For the typical case of a linear form over , the form can be seen just as a row vector with n elements, the full form being specified by the value of each of the basis vectors.
Punycode inscription Updated 2025-07-16
Namecoin examples are catalogued at: punycodes.xyz. The are small Unicode art or emoji code.
There seems to be nothing of particular artistic value as far as we've seen so far, the only interest in such tokens seems to be that:
RimWorld Updated 2025-07-16
Sexual arousal Updated 2025-07-16
Analects translation by Robert Eno (2015) 16.7:
The Junzi has three cautions.
When he is young and his blood and energy are not yet settled, he is cautious about sex.
When he is in his prime and his blood and energy have newly achieved strength, he is cautious about combativeness.
When he is old and his blood and energy are declining, he is cautious about acquisitiveness.
Amitābha Updated 2025-07-16
More important than the monk itself in Chinese culture, it is used as a Budhist Amen. TODO find some usage in some Chinese television series.
Bridge amplification Updated 2025-07-16
This is one of the the key innovations of the Illumina (originally Solexa) sequencing.
This step is genius because sequencing is basically a signal-to-noise problem, as you are trying to observe individual tiny nucleotides mixed with billions of other tiny nucleotides.
With bridge amplification, we group some of the nucleotides together, and multiply the signal millions of times for that part of the DNA.
Bristol (synthesizer) Updated 2025-07-16
Simulates vintage hardware synthesizers, and includes some pretty complex ones!
Aims to show an UI that looks exactly like the synthesizers in question.
For example for the Minimoog on Ubuntu 20.04:
sudo apt install bristol
startBristol -mini -alsa
This is a really good piece of software. You can search on YouTube how some classic synths, work, and the immediately start playing them!
The Simpsons Updated 2025-07-16
Video 1.
The Fall of The Simpsons: How it Happened by Super Eyepatch Wolf (2017)
Source. This interesting video essay makes the main point that the Simpsons used to be good because they mocked mainstream. But then they became mainstream, which basically defeated their purpose. Think different from Apple comes to mind.
Distributive property Updated 2025-07-16
One of the defining properties of algebraic structure with two operations such as ring and field:
This property shows how the two operations interact.
Four-vector Updated 2025-07-16
Ubuntu 21.04 Updated 2025-07-16
They are sorted in order of "most likely to get done first".
Top one: OurBigBook.com.
Broadcom Updated 2025-07-16
Brownian motion Updated 2025-07-16
Small microscopic visible particles move randomly around in water.
If water were continuous, this shouldn't happen. Therefore this serves as one important evidence of atomic theory.
The amount it moves also quantitatively matches with the expected properties of water and the floating particles, was was settled in 1905 by Einstein at: investigations on the theory of the Brownian movement by Einstein (1905).
This suggestion that Brownian motion comes from the movement of atoms had been made much before Einstein however, and passed tortuous discussions. Subtle is the Lord by Abraham Pais (1982) page 93 explains it well. There had already been infinite discussion on possible causes of those movements besides atomic theory, and many ideas were rejected as incompatible with observations:
Further investigations eliminated such causes as temperature gradients, mechanical disturbances, capillary actions, irradiation of the liquid (as long as the resulting temperature increase can be neglected), and the presence of convection currents within the liquid.
The first suggestions of atomic theory were from the 1860s.
Tiny uniform plastic beads called "microbeads" are the preferred 2019 modern method of doing this: en.wikipedia.org/wiki/Microbead
Original well known observation in 1827 by Brown, with further experiments and interpretation in 1908 by Jean Baptiste Perrin. Possible precursor observation in 1785 by Jan Ingenhousz, not sure why he wasn't credited better.
Video 1.
Observing Brownian motion of micro beads by Forrest Charnock (2016)
Source.
Four-gradient Updated 2025-07-16
A 4D gradient with some small special relativity specifics added in (the light of speed and sign change for the time).

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