electrodynamics Lecture at University of Auckland (1979).
The difficulty is then proving that the total probability remains at 1, and maybe causality is hard too.
The path integral formulation can be seen as a generalization of the double-slit experiment to infinitely many slits.
Feynman first stared working it out for non-relativistic quantum mechanics, with the relativistic goal in mind, and only later on he attained the relativistic goal.
TODO why intuitively did he take that approach? Likely is makes it easier to add special relativity.
This approach more directly suggests the idea that quantum particles take all possible paths.
Lysozyme structure resolution (1965) by Ciro Santilli 37 Updated 2025-06-02 +Created 1970-01-01
Ciro Santilli 37 Updated 2025-06-02 +Created 1970-01-01With X-ray crystallography by David Chilton Phillips. The second protein to be resolved fter after myoglobin, and the first enzyme.
Published at: Structure of Hen Egg-White Lysozyme: A Three-dimensional Fourier Synthesis at 2 Å Resolution (1965). The work was done while at the Davy Faraday Research Laboratory of the Royal Institution.
Phillips also published a lower resolution (6angstrom) of the enzyme-inhibitor complexes at about the same time: Structure of Some Crystalline Lysozyme-Inhibitor Complexes Determined by X-Ray Analysis At 6 Å Resolution (1965). The point of doing this is that it points out the active site of the enzyme.
en.wikipedia.org/wiki/Logarithm_of_a_matrix#Existence mentions it always exists for all invertible complex matrices. But the real condition is more complicated. Notable counter example: -1 cannot be reached by any real .
The Lie algebra exponential covering problem can be seen as a generalized version of this problem, because
- Lie algebra of is just the entire
- we can immediately exclude non-invertible matrices from being the result of the exponential, because has inverse , so we already know that non-invertible matrices are not reachable
Lots of similar ideologies to Ciro Santilli, love it:
- sandymaguire.me/blog/reaching-climbing/: don't be a pussyOne is also reminded of Gwern Branwen. Sandy is also into self-improvement stuff, so even more like Gwern. This is a point Ciro diverges on. Ciro works actively on self-worsening.
Last Friday was my final day at work. According to my facebook profile, I am now "happily retired." As of today, I don't plan to do another day of "traditional work" in my life. That's not to say that I'll be sitting idle playing tiddly winks. I want to build things, to dedicate my life to independent study, and to get really, really good with building communities. I don't have time for any of this "work" stuff that somehow pervades our entire culture, choking our inspiration and sapping our energy away from the things we'd rather be doing.
- he thinks university is useless:
- sandymaguire.me/blog/where-uni-fails/ Where University Fails (2018), mostly talking about backward design
- sandymaguire.me/blog/gatekept/ rejected from Imperial College PhD program due to grade being slightly too low for their stupid requirements, even though he had a referral already, and an amazing CV
- he likes jazz: sandymaguire.me/blog/too-smart/
Other interesting points:
- sandymaguire.me/blog/sandy-runback/ he changed his own name to Sandy because he didn't like it, he was born Alexander
- algebradriven.design/ closed source books though, ouch. At least they seem to have been made with leanpub though, could be worse.
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