It's not only in the abstract - "category" occurs all over the document. Possibly he's poking fun at category theory/theorists.
236 karma · joined September 23, 2012
In a chaotic system, minute differences in initial conditions are quickly amplified, making long time predictions impossible. A striking example of this is the potential instability of the solar system; we cannot rule out that a planet (earth!?) shoots off into space long before the sun turns into a red giant. On the other hand, in the wavelike world of quantum mechanics, trajectories are ``smeared out'' because of the uncertainty principle, and this seems to preclude the complicated picture of interlocking, yet divergent trajectories present in chaotic systems.
Thus, a fundamental (and somewhat philosophical) question is: how can macroscopic chaos arise in a world governed by quantum mechanics? The answer to this has been the subject of debate, but from the point of view of mathematical physics, a more concrete question is at the center: in what ways does chaos in classical dynamical systems manifest itself quantum mechanically, in particular in terms of spectral properties of "quantized Hamiltonians".
There is a fascinating connection between quantum chaos and number theory (the Riemann zeta function): the distribution of (normalized) gaps between zeros of the Riemann zeta function appears to be the "same" as the distribution of gaps between eigenvalues of quantized Hamiltonians associated to classically chaotic systems. There is a fun story of how H. Montgomery had (partially) computed the "pair correlation" ofthe gaps between Riemann zeta zeros, and at tea time at IAS he mentioned this to F. Dyson, who immeditely told him that this is the same as for random matrices, more details can be found in
http://www.bourbaphy.fr/keating.pdf
Some further info about quantum chaos:
http://www.ams.org/notices/200801/tx080100032p.pdf
https://en.wikipedia.org/wiki/Quantum_chaos
https://www.scientificamerican.com/article/quantum-chaos-sub...
2012: work starts on Mars station.
Elon, hurry up! :-)
"I’m suddenly concerned that all of published math is wrong because mathematicians are not checking the details, and I’ve seen them wrong before,”
Anyhow, for a computer with 16 bit wide data bus, having 16 bit ints might be justified by performance (and/or reducing memory usage.)
The engineers were very optimistic about selling this even as small municipal thermal power plants (for heating water) very close to city centers. The idea of passive safety is quite beatiful, but it seems no PIUS reactors were produced. Rosatom seems to have had some success.
More info about PIUS can be found at
https://www.iaea.org/sites/default/files/publications/magazi...
There are tons of good expositions on the FFT-way, e.g. check out
"Prime Numbers - A Computational Perspective" by Crandall-Pomerance see ch. 9, Fast algorithms for large-integer arithmetic
Ideally your organization should keep updated (public) host keys somewhere, say on some https-protected website so you can double check yourself. How common is this?
(I mainly use ssh for interactive/tunneling use, but with a bit of bad luck the host key would change just in time for scp. BTW, don't rsync/unison use scp sometimes?)
"Only then did I discover that the proof of a key lemma in my paper contained a mistake and that the lemma, as stated, could not be salvaged. Fortunately, I was able to prove a weaker and more complicated lemma, which turned out to be sufficient for all applications. A corrected sequence of arguments was published in 2006.
This story got me scared. Starting from 1993, multiple groups of mathematicians studied my paper at seminars and used it in their work and none of them noticed the mistake. And it clearly was not an accident."
More details on page 8 in the IAS newsletter article
https://www.ias.edu/sites/default/files/pdfs/publications/le...
There is also a Quanta article:
https://www.quantamagazine.org/univalent-foundations-redefin...
"Well, no," he continued. "Much more likely is that any family that has 100 children's books in the home is likely to be pretty highly educated to begin with, is starting out with a pretty high IQ, and values or treasures or rewards education to begin with."
The main point of the article is not about longevity, but rather: does the award lead to better or worse research? (It is awarded relatively early.)
"In fact I'm looking at the RAID-Z code right now. This scenario would be literally impossible because the code keeps everything read from the disk in memory in separate buffers - i.e. reconstructed data and bad data do not occupy or reuse the same memory space, and are concurrently allocated. The parity data is itself checksummed, as ZFS assumes it might be reading bad parity by default."
His full comment can be found here:
Question: What is the origin of STL? Has STL been conceived to be what it is now, that is "the" C++ Standard Library, or does it come from some other project? Could you tell us a history of STL?
Answer: In 1976, still back in the USSR, I got a very serious case of food poisoning from eating raw fish. While in the hospital, in the state of delirium, I suddenly realized that the ability to add numbers in parallel depends on the fact that addition is associative. (So, putting it simply, STL is the result of a bacterial infection.) In other words, I realized that a parallel reduction algorithm is associated with a semigroup structure type.
The full interview can be found at:
electricsheepcomix.com/almostguy/