Phylogenetic tree Updated 2025-07-16
It is important to note that due to horizontal gene transfer, the early days of life, and still bacteria to this day due to bacterial conjugation, are actually a graph and not a tree, see also: Figure "Graph of life".
Definitely have a look at: coral of life representations.
Underlying field of a vector space Updated 2025-07-16
Every vector space is defined over a field.
E.g. in , the underlying field is , the real numbers. And in the underlying field is , the complex numbers.
Any field can be used, including finite field. But the underlying thing has to be a field, because the definitions of a vector need all field properties to hold to make sense.
Elements of the underlying field of a vector space are known as scalar.
UNION (SQL) Updated 2025-07-16
Basic example tested on SQLite 3.40.1, Ubuntu 23.04:
sqlite3 :memory: 'select 1 union select 2'
output:
1
2
Two columns two rows:
sqlite3 :memory: <<EOF
select * from (values (1, 2), (2, 3))
union
select * from (values (2, 3), (3, 4))
EOF
output:
1|2
2|3
3|4
Note how duplicates are removed, to keep them we UNION ALL instead:
sqlite3 :memory: <<EOF
select * from (values (1, 2), (2, 3))
union all
select * from (values (2, 3), (3, 4))
EOF
output:
1|2
2|3
2|3
3|4
United Kingdom Updated 2025-07-16
The United Kingdom is one big field.
Everything is extremely uniform and fully controlled by humans. Maybe this is partially due to it being an island with extensive flood plains. Loots of white mana floating around there.
Some impressively sounding natural parks look more like cute countryside that is slightly hillier than the surrounding countryside.
This uniformity does however make it quite comfortable for its Hobbit inhabitants.
It also means that whenever slightly out of the ordinary happens, e.g., a bit of slightly heavier rain, everything floods. In some way however, the Brits are very pragmatic, and as long as the flood is not too bad, they just let it be, it might be cheaper.
Universe Updated 2025-07-16
Epsilon (letter) Updated 2025-07-16
Confusingly, in LaTeX:
  • \varepsilon rendered , is the default modern Greek glyph
  • \epsilon rendered is the lunate variant
Erhu Updated 2025-07-16
Figure 1.
A blind erhu street performer playing in Jingzhou, Hubei (2006)
Source. Playing the erhu is a traditional occupation for blind people in China, a notable example being Abing.
Video 1.
Suwu herding sheep played by Song Fei (2017)
Source.
Video 2.
The 12 Most Famous Erhu Melodies in China (2021)
Source. TODO transcribe list.
This section is about the version of the course offered on Hilary term 2023 (January).
United States Updated 2025-07-16
The ruler of the 1950-2020 world by Dollar and nuke count.
Capable of evil like any other country, and somewhat merciless to its poor and overly egocentric, but not nearly as evil as any dictatorship.
Has the huge advantage of being one large country which speaks English.
Countries of the world have only two choices as of 2019: either rally behind the US and support democracy, or rally behind China and support dictatorship. The choice is up to you, voters. The more you deal with China, the more you lose your democracy and freedom. All dictatorships have no doubt that they must stick together.
And Americans, please stop that America Number 1 bullshit. Obviously everyone has to strive to be the best, so when you say it like that, it sounds like "even if at the expense of everyone else". The motto has to be "democracy number 1" or else you will scare off all allies. If all other countries sell out to China, you are fucked.
Blockchain.info Updated 2025-07-16
TODO who owns it? Are they reliable?
This helper dumps a transaction JSON to a binary:
bitcoin-tx-out-scripts() (
    # Dump data contained in out scripts. Remove first 3 last 2 bytes of
    # standard transaction boilerplate.
    h="$1"
    echo curl "https://blockchain.info/tx/${h}?format=json" |
    jq '.out[].script' tmp.json |
    sed 's/"76a914//;s/88ac"//' |
    xxd -r -p > "${h}.bin"
)
Their API limit witout key is 1 query per 10 seconds!!!
A good project to see UARTs at work in all their beauty is to connect two Raspberry Pis via UART, and then:
Part of the beauty of this is that you can just connect both boards directly manually with a few wire-to-wire connections with simple jump wire. Its simplicity is just quite refreshing. Sure, you could do something like that for any physical layer link presumably...
Remember that you can only have one GNU screen connected at a time or else they will mess each other up: unix.stackexchange.com/questions/93892/why-is-screen-is-terminating-without-root/367549#367549
On Ubuntu 22.04 you can screen without sudo by adding yourself to the dialout group with:
sudo usermod -a -G dialout $USER
Universal quantum gates Updated 2025-07-16
Just like as for classic gates, we would like to be able to select quantum computer physical implementations that can represent one or a few gates that can be used to create any quantum circuit.
Unfortunately, in the case of quantum circuits this is obviously impossible, since the space of N x N unitary matrices is infinite and continuous.
Therefore, when we say that certain gates form a "set of universal quantum gates", we actually mean that "any unitary matrix can be approximated to arbitrary precision with enough of these gates".
Or if you like fancy Mathy words, you can say that the subgroup of the unitary group generated by our basic gate set is a dense subset of the unitary group.

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