Ciro Santilli @cirosantilli 35

silkqin.com entry: www.silkqin.com/02qnpu/07sqmp/sq46lsc.htm

Composed by Bo Ya for the guqin.

But there is an awesome guzheng adaptation which is perhaps better known in modern times, partly because it is not as long/slow. TODO origin.

韦编三绝 is a chengyu that means "to study diligently", i.e. to read so much to the point that your book starts to wear down.

There is a Chinese Wiki page for this song: zh.wikipedia.org/wiki/韦编三绝 which says it dates from the early Qing dynasty

Ubuntu 23.10:

glmark2 -b build:duration=3:model=horse

~22K

The key question is: why is this not symmetrical?

One answer is: because one of the twin accelerates, and therefore changes inertial frames.

But the better answer is: understand what happens when the stationary twin sends light signals at constant time intervals to each other. When does the travelling twin receives them?

By doing that, we see that "all the extra aging happens immediately when the twin turns around":

Another way of understanding it is: you have to make all calculations on a single inertial frame for the entire trip.

Supposing the sibling quickly accelerates out (or magically starts moving at constant speed), travels at constant speed, and quickly accelerates back, and travels at constant speed setup, there are three frames that seem reasonable:

If you do that, all three calculations give the exact same result, which is reassuring.

Another way to understand it is to do explicit integrations of the acceleration: physics.stackexchange.com/questions/242043/what-is-the-proper-way-to-explain-the-twin-paradox/242044#242044 This is the least insightful however :-)

Bibliography:

The set of all invertible matrices forms a group: the general linear group with matrix multiplication. Non-invertible matrices don't form a group due to the lack of inverse.

For this sub-case, we can define the Lie algebra of a Lie group $G$ as the set of all matrices $M\in G$ such that for all $t\in \mathbb{R}$:If we fix a given $M$ and vary $t$, we obtain a subgroup of $G$. This type of subgroup is known as a one parameter subgroup.

The immediate question is then if every element of $G$ can be reached in a unique way (i.e. is the exponential map a bijection). By looking at the matrix logarithm however we conclude that this is not the case for real matrices, but it is for complex matrices.

Examples:

TODO example it can be seen that the Lie algebra is not closed matrix multiplication, even though the corresponding group is by definition. But it is closed under the Lie bracket operation.

Subcase of a normed vector space, therefore also necessarily a vector space.

Composed by Wang Huiran in 1960.

The Yi people are one of the 55 Chinese ethnic minorities officially recognized by the Chinese government.

Virgin hub 3.0. mega minimal manual: web.archive.org/web/20220930011319/https://www.virginmedia.com/content/dam/virginmedia/dotcom/documents/corporate/userg-guide_broadband_superhub3.pdf

Home 2023:

Toy model of matter that exhibits phase transition in dimension 2 and greater. It does not provide numerically exact results by itself, but can serve as a tool to theorize existing and new phase transitions.

Each point in the lattice has two possible states: TODO insert image.

As mentioned at: stanford.edu/~jeffjar/statmech/intro4.html some systems which can be seen as modelled by it include:

Also has some funky relations to renormalization TODO.

Bibliography: