Ciro Santilli @cirosantilli 40

Open source driver/hardware interface specification??? E.g. on Ubuntu, a large part of the nastiest UI breaking bugs Ciro Santilli encountered over the years have been GPU related. Do you think that is a coincidence??? E.g. ubuntu 21.10 does not wake up from suspend.

The finite element method is one of the most common ways to solve PDEs in practice.

Why would physicists use a letter such that:Why? Why?????????

Ciro Santilli is mildly obsessed by nuclear reactions, because they are so quirky. How can a little ball destroy a city? How can putting too much of it together produce criticality and kill people like in the Slotin accident or the Tokaimura criticality accident. It is mind blowing really.

Uranium vs plutonium: Section "Uranium vs plutonium Quora answer by Ciro Santilli".

More fun nuclear stuff to watch:

Some of the most notable ones:

One major difference between the elliptic curve over a finite field or the elliptic curve over the rational numbers the elliptic curve over the real numbers is that not every possible $x$ generates a member of the curve.

This is because on the Equation "Definition of the elliptic curves" we see that given an $x$, we calculate $x^3+ax+b$, which always produces an element $y^2$.

But then we are not necessarily able to find an $y$ for the $y^2$, because not all fields are not quadratically closed fields.

For example: with $a=1$ and $b=1$, taking $x=1$ gives:and therefore there is no $y\in \mathbb{Q}$ that satisfies the equation. So $x=1$ is not on the curve if we consider this elliptic curve over the rational numbers.

That $x$ would also not belong to Elliptic curve over the finite field ${\mathbb{F}}_4$, because doing everything $\mathrm{mod}4$ we have:Therefore, there is no element $y\in {\mathbb{F}}_4$ such that $y\times y=2$ or $y\times y=3$, i.e. $2$ and $3$ don't have a multiplicative inverse.

For the real numbers, it would work however, because the real numbers are a quadratically closed field, and $\sqrt{3}\in \mathbb{R}$.

For this reason, it is not necessarily trivial to determine the number of elements of an elliptic curve.

Given:the norm ends up being:

E.g. in ${\mathbb{C}}^2$:

Ultimate explanation: math.stackexchange.com/questions/776039/intuition-behind-normal-subgroups/3732426#3732426

Only normal subgroups can be used to form quotient groups: their key definition is that they plus their cosets form a group.

Intuition:

One key intuition is that "a normal subgroup is the kernel" of a group homomorphism, and the normal subgroup plus cosets are isomorphic to the image of the isomorphism, which is what the fundamental theorem on homomorphisms says.

Therefore "there aren't that many group homomorphism", and a normal subgroup it is a concrete and natural way to uniquely represent that homomorphism.

The best way to think about the, is to always think first: what is the homomorphism? And then work out everything else from there.

Era of quantum computing before we reach physical errors small enough to do perfect quantum error correction as demonstrated by the quantum threshold theorem.

Setting: you are sending bits through a communication channel, each bit has a random probability of getting flipped, and so you use some error correction code to achieve some minimal error, at the expense of longer messages.

This theorem sets an upper bound on how efficient you can be in your encoding, for any encoding.

The next big question, which the theorem does not cover is how to construct codes that reach or approach the limit. Important such codes include:

But besides this, there is also the practical consideration of if you can encode/decode fast enough to keep up with the coded bandwidth given your hardware capabilities.

news.mit.edu/2010/gallager-codes-0121 explains how turbo codes were first reached without a very good mathematical proof behind them, but were still revolutionary in experimental performance, e.g. turbo codes were used in 3G/4G.

But this motivated researchers to find other such algorithms that they would be able to prove things about, and so they rediscovered the much earlier low-density parity-check code, which had been published in the 60's but was forgotten, partially because it was computationally expensive.

www.knfusa.com/en/laboport/ (archive).

It runs one instance of the Linux kernel and has one IP address. Each node is therefore a complete computer. As such is must also contain RAM memory, disk storage and a network interface controller.

And the articles that really matter:

Web of Stories contains amazing interviews with many (mostly American) winners.

See Surely You're Joking, Mr. Feynman chapter Alfred Nobel's Other Mistake's amazing comments about the Nobel Prize.

TODO who is the digital switch person he mentions?

NIST database for spectral line: physics.nist.gov/PhysRefData/ASD/lines_form.html

Let's do a sanity check.

Searching for "H" for hydrogen leads to: physics.nist.gov/cgi-bin/ASD/lines1.pl?spectra=H&limits_type=0&low_w=&upp_w=&unit=1&submit=Retrieve+Data&de=0&format=0&line_out=0&en_unit=0&output=0&bibrefs=1&page_size=15&show_obs_wl=1&show_calc_wl=1&unc_out=1&order_out=0&max_low_enrg=&show_av=2&max_upp_enrg=&tsb_value=0&min_str=&A_out=0&intens_out=on&max_str=&allowed_out=1&forbid_out=1&min_accur=&min_intens=&conf_out=on&term_out=on&enrg_out=on&J_out=on

From there we can see for example the 1 to 2 lines:

We see that the table is sorted from lower from level first and then by upper level second.

So it is good to see that we are in the same 121nm ballpark as mentioned at hydrogen spectral line.

TODO why I can't see 2s to 2p transitions there to get the fine structure?