Ciro Santilli @cirosantilli 40

Many bad films have good aspects. They just didn't cross the elusive threshold of a good film.

Semi-comical student website to review the toilets of the University of São Paulo. Some of the toilets had a reputation for being terrible.

One is reminded of Crushbridge.

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.

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?

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.

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.

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.

iubmb.onlinelibrary.wiley.com/doi/full/10.1002/bmb.2002.494030030067 Surprises and revelations in biochemistry: 1950-2000 by Perry A. Frey (2006). This should be worth a read.

Reference implementation?

Links:

Executables provided:

This is the most extreme and final form of peer tutoring, it's natural final consequence given the Internet Age.

Uses the frequency of the hyperfine structure of caesium-133 ground state, i.e spin up vs spin down of its valence electron $6s^1$, to define the second.

International System of Units definition of the second since 1967, because this is what atomic clocks use.

TODO why does this have more energy than the hyperfine split of the hydrogen line given that it is further from the nucleus?

Why caesium hyperfine structure is used: