Ciro Santilli @cirosantilli  40

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Fine structure constant Updated 2025-07-16

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Hyperfine structure Updated 2025-07-16

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:

hydrogen line useful in astronomy, and also the simplest possible case between 1s
caesium standard, which is used to define the second in the International System of Units since 1967.

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Financial crisis of 2007-2008 Updated 2025-07-16

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Dot-com bubble Updated 2025-07-16

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Finance is a cancer of society Updated 2025-07-16

The financial industry does not serve society nowhere near its magnitude (London of course being the epitome of that). It serves only itself. It just grows without bound.

www.theatlantic.com/technology/archive/2011/05/on-the-floor-laughing-traders-are-having-a-new-kind-of-fun/238570/ On the Floor Laughing: Traders Are Having a New Kind of Fun (2011) by James Somers describes trading as a kind of game.

Why I chose quant trading to retire early by Lit Nomad

. Source. Ciro Santilli was not sure under which section classify this video. It is worthwhile despite the title

youtu.be/exPt6mVgpfY?t=123 describes how at Lockheed Martin they were playing the "we are doing it for national defense, not for money card" on employees. Ciro Santilli came to understand and despise similar hypocrisy via Ciro's everyone gets a raise story

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Bank Updated 2025-07-16

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Financial fraud Updated 2025-07-16

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High-frequency trading Updated 2025-07-16

High Frequency Trading by WEED e.V. (2014)

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Feynman diagram solver Updated 2025-07-16

physics.stackexchange.com/questions/96510/software-for-calculating-feynman-diagrams

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Does the exact position of vertices matter in Feynman diagrams? Updated 2025-07-16

No, but why?

physics.stackexchange.com/questions/297004/feynman-diagram-and-uncertainty/297006

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Cavendish experiment Updated 2025-07-16

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Equations of motion Updated 2025-07-16

These are the final equations that you derive from the Lagrangian via the Euler-Lagrange equation which specify how the system evolves with time.

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There are no known eukaryotes which never had mitochondria Updated 2025-07-16

As of 2020, there are no known eukaryotes which have never had mitochondria.

Known eukaryotes without mitochondria, which are very rare, have lost mitochondria they previously had.

Having mitochondria appears to be a requisite for being an eukaryote. This is one of the central thesis of Power, Sex, Suicide by Nick Lane (2006).

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Time-energy uncertainty principle Updated 2025-07-16

There is also a time-energy uncertainty principle, because those two operators are also complementary.

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Elliptic-curve Diffie-Hellman Updated 2025-07-16

The algorithm is completely analogous to Diffie-Hellman key exchange in that you efficiently raise a number to a power

n

times and send the result over while keeping

n

as private key.

The only difference is that a different group is used: instead of using the cyclic group, we use the elliptic curve group of an elliptic curve over a finite field.

Elliptic curves by Computerphile (2018)

Source. youtu.be/NF1pwjL9-DE?t=143 shows the continuous group well, but then fails to explain the discrete part.

Variant of Diffie-Hellman key exchange based on elliptic curve cryptography.

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ELF Hello World Tutorial / Introduction Updated 2025-07-16

ELF is the dominating file format for Linux. It competes with Mach-O for OS X and PE for Windows.

ELF supersedes .coff, which supersedes a.out.

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ELF Hello World Tutorial / Minimal ELF file Updated 2025-07-16

It is non-trivial to determine what is the smallest legal ELF file, or the smaller one that will do something trivial in Linux.

Some impressive attempts:

In this example we will consider a saner hello world example that will better capture real life cases.

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ELF Hello World Tutorial / Generate the example Updated 2025-07-16

Let's break down a minimal runnable Linux x86-64 example:

hello_world.asm

section .data
    hello_world db "Hello world!", 10
    hello_world_len  equ $ - hello_world
section .text
    global _start
    _start:
        mov rax, 1
        mov rdi, 1
        mov rsi, hello_world
        mov rdx, hello_world_len
        syscall
        mov rax, 60
        mov rdi, 0
        syscall

Compiled with:

nasm -w+all -f elf64 -o 'hello_world.o' 'hello_world.asm'
ld -o 'hello_world.out' 'hello_world.o'

TODO: use a minimal linker script with -T to be more precise and minimal.

Versions:

NASM 2.10.09
Binutils version 2.24 (contains ld)
Ubuntu 14.04

We don't use a C program as that would complicate the analysis, that will be level 2 :-)

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ELF Hello World Tutorial / Object hd Updated 2025-07-16

Running:

hd hello_world.o

gives:

00000000  7f 45 4c 46 02 01 01 00  00 00 00 00 00 00 00 00  |.ELF............|
00000010  01 00 3e 00 01 00 00 00  00 00 00 00 00 00 00 00  |..>.............|
00000020  00 00 00 00 00 00 00 00  40 00 00 00 00 00 00 00  |........@.......|
00000030  00 00 00 00 40 00 00 00  00 00 40 00 07 00 03 00  |....@.....@.....|
00000040  00 00 00 00 00 00 00 00  00 00 00 00 00 00 00 00  |................|
*
00000080  01 00 00 00 01 00 00 00  03 00 00 00 00 00 00 00  |................|
00000090  00 00 00 00 00 00 00 00  00 02 00 00 00 00 00 00  |................|
000000a0  0d 00 00 00 00 00 00 00  00 00 00 00 00 00 00 00  |................|
000000b0  04 00 00 00 00 00 00 00  00 00 00 00 00 00 00 00  |................|
000000c0  07 00 00 00 01 00 00 00  06 00 00 00 00 00 00 00  |................|
000000d0  00 00 00 00 00 00 00 00  10 02 00 00 00 00 00 00  |................|
000000e0  27 00 00 00 00 00 00 00  00 00 00 00 00 00 00 00  |'...............|
000000f0  10 00 00 00 00 00 00 00  00 00 00 00 00 00 00 00  |................|
00000100  0d 00 00 00 03 00 00 00  00 00 00 00 00 00 00 00  |................|
00000110  00 00 00 00 00 00 00 00  40 02 00 00 00 00 00 00  |........@.......|
00000120  32 00 00 00 00 00 00 00  00 00 00 00 00 00 00 00  |2...............|
00000130  01 00 00 00 00 00 00 00  00 00 00 00 00 00 00 00  |................|
00000140  17 00 00 00 02 00 00 00  00 00 00 00 00 00 00 00  |................|
00000150  00 00 00 00 00 00 00 00  80 02 00 00 00 00 00 00  |................|
00000160  a8 00 00 00 00 00 00 00  05 00 00 00 06 00 00 00  |................|
00000170  04 00 00 00 00 00 00 00  18 00 00 00 00 00 00 00  |................|
00000180  1f 00 00 00 03 00 00 00  00 00 00 00 00 00 00 00  |................|
00000190  00 00 00 00 00 00 00 00  30 03 00 00 00 00 00 00  |........0.......|
000001a0  34 00 00 00 00 00 00 00  00 00 00 00 00 00 00 00  |4...............|
000001b0  01 00 00 00 00 00 00 00  00 00 00 00 00 00 00 00  |................|
000001c0  27 00 00 00 04 00 00 00  00 00 00 00 00 00 00 00  |'...............|
000001d0  00 00 00 00 00 00 00 00  70 03 00 00 00 00 00 00  |........p.......|
000001e0  18 00 00 00 00 00 00 00  04 00 00 00 02 00 00 00  |................|
000001f0  04 00 00 00 00 00 00 00  18 00 00 00 00 00 00 00  |................|
00000200  48 65 6c 6c 6f 20 77 6f  72 6c 64 21 0a 00 00 00  |Hello world!....|
00000210  b8 01 00 00 00 bf 01 00  00 00 48 be 00 00 00 00  |..........H.....|
00000220  00 00 00 00 ba 0d 00 00  00 0f 05 b8 3c 00 00 00  |............<...|
00000230  bf 00 00 00 00 0f 05 00  00 00 00 00 00 00 00 00  |................|
00000240  00 2e 64 61 74 61 00 2e  74 65 78 74 00 2e 73 68  |..data..text..sh|
00000250  73 74 72 74 61 62 00 2e  73 79 6d 74 61 62 00 2e  |strtab..symtab..|
00000260  73 74 72 74 61 62 00 2e  72 65 6c 61 2e 74 65 78  |strtab..rela.tex|
00000270  74 00 00 00 00 00 00 00  00 00 00 00 00 00 00 00  |t...............|
00000280  00 00 00 00 00 00 00 00  00 00 00 00 00 00 00 00  |................|
00000290  00 00 00 00 00 00 00 00  01 00 00 00 04 00 f1 ff  |................|
000002a0  00 00 00 00 00 00 00 00  00 00 00 00 00 00 00 00  |................|
000002b0  00 00 00 00 03 00 01 00  00 00 00 00 00 00 00 00  |................|
000002c0  00 00 00 00 00 00 00 00  00 00 00 00 03 00 02 00  |................|
000002d0  00 00 00 00 00 00 00 00  00 00 00 00 00 00 00 00  |................|
000002e0  11 00 00 00 00 00 01 00  00 00 00 00 00 00 00 00  |................|
000002f0  00 00 00 00 00 00 00 00  1d 00 00 00 00 00 f1 ff  |................|
00000300  0d 00 00 00 00 00 00 00  00 00 00 00 00 00 00 00  |................|
00000310  2d 00 00 00 10 00 02 00  00 00 00 00 00 00 00 00  |-...............|
00000320  00 00 00 00 00 00 00 00  00 00 00 00 00 00 00 00  |................|
00000330  00 68 65 6c 6c 6f 5f 77  6f 72 6c 64 2e 61 73 6d  |.hello_world.asm|
00000340  00 68 65 6c 6c 6f 5f 77  6f 72 6c 64 00 68 65 6c  |.hello_world.hel|
00000350  6c 6f 5f 77 6f 72 6c 64  5f 6c 65 6e 00 5f 73 74  |lo_world_len._st|
00000360  61 72 74 00 00 00 00 00  00 00 00 00 00 00 00 00  |art.............|
00000370  0c 00 00 00 00 00 00 00  01 00 00 00 02 00 00 00  |................|
00000380  00 00 00 00 00 00 00 00  00 00 00 00 00 00 00 00  |................|
00000390

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ELF Hello World Tutorial / Executable hd Updated 2025-07-16

Running:

hd hello_world.out

gives:

00000000  7f 45 4c 46 02 01 01 00  00 00 00 00 00 00 00 00  |.ELF............|
00000010  02 00 3e 00 01 00 00 00  b0 00 40 00 00 00 00 00  |..>.......@.....|
00000020  40 00 00 00 00 00 00 00  10 01 00 00 00 00 00 00  |@...............|
00000030  00 00 00 00 40 00 38 00  02 00 40 00 06 00 03 00  |[email protected]...@.....|
00000040  01 00 00 00 05 00 00 00  00 00 00 00 00 00 00 00  |................|
00000050  00 00 40 00 00 00 00 00  00 00 40 00 00 00 00 00  |..@.......@.....|
00000060  d7 00 00 00 00 00 00 00  d7 00 00 00 00 00 00 00  |................|
00000070  00 00 20 00 00 00 00 00  01 00 00 00 06 00 00 00  |.. .............|
00000080  d8 00 00 00 00 00 00 00  d8 00 60 00 00 00 00 00  |..........`.....|
00000090  d8 00 60 00 00 00 00 00  0d 00 00 00 00 00 00 00  |..`.............|
000000a0  0d 00 00 00 00 00 00 00  00 00 20 00 00 00 00 00  |.......... .....|
000000b0  b8 01 00 00 00 bf 01 00  00 00 48 be d8 00 60 00  |..........H...`.|
000000c0  00 00 00 00 ba 0d 00 00  00 0f 05 b8 3c 00 00 00  |............<...|
000000d0  bf 00 00 00 00 0f 05 00  48 65 6c 6c 6f 20 77 6f  |........Hello wo|
000000e0  72 6c 64 21 0a 00 2e 73  79 6d 74 61 62 00 2e 73  |rld!...symtab..s|
000000f0  74 72 74 61 62 00 2e 73  68 73 74 72 74 61 62 00  |trtab..shstrtab.|
00000100  2e 74 65 78 74 00 2e 64  61 74 61 00 00 00 00 00  |.text..data.....|
00000110  00 00 00 00 00 00 00 00  00 00 00 00 00 00 00 00  |................|
*
00000150  1b 00 00 00 01 00 00 00  06 00 00 00 00 00 00 00  |................|
00000160  b0 00 40 00 00 00 00 00  b0 00 00 00 00 00 00 00  |..@.............|
00000170  27 00 00 00 00 00 00 00  00 00 00 00 00 00 00 00  |'...............|
00000180  10 00 00 00 00 00 00 00  00 00 00 00 00 00 00 00  |................|
00000190  21 00 00 00 01 00 00 00  03 00 00 00 00 00 00 00  |!...............|
000001a0  d8 00 60 00 00 00 00 00  d8 00 00 00 00 00 00 00  |..`.............|
000001b0  0d 00 00 00 00 00 00 00  00 00 00 00 00 00 00 00  |................|
000001c0  04 00 00 00 00 00 00 00  00 00 00 00 00 00 00 00  |................|
000001d0  11 00 00 00 03 00 00 00  00 00 00 00 00 00 00 00  |................|
000001e0  00 00 00 00 00 00 00 00  e5 00 00 00 00 00 00 00  |................|
000001f0  27 00 00 00 00 00 00 00  00 00 00 00 00 00 00 00  |'...............|
00000200  01 00 00 00 00 00 00 00  00 00 00 00 00 00 00 00  |................|
00000210  01 00 00 00 02 00 00 00  00 00 00 00 00 00 00 00  |................|
00000220  00 00 00 00 00 00 00 00  90 02 00 00 00 00 00 00  |................|
00000230  08 01 00 00 00 00 00 00  05 00 00 00 07 00 00 00  |................|
00000240  08 00 00 00 00 00 00 00  18 00 00 00 00 00 00 00  |................|
00000250  09 00 00 00 03 00 00 00  00 00 00 00 00 00 00 00  |................|
00000260  00 00 00 00 00 00 00 00  98 03 00 00 00 00 00 00  |................|
00000270  4c 00 00 00 00 00 00 00  00 00 00 00 00 00 00 00  |L...............|
00000280  01 00 00 00 00 00 00 00  00 00 00 00 00 00 00 00  |................|
00000290  00 00 00 00 00 00 00 00  00 00 00 00 00 00 00 00  |................|
000002a0  00 00 00 00 00 00 00 00  00 00 00 00 03 00 01 00  |................|
000002b0  b0 00 40 00 00 00 00 00  00 00 00 00 00 00 00 00  |..@.............|
000002c0  00 00 00 00 03 00 02 00  d8 00 60 00 00 00 00 00  |..........`.....|
000002d0  00 00 00 00 00 00 00 00  01 00 00 00 04 00 f1 ff  |................|
000002e0  00 00 00 00 00 00 00 00  00 00 00 00 00 00 00 00  |................|
000002f0  11 00 00 00 00 00 02 00  d8 00 60 00 00 00 00 00  |..........`.....|
00000300  00 00 00 00 00 00 00 00  1d 00 00 00 00 00 f1 ff  |................|
00000310  0d 00 00 00 00 00 00 00  00 00 00 00 00 00 00 00  |................|
00000320  00 00 00 00 04 00 f1 ff  00 00 00 00 00 00 00 00  |................|
00000330  00 00 00 00 00 00 00 00  2d 00 00 00 10 00 01 00  |........-.......|
00000340  b0 00 40 00 00 00 00 00  00 00 00 00 00 00 00 00  |..@.............|
00000350  34 00 00 00 10 00 02 00  e5 00 60 00 00 00 00 00  |4.........`.....|
00000360  00 00 00 00 00 00 00 00  40 00 00 00 10 00 02 00  |........@.......|
00000370  e5 00 60 00 00 00 00 00  00 00 00 00 00 00 00 00  |..`.............|
00000380  47 00 00 00 10 00 02 00  e8 00 60 00 00 00 00 00  |G.........`.....|
00000390  00 00 00 00 00 00 00 00  00 68 65 6c 6c 6f 5f 77  |.........hello_w|
000003a0  6f 72 6c 64 2e 61 73 6d  00 68 65 6c 6c 6f 5f 77  |orld.asm.hello_w|
000003b0  6f 72 6c 64 00 68 65 6c  6c 6f 5f 77 6f 72 6c 64  |orld.hello_world|
000003c0  5f 6c 65 6e 00 5f 73 74  61 72 74 00 5f 5f 62 73  |_len._start.__bs|
000003d0  73 5f 73 74 61 72 74 00  5f 65 64 61 74 61 00 5f  |s_start._edata._|
000003e0  65 6e 64 00                                       |end.|
000003e4

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