In "practice" it is likely "useless", because the functions that it can integrate that Riemann can't are just too funky to appear in practice :-)
Its value is much more indirect and subtle, as in "it serves as a solid basis of quantum mechanics" due to the definition of Hilbert spaces.
Solving differential equations was apparently Lie's original motivation for developing Lie groups. It is therefore likely one of the most understandable ways to approach it.
It appears that Lie's goal was to understand when can a differential equation have an explicitly written solution, much like Galois theory had done for algebraic equations. Both approaches use symmetry as the key tool.
- www.researchgate.net/profile/Michael_Frewer/publication/269465435_Lie-Groups_as_a_Tool_for_Solving_Differential_Equations/links/548cbf250cf214269f20e267/Lie-Groups-as-a-Tool-for-Solving-Differential-Equations.pdf Lie-Groups as a Tool for Solving Differential Equations by Michael Frewer. Slides with good examples.
Ciro Santilli's favorite music genre.
Ciro's 2020 perfect Friday evening: jazz fusion + study quantum field theory on an Amazon Kindle. Ahhhhhh.
This script tests all executables under a selected directory.
Ciro Santilli has been writing scripts of that type for a long time in order to test his programming self-learning setups with asserts.
The most advanced of those being the test system of Linux Kernel Module Cheat.
But had too much stuff that would be specific to that project, so Ciro decided to start this new one in Node.js, hopefully it will also be the last he ever writes.
A sample usage of the test library can be seen at: nodejs/sequelize/test.
This example shows how you could manually include the
dist/index.js that is output from webpack into your index.html.This is generally not what you want to do, because what you actually want to do is to use a Js output name with a hash in it, so that browsers only need to refetch when the name changes.
And to do that, we have to let webpack dynamically inject that unpredictable hash as done in webpack/template with:
new HtmlWebpackPlugin({
filename: 'index.html',
// Inject the include to our hashed filename,
// since it is not deterministic due to the hash.
inject: true,
template: path.resolve(__dirname, 'index.html'),
}),Dummy example of using a React
ref This example is useless and to the end user seems functionally equivalent to react/hello.html.It does however serve as a good example of what react does that is useful: it provides a "clear" separation between state and render code (which becomes once again much less clear in React function components.
Notably, this example is insane because at:we are extracing state from some random HTML string rather than having a clean JavaScript variable containing that value.
<button onClick={() => {
elem.innerHTML = (parseInt(elem.innerHTML) + 1).toString()In this case we managed to get away with it, but this is in general not easy/possible.
This seems like a cool dude. Besides a hardcore scientist, he also made many important contributions to the French education and research system.
And by artificial intelligence, read of course (non-human-identical) artificial general intelligence.
Today-2022, this is placed under the science fiction film category. But maybe this might change during Ciro Santilli's own lifetime?
The basic criteria of "is a film about artificial intelligence good or not" to Ciro Santilli is: does the AI inhabit humanoid, or fully human looking, bodies? Bodies is a bad sign due to:
- the best science fiction works deeply explore the consequences of one single technology: efficient humanoid bodies are a second technological breakthrough besides AI itself. The first AI will obviously be a supercomputer without a body
- it is hard to imagine that the AI wouldn't organize itself as one huge central computer and R&D/command center. Perhaps there will be need for a few separate ones to optimize usage of natural resources, and to have some redundance in case a nuke blows the region, but there would be very very few of the think tanks. But having big centers is fundamental, because you centralize all the flow of ideas and their combination leading to new better outcomes for the AI. The mobile robot actors controlled by this center, if any exist, would then be slaves with some degree of autonomy and infinitely less computational powerful than the think tank.
AMD Founder Jerry Sanders Interview (2002)
Source. Source: exhibits.stanford.edu/silicongenesis/catalog/hr396zc0393. Fun to watch.- youtu.be/HqWWoaA8pIs?t=779 Newton Minow mandated UHF on all television sets in 1961, and the oscillator needed for the tuner was one of the first major non-military products from Fairchild, the 28918 (?).
- youtu.be/HqWWoaA8pIs?t=1053 Fairchild had won the first round of a Minuteman contract, but lost the second one due to poor management
In Ciro's ASCII art circuit diagram notation, it is a loop with three Josephson junctions:
+----X-----+
| |
| |
| |
+--X----X--+
Superconducting Qubit by NTT SCL (2015)
Source. Offers an interesting interpretation of superposition in that type of device (TODO precise name, seems to be a flux qubit): current going clockwise or current going counter clockwise at the same time. youtu.be/xjlGL4Mvq7A?t=1348 clarifies that this is just one of the types of qubits, and that it was developed by Hans Mooij et. al., with a proposal in 1999 and experiments in 2000. The other type is dual to this one, and the superposition of the other type is between N and N + 1 copper pairs stored in a box.
Their circuit is a loop with three Josephson junctions, in Ciro's ASCII art circuit diagram notation:
+----X-----+
| |
| |
| |
+--X----X--+They name the clockwise and counter clockwise states and (named for Left and Right).
When half the magnetic flux quantum is applied as microwaves, this produces the ground state:where and cancel each other out. And the first excited state is:Then he mentions that:
- to go from 0 to 1, they apply the difference in energy
- if the duration is reduced by half, it creates a superposition of .
Ciro Santilli's admiration for Dyson goes beyond his "unify all the things approach", which Ciro loves, but also extends to the way he talks and the things he says. Dyson is one of Ciro's favorite physicist.
Besides this, he was also very idealistic compassionate, and supported a peaceful resolution until World War II with United Kingdom was basically inevitable. Note that this was a strategic mistake.
Dyson is "hawk nosed" as mentioned in Genius: Richard Feynman and Modern Physics by James Gleick (1994) chapter "Dyson". But he wasn't when he was young, see e.g. i2.wp.com/www.brainpickings.org/wp-content/uploads/2016/03/freemandyson_child-1.jpg?resize=768%2C1064&ssl=1 It sems that his nose just never stopped growing after puberty.
He also has some fun stories, like him practicing night climbing while at Cambridge University, and having walked from Cambridge to London (~86km!) in a day with his wheelchair bound friend.
Ciro Santilli feels that the label child prodigy applies even more so to him than to Feynman and Julian Schwinger.
Bibliography:
- QED and the men who made it: Dyson, Feynman, Schwinger, and Tomonaga by Silvan Schweber (1994) chapter 9 Freeman Dyson and the Structure of Quantum Field Theory
Old town sign of Fugging, Upper Austria
. Source. Welcome to Austria!
The language all browsers converted to as of 2019, and therefore the easiest one to distribute and most widely implemented programming language.
Hopefully will be killed by WebAssembly one day.
Because JavaScript is a relatively crap/ad-hoc language, it ended up some decent tooling to make up for that, e.g. stuff like linting via ESLint and reformatting through Prettier is much more widespread than in other languages.
JavaScript data structure are also quite a bit anemic, which makes libraries such as lodash incredibly popular. But most of that stuff should be in the stdlib.
Our JavaScript examples can be found at:
- Node.js example: examples that don't interact with any browser feature. We are just testing those on the CLI which is much more convenient.
- JavaScript browser example: examples that interact with browser-specific features, notably the DOM
Richard Feynman's mentor at Princeton University, and notable contributor to his development of quantum electrodynamics.
Worked with Niels Bohr at one point.
Web of Stories interview (1996): www.youtube.com/playlist?list=PLVV0r6CmEsFzVlqiUh95Q881umWUPjQbB. He's a bit slow, you wonder if he's going to continute or not! One wonders if it is because of age, or he's always been like that.
The definition is not very precise, as in many games with random elements there is a mixture of both skill and luck.
So we just use the precise Non-deterministic game term instead for any game that has any random element beyond the control of the players.
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