Ciro Santilli @cirosantilli 37

Ciro Santilli 37 Updated 2025-07-16

Ciro Santilli believes that the Donald Trump bans were extremely unfair, and highlight the need for government to ensure greater freedom of speech in social media, more information at: cirosantilli.com/china-dictatorship/unjust-social-media-censorship-in-the-west, related: globalization reduces the power of governments.

techcrunch.com/2021/05/24/floridas-ban-on-bans-will-test-first-amendment-rights-of-social-media-companies/

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Short-read DNA sequencing by

Ciro Santilli 37 Updated 2025-07-16

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Fog computing by

Ciro Santilli 37 Updated 2025-07-16

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Our definition of fog computing: a system that uses the computational resources of individuals who volunteer their own devices, in which you give each of the volunteers part of a computational problem that you want to solve.

Folding@home and SETI@home are perfect example of that definition.

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Antimatter by

Ciro Santilli 37 Updated 2025-07-16

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Predicted by the Dirac equation.

Can be easily seen from the solution of Equation "Expanded Dirac equation in Planck units" when the particle is at rest as shown at Video "Quantum Mechanics 12b - Dirac Equation II by ViaScience (2015)".

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Klein-Gordon equation by

Ciro Santilli 37 Updated 2025-07-16

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A relativistic version of the Schrödinger equation.

Correctly describes spin 0 particles.

The most memorable version of the equation can be written as shown at Section "Klein-Gordon equation in Einstein notation" with Einstein notation and Planck units:

\partial_{i} \partial^{i} ψ - m^{2} ψ = 0

(1)

Has some issues which are solved by the Dirac equation:

it has a second time derivative of the wave function. Therefore, to solve it we must specify not only the initial value of the wave equation, but also the derivative of the wave equation,
As mentioned at Advanced quantum mechanics by Freeman Dyson (1951) and further clarified at: physics.stackexchange.com/questions/340023/cant-the-negative-probabilities-of-klein-gordon-equation-be-avoided, this would lead to negative probabilities.
the modulus of the wave function is not constant and therefore not always one, and therefore cannot be interpreted as a probability density anymore
since we are working with the square of the energy, we have both positive and negative value solutions. This is also a features of the Dirac equation however.

Bibliography:

Video "Quantum Mechanics 12a - Dirac Equation I by ViaScience (2015)" at youtu.be/OCuaBmAzqek?t=600
An Introduction to QED and QCD by Jeff Forshaw (1997) 1.2 "Relativistic Wave Equations" and 1.4 "The Klein Gordon Equation" gives some key ideas
2011 PHYS 485 lecture videos by Roger Moore from the University of Alberta at around 7:30
www.youtube.com/watch?v=WqoIW85xwoU&list=PL54DF0652B30D99A4&index=65 "L2. The Klein-Gordon Equation" by doctorphys
sites.ualberta.ca/~gingrich/courses/phys512/node21.html from Advanced quantum mechanics II by Douglas Gingrich (2004)
- sites.ualberta.ca/~gingrich/courses/phys512/node23.html gives Lorentz invariance

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Cryogen-free dilution refrigerator by

Ciro Santilli 37 Updated 2025-07-16

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Developmental genetics by

Ciro Santilli 37 Updated 2025-07-16

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How genes form bodies.

Video 1.

Developmental Genetics 1 by Joseph Ross (2020)

Source. Talks about homeobox genes.

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The orthogonal group is the group of all matrices that preserve the dot product by

Ciro Santilli 37 Updated 2025-07-16

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When viewed as matrices, it is the group of all matrices that preserve the dot product, i.e.:

O (n) = O \in M (n) ∣\forall x, y, x^{T} y = (O x)^{T} (O y)

(1)

This implies that it also preserves important geometric notions such as norm (intuitively: distance between two points) and angles.

This is perhaps the best "default definition".

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Product definition of the exponential function by

Ciro Santilli 37 Updated 2025-07-16

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e^{x} = lim_{n \to \infty} (1 + \frac{x}{n})^{n}

(1)

The basic intuition for this is to start from the origin and make small changes to the function based on its known derivative at the origin.

More precisely, we know that for any base b, exponentiation satisfies:

$b^{x + y} = b^{x} b^{y}$ .
$b^{0} = 1$ .

And we also know that for

b = e

in particular that we satisfy the exponential function differential equation and so:

\frac{d e ^{x}}{d x} (0) = 1

(2)

One interesting fact is that the only thing we use from the exponential function differential equation is the value around

x = 0

, which is quite little information! This idea is basically what is behind the importance of the ralationship between Lie group-Lie algebra correspondence via the exponential map. In the more general settings of groups and manifolds, restricting ourselves to be near the origin is a huge advantage.

Now suppose that we want to calculate

e^{1}

. The idea is to start from

e^{0}

and then then to use the first order of the Taylor series to extend the known value of

e^{0}

e^{1}

E.g., if we split into 2 parts, we know that:

e^{1} = e^{1/2} e^{1/2}

(3)

or in three parts:

e^{1} = e^{1/3} e^{1/3} e^{1/3}

(4)

so we can just use arbitrarily many parts

e^{1/ n}

that are arbitrarily close to

x = 0

e^{1} = (e^{1/ n})^{n}

(5)

and more generally for any

x

we have:

e^{x} = (e^{x / n})^{n}

(6)

Let's see what happens with the Taylor series. We have near

y = 0

in little-o notation:

e^{y} = 1 + y + o (y)

(7)

Therefore, for

y = x / n

, which is near

y = 0

for any fixed

x

e^{x / n} = 1 + x / n + o (1/ n)

(8)

and therefore:

e^{x} = (e^{x / n})^{n} = (1 + x / n + o (1/ n))^{n}

(9)

which is basically the formula tha we wanted. We just have to convince ourselves that at

lim_{n \to \infty}

, the

o (1/ n)

disappears, i.e.:

(1 + x / n + o (1/ n))^{n} = (1 + x / n)^{n}

(10)

To do that, let's multiply

e^{y}

by itself once:

e^{y} e^{y} = (1 + y + o (y)) (1 + y + o (y)) = 1 + 2 y + o (y)

(11)

and multiplying a third time:

e^{y} e^{y} e^{y} = (1 + 2 y + o (y)) (1 + y + o (y)) = 1 + 3 y + o (y)

(12)

TODO conclude.

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Debugger by

Ciro Santilli 37 Updated 2025-07-16

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List of data breaches by

Ciro Santilli 37 Updated 2025-07-16

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CC BY-NC-SA by

Ciro Santilli 37 Updated 2025-07-16

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Too restrictive. People should be able to make money from stuff.

The definition of "commercial" could also be taken in extremely broad senses, making serious reuse risky in many applications.

Notably, many university courses use it, notably MIT OpenCourseWare. Ciro wonders if it is because academics are wary of industry, or if they want to make money from it themselves. This reminds Ciro of a documentary he watched about the origins of one an early web browsers in some American university. And then that university wanted to retain copyright to make money from it. But the PhDs made a separate company nonetheless. And someone from the company rightly said something along the lines of:

The goal of universities is to help create companies and to give back to society like that. Not to try and make money from inventions.

TODO source.

The GNU project does not like it either www.gnu.org/licenses/license-list.en.html#CC-BY-NC:

This license does not qualify as free, because there are restrictions on charging money for copies. Thus, we recommend you do not use this license for documentation.
In addition, it has a drawback for any sort of work: when a modified version has many authors, in practice getting permission for commercial use from all of them would become infeasible.

en.wikipedia.org/wiki/Creative_Commons_NonCommercial_license#Defining_%22Noncommercial%22 also talks about the obvious confusion this generates: nobody can agree what counts as commercial or not!

In September 2009 Creative Commons published a report titled, "Defining 'Noncommercial'". The report featured survey data, analysis, and expert opinions on what "noncommercial" means, how it applied to contemporary media, and how people who share media interpret the term. The report found that in some aspects there was public agreement on the meaning of "noncommercial", but for other aspects, there is wide variation in expectation of what the term means.

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Dan Kaminsky by

Ciro Santilli 37 Updated 2025-07-16

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A superstar security researcher with some major exploits from in the 2000's.

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PlanetMath by

Ciro Santilli 37 Updated 2025-07-16

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planetmath.org/

Based on GitHub pull requests: github.com/planetmath

Joe Corneli, of of the contributors, mentions this in a cool-sounding "Peeragogy" context at metameso.org/~joe/:

I earned my doctorate at The Open University in Milton Keynes, with a thesis focused on peer produced support for peer learning in the mathematics domain. The main case study was planetmath.org; the ideas also informed the development of “Peeragogy”.

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Atlas (topology) by

Ciro Santilli 37 Updated 2025-07-16

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Collection of coordinate charts.

The key element in the definition of a manifold.

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Chinese character by

Ciro Santilli 37 Updated 2025-07-16

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cirosantilli.com/china-dictatorship/schinese-characters-are-insane

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Lotus-Eater Machine by

Ciro Santilli 37 Updated 2025-07-16

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tvtropes.org/pmwiki/pmwiki.php/Main/LotusEaterMachine

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Supernatural martial arts by

Ciro Santilli 37 Updated 2025-07-16

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tvtropes.org/pmwiki/pmwiki.php/Main/SupernaturalMartialArts

Shame that the Chinese in the lat 20th early 21st like that bullshit so much. It just weakens everything. Just imaginge those works with more realistic fighting! Would be amazing.

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Coursera by

Ciro Santilli 37 Updated 2025-07-16

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Some courses at least allow you to see material for free, e.g.: www.coursera.org/learn/quantum-optics-single-photon/lecture/UYjLu/1-1-canonical-quantization. Lots of video focus as usual for MOOCs.

Some are paywalled: www.coursera.org/learn/theory-of-angular-momentum?specialization=quantum-mechanics-for-engineers

It is extremely hard to find the course materials without enrolling, even if enrolling for free! By trying to make money, they make their website shit.

The comment section does have a lot of activity: www.coursera.org/learn/statistical-mechanics/discussions/weeks/2! Nice. And works like a proper issue tracker. But it is also very hidden.

November 2023 topics:

quantum field theory: no
condensed matter: 1 by Rahul Nandkishore from Colorado Boulder: www.coursera.org/specializations/the-physics-of-emergence-introduction-to-condensed-matter

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 There are unlisted articles, also show them or only show them.