Kaggle Updated 2026-01-30
To be fair, this is one of the least worse ones.
Synthetic geometry of the real projective plane Updated 2025-07-16
It good to think about how Euclid's postulates look like in the real projective plane:
- Since there is one point of infinity for each direction, there is one such point for every direction the two parallel lines might be at. The parallel postulate does not hold, and is replaced with a simpler more elegant version: every two lines meet at exactly one point.One thing to note however is that ther real projective plane does not have angles defined on it by definition. Those can be defined, forming elliptic geometry through the projective model of elliptic geometry, but we can interpret the "parallel lines" as "two lines that meet at a point at infinity"
- points in the real projective plane are lines in
- lines in the real projective plane are planes in .For every two projective points there is a single projective line that passes through them.Note however that not all lines in the real plane correspond to a projective line: only lines tangent to a circle at zero do.
Unlike the real projective line which is homotopic to the circle, the real projective plane is not homotopic to the sphere.
The topological difference bewteen the sphere and the real projective space is that for the sphere all those points in the x-y circle are identified to a single point.
One more generalized argument of this is the classification of closed surfaces, in which the real projective plane is a sphere with a hole cut and one Möbius strip glued in.
Symmetry breaking in superconductors Updated 2025-07-16
As mentioned in True Genius: The Life and Science of John Bardeen page 224, the idea of symmetry breaking was a major motivation in Josephson's study of the Josephson effect.
Sylvester's law of inertia Updated 2025-07-16
The main interest of this theorem is in classifying the indefinite orthogonal groups, which in turn is fundamental because the Lorentz group is an indefinite orthogonal groups, see: all indefinite orthogonal groups of matrices of equal metric signature are isomorphic.
It also tells us that a change of basis does not the alter the metric signature of a bilinear form, see matrix congruence can be seen as the change of basis of a bilinear form.
The theorem states that the number of 0, 1 and -1 in the metric signature is the same for two symmetric matrices that are congruent matrices.
For example, consider:
The eigenvalues of are and , and the associated eigenvectors are:symPy code:and from the eigendecomposition of a real symmetric matrix we know that:
A = Matrix([[2, sqrt(2)], [sqrt(2), 3]])
A.eigenvects()Now, instead of , we could use , where is an arbitrary diagonal matrix of type:With this, would reach a new matrix :Therefore, with this congruence, we are able to multiply the eigenvalues of by any positive number and . Since we are multiplying by two arbitrary positive numbers, we cannot change the signs of the original eigenvalues, and so the metric signature is maintained, but respecting that any value can be reached.
Note that the matrix congruence relation looks a bit like the eigendecomposition of a matrix:but note that does not have to contain eigenvalues, unlike the eigendecomposition of a matrix. This is because here is not fixed to having eigenvectors in its columns.
But because the matrix is symmetric however, we could always choose to actually diagonalize as mentioned at eigendecomposition of a real symmetric matrix. Therefore, the metric signature can be seen directly from eigenvalues.
What this does represent, is a general change of basis that maintains the matrix a symmetric matrix.
Super Mario 64 A press challenge Updated 2025-07-16
Superconductivity Updated 2025-07-16
Experiments:
- "An introduction to superconductivity" by Alfred Leitner originally published in 1965, source: www.alfredleitner.com/
- Isotope effect on the critical temperature. hyperphysics.phy-astr.gsu.edu/hbase/Solids/coop.html mentions that:
If electrical conduction in mercury were purely electronic, there should be no dependence upon the nuclear masses. This dependence of the critical temperature for superconductivity upon isotopic mass was the first direct evidence for interaction between the electrons and the lattice. This supported the BCS Theory of lattice coupling of electron pairs.
20. Fermi gases, BEC-BCS crossover by Wolfgang Ketterle (2014)
Source. Part of the "Atomic and Optical Physics" series, uploaded by MIT OpenCourseWare.Actually goes into the equations.
Notably, youtu.be/O_zjGYvP4Ps?t=3278 describes extremely briefly an experimental setup that more directly observes pair condensation.
Lecture notes:
Transition into superconductivity can be seen as a phase transition, which happens to be a second-order phase transition.
Superconducting tunnel junction Updated 2025-07-16
Specific type of Josephson junction. Probably can be made tiny and in huge numbers through photolithography.
Superconducting qubits are good because superconductivity is macroscopic Updated 2025-07-16
Superconducting qubits are regarded as promising because superconductivity is a macroscopic quantum phenomena of Bose Einstein condensation, and so as a macroscopic phenomena, it is easier to control and observe.
This is mentioned e.g. in this relatively early: physicsworld.com/a/superconducting-quantum-bits/. While most quantum phenomena is observed at the atomic scale, superconducting qubits are micrometer scale, which is huge!
Physicists are comfortable with the use of quantum mechanics to describe atomic and subatomic particles. However, in recent years we have discovered that micron-sized objects that have been produced using standard semiconductor-fabrication techniques – objects that are small on everyday scales but large compared with atoms – can also behave as quantum particles.
Sun Wukong Updated 2025-07-16
Only after Ciro became an adult did he finally understand that Sun Wukong was the basis for Dragon Ball as mentioned at: Figure "19th century illustration of the Journey to the West protagonist Sun Wukong". And that Sun Wukong was a million times more famous overall. Mind blown.
His given name "Wukong" literally means "the one who mastered the void" (Wu = Comprehend, Kong = void), so clearly a Dharma name. Edit: it is actually given in the novel, he was born without name. They seem to be Taoist however.
The family name sun1 孙 is the same character as "grandson", but most educated Chinese people seem to be able to recognize it as a reference to "monkey" from some archaic context not anymore in current usage.
19th century illustration of Sun Wukong
. Source. TODO check that it is actually 19th century. Because en.wikipedia.org/wiki/File:Xiyou2.PNG for Zhu Bajie, obviously from the same print, says it is 15th centure.
20 Sun Wukong depiction in Peking opera
. Source. Sun Microsystems Updated 2025-07-16
Although Ciro Santilli is a bit past their era, there's an aura of technical excellence about those people. It just seems that they sucked at business. Those open source hippies. Erm, wait.
Bibliography:
- archive.org/details/sunburstascentof00hall Sunburst: the ascent of Sun Microsystems by Mark Hall (1990)
stress-ng Updated 2025-07-16
STED microscopy Updated 2025-07-16
Instead of shining a light over the entire sample to saturate it, you illuminate just a small bit instead.
He was basically saying that this truly brings the resolution to the actual physical limits, going much much beyond 2014 Nobel prize levels.
Illumination patterns for STED microscopy
. Source. Stars nearest to the Sun Updated 2025-07-16
Some notable ones:
Standard cell library Updated 2025-07-16
Basically what register transfer level compiles to in order to achieve a real chip implementation.
After this is done, the final step is place and route.
They can be designed by third parties besides the semiconductor fabrication plants. E.g. Arm Ltd. markets its Artisan Standard Cell Libraries as mentioned e.g. at: web.archive.org/web/20211007050341/https://developer.arm.com/ip-products/physical-ip/logic This came from a 2004 acquisition: www.eetimes.com/arm-to-acquire-artisan-components-for-913-million/, obviously.
The standard cell library is typically composed of a bunch of versions of somewhat simple gates, e.g.:and so on.
Each of those gates has to be designed by hand as a 3D structure that can be produced in a given fab.
Simulations are then carried out, and the electric properties of those structures are characterized in a standard way as a bunch of tables of numbers that specify things like:Those are then used in power, performance and area estimates.
Stabilizer (group) Updated 2025-07-16
If we pick k elements of the set, the stabilizer subgroup of those k elements is a subgroup of the given permutation group that keeps those elements unchanged.
Note that an analogous definition can be given for non-finite groups. Also note that the case for all finite groups is covered by the permutation definition since all groups are isomorphic to a subgroup of the symmetric group
TODO existence and uniqueness. Existence is obvious for the identity permutation, but proper subgroup likely does not exist in general.
SQL TRIGGER Updated 2025-07-16
In particular, everything that happens in a trigger happens as if it were in a transaction. This way, you can do less explicit transactions when you use triggers. It is a bit like the advantages of SQL CASCADE.
DBMS:
SQL RECURSIVE prevent infinite recursion Updated 2025-07-16
Example under: nodejs/sequelize/raw/tree.js
sqlite3 Node.js package Updated 2025-07-16Includes its own copy of sqlite3, you don't use the system one, which is good to ensure compatibility. The version is shown at: github.com/mapbox/node-sqlite3/blob/918052b538b0effe6c4a44c74a16b2749c08a0d2/deps/common-sqlite.gypi#L3 SQLite source is tracked compressed in-tree: github.com/mapbox/node-sqlite3/blob/918052b538b0effe6c4a44c74a16b2749c08a0d2/deps/sqlite-autoconf-3360000.tar.gz horrendous. This explains why it takes forever to clone that repository. People who don't believe in git submodules, there's even an official Git mirror at: github.com/sqlite/sqlite
It appears to spawn its own threads via its C extension (since JavaScript is single threaded and and SQLite is not server-based), which allows for parallel queries using multiple threads: github.com/mapbox/node-sqlite3/blob/v5.0.2/src/threading.h
Hello world example: nodejs/node-sqlite3/index.js.
As of 2021, this had slumped back a bit, as maintainers got tired. Unmerged pull requests started piling more, and
better-sqlite3 Node.js package started pulling ahead a little.- github.com/mapbox/node-sqlite3/issues/1381
FATAL ERROR: Error::ThrowAsJavaScriptException napi_throwwith Node.jsworker_threadsvsbetter-sqlite3Node.js package github.com/JoshuaWise/better-sqlite3/issues/237
Sponsor Ciro Santilli's work on OurBigBook.com Taxation Updated 2026-01-30
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:
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:
Spontaneous parametric down-conversion Updated 2025-07-16
You can then detect one of the photons, and when you do you know that the other one is there as well and ready to be used. two photon interference experiment comes to mind, which is the basis of photonic quantum computer, where you need two photons to be produced at the exact same time to produce quantum entanglement.
Features Alan Migdall of the National Institute of Standards and Technology. Produced by the Joint Quantum Institute (JQI).
Mentions that this phenomena is useful to determine the efficiency of a single photon detector, as you have the second photon of the pair as a control.
Also briefly describes how the input energy and momentum must balance out the output energy and momentum of the two photons coming out (determined by the output frequency and angle).
Shows the crystal close up of the crystal branded "Cleveland Crystals Inc.". Mentions that only one in a billion photon gets scattered.
Also shows a photomultiplier tube.
Then shows their actual optical table setup, with two tunnels of adjustable angle to get photons with different properties.
Very short whiteboard video by Peter Mosley from the University of Bath, but it's worth it for newbs. Basically describes spontaneous parametric down-conversion.
One interesting thing he mentions is that you could get single photons by making your sunglasses thicker and thicker to reduce how many photons pass, but one big downside problem is that then you don't know when the photon is going to come through, that becomes essentially random, and then you can't use this technique if you need two photons at the same time, which is often the case, see also: two photon interference experiment.
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