Erdős' conjecture on powers of 2 Updated 2025-10-27
Described at: arxiv.org/pdf/2107.12475.pdf where a relation to the Busy beaver scale is proven, and the intuitive relation to the Collatz conjecture described. Perhaps more directly: demonstrations.wolfram.com/CollatzSequenceComputedByATuringMachine/
Entropy Updated 2025-07-16
OK, can someone please just stop the philosophy and give numerical predictions of how entropy helps you predict the future?
The original notion of entropy, and the first one you should study, is the Clausius entropy.
Video 1.
The Unexpected Side of Entropy by Daan Frenkel
. Source. 2021.
Video 2.
The Biggest Ideas in the Universe | 20. Entropy and Information by Sean Carroll (2020)
Source. In usual Sean Carroll fashion, it glosses over the subject. This one might be worth watching. It mentions 4 possible definitions of entropy: Boltzmann, Gibbs, Shannon (information theory) and John von Neumann (quantum mechanics).
enwiki-latest-category.sql Updated 2025-07-16
dumps.wikimedia.org/enwiki/latest/enwiki-latest-category.sql.gz contains a list of categories. It only contains the categories and some counts, but it doesn't contain the subcategories and pages under each category, so it is a bit pointless.
The SQL first defines the table:
CREATE TABLE `category` (
  `cat_id` int(10) unsigned NOT NULL AUTO_INCREMENT,
  `cat_title` varbinary(255) NOT NULL DEFAULT '',
  `cat_pages` int(11) NOT NULL DEFAULT 0,
  `cat_subcats` int(11) NOT NULL DEFAULT 0,
  `cat_files` int(11) NOT NULL DEFAULT 0,
  PRIMARY KEY (`cat_id`),
  UNIQUE KEY `cat_title` (`cat_title`),
  KEY `cat_pages` (`cat_pages`)
) ENGINE=InnoDB AUTO_INCREMENT=249228235 DEFAULT CHARSET=binary ROW_FORMAT=COMPRESSED;
followed by a few humongous inserts:
INSERT INTO `category` VALUES (2,'Unprintworthy_redirects',1597224,20,0),(3,'Computer_storage_devices',88,11,0)
which we can see at: en.wikipedia.org/wiki/Category:Computer_storage_devices
Se see that en.wikipedia.org/wiki/Category:Computer_storage_devices_by_company
so it contains only categories.
We can check this with:
sed -s 's/),/\n/g' enwiki-latest-category.sql | grep Computer_storage_devices
and it shows:
(3,'Computer_storage_devices',88,11,0
(521773,'Computer_storage_devices_by_company',6,6,0
There doesn't seem to be any interlink between the categories, only page and subcategory counts therefore.
Epic Rap Battles of History Updated 2025-07-16
Most of the videos are crap, but the following ones almost killed Ciro Santilli of laughter:
Monty Python has a few precursors to the "random famous people mixed together compting" format, although not in the rap fight format:
Video 3. Source. If you can understand the jokes, your philosophy level is pretty good. Like more than zero. Wiki page: en.wikipedia.org/wiki/The_Philosophers%27_Football_Match. Ciro loves how that page currently uses a standard footbal match template to describe the match!
Stockfish CLI Updated 2025-10-14
Most of what follows is part of the Universal Chess Interface. Tested on Ubuntu 22.10, Stockfish 14.1.
After starting stockfish on the command line, d (presumably display) contains:
 +---+---+---+---+---+---+---+---+
 | r | n | b | q | k | b | n | r | 8
 +---+---+---+---+---+---+---+---+
 | p | p | p | p | p | p | p | p | 7
 +---+---+---+---+---+---+---+---+
 |   |   |   |   |   |   |   |   | 6
 +---+---+---+---+---+---+---+---+
 |   |   |   |   |   |   |   |   | 5
 +---+---+---+---+---+---+---+---+
 |   |   |   |   |   |   |   |   | 4
 +---+---+---+---+---+---+---+---+
 |   |   |   |   |   |   |   |   | 3
 +---+---+---+---+---+---+---+---+
 | P | P | P | P | P | P | P | P | 2
 +---+---+---+---+---+---+---+---+
 | R | N | B | Q | K | B | N | R | 1
 +---+---+---+---+---+---+---+---+
   a   b   c   d   e   f   g   h

Fen: rnbqkbnr/pppppppp/8/8/8/8/PPPPPPPP/RNBQKBNR w KQkq - 0 1
Key: 8F8F01D4562F59FB
Sweet ASCII art. where:
Move white king's pawn from e2 to e4:
position startpos moves e2e4
Then display again:
d
gives:
 +---+---+---+---+---+---+---+---+
 | r | n | b | q | k | b | n | r | 8
 +---+---+---+---+---+---+---+---+
 | p | p | p | p | p | p | p | p | 7
 +---+---+---+---+---+---+---+---+
 |   |   |   |   |   |   |   |   | 6
 +---+---+---+---+---+---+---+---+
 |   |   |   |   |   |   |   |   | 5
 +---+---+---+---+---+---+---+---+
 |   |   |   |   | P |   |   |   | 4
 +---+---+---+---+---+---+---+---+
 |   |   |   |   |   |   |   |   | 3
 +---+---+---+---+---+---+---+---+
 | P | P | P | P |   | P | P | P | 2
 +---+---+---+---+---+---+---+---+
 | R | N | B | Q | K | B | N | R | 1
 +---+---+---+---+---+---+---+---+
   a   b   c   d   e   f   g   h

Fen: rnbqkbnr/pppppppp/8/8/4P3/8/PPPP1PPP/RNBQKBNR b KQkq - 0 1
Key: B46022469E3DD31B
so we see that the pawn moved.
Now let's make Stockfish think for one second what is the next best move for black:
go movetime 1000
gives as the last line:
bestmove c7c5 ponder g1f3
TODO:
  • what is ponder? Something to do with thinking on the opponent's turn: permanent brain.
  • understand the previous lines
To make the move it as suggested for black, we have to either repeat the entire sequence of movements:
position startpos moves e2e4 c7c5
d:
 +---+---+---+---+---+---+---+---+
 | r | n | b | q | k | b | n | r | 8
 +---+---+---+---+---+---+---+---+
 | p | p |   | p | p | p | p | p | 7
 +---+---+---+---+---+---+---+---+
 |   |   |   |   |   |   |   |   | 6
 +---+---+---+---+---+---+---+---+
 |   |   | p |   |   |   |   |   | 5
 +---+---+---+---+---+---+---+---+
 |   |   |   |   | P |   |   |   | 4
 +---+---+---+---+---+---+---+---+
 |   |   |   |   |   |   |   |   | 3
 +---+---+---+---+---+---+---+---+
 | P | P | P | P |   | P | P | P | 2
 +---+---+---+---+---+---+---+---+
 | R | N | B | Q | K | B | N | R | 1
 +---+---+---+---+---+---+---+---+
   a   b   c   d   e   f   g   h

Fen: rnbqkbnr/pp1ppppp/8/2p5/4P3/8/PPPP1PPP/RNBQKBNR w KQkq - 0 2
Key: 4CA78BCE9C2980B0
or alternatively we could also use the previous FEN notation as a starting point;
position fen rnbqkbnr/pppppppp/8/8/4P3/8/PPPP1PPP/RNBQKBNR b KQkq - 0 1 moves c7c5
Note how the Universal Chess Interface interface is very simple: we just load a state and then decide what to do next for that one state. The engine holds only one and exactly one state at a time, and you can't even modify it differentially without loading new one from scratch.
Let's move white again with our brain with either:
position startpos moves e2e4 c7c5 d2d3
position fen rnbqkbnr/pp1ppppp/8/2p5/4P3/8/PPPP1PPP/RNBQKBNR w KQkq - 0 2 moves d2d3
Set a specific position from fen:
position fen rnbqkbnr/pppppppp/8/8/4P3/8/PPPP1PPP/RNBQKBNR b KQkq - 0 1
Primate Updated 2025-07-16
Street reclamation Updated 2025-07-16
Only people who need to drive a car should be allowed to drive a car anywhere near a city, e.g. people who work door to door, people who are disabled, etc.
Countryside driving is fine. If going to a city, you just have to drive to a parking outside of the city where you then take the public transport. And those who live in cities must leave their cars there too.
Everyone else must walk or cycle from home to public transport.
Cars just destroy everything, they make everything ugly:
  • this was extremely clear to Ciro Santilli as a cyclist. He previously lived in a place with few cars and the countryside was so pleasant. Then he moved to a place with more cars and it was shocking. It's a mixture of pollution, noise, and the fact that roads cut up the countryside that just make things not pleasant at all. Dual lane roads in particular are just a terrible thing. You can hear them from afar, much before you see them.
    You can just see as tiny little villages surrounding the bit city and it's oversized motorways are more or less homogenized into one big city mass, the process is clearly visible as you cycle out of the big city and the villages become nicer and more unique as you go along further out.
  • even within cities, cars completely dehumanize the streets. For example, Ciro once lived in a small dead end street, and he would have gladly opened his front window more often to meet the neighbours. But just the noise of cars passing by every so often makes it impractical to work like that.
The Zatoichi effect applies well to the problem of cyclists:
  • they are not really pedestrians, and pedestrian paths are not suitable to them because they are too narrow, of not smooth, or curved. But pedestrians will always have enough political power to have their paths, because they live around the paths
  • they are not really motor vehicles, because motor vehicle paths are too wide and too fast for them. But motor vehicles will always have enough political power to have their paths, because people are lazy and stupid, and because as the world stands, individually you just don't have any reasonable choice to go anywhere.
This is the main drama faced by cyclists.
Lobbying groups:
Video 1.
Why isn't cycling normal in London? by Jay Foreman (2018)
Source.
String polarization Updated 2025-07-16
This is about the polarization of a string in 3D space. That is the first concept of polarization you must have in mind!
This is one of the main reasons why Ciro Santilli invested in OurBigBook.com.
Ciro believes that the only thing students must be forced to learn is to speak read and write English and that a teacher's main job after that is to help students find their next big goals and also ties into the backward design philosophy.
Everything else, the student must choose.
This idea is generally known as self-directed learning.
This is most notable in University entry examinations of poor countries, where students often have to waste one extra year of their lives to go through preparation for the useless university entry exams. And then, surprise surprise, if they actually get in, they find that this is not what they really wanted to do, and they just go through to the end miserably because they understandably they don't want to risk another year of their lives.
Ciro saw this first hand École Polytechnique which was way freer than his university in Brazil.
Video 1.
The Purpose of Education by Noam Chomsky (2012)
Source.
  • 0:00 discusses Education as a system of indoctrination: indoctrination for people to comply with the Establishment and pass tests, vs the Age of Enlightenment in which education should help you achieve your own intellectual/life goals. He suggests without specific evidence that after the 60's there was explicit intervention in the US to increase the indoctrination aspect, of which debt is a part.
  • 15.45: assessment vs autonomy: exams are useless, except as a tool to help improve teaching and self assess. Tells anecdote about little girl who wanted to learn more about a subject, asked teacher how to learn more, teacher said you can't, you have to study for this useless national exam instead which will determine your future, and if I'm rehired or not.
Godfrey Hounsfield, 1979 Nobel Prize in Physiology and Medicine:[ref]
They tried hard to educate me but I responded only to physics and mathematics
UniProt for example describes YaaX as "Uncharacterized protein YaaX".
As function is discovered, they then change it to a better name, e.g. to names such as the E. Coli K-12 MG1655 transcription unit thrLABC proteins all of which have a clear name due to threonine.
There are many other y??? as of 2021! Though they do tend to be smaller molecules.
Sum of three cubes Updated 2025-07-16
Compared to Waring's problem, this is potentially much harder, as we can go infinitely negative in our attempts, there isn't a bound on how many tries we can have for each number.
In other words, it is unlikely to have a Conjecture reduction to a halting problem.
Video 1.
3 as the sum of the 3 cubes by Numberphile (2019)
Source.
Sun Erniang Updated 2025-07-16
Erniang is way more popular than her ranking in the 108 Stars of Destiny.
This is of course in part because she is one of the only 3 108 Stars of Destiny women. But her story about making human mantou is particularly fun!
She's also quite seductive, which gives directors a good opportunity for a bit of fan service. See e.g. kknews.cc/history/6epp2pp.html for a still from The Water Margin showing some good cleavage for example.
Quantum logic gate Updated 2025-07-16
At Section "Quantum computing is just matrix multiplication" we saw that making a quantum circuit actually comes down to designing one big unitary matrix.
We have to say though that that was a bit of a lie.
Quantum programmers normally don't just produce those big matrices manually from scratch.
Instead, they use quantum logic gates.

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