Saylor Academy Updated 2025-07-16
This is an interesting initiative which has some similarities to Ciro Santilli's OurBigBook project.
The fatal flaw of the initiative in Ciro Santilli's opinion is the lack of user-generated content. We will never get there without UGC and algorithms, never.
Also as of 2021, it mostly useless business courses: learn.saylor.org unfortunately.
But it has several redeeming factors which Ciro Santilli aproves of:
- exam as a service-like
- they have a GitHub: github.com/saylordotorgo
The founder Michael J. Saylor looks a bit crooked, Rich people who create charitable prizes are often crooked comes to mind. But maybe he's just weird.
Michael Saylor interview by Lex Fridman (2022)
Source. At the timestamp:What statement... maybe he's actually not crooked, maybe it was just an accounting mistake... God, why.
When I go, all my assets will flow into a foundation, and the foundation's mission is to make education free for everybody forever.
If only Ciro Santilli knew how to contact him and convince him that his current approach is innefective and that Ciro has something better! Michael, please Google into this page some day, Ciro Santilli needs funding for OurBigBook.com. A hopeless Tweet at: twitter.com/cirosantilli/status/1548350114623660035. Also tried to hit his
saylor@strategy.com. Riemann hypothesis Updated 2025-07-16
visualizing the Riemann hypothesis and analytic continuation by 3Blue1Brown (2016) is a good quick visual non-mathematical introduction is to it.
One of the Millennium Prize Problems and Hilbert's problems.
What is the Riemann hypothesis REALLY about? by HexagonVideos (2022)
Source. Richard Feynman's drug use Updated 2025-07-16
From Surely You're Joking, Mr. Feynman chapter O Americano, Outra Vez!:
The people from the airlines were somewhat bored with their lives, strangely enough, and at night they would often go to bars to drink. I liked them all, and in order to be sociable, I would go with them to the bar to have a few drinks, several nights a week.One day, about 3:30 in the afternoon, I was walking along the sidewalk opposite the beach at Copacabana past a bar. I suddenly got this treMENdous, strong feeling: "That's just what I want; that'll fit just right. I'd just love to have a drink right now!"I started to walk into the bar, and I suddenly thought to myself, "Wait a minute! It's the middle of the afternoon. There's nobody here, There's no social reason to drink. Why do you have such a terribly strong feeling that you have to have a drink?" - and I got scared.I never drank ever again, since then. I suppose I really wasn't in any danger, because I found it very easy to stop. But that strong feeling that I didn't understand frightened me. You see, I get such fun out of thinking that I don't want to destroy this most pleasant machine that makes life such a big kick. It's the same reason that, later on, I was reluctant to try experiments with LSD in spite of my curiosity about hallucinations.
One notable drug early teens Ciro consumed was Magic: The Gathering, see also: Section "Magic: The Gathering is addictive".
Resonance Updated 2025-07-16
Examples:
- mechanical resonance, notably:
- pipe instruments
- electronic oscillators, notably:
- LC oscillator, and notably the lossy version RLC circuit
Perhaps a key insight of resonance is that the reonant any lossy system tends to look like the resonance frequency quite quickly even if the initial condition is not the resonant condition itself, because everything that is not the resonant frequency interferes destructively and becomes noise. Some examples of that:
- striking a bell or drum can be modelled by applying an impuse to the system
- playing a pipe instrument comes down to blowing a piece that vibrates randomly, and then leads the pipe to vibrate mostly in the resonant frequency. Likely the same applies to bowed string instruments, the bow must be creating a random vibration.
- playing a plucked string instrument comes down to initializing the system to an triangular wave form and then letting it evolve. TODO find a simulation of that!
Another cool aspect of resonance is that it was kind of the motivation for de Broglie hypothesis, as de Broglie was kind of thinking that electroncs might show discrete jumps on atomic spectra because of constructive interference.
Representation theory Updated 2025-07-16
Basically, a "representation" means associating each group element as an invertible matrices, i.e. a matrix in (possibly some subset of) , that has the same properties as the group.
Or in other words, associating to the more abstract notion of a group more concrete objects with which we are familiar (e.g. a matrix).
This is basically what everyone does (or should do!) when starting to study Lie groups: we start looking at matrix Lie groups, which are very concrete.
Or more precisely, mapping each group element to a linear map over some vector field (which can be represented by a matrix infinite dimension), in a way that respects the group operations:
As shown at Physics from Symmetry by Jakob Schwichtenberg (2015)
- page 51, a representation is not unique, we can even use matrices of different dimensions to represent the same group
- 3.6 classifies the representations of . There is only one possibility per dimension!
- 3.7 "The Lorentz Group O(1,3)" mentions that even for a "simple" group such as the Lorentz group, not all representations can be described in terms of matrices, and that we can construct such representations with the help of Lie group theory, and that they have fundamental physical application
Bibliography:
- www.youtube.com/watch?v=9rDzaKASMTM "RT1: Representation Theory Basics" by MathDoctorBob (2011). Too much theory, give me the motivation!
- www.quantamagazine.org/the-useless-perspective-that-transformed-mathematics-20200609 The "Useless" Perspective That Transformed Mathematics by Quanta Magazine (2020). Maybe there is something in there amidst the "the reader might not know what a matrix is" stuff.
Real time live plot from streaming data Updated 2025-07-16
E.g. showing live data from a scientific instrument! TODO:
- superuser.com/questions/825588/what-is-the-easiest-way-of-visualizing-data-from-stdout-as-a-graph
- unix.stackexchange.com/questions/190337/how-can-i-make-a-graphical-plot-of-a-sequence-of-numbers-from-the-standard-input
- stackoverflow.com/questions/44470965/how-can-you-watch-gnuplot-realtime-data-plots-as-a-live-graph-with-automatic-up
- stackoverflow.com/questions/14074790/plotting-a-string-of-csv-data-in-realtime-using-linux
- stackoverflow.com/questions/11874767/how-do-i-plot-in-real-time-in-a-while-loop-using-matplotlib
Real-time attack speedrun Updated 2025-07-16
A non-tool-assisted speedrun.
Ciro Santilli views humans as biological robots, and therefore RTA videos can be thought of as probabilistic TAS with human achievable reflex constraints.
This aspect is especially highlighted in "speed run record evolution videos", which can be quite fun, e.g. www.youtube.com/watch?v=pmS9e7kzgS4 Ocarina of Time - World Record History and Progression (Any% Speedrun, 1990s-2017) by retro (2017)
From a similar point of view, Ciro also sometimes watches/learns a bit about competitive PvP games from a "could a computer play this better than a human" point of view.
Ciro also likes to watch commented manual speedruns of games as a way of experiencing the game at a high level without spending too much time on it, often from Games Done Quick. Their format is good because it generally showcases one player focusing more on the gameplay, and three couch commentators to give context, that's a good setup.
It is a
Real coordinate space of dimension three Updated 2025-07-16
Quantum Mechanical View of Reality by Richard Feynman (1983) Updated 2025-07-16
Sample playlist: www.youtube.com/playlist?list=PLW_HsOU6YZRkdhFFznHNEfua9NK3deBQy
Basically the same content as: Richard Feynman Quantum Electrodynamics Lecture at University of Auckland (1979), but maybe there is some merit to this talk, as it is a bit more direct in some points. This is consistent with what is mentioned at www.feynman.com/science/qed-lectures-in-new-zealand/ that the Auckland lecture was the first attempt.
Some more information at: iucat.iu.edu/iub/5327621
By Mill Valley, CA based producer "Sound Photosynthesis", some info on their website: sound.photosynthesis.com/Richard_Feynman.html
They are mostly a New Age production company it seems, which highlights Feynman's absolute cult status. E.g. on the last video, he's not wearing shoes, like a proper guru.
Feynman liked to meet all kinds of weird people, and at some point he got interested in the New Age Esalen Institute. Surely You're Joking, Mr. Feynman this kind of experience a bit, there was nude bathing on a pool that oversaw the sea, and a guy offered to give a massage to the he nude girl and the accepted.
youtu.be/rZvgGekvHest=5105 actually talks about spin, notably that the endpoint events also have a spin, and that the transition rules take spin into account by rotating thing, and that the transition rules take spin into account by rotating things.
Quantum matter physics course of the University of Oxford Updated 2025-07-16
2011- professor: Steven H. Simon. His start date is given e.g. at: www-thphys.physics.ox.ac.uk/people/SteveSimon/condmat2012/LectureNotes2012.pdf which is presumably an older version of: www-thphys.physics.ox.ac.uk/people/SteveSimon/QCM2022/QuantumMatter.pdf
Notes/book: www-thphys.physics.ox.ac.uk/people/SteveSimon/QCM2022/QuantumMatter.pdf Marked as being for Oxford MMathPhys, so it appears that this is a 4th year course normally. TODO but where is it listed under the course list of MMapthPhys? mmathphys.physics.ox.ac.uk/course-schedule
Course page index: www-thphys.physics.ox.ac.uk/people/SteveSimon/
www-thphys.physics.ox.ac.uk/people/SteveSimon/QCM2023/quantummatter.html mentions it is given in Hilary term
2023 syllabus as per www-thphys.physics.ox.ac.uk/people/SteveSimon/QCM2023/quantummatter.html#Syllabus:
- Fermi Liquids
- Weakly Interacting Fermions
- Response Functions and Screening
- Thomas Fermi
- RPA
- Plasmons
- Landau Fermi Liquid Theory
- Superfluidity
- Two Fluid Model and Quantized Circulation
- Landau Criterion for Superfluidity
- Two Fluid Model for Superconductors
- London Theory
- Flux Vortices
- Type I and Type II superconductors
- Microscopic Superfluidity
- Coherent States
- Bose Condensation
- Gross Pitaevskii Equation
- Off Diagonal Long Range Order
- Feynman Theory of Superfluidity (in book, but will skip in lectures. Not examinable)
- Ginzburg Landau Theory of Superfluids
- BCS Theory of Superconductors
SMIC Updated 2025-07-16
SMIC, Explained by Asianometry (2021)
Source. Quantum logic gates are needed because you can't compute the matrix explicitly as it grows exponentially Updated 2025-07-16
One key insight, is that the matrix of a non-trivial quantum circuit is going to be huge, and won't fit into any amount classical memory that can be present in this universe.
This is because the matrix is exponential in the number qubits, and is more than the number of atoms in the universe!
Therefore, off the bat we know that we cannot possibly describe those matrices in an explicit form, but rather must use some kind of shorthand.
But it gets worse.
This is because knowing the matrix, basically means knowing the probability result for all possible outputs for each of the possible inputs.
But if we had those probabilities, our algorithmic problem would already be solved in the first place! We would "just" go over each of those output probabilities (OK, there are of those, which is also an insurmountable problem in itself), and the largest probability would be the answer.
So if we could calculate those probabilities on a classical machine, we would also be able to simulate the quantum computer on the classical machine, and quantum computing would not be able to give exponential speedups, which we know it does.
To see this, consider that for a given input, say and therefore when you multiply it by the unitary matrix of the quantum circuit, what you get is the first column of the unitary matrix of the quantum circuit. And
000 on a 3 qubit machine, the corresponding 8-sized quantum state looks like:000 -> 1000 0000 == (1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0)001, gives the second column and so on.As a result, to prove that a quantum algorithm is correct, we need to be a bit smarter than "just calculate the full matrix".
Which is why you should now go and read: Section "Quantum algorithm".
This type of thinking links back to how physical experiments relate to quantum computing: a quantum computer realizes a physical experiment to which we cannot calculate the probabilities of outcomes without exponential time.
So for example in the case of a photonic quantum computer, you are not able to calculate from theory the probability that photons will show up on certain wires or not.
Quantum field theory lecture notes Updated 2025-07-16
Lecture notes found by Googling "quantum field theory pdf":
- www.ppd.stfc.ac.uk/Pages/Dasgupta_08_Intro_to_QFT.pdf "An Introduction to Quantum Field Theory" by Mrinal Dasgupta from the University of Manchester (2008). 48 pages.
- www.thphys.uni-heidelberg.de/~weigand/QFT2-14/SkriptQFT2.pdf "Quantum Field Theory I + II" by Timo Weigand from the Heidelberg University. Unknown year, references up to 2008.
- edu.itp.phys.ethz.ch/hs12/qft1/ Quantum Field Theory 1 by Niklas Beisert
Quantum error correction Updated 2025-07-16
Technique that uses multiple non-ideal qubits (physical qubits) to simulate/produce one perfect qubit (logical).
One is philosophically reminded of classical error correction codes, where we also have multiple input bits per actual information bit.
TODO understand in detail. This appears to be a fundamental technique since all physical systems we can manufacture are imperfect.
Part of the fundamental interest of this technique is due to the quantum threshold theorem.
For example, when PsiQuantum raised 215M in 2020, they announced that they intended to reach 1 million physical qubits, which would achieve between 100 and 300 logical qubits.
Video "Jeremy O'Brien: "Quantum Technologies" by GoogleTechTalks (2014)" youtu.be/7wCBkAQYBZA?t=2778 describes an error correction approach for a photonic quantum computer.
Bibliography:
Quantum dot Updated 2025-07-16
TODO WTF is this? How is it built? What is special about it?
Mentioned a lot in the context of superconducting quantum computers, e.g. youtu.be/t5nxusm_Umk?t=268 from Video "Quantum Computing with Superconducting Qubits by Alexandre Blais (2012)",
Quantum Computing Inc. Updated 2025-10-14
Really weird and obscure company, good coverage: thequantuminsider.com/2020/02/06/quantum-computing-incorporated-the-first-publicly-traded-quantum-computing-stock/
Publicly traded in 2007, but only pivoted to quantum computing much later.
Quantum computers as experiments that are hard to predict outcomes Updated 2025-07-16
One possibly interesting and possibly obvious point of view, is that a quantum computer is an experimental device that executes a quantum probabilistic experiment for which the probabilities cannot be calculated theoretically efficiently by a nuclear weapon.
This is how quantum computing was originally theorized by the likes of Richard Feynman: they noticed that "Hey, here's a well formulated quantum mechanics problem, which I know the algorithm to solve (calculate the probability of outcomes), but it would take exponential time on the problem size".
The converse is then of course that if you were able to encode useful problems in such an experiment, then you have a computer that allows for exponential speedups.
This can be seen very directly by studying one specific quantum computer implementation. E.g. if you take the simplest to understand one, photonic quantum computer, you can make systems for which you need exponential time to calculate the probabilities that photons will exit through certain holes and not others.
The obvious aspect of this idea is by coming from quantum logic gates are needed because you can't compute the matrix explicitly as it grows exponentially: knowing the full explicit matrix is impossible in practice, and knowing the matrix is equivalent to knowing the probabilities of every outcome.
Quantum computer benchmark Updated 2025-07-16
One important area of research and development of quantum computing is the development of benchmarks that allow us to compare different quantum computers to decide which one is more powerful than the other.
Ideally, we would like to be able to have a single number that predicts which computer is more powerful than the other for a wide range of algorithms.
However, much like in CPU benchmarking, this is a very complex problem, since different algorithms might perform differently in different architectures, making it very hard to sum up the architecture's capabilities to a single number as we would like.
The only thing that is directly comparable across computers is how two machines perform for a single algorithm, but we want a single number that is representative of many algorithms.
For example, the number of qubits would be a simple naive choice of such performance predictor number. But it is very imprecise, since other factors are also very important:
Quantum volume is another less naive attempt at such metric.
Quantum Computation and Quantum Information by Nielsen and Chuang Updated 2025-07-16
Quantum chromodynamics Updated 2025-07-16
Quarks, Gluon flux tubes, Strong Nuclear Force, & Quantum Chromodynamics by Physics Videos by Eugene Khutoryansky (2018)
Source. Some decent visualizations of how the field lines don't expand out like they do in electromagnetism, suggesting color confinement. There are unlisted articles, also show them or only show them.