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.
The heart/main innovation of GitHub!
The Evolution of Bacteria on a 'Mega-Plate' Petri dish by Kishony Lab (2016)
Source. They've made a huge Petri dish with bands of different concentrations of antibiotic, and then they visualize Escherichia coli mutations as new strains manage to make their way into the highest antibiotic concentration strip. mind blowing.Previously known as "Food From Electricity", "NeoCarbonFood" sounds like a more commercializable version of it.
Uses electricity to electrolyse water into hydrogen and oxygen molecules, and then use bacteria that do hydrogen chemosynthesis to convert it into food.
Ciro Santilli is agnostic, see also: github.com/cirosantilli/china-dictatorship/tree/965430af9f50a93ac23dfbb72719eee0f93c8c5c#do-you-believe-in-or-practice-falun-gong
His father always told him a story about how when Ciro was small, someone raised the question of the existence of God, to which Ciro replied very directly and naturally, without any doubts:It's a genetic thing it seems.
That doesn't exist.
With major mathematicians holding ideas such as:it is not surprise that the state of STEM education is so shit as of 2020, especially at the the missing link between basic and advanced! This also implies that the number of people that can appreciate any advanced mathematics research is tiny, and consequently so is the funding.
Exposition, criticism, appreciation, is work for second-rate minds. [...] It is a melancholy experience for a professional mathematician to find himself writing about mathematics. The function of a mathematician is to do something, to prove new theorems, to add to mathematics, and not to talk about what he or other mathematicians have done.
Let's see:
- www.linkedin.com/in/xahlee/
- xahlee.org/Nice Second brain vibe.
Siphon my knowledge into your brain. Assimilate my sensibilities to your spine.
- youtu.be/a6J62TwOreY?t=271 OMG he also uses a Kinesis Advantage 2 keyboard-like keyboard! Maybe there is something here after all.
- he's also a mad tutorial writer: xahlee.info/Wallpaper_dir/c4_Derivation.html#gc2.2.2.1 like Ciro's Stack Overflow
- www.patreon.com/xahlee £835.2/month from ony 27 members as of 2023, holy crap not bad!
- he was in a bad spot as of 2014: xahlee.info/emacs/misc/xah_as_good_as_dead.htmlThread: www.reddit.com/r/programming/comments/25pypq/im_about_as_good_as_dead_the_end_of_xah_lee/
i live on $3 per day for food in past 3 years. Eating noodles and oats with salt
One is reminded of Chill and eat your bread in peace and Quote "Omar Khayyam's chill out quote". xahlee.org/PageTwo_dir/Personal_dir/xah.html autobiography is also of interest.
Equivalent to Lagrangian mechanics but formulated in a different way.
Motivation: Lagrangian vs Hamiltonian.
TODO understand original historical motivation, www.youtube.com/watch?v=SZXHoWwBcDc says it is from optics.
Intuitively, the Hamiltonian is the total energy of the system in terms of arbitrary parameters, a bit like Lagrangian mechanics.
Bibliography:
PDF table of contents feature requests: twitter.com/cirosantilli/status/1459844683925008385
There are unlisted articles, also show them or only show them.