Ciro Santilli @cirosantilli 37

Someone once called Ciro Santilli that: archive.is/W1ocv. It's an overstatement, considering that Ciro's parents have some money. Not infinite. But still. Changes everything. A real Based God is someone like Charles Bukowski, who had to work decades at the post office.

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BCS Theory Updated 2025-07-16

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Main theory to explain Type I superconductors very successfully.

TODO can someone please just give the final predictions of BCS, and how they compare to experiments, first of all? Then derive them.

High level concepts:

the wave functions of pairs of electrons (fermions) get together to form bosons. This is a phase transition effect, thus the specific sudden transition temperature.
the pairs form a Bose-Einstein condensate
once this new state is reached, all pairs are somehow entangled into one big wave function, and you so individual lattice imperfections can't move just one single electron off trajectory and make it lose energy

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Beeching cuts Updated 2025-07-16

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A disaster. More cars and less trains...

Bibliograpy:

Losing Track by Channel 4 (1984), especially episode 5
www.theguardian.com/uk/2013/mar/02/beeching-wrong-about-britains-railways
Today the makeup of UK transport looks very different from the one envisaged by Dr Beeching. Rail passenger figures have almost doubled over the past 10 years; commuter trains are crammed; young people are deserting the car for the train; and Britain's railway bosses are struggling to meet soaring demands for seats. The legacy of Beeching - dug-up lines, sold-off track beds and demolished bridges - has only hindered plans to revitalise the network, revealing the dangers of having a single, inflexible vision when planning infrastructure.
"The crucial lesson to take from the Beeching anniversary is that you have to be flexible when planning transport infrastructure. Beeching was not," says Colin Divall, professor of rail history at York University. "Yes, many loss-making lines did need closing down, but nowhere near the number earmarked by Beeching, as we can now see with terrible hindsight."

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Lagrangian density Updated 2025-07-16

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

A c t i o n = \int_{t_{0}}^{t} L (x (t), \frac{\partial x ( t )}{\partial t}, t) d t

(1)

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)

A c t i o n = \int_{t_{0}}^{t} L (f (x, y, t), \frac{\partial f ( x , y , t )}{\partial x}, \frac{\partial f ( x , y , t )}{\partial y}, \frac{\partial f ( x , y , t )}{\partial t}, x, y, t) d x d y d t

(2)

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 R^{2}

A c t i o n = \int_{t_{0}}^{t} L (f (x, t), \nabla f (x, t), x, t) d x d t

(3)

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.

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Lagrangian vs Hamiltonian Updated 2025-07-16

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The key difference from Lagrangian mechanics is that the Hamiltonian approach groups variables into pairs of coordinates called the phase space coordinates:

generalized coordinates, generally positions or angles
their corresponding conjugate momenta, generally velocities, or angular velocities

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:

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Laplace's equation Updated 2025-07-16

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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.

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Largest known ranks of an elliptic curve over the rational numbers Updated 2025-07-16

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web.math.pmf.unizg.hr/~duje/tors/rankhist.html gives a list with Elkies (2006) on top with:

y^{2} + x y + y = x^{3} - x^{2} - 20067762415575526585033208209338542750930230312178956502 x + 34481611795030556467032985690390720374855944359319180361266008296291939448732243429

(1)

TODO why this non standard formulation?

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Being naughty and creative are correlated Updated 2025-07-16

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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:

Jobs and Wozniak's blue box
Robert Noyce's stealing a pig for a university party somewhat as a joke. This was actually a felony, but he got away with a compromise by paying the owner and being suspended for 6 months. The law is not blind, and thanks for that sometimes.
Oh, and apparently he also got a university girlfriend pregnant, and she had an abortion.
Mark Zuckerberg's FaceMash