Ciro Santilli @cirosantilli 40

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?

This is the one that hit Ciro Santilli the hardest, coming in at the point in which he started to discern between games and the real world a little better. His parents bought it for him during a trip to Disney World in Florida in 1996 (?), since electronics were much cheaper in the USA.

So as Ciro became older, and turned into a software engineer, he started to become more and more morbidly curious about "N64 internals": tool-assisted speedrun, how the devkit looks like, how games were developed for it, hardware leaks, etc.

Luckily Ciro's mind is not interested enough by that useless shit for Ciro to seriously study it himself. But that's what YouTube is for, right? Why do useless stuff when other more useless people can do it for you?

The console has only 4 MB of RAM memory. It is quite incredible what can be done with 8 MB, from the point of view of a 2020 worls where 16 GB laptops are the norm.

As mentioned at Video "Are we living in the matrix? by David Tong (2020)" somehow implies that it is difficult or impossible to simulate physics on a computer. Big news!!!

Chinese descent: thesportsgrail.com/who-is-nicole-shanahan-wife-of-sergey-brin-google-co-founder-biography-age-first-husband-parents-chinese-mother-child-net-worth-instagram/ Good old Sergey likes Asians.

Ciro Santilli's answer to How credible is Nick Lucid, of YouTube's "The Science Asylum"? on Quora.

Our examples are located under nodejs/next:

Solved ones: