Ciro Santilli @cirosantilli 34

The Busy beaver scale allows us to gauge the difficulty of proving certain (yet unproven!) mathematical conjectures!

To to this, people have reduced certain mathematical problems to deciding the halting problem of a specific Turing machine.

A good example is perhaps the Goldbach's conjecture. We just make a Turing machine that successively checks for each even number of it is a sum of two primes by naively looping down and trying every possible pair. Let the machine halt if the check fails. So this machine halts iff the Goldbach's conjecture is false! See also Conjecture reduction to a halting problem.

Therefore, if we were able to compute $BB(n)$, we would be able to prove those conjectures automatically, by letting the machine run up to $BB(n)$, and if it hadn't halted by then, we would know that it would never halt.

Of course, in practice, $BB$ is generally uncomputable, so we will never know it. And furthermore, even if it were computable, it would take a lot longer than the age of the universe to compute any of it, so it would be useless.

However, philosophically speaking at least, the number of states of the equivalent Turing machine gives us a philosophical idea of the complexity of the problem.

The busy beaver scale is likely mostly useless, since we are able to prove that many non-trivial Turing machines do halt, often by reducing problems to simpler known cases. But still, it is cute.

But maybe, just maybe, reduction to Turing machine form could be useful. E.g. The Busy Beaver Challenge and other attempts to solve BB(5) have come up with large number of automated (usually parametrized up to a certain threshold) Turing machine decider programs that automatically determine if certain (often large numbers of) Turing machines run forever.

So it it not impossible that after some reduction to a standard Turing machine form, some conjecture just gets automatically brute-forced by one of the deciders, this is a path to

Highly radioactive isotope of caesium with half-life of 30.17 y. Produced from the nuclear fission of uranium, TODO exact reaction, not found in nature.

The fucked thing about this byproduct is that it is in the same chemical family as sodium, and therefore forms a salt that looks like regular table salt, and dissolves in water and therefore easily enters your body and sticks to things.

Another problem is that its half-life is long enough that it doesn't lose radioactivity very quickly compared to the life of a human person, although it is short enough to make it highly toxic, making it a terrible pollutant when released.

This is why for example in the goiânia accident a girl ended up ingesting Caesium-137 after eating an egg after touching the Caesium with her hands.

Like a heat equation but for functions without time dependence, space-only.

TODO confirm: does the solution of the heat equation always converge to the solution of the Laplace equation as time tends to infinity?

In one dimension, the Laplace equation is boring as it is just a straight line since the second derivative must be 0. That also matches our intuition of the limit solution of the heat equation.

Uniqueness: Uniqueness theorem for Poisson's equation.

Founder: Peter Armstrong

The general idea is publishing entire books with usual copyright, but with gradual updates.

ruboss.com/ documents their stack, a somewhat similar choice to OurBigBook.com as of 2021, notably Next.js. But backend in Ruby on Rails. They actually managed Apollo/GraphQL, which Ciro Santilli would have liked, but din't have the patience for.

The founder/CEO Peter Armstrong www.linkedin.com/in/peterburtonarmstrong/ He looks like a nice guy.

This is the cutest product name ever.

Used e.g. at Video "Superconducting Quantum Interference Devices by UNSW Physics (2020)"

Their manual: www.phys.ksu.edu/personal/cocke/classes/phys506/squidman.pdf

YBCO device, runs on liquid nitrogen.

PostgreSQL feels good.

Its feature set is insanely large! Just look at stuff like: stackoverflow.com/questions/1986491/sql-split-string-by-space-into-table-in-postgresql/1993058#1993058

Had a look at the source tree, and also felt good.

If Oracle is the Microsoft of database, Postgres is the Linux, and MySQL (or more precisely MariaDB) is the FreeBSD (i.e. the one that got delayed by legal issues). Except that their software licenses were accidentally swapped.

The only problem with Postgres is its name. PostgreSQL is so unpronounceable and so untypeable that you should just call it "Postgres" like everyone else.

The Fourier series of an $L^2$ function (i.e. the function generated from the infinite sum of weighted sines) converges to the function pointwise almost everywhere.

The theorem also seems to hold (maybe trivially given the transform result) for the Fourier series (TODO if trivially, why trivially).

Only proved in 1966, and known to be a hard result without any known simple proof.

This theorem of course implies that Fourier basis is complete for $L^2$, as it explicitly constructs a decomposition into the Fourier basis for every single function.

TODO vs Riesz-Fischer theorem. Is this just a stronger pointwise result, while Riesz-Fischer is about norms only?

One of the many fourier inversion theorems.

Early transmitters such as the spark-gap transmitter could only send noises to send Morse code.

To send voice and music, amplitude modulation had to be developed. And a key ingredient of this is the carrier wave.

The problem is, the carrier wave needs to have somewhat high frequencies, in the hundreds of kHz TODO why. But as you might imagine, that is hard to achieve by mechanical means such as a hand cranck like Hippolyte Pixiis alternator!

Interestingly, some of the first carrier wave generators were actually mechanical, e.g. the Alexanderson alternator.

But clearly such mechanical machines were not very scalable, and soon more electronic devices were introduced, notably the vacuum tube.

You select a generating set of a group, and then you name every node with them, and you specify:

Not unique: different generating sets lead to different graphs, see e.g. two possible en.wikipedia.org/w/index.php?title=Cayley_graph&oldid=1028775401#Examples for the

Centerpiece of the CEA since the beginning of the French nuclear weapons program, headquarters since 2006.

As of 2023 the place was blurred on Google Maps satellite view, no wonder.

The most important publisher, AKA "CRC Jianian". TODO meaning of Jianian?

Chinese government owned unfortunately.

Their website takes forever to load: www.china-crc.com.cn/, and features mostly Communist shit, and I can't find the decent traditional music listed there.

One thing to try is an Amazon advanced search by label "China Record Co": www.amazon.com/s?i=digital-music&rh=p_33%3AChina+Record+Co&s=relevancerank&Adv-Srch-MP3-Submit.x=42&Adv-Srch-MP3-Submit.y=4&unfiltered=1&ref=sr_adv_m_digital

Considering e.g. Newton's laws of motion, you take a system that is a function of time $f(t)$, e.g. the position of many point particles, and then you reverse the speeds of all particles, then $f(-t)$ is a solution to that.

Why Wikipedia sucks: Section "Wikipedia".

Best languages:

The most important page of Wikipedia is undoubtedly: en.wikipedia.org/wiki/Wikipedia:Reliable_sources/Perennial_sources which lists the accepted and non accepted sources. Basically, the decision of what is true in this world.

Wikipedia is incredibly picky about copyright. E.g.: en.wikipedia.org/wiki/Wikipedia:Deletion_of_all_fair_use_images_of_living_people because "such portrait could be created". Yes, with a time machine, no problem! This does more harm than good... excessive!

Citing in Wikipedia is painful. Partly because of they have a billion different templates that you have to navigate. They should really have a system where you can easily reuse existing sources across articles! Section "How to use a single source multiple times in a Wikipedia article?"

This is what happens when you apply a DC voltage across a Josephson junction.

It is called "AC effect" because when we apply a DC voltage, it produces an alternating current on the device.

By looking at the Josephson equations, we see that $V(t)=k$ a positive constant, then $\phi$ just increases linearly without bound.

Therefore, from the first equation:we see that the current will just vary sinusoidally between $\pm I_c$.

This meas that we can use a Josephson junction as a perfect voltage to frequency converter.

Wikipedia mentions that this frequency is $484GHz/mV$, so it is very very high, so we are not able to view individual points of the sine curve separately with our instruments.

Also it is likely not going to be very useful for many practical applications in this mode.

An I-V curve can also be seen at: Figure "Electron microscope image of a Josephson junction its I-V curve".

whoisxmlapi WHOIS history March 22, 2011:

77K. Low enough for "high temperature superconductors" such as yttrium barium copper oxide, but for "low temperature superconductors", you need to go much lower, typically with liquid helium, which is likely much more expensive. TODO by how much?

Early on, he's usually called by others as Major Lu (魯提轄).

His original name is Lu Da 魯達

He then receives the Buddhist name Zhishen (智深, profound wisdom) during conversion.