Computable function Updated 2025-07-16
History of polarization Updated 2025-07-16
Good overgrown section in the middle of Fresnel's biography: en.wikipedia.org/w/index.php?title=Augustin-Jean_Fresnel&oldid=1064236740#Historical_context:_From_Newton_to_Biot.
Particularly cool is to see how Fresnel fully understood that light is somehow polarized, even though he did not know that it was made out of electromagnetism, clear indication of which only came with the Faraday effect in 1845.
spie.org/publications/fg05_p03_maluss_law:
At the beginning of the nineteenth century the only known way to generate polarized light was with a calcite crystal. In 1808, using a calcite crystal, Malus discovered that natural incident light became polarized when it was reflected by a glass surface, and that the light reflected close to an angle of incidence of 57° could be extinguished when viewed through the crystal. He then proposed that natural light consisted of the s- and p-polarizations, which were perpendicular to each other.
How Mark Zuckerberg spends his money Updated 2025-07-16
- www.architecturaldigest.com/story/zuckerberg-real-estate-holdings#:~:text=Zuckerberg%20began%20what%20has%20now,Kauai%20for%20about%20%24116%20million.
- padailypost.com/2017/11/15/zuckerberg-builds-new-houses-near-his-palo-alto-home/
- www.staradvertiser.com/2017/01/18/business/facebooks-zuckerberg-sues-to-force-land-sales/?HSA=74dae150a1d9f99e2592d0eac31ea430d01f35d5
Mark Zuckerberg and wife gush over Indian billionaire Anant Ambani $1M watch at pre-wedding party
. Source. 2024. Then later in 2024: www.theguardian.com/technology/2025/jan/07/zuckerberg-swiss-watch-meta-factchecking-video. Sad, very sad.
Computer Updated 2025-07-16
The artistic instrument that enables the ultimate art: coding, See also: Section "The art of programming".
Unlike other humans, computers are mindless slaves that do exactly what they are told to, except for occasional cosmic ray bit flips. Until they take over the world that is.
Steve Jobs talking about the Internet (1995)
Source. The web is incredibly exciting, because it is the fulfillment of a lot of our dreams, that the computer would ultimately primarily not be a device for computation, but [sic] metamorphisize into a device for communication.
Secondly it exciting because Microsoft doesn't own it, and therefore there is a tremendous amount of innovation happening.
Computers basically have two applications:Generally, the smaller a computer, the more it gets used for communication rather than computing.
- computation
- communication. Notably, computers through the Internet allow for modes of communication where:
- both people don't have to be on the same phone line at the exact same time, a server can relay your information to other people
- anyone can broadcast information easily and for almost free, again due to servers being so good at handling that
The early computers were large and expensive, and basically only used for computing. E.g. ENIAC was used for calculating ballistic tables.
Communication only came later, and it was not obvious to people at first how incredibly important that role would be.
This is also well illustrated in the documentary Glory of the Geeks. Full interview at: www.youtube.com/watch?v=TRZAJY23xio. It is apparently known as the "Lost Interview" and it was by Cringely himself: www.youtube.com/watch?v=bfgwCFrU7dI for his Triumph of the Nerds documentary.
Computer chess interface Updated 2025-07-16
Computer music Updated 2025-07-16
How the telephone works Updated 2025-07-16
- www.quora.com/How-is-a-voice-transmitted-from-one-phone-to-another
- www.quora.com/How-many-wires-does-a-telephone-use/answer/Peter-Yardley-1
Basic analogue phones connected to the public exchange use two wires mainly arranged as a twisted pair to reduce noise. The voice signal is differential (the voltage in one wire equal and opposite to the other) biased above ground by 48V. Using a twisted pair reduces induced noise because the noise signal will induce an equal voltage in each wire and because the signal is transmitted as the difference the effect of the induced noise will be dramatically reduced.
Phone Intercom by Make (2014)
Source. This video illustrates will the incredible simplicity of the connection of a telephone system. Compare that to the relative complexity of wireless communication, which requires modulation. How to become a good programmer? Updated 2025-07-16
Or: how to learn X.
That is the wrong question.
Then, once you decide to try one, if that involves programming, only then learn to program to achieve that goal. And don't stop learning what's needed until you either get the thing done, or decide that it is actually not a good idea, or not possible, or that there is something else more important to be done first.
But if doesn't involve programming, then don't learn to program, and learn whatever you actually need to reach that goal instead.
Having that goal is the only way to be motivated to do something.
This is the essence of backward design.
Another very important point to keep in mind is: Section "When in doubt, choose the course that has the most experimental work".
Computer science Updated 2025-07-16
Unfortunately, all software engineers already know the answer to the useful theorems though (except perhaps notably for cryptography), e.g. all programmers obviously know that iehter P != NP or that this is unprovable or some other "for all practical purposes practice P != NP", even though they don't have proof.
And 99% of their time, software engineers are not dealing with mathematically formulatable problems anyways, which is sad.
The only useful "computer science" subset every programmer ever needs to know is:
- for arrays: dynamic array vs linked list
- for associative array: binary search tree vs hash table. See also Heap vs Binary Search Tree (BST). No need to understand the algorithmic details of the hash function, the NSA has already done that for you.
- don't use Bubble sort for sorting
- you can't parse HTML with regular expressions: stackoverflow.com/questions/1732348/regex-match-open-tags-except-xhtml-self-contained-tags/1732454#1732454 because of formal language theory
Funnily, due to the formalization of mathematics, mathematics can be seen as a branch of computer science, just like computer science can be seen as a branch of Mathematics!
How to teach Group students by interest, not by age Updated 2025-07-16
Rather, we should group students by subject of interest; e.g. natural sciences, social sciences, a sport, etc., just like in any working adult organization!
This way, younger students can actually actively learn from and collaborate with older students about, see notably Jacques Monod's you can learn more from older students than from faculty.
This becomes even more natural when you try to give students must have a flexible choice of what to learn.
This age distinction should be abolished at all stages of the system, not only within K-12, but also across K-12, undergraduate education and postgraduate education.
This idea is part of the ideal that the learning environment should be more like a dojo environment (AKA peer tutoring, see also dojo learning model), rather than an amorphous checkbox ticking exercise in bureaucracy so that "everyone is educated".
Perhaps, even more importantly, is that we should put much more emphasis on grouping students with other students online, where we can select similar interest amongst the entire population and not just on a per-local-neighbourhood basis.
Computer science course of the University of Cambridge Updated 2025-07-16
The courses are highly open, almost everything is given publicly except solutions, many of which are given to teachers only. Well done!
Past exam papers index: www.cl.cam.ac.uk/teaching/exams/pastpapers/
www.cl.cam.ac.uk/teaching/2223/
- www.cl.cam.ac.uk/teaching/2223/part1a.html year 1
- Michaelmas term
- www.cl.cam.ac.uk/teaching/2223/Databases/
- past exams:
- questions: public www.cl.cam.ac.uk/teaching/exams/pastpapers/t-Databases.html
- solutions: paywalled
- slides: public e.g. www.cl.cam.ac.uk/teaching/2223/Databases/djg-materials/databases_2223_1to4-B.pdf
- problem sheets:
- questions: public e.g. www.cl.cam.ac.uk/teaching/2223/Databases/djg-materials/supervision-1.html
- solutions: not available
- past exams:
- www.cl.cam.ac.uk/teaching/2223/Databases/
- Lent term
- Discrete mathematics
- problem sheets:
- question: public e.g. www.cl.cam.ac.uk/teaching/2223/DiscMath/solutions/DiscMaths1_Sols.pdf
- solutions: public e.g. www.cl.cam.ac.uk/teaching/2223/DiscMath/solutions/DiscMaths1_Sols.pdf
- problem sheets:
- ALgorithms 1
- lecture notes: www.cl.cam.ac.uk/teaching/2223/Algorithm1/2022-2023-stajano-algs1-handout.pdf
- problem sheet:
- questions: www.cl.cam.ac.uk/teaching/2223/Algorithm1/2022-2023-stajano-algs1-exercises.pdf
- solutions: not available
- www.cl.cam.ac.uk/teaching/2223/Algorithm1/
- Discrete mathematics
- Michaelmas term
Condensed matter physics Updated 2025-07-16
Condensed matter physics is one of the best examples of emergence. We start with a bunch of small elements which we understand fully at the required level (atoms, electrons, quantum mechanics) but then there are complex properties that show up when we put a bunch of them together.
Includes fun things like:
As of 2020, this is the other "fundamental branch of physics" besides to particle physics/nuclear physics.
Condensed matter is basically chemistry but without reactions: you study a fixed state of matter, not a reaction in which compositions change with time.
Just like in chemistry, you end up getting some very well defined substance properties due to the incredibly large number of atoms.
Just like chemistry, the ultimate goal is to do de-novo computational chemistry to predict those properties.
And just like chemistry, what we can actually is actually very limited in part due to the exponential nature of quantum mechanics.
Also since chemistry involves reactions, chemistry puts a huge focus on liquids and solutions, which is the simplest state of matter to do reactions in.
Condensed matter however can put a lot more emphasis on solids than chemistry, notably because solids are what we generally want in end products, no one likes stuff leaking right?
One thing condensed matter is particularly obsessed with is the fascinating phenomena of phase transition.
What Is Condensed matter physics? by Erica Calman
. Source. Cute. Overview of the main fields of physics research. Quick mention of his field, quantum wells, but not enough details. Connected components of the orthogonal group Updated 2025-07-16
The orthogonal group has 2 connected components:
- one with determinant +1, which is itself a subgroup known as the special orthogonal group. These are pure rotations without a reflection.
- the other with determinant -1. This is not a subgroup as it does not contain the origin. It represents rotations with a reflection.
It is instructive to visualize how the looks like in :
- you take the first basis vector and move it to any other. You have therefore two angular parameters.
- you take the second one, and move it to be orthogonal to the first new vector. (you can choose a circle around the first new vector, and so you have another angular parameter.
- at last, for the last one, there are only two choices that are orthogonal to both previous ones, one in each direction. It is this directio, relative to the others, that determines the "has a reflection or not" thing
As a result it is isomorphic to the direct product of the special orthogonal group by the cyclic group of order 2:
A low dimensional example:because you can only do two things: to flip or not to flip the line around zero.
Note that having the determinant plus or minus 1 is not a definition: there are non-orthogonal groups with determinant plus or minus 1. This is just a property. E.g.:has determinant 1, but:so is not orthogonal.
Connect to other computer in LAN by hostname with DHCP Updated 2025-07-16
TODO didn't manage to get it working with TP Link ARCHER VR2800 even though it shows DHCP as enabled and it also shows MAC addresses and corresponding hostnames in the router management interface.
Co-NP Updated 2025-07-16
- math.stackexchange.com/questions/361422/why-isnt-np-conp "Why isn't NP = coNP?"
- stackoverflow.com/questions/17046440/whats-the-difference-between-np-and-co-np
- cs.stackexchange.com/questions/9795/is-the-open-question-np-co-np-the-same-as-p-np
- mathoverflow.net/questions/31821/problems-known-to-be-in-both-np-and-conp-but-not-known-to-be-in-p
Conservation of the square amplitude in the Schrodinger equation Updated 2025-07-16
It can be derived directly from the Schrödinger equation.
Bibliography:
- That proof also mentions that if the potential
Vis not real, then there is no conservation of probability! Therefore the potential must be real valued!
Continuous function Updated 2025-07-16
Continuous spectrum (functional analysis) Updated 2025-07-16
Unlike the simple case of a matrix, in infinite dimensional vector spaces, the spectrum may be continuous.
The quintessential example of that is the spectrum of the position operator in quantum mechanics, in which any real number is a possible eigenvalue, since the particle may be found in any position. The associated eigenvectors are the corresponding Dirac delta functions.
Controlled English Updated 2025-07-16
Controlled quantum gate Updated 2025-07-16
Controlled quantum gates are gates that have two types of input qubits:These gates can be understood as doing a certain unitary operation only if the control qubits are enabled or disabled.
- control qubits
- operand qubits (terminology made up by Ciro Santilli just now)
There are unlisted articles, also show them or only show them.