Linear operator Updated 2025-07-16
We define it as a linear map where the domain is the same as the image, i.e. an endofunction.
Examples:
Second quantization Updated 2025-07-16
Second quantization also appears to be useful not only for relativistic quantum mechanics, but also for condensed matter physics. The reason is that the basis idea is to use the number occupation basis. This basis is:
Bibliography:
Second law of thermodynamics Updated 2025-07-16
Subtle is the Lord by Abraham Pais (1982) chapter 4 "Entropy and Probability" mentions well how Boltzmann first thought that the second law was an actual base physical law of the universe while he was calculating numerical stuff for it, including as late as 1872.
But then he saw an argument by Johann Joseph Loschmidt that given the time reversibility of classical mechanics, and because they were thinking of atoms as classical balls as in the kinetic theory of gases, then there always exist a valid physical state where entropy decreases, by just reversing the direction of time and all particle speeds.
So from this he understood that the second law can only be probabilistic, and not a fundamental law of physics, which he published clearly in 1877.
Pleistocene Updated 2025-07-16
Agriculture is not the official definition of the age. But it is good enough. Likely related to the official end of glaciations thing.
Planned obsolescence Updated 2025-07-16
The first time Ciro Santilli Googled this was when trying to repair his cell phone.
2019 cell phones are glued together with adhesive, which makes them impossible to repair them unless you have a heat gun, spend hours and hours learning and planning, and accept the risk of breaking the screen
If you take a phone less than 300 dollars to a repair shop in the first world, they will say: I've never repaired this crap, and likely for the price of the repair you should just buy a new one, and so to the trash goes the old one, polluting the planet, and in comes a new one, enriching the manufacturer further.
Life difficulty level meme Updated 2025-07-16
TODO there was one which was relly good, can't find it anymore. One day.
Figure 1.
Life difficulty level meme with West Europe, East Europe, Turkey and Middle east
. Source.
Leo Szilard Updated 2025-07-16
Video 1.
Leo Szilard: The Genius Behind the Bomb
. Source. 1992. TODO an external link to the production? Producers credited at end: Helen Weiss and Alain Jehlen. As indicated at: archive.org/details/TheGeniusBehindtheBomb it was apparently produced by WGBH, public radio station from Boston.
Level: Asian Updated 2025-07-16
This is true. The level of competition in university entry exams in Asia in insane in the early 21st century compared to the West.
Fermat's last theorem Updated 2026-01-30
A generalization of the Pythagorean triple infinity question.
Ciro Santilli is a UK resident. He will register as a "solo trader" (slightly funny legal term) and treat donations that he uses for projects as grants, which pay regular income tax:The rates are given at: www.gov.uk/income-tax-rates and are as of writing:
  • 0 - £12,570 0%
  • £12,571 - £50,270: 20%
  • £50,271 - to £125,140: 40%
  • £125,140: 45%
National insurance is also likely going to be paid: www.gov.uk/self-employed-national-insurance-rates:
  • 6% on profits between £12,570 and £50,270
  • 2% on profits over £50,270
Fortunately however VAT does not need to be paid.
The amount that will be declared is the same as he grant amount that was requested, e.g. if 100k USD is requested for 1 year, then 100k USD will be pro-rata declared on that year.
Any remaining donations that don't yet meet specific grant goals will be initially treated as cash gifts which pay no tax. If in the future they are used as grant money after further goal amounts are reached, then they will taxed as grants.
Note however that if the donor is UK-based and dies within 7 years of the gift being given, inheritance tax has to be paid on them as per: www.gov.uk/inheritance-tax/gifts, at a maximum of 32% and going to to 0% at 7 years, so let me know from the afterlife.
Ciro paid his bill for £24,321.87 ($32,729.70) on 2026-01-02. Announcements:

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