Ciro Santilli @cirosantilli 34

Datasheet: datasheets.raspberrypi.com/picow/pico-w-datasheet.pdf

This is a good approach. The downside is that while you are developing the implementation and testing interactively you might notice that the requirements are wrong, and then the tests have to change.

One intermediate approach Ciro Santilli likes is to do the implementation and be happy with interactive usage, then create the test, make it pass, then remove the code that would make it pass, and see it fail. This does have a risk that you will forget to test something, but Ciro finds it is a worth it generally. Unless it really is one of those features that you are unable to develop without an automated test, generally more "logical/mathematical" stuff. This is a sort of laziness Driven Development.

Includes:

The exact relationships between those clades is not very clear as there's a bunch of extinct species in the middle we are not sure exactly where they go exactly, some hypothesis are listed at: en.wikipedia.org/w/index.php?title=Tetrapod&oldid=1053601110#Temnospondyl_hypothesis_(TH)

But at least it seems rock solid that those three are actually clades.

mathoverflow.net/questions/20112/interesting-results-in-algebraic-geometry-accessible-to-3rd-year-undergraduates Interesting results in algebraic geometry accessible to 3rd year undergraduates

The ELF standard specifies multiple file formats:

In this tutorial, we consider only object and executable files.

When we particles particles, the action is obtained by integrating the Lagrangian over time:

In the case of field however, we can expand the Lagrangian out further, to also integrate over the space coordinates and their derivatives.

Since we are now working with something that gets integrated over space to obtain the total action, much like density would be integrated over space to obtain a total mass, the name "Lagrangian density" is fitting.

E.g. for a 2-dimensional field $f(x,y,t)$:

Of course, if we were to write it like that all the time we would go mad, so we can just write a much more condensed vectorized version using the gradient with $x\in {\mathbb{R}}^2$:

And in the context of special relativity, people condense that even further by adding $t$ to the spacetime Four-vector as well, so you don't even need to write that separate pesky $t$.

The main point of talking about the Lagrangian density instead of a Lagrangian for fields is likely that it treats space and time in a more uniform way, which is a basic requirement of special relativity: we have to be able to mix them up somehow to do Lorentz transformations. Notably, this is a key ingredient in a/the formulation of quantum field theory.

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.

These are basically technically minded people that Ciro Santilli feels have similar interests/psychology to him, and who write too much for their own good:

Maybe one day these will also be legendary, who knows:

Another category Ciro admires are the "computational physics visualization" people, these people will go to Heaven:

Related:

Institution led:

Other mentions:

Take the group of all Translation in ${\mathbb{R}}^1$.

Let's see how the generator of this group is the derivative operator:

The way to think about this is:

So let's take the exponential map: and we notice that this is exactly the Taylor series of $f(x)$ around the identity element of the translation group, which is 0! Therefore, if $f(x)$ behaves nicely enough, within some radius of convergence around the origin we have for finite $x_0$:

This example shows clearly how the exponential map applied to a (differential) operator can generate finite (non-infinitesimal) Translation!

The language all browsers converted to as of 2019, and therefore the easiest one to distribute and most widely implemented programming language.

Hopefully will be killed by WebAssembly one day.

Because JavaScript is a relatively crap/ad-hoc language, it ended up some decent tooling to make up for that, e.g. stuff like linting via ESLint and reformatting through Prettier is much more widespread than in other languages.

JavaScript data structure are also quite a bit anemic, which makes libraries such as lodash incredibly popular. But most of that stuff should be in the stdlib.

Our JavaScript examples can be found at:

The key difference from Lagrangian mechanics is that the Hamiltonian approach groups variables into pairs of coordinates called the phase space coordinates:This leads to having two times more unknown functions than in the Lagrangian. However, it also leads to a system of partial differential equations with only first order derivatives, which is nicer. Notably, it can be more clearly seen in phase space.

Bibliography:

In Ciro Santilli's view, the following three artists form a Holy Trinity of popular Brazilian music:

Elis Regina is not far though.

Ciro remembers quite clearly when he was riding the car with his parents when he pre teen, and he could not understand why they seemed so obsessed with The Trinity et al. Ciro in particular remembers listening to Video "Refazenda by Gilberto Gil (1975)". They had picked it up of course from the 70's and 80's when they were younger.

Young Ciro would also always confuse who was whom from the three of them.

Then Ciro got older, and he understood, they are mind blowing. You do have to look back in time a bit though, lots of lukewarm stuff on later periods. The military dictatorship in Brazil was good for music.

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.

This is the actual main function of university for many people as of the 2020s. And it fulfills it quite well. A breeding ground.

In a closely related sense, university is simply a symbol of personal status. Not a place where you go to learn. And especially in the Anglophone world of fancy colleges, university also doubles down as a form of long term luxury hotel. Even if it ends up meaning debt.

There's nothing wrong with sexual selection. This type of natural eugenics is an important part of humankind. It is however just sad that any type of learning falls so much behind. A close second would be fine. But as it stands, it is just too far off.

Related:

As of 2019, the Standard Model and general relativity are incompatible. Once those are unified, we will have one equation to describe the entirety of physics.

There are also however also unsolved problems in electroweak interaction + strong interaction, which if achieved is referred to as a Grand Unified Theory. Reaching a GUT is considered a sensible intermediate step before TOE.

The current state of Physics has been the result of several previous unifications as shown at: en.wikipedia.org/wiki/Theory_of_everything#Conventional_sequence_of_theories so it is expected that this last missing unification is likely to happen one day, potentially conditional on humanity having enough energy to observe new phenomena.

Notable mentions:

Other notable people that are likely also awesome but Ciro has less familiarity with their contributions: