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(no subject)
Feb. 2nd, 2025 11:18 pmI keep coming back to this video about the relationship between (pre-)sheafs and cohomology. Here he says that "the number one technique in mathematics is turning any problem into a linear algebra problem.
More generally, Lawvere often talks about mapping geometry to algebra.
https://youtu.be/RPuWHN0BTio?si=U0h7YM-3GlcyvnS5&t=1890
D --> J <-- T ( c: D --> T is the solution to a choice problem, per Lawvere).
d: D --> J
e: T --> J
c: D --> T
This diagram is a regular Kan extension problem, with a cohomology twist, i.e. assigning values to both objects and arrows.
More generally, Lawvere often talks about mapping geometry to algebra.
https://youtu.be/RPuWHN0BTio?si=U0h7YM-3GlcyvnS5&t=1890
D --> J <-- T ( c: D --> T is the solution to a choice problem, per Lawvere).
d: D --> J
e: T --> J
c: D --> T
This diagram is a regular Kan extension problem, with a cohomology twist, i.e. assigning values to both objects and arrows.
(no subject)
Sep. 14th, 2024 10:31 amFDA approved Airpods2 as hearing aids for people with mild to medium hearing loss. https://www.wsj.com/tech/personal-tech/apple-airpods-pro-hearing-aid-features-af0f2714
As soon as it rolls out the software update this fall, Apple will instantly make the AirPods Pro 2 into a medical device, essentially turning every pair of the company’s top-selling headphones into over-the-counter hearing aids.
...
75% of people with hearing loss let it go untreated, according to the Apple Hearing Study, a project run with the University of Michigan. In case you don’t trust medical statistics from a trillion-dollar company trying to sell you something, the audiologists I consulted told me that number sounded right.
(no subject)
Aug. 15th, 2024 11:33 am
Ukrainian forces said they accepted the surrender of the largest single group of Russian soldiers since the start of the war more than two years ago, as Kyiv’s military claimed to continue expanding its cross-border incursion.
A Ukrainian Security Service unit operating in Russia’s Kursk region took 102 Russian servicemen as prisoners-of-war, according to a person with knowledge of the operation, who asked not to be identified because the matter is sensitive.
https://www.bloomberg.com/news/articles/2024-08-15/ukraine-reports-largest-surrender-by-russian-troops-of-the-war
(no subject)
Feb. 27th, 2024 08:08 pmThe development of computerized simulations and techniques for real-time imaging at microscopic scales provides a partial solution to the problem of visu- alizing such n-dimensional entities, by providing, in effect, 4D projections of them. With these techniques, the scientist or any other viewer of the imagery is removed from the production of the representation, however, which negatively affects the quality of insight and inference.
Quoted from Drawing Processes of Life, 2024.
One purpose of going from viewing to insight development would be discovery of transition points in the process of change, see e.g.
For example, the emergence of new opportunities and related decision forks can be represented as a critical point within the Morse-Smale theory.
(no subject)
Oct. 31st, 2023 09:38 pmTruth is not "relative" and certainly not "subjective" in the popular sense of the word. It is always, or almost always, completely determined within a thought style.
...
Truth is not a convention, but rather (1) in historical perspective, an event in the history of thought, (2) in its contemporary context, stylized thought constraint.
--- Ludwik Fleck, Genesis and development of a scientific fact.
The relationship to thought constraint sounds interesting. Also, we can probably model it as a topos of dynamical systems.
(no subject)
Aug. 28th, 2023 10:50 pmAn excerpt from The Good Shepherd (2006) script:
The movie bombed, both at the box and among the critics. But I really like the script, so far.
The movie bombed, both at the box and among the critics. But I really like the script, so far.
(no subject)
Jun. 8th, 2023 01:40 pm
Make Ukraine Putin-proof—and Trump-proof
Short of an explicit treaty that will be hard, but not impossible. America, for instance, has legal commitments that oblige it to provide Israel and Taiwan with the arms they need to defend themselves. The guarantees should cover weapons systems, ammunition, training and support to beef up Ukraine’s own defence industries. The more countries that sign up to them, the more convincing they would become—and the harder they would be to overturn if a Ukraine-sceptic like Donald Trump were elected. After the fighting stops, Western “tripwire” forces could be stationed on Ukrainian soil.
Ukraine’s fear, and Mr Putin’s hope, is that the West will lose focus. Only a successful counter-offensive and credible security pledges can get Russians to realise that Mr Putin’s war is futile—that he will never succeed, but can only fail, or fall.
