Ciro Santilli @cirosantilli 35

Original playlist name: "PHYSICS 68 ADVANCED MECHANICS: LAGRANGIAN MECHANICS"

Author: Michel van Biezen.

High school classical mechanics material, no mention of the key continuous symmetry part.

But does have a few classic pendulum/pulley/spring worked out examples that would be really wise to get under your belt first.

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:

Like Jimmy Wales, he used to work in finance and then quit. What is it with those successful e-learning people??

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.

Besides being useful in engineering, it was very important historically from a "development of mathematics point of view", e.g. it was the initial motivation for the Fourier series.

Some interesting properties:

Sample numerical solutions:

The group of all transformations that preserve some bilinear form, notable examples:

You just map the value (1, 1) $C_m\times C_n$ to the value 1 of $C_{mn}$, and it works out. E.g. for $C_2\times C_3$, the group generated by of (1, 1) is:

This is a general principle of software/hardware design that Ciro feels holds wide applicability.

The most extreme case of this is of course the integrated circuit itself, in which it is essentially impossible (?) to observe the specific value of some indidual wire at some point.

Somewhat on the other extreme, we have high level programming languages running on top of an operating system: at this point, you can just GDB step debug your program, print the value of any variable/memory location, and fully understand anything that you want. Provided that you manage to easily reach that point of interest.

And for anything in between we have various intermediate levels of complication. The most notable perhaps being developing the operating system itself. At this level, you can't so easily step debug (although techniques do exist). For early boot or bootloaders for example, you might want to use JTAG for example on real hardware.

In parallel to this, there is also another very important pair of closely linked tradeoffs:

Emulation also has another potential downside: unless you are very careful at implementing things correctly, your model might not be representative of the real thing. Also, there may be important tradeoffs between how much the model looks like the real thing, and how fast it runs. For example, QEMU's use of binary translation allows it to run orders of magnitude faster than gem5. However, you are unable to make any predictions about system performance with QEMU, since you are not modelling key elements like the cache or CPU pipeline.

Instrumentation is another technique that has can be considered to achieve greater observability.

Weight: heavy.

MIDI support is kind of secondary: www.youtube.com/watch?v=vnkJ0uYXMG8, e.g. how to export MIDI? discourse.ardour.org/t/export-an-entire-project-into-a-midi-file/88116

Ardour vmpk input: askubuntu.com/questions/709673/save-as-midi-when-playing-from-vmpk-qsynth/1298231#1298231

This vocabulary likely entered Ciro Santilli's vernacular through playing Counter-Strike when he was a teenager.