Ciro Santilli @cirosantilli 35

This makes it clear how the Lie bracket can be seen as a "measure of non-commutativity"

Because the Lie bracket has to be a bilinear map, all we need to do to specify it uniquely is to specify how it acts on every pair of some basis of the Lie algebra.

Then, together with the Baker-Campbell-Hausdorff formula and the Lie group-Lie algebra correspondence, this forms an exceptionally compact description of a Lie group.

The one parameter subgroup of a Lie group for a given element $M$ of its Lie algebra is a subgroup of $G$ given by:

Intuitively, $M$ is a direction, and $t$ is how far we move along a given direction. This intuition is especially vivid in for example in the case of the Lie algebra of $SO(3)$, the rotation group.

One parameter subgroups can be seen as the continuous analogue to the cycle of an element of a group.

The first Bitcoin exchange. Coded as a hack, and they didn't manage to fix the hacks as the site evolved in a major way, which led to massive hacks.

Their creation is clearly visible on the archive history of bitcoin.org: web.archive.org/web/20100701000000*/bitcoin.org which started having massively more archives since Mt. Gox opened.

This is true. The level of competition in university entry exams in Asia in insane in the early 21st century compared to the West.

This is actually both good and bad. Good because it selects some very good exam passers. And bad because it selects some very good exam passers.

Is a decision problem of determining if something belongs to a non-recursive language.

Or in other words: there is no Turing machine that always halts for every input with the yes/no output.

Every undecidable problem must obviously have an infinite number of "possibilities of stuff you can try": if there is only a finite number, then you can brute-force it.

Some undecidable problems are of recursively enumerable language, e.g. the halting problem.

Lists of undecidable problems.

Coolest ones besides the obvious boring halting problem:

Nice, nice place. Natural sciences only, no bullshit.

One "LevelDB" database contains multiple file in a directory. Off the bat inferior to SQLite which stores everything in a single file!