Ciro Santilli @cirosantilli 37

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.

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:

Like a heat equation but for functions without time dependence, space-only.

TODO confirm: does the solution of the heat equation always converge to the solution of the Laplace equation as time tends to infinity?

In one dimension, the Laplace equation is boring as it is just a straight line since the second derivative must be 0. That also matches our intuition of the limit solution of the heat equation.

Uniqueness: Uniqueness theorem for Poisson's equation.

web.math.pmf.unizg.hr/~duje/tors/rankhist.html gives a list with Elkies (2006) on top with:TODO why this non standard formulation?

An elliptic curve is defined by numbers $a$ and $b$. The curve is the set of all points $(x,y)$ of the real plane that satisfy the Equation 1. "Definition of the elliptic curves"

Equation 1. "Definition of the elliptic curves" definies elliptic curves over any field, it doesn't have to the real numbers. Notably, the definition also works for finite fields, leading to elliptic curve over a finite fields, which are the ones used in Elliptic-curve Diffie-Hellman cyprotgraphy.

Ciro Santilli believes that there is a close link between the ability to create disruptive technology, and the desire to find bugs/exploits in systems.

Both of them destabilize society and enterprises.

Some examples:

And yes, this sometimes leads into a fine line between legality and illegality:

Ciro Santilli's own naughty projects are listed at: Section "Ciro Santilli's naughty projects".

The outcome of Larry Page and Sergey Brin performing a Dragon Ball fusion dance.

Both of them attended Montessori education at some point. Interesting! Mentioned in a talk by Sergey and highlighted at The Google Story.

They stepped down from leading Google roles in 2019: www.npr.org/2019/12/03/784570156/google-founders-brin-page-step-down-pichai-takes-over-as-alphabet-ceo

But in 2023 they were somewhat pulled back in by the AI race and competition with ChatGPT.^[ref]

As The Google Story puts it about Largey:Ciro Santilli likes that.

A quantum circuit which when fed with input $|00⟩$ produces the Bell state.

In Qiskit at: qiskit/hello.py.

101 Crawfords Corner Rd Holmdel, NJ 07733 USA

It started with radio research apparently, including Karl Guthe Jansky.

They had a smaller building first: youtu.be/BPq_ZyOvbsg?t=51 and in 1962 opened the large new building.

600 Mountain Ave bldg 5, New Providence, NJ 07974, United States.

Became headquarters in 1967,

Drone footage: www.youtube.com/watch?v=z0Ld2KFjaC8 Bell LABS Headquarters Murray Hill NJ in 4K Drone Flight by ESTOUCHFPV (2017)

Notable inventions made there:

Some of the most remarkable ones seem to be:

Some good mentions on Inside Job (2010).

Depicted at: Len Sassaman tribute.

Won 2022 Nobel Prize.

www.facebook.com/watch/live/?mibextid=qC1gEa&ref=watch_permalink&v=10100156534675351 claims to have a video of Benji Wojin and his cousin Marco Troper from 2018. www.linkedin.com/posts/superintendents_marco-and-benji-wojin-love-these-kids-and-activity-7164448664772435968-siUC/ that links to it is lamenting Marco Troper 's death in 2024.

Claimed photos can be found at:All of the above are likely of the same child.

Co-founder of PowerDNS, an open source dNS implementation.

Homepage: berthub.eu/ says:.
All stuff Ciro cares about too! Cool dude! In particular Ciro loved his quote of I should have loved biology.

He's writing a fun-sounding book about molecular biology as of 2022: berthub.eu/dna-book. Appears to be closed source though. Ciro wonders if he really needs to sell the book for money after all those years though, rather than just publishing it online for free.

Looking at Bert just brings the Dutch Golden Age, and more in particular Antonie van Leeuwenhoek to mind. Epic.

Shows up when trying to solve 2D wave equation on a circular domain in polar coordinates with separation of variables, where we have to decompose the initial condition in termes of a fourier-Bessel series, exactly like the Fourier series appears when solving the wave equation in linear coordinates.

For the same fundamental reasons, also appears when calculating the Schrödinger equation solution for the hydrogen atom.

Issue report at: github.com/ourbigbook/ourbigbook/issues/198 Suppose you had:

programming-language.ciro

= Programming language

\Image[https://raw.githubusercontent.com/cirosantilli/media/master/python-logo.jpg]
{title=The \x[python-programming-language] logo}

== Python
{c}
{disambiguate=programming-language}

logos-i-like.ciro

= Logos I like

\x[image-the-python-logo]

Now, when rendering \x[image-the-python-logo], we would need to fetch two IDs:

But after group all SQL queries together was done, there was no way to know that rendering image-the-python-logo would imply also fetching python-programming-language.

This was solved by adding a new database entry type, REFS_TABLE_X_TITLE_TITLE to the existing References table, which tracks dependencies between IDs.

After this was setup, we can now know that image-the-python-logo depends on image-the-python-logo, and then fetch both of them together in a single JOIN.

What makes lasers so special: Lasers vs other light sources.

Bibliography:

The elliptic curve group of an elliptic curve is a group in which the elements of the group are points on an elliptic curve.

The group operation is called elliptic curve point addition.

Bibliography:

This is a family of notations related to the big O notation. A good mnemonic summary of all notations would be:

Analogous to a linear form, a bilinear form is a Bilinear map where the image is the underlying field of the vector space, e.g. ${\mathbb{R}}^n\times {\mathbb{R}}^m\to \mathbb{R}$.

Some definitions require both of the input spaces to be the same, e.g. ${\mathbb{R}}^n\times {\mathbb{R}}^n\to \mathbb{R}$, but it doesn't make much different in general.

The most important example of a bilinear form is the dot product. It is only defined if both the input spaces are the same.