Ciro Santilli @cirosantilli 37

People will be more interested if they see how the stuff they are learning is useful.

Useful 99% of the time means you can make money with it.

Achieving novel results for science, or charitable goals (e.g. creating novel tutorials) are also equaly valid. Note that those also imply you being able to make a living out of something, just that you will be getting donations and not become infinitey rich. and that is fine.

Projects don't need of course to reach the level of novel result. But they must at least aim at moving towards that.

This is one of the greatest challenges of education, since a huge part of the useful information is locked under enterprise or military secrecy, or even open academic incomprehensibility, making it nearly to impossible for the front-line educators to actually find and teach real use cases.

And if you really can't make money from a subject, there is only one other thing people crave: beauty.

You have to give the beauty motivations upfront, before boring people to death with endless prerequisites, otherwise no one will ever want to learn it.

The key takeaway is that setting an explicit value function to an AGI entity is a good way to destroy the world due to poor AI alignment. We are more likely to not destroy by creating an AI whose goals is to "do want humans what it to do", but in a way that it does not know before hand what it is that humans want, and it has to learn from them. This approach appears to be known as reward modeling.

Some other cool ideas:

As of 2020's and earlier, humans were far far behind. As of 2020s and earlier, even an average personal computers without a GPU, the hallmark of deep learning beats every human.

Chess is just too easy!

21 cm is very long and very low energy, because he energy split is very small!

Compare it e.g. with the hydrogen 1-2 spectral line which is 121.6 nm!

square, cube. 4D case known as tesseract.

Convex hull of all $\{-1,1{\}}^D$ (Cartesian product power) D-tuples, e.g. in 3D:

From this we see that there are $2^D$ vertices.

Two vertices are linked iff they differ by a single number. So each vertex has D neighbors.

Small splits present in all levels due to interaction between the electron spin and the nuclear spin if it is present, i.e. the nucleus has an even number of nucleons.

As the name suggests, this energy split is very small, since the influence of the nucleus spin on the electron spin is relatively small compared to other fine structure.

TODO confirm: does it need quantum electrodynamics or is the Dirac equation enough?

The most important examples:

Created by Dr. Rod Nave from Georgia State University, where he worked from 1968 after his post-doc in North Wales on molecular spectroscopy.

While there is value to that website, it always feels like it falls a bit too short as too "encyclopedic" and too little "tutorial-like". Most notably, it has very little on the history of physics/experiments.

Ciro Santilli likes this Rod, he really practices some good braindumping, just look at how he documented his life in the pre-social media Internet dark ages: hyperphysics.phy-astr.gsu.edu/Nave-html/nave.html

The website evolved from a HyperCard stack, as suggested by the website name, mentioned at: hyperphysics.phy-astr.gsu.edu/hbase/index.html.

Shame he was too old for CC BY-SA, see "Please respect the Copyright" at hyperphysics.phy-astr.gsu.edu/hbase/index.html.

exhibits.library.gsu.edu/kell/exhibits/show/nave-kell-hall/capturing-a-career has some good photo selection focused on showing the department, and has an interview.

Kell hall is a building of GSU that was demolished in 2019: atlanta.curbed.com/2020/1/31/21115980/gsu-georgia-state-atlanta-kell-hall-demolition-park-library-north

Very similar to OurBigBook.com!

People who worked on it:

Bibliography:

Ahh, Ciro Santilli was certain this was some slang neologism, but it is actually Greek! So funny. Introduced into English in the 19th century according to: www.merriam-webster.com/dictionary/kudo.

$L^p$ for $p==2$.

$L^2$ is by far the most important of $L^p$ because it is quantum mechanics states live, because the total probability of being in any state has to be 1!

$L^2$ has some crucially important properties that other $L^p$ don't (TODO confirm and make those more precise):

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.

Published as "Fine Structure of the Hydrogen Atom by a Microwave Method" by Willis Lamb and Robert Retherford (1947) on Physical Review. This one actually has open accesses as of 2021, miracle! journals.aps.org/pr/pdf/10.1103/PhysRev.72.241

Microwave technology was developed in World War II for radar, notably at the MIT Radiation Laboratory. Before that, people were using much higher frequencies such as the visible spectrum. But to detect small energy differences, you need to look into longer wavelengths.

This experiment was fundamental to the development of quantum electrodynamics. As mentioned at Genius: Richard Feynman and Modern Physics by James Gleick (1994) chapter "Shrinking the infinities", before the experiment, people already knew that trying to add electromagnetism to the Dirac equation led to infinities using previous methods, and something needed to change urgently. However for the first time now the theorists had one precise number to try and hack their formulas to reach, not just a philosophical debate about infinities, and this led to major breakthroughs. The same book also describes the experiment briefly as:

It is two pages and a half long.

They were at Columbia University in the Columbia Radiation Laboratory. Robert was Willis' graduate student.

Previous less experiments had already hinted at this effect, but they were too imprecise to be sure.

Consider a real valued function of three variables:

Its Laplacian can be written as:

It is common to just omit the variables of the function, so we tend to just say:or equivalently when referring just to the operator:

This is a good first concrete example of a Lie algebra. Shown at Lie Groups, Physics, and Geometry by Robert Gilmore (2008) Chapter 4.2 "How to linearize a Lie Group" has an example.

We can use use the following parametrization of the special linear group on variables $x$, $y$ and $z$:

Every element with this parametrization has determinant 1:Furthermore, any element can be reached, because by independently settting $x$, $y$ and $z$, $M_{00}$, $M_{01}$ and $M_{10}$ can have any value, and once those three are set, $M_{11}$ is fixed by the determinant.

To find the elements of the Lie algebra, we evaluate the derivative on each parameter at 0:

Remembering that the Lie bracket of a matrix Lie group is really simple, we can then observe the following Lie bracket relations between them:

One key thing to note is that the specific matrices $M_x$, $M_y$ and $M_z$ are not really fundamental: we could easily have had different matrices if we had chosen any other parametrization of the group.

TODO confirm: however, no matter which parametrization we choose, the Lie bracket relations between the three elements would always be the same, since it is the number of elements, and the definition of the Lie bracket, that is truly fundamental.

Lie Groups, Physics, and Geometry by Robert Gilmore (2008) Chapter 4.2 "How to linearize a Lie Group" then calculates the exponential map of the vector $x{M}_x+y{M}_y+z{M}_z$ as:with:

TODO now the natural question is: can we cover the entire Lie group with this exponential? Lie Groups, Physics, and Geometry by Robert Gilmore (2008) Chapter 7 "EXPonentiation" explains why not.

The key and central motivation for studying Lie groups and their Lie algebras appears to be to characterize symmetry in Lagrangian mechanics through Noether's theorem, just start from there.

Notably local symmetries appear to map to forces, and local means "around the identity", notably: local symmetries of the Lagrangian imply conserved currents.

More precisely: local symmetries of the Lagrangian imply conserved currents.

TODO Ciro Santilli really wants to understand what all the fuss is about:

Oh, there is a low dimensional classification! Ciro is a sucker for classification theorems! en.wikipedia.org/wiki/Classification_of_low-dimensional_real_Lie_algebras

The fact that there are elements arbitrarily close to the identity, which is only possible due to the group being continuous, is the key factor that simplifies the treatment of Lie groups, and follows the philosophy of continuous problems are simpler than discrete ones.

Bibliography:

A subset of Spacetime diagram.

The key insights that it gives are:

That makes Ciro Santilli most mad about this film is the fact that the dude was passionate about writing, and when he became a genius, rather than write the best novels ever written, he decided instead to play the stock market instead. This paints an accurate picture of 2020's society, where finance jobs make infinitely more money than other real engineering jobs, and end up attracting much of the talent.

Another enraging thing is how his girlfriend starts liking him again once he is a genius, and instead of telling her to fuck off, he stays with her.

The other really bad thing is the ending. He fixed the drug by himself? He scared off De Niro just like that?

Lance instructor of the 800,000 Imperial Guards (八十万禁军枪棒教头). TODO understand the "枪棒" part: zhidao.baidu.com/question/206659649.html.

The adopted son of Gao Qiu wanted to fuck his wife, and because of this they frame him of planning to take revenge by killing Go Qiu, even though Lin Chong had decided not to take revenge to avoid harming his wife further.

They just keep trying to kill him, until at one point he just gives up and becomes a fugitive.

His story is well told in The Water Margin.

Usually called by others as 林教头 (lin jiaotou, literally Head Instructor Lin, but usually translated as just Instructor Lin).

A linear map is a function $f:V_1(F)\to V_2(F)$ where $V_1(F)$ and $V_2(F)$ are two vector spaces over underlying fields $F$ such that:

A common case is $F=\mathbb{R}$, $V_1={\mathbb{R}}_m$ and $V_2={\mathbb{R}}_n$.

One thing that makes such functions particularly simple is that they can be fully specified by specifyin how they act on all possible combinations of input basis vectors: they are therefore specified by only a finite number of elements of $F$.

Every linear map in finite dimension can be represented by a matrix, the points of the domain being represented as vectors.

As such, when we say "linear map", we can think of a generalization of matrix multiplication that makes sense in infinite dimensional spaces like Hilbert spaces, since calling such infinite dimensional maps "matrices" is stretching it a bit, since we would need to specify infinitely many rows and columns.

The prototypical building block of infinite dimensional linear map is the derivative. In that case, the vectors being operated upon are functions, which cannot therefore be specified by a finite number of parameters, e.g.

For example, the left side of the time-independent Schrödinger equation is a linear map. And the time-independent Schrödinger equation can be seen as a eigenvalue problem.