Ciro Santilli @cirosantilli 37

This book really tries to recall basic things to ensure that the reader will be able to understand the more advanced ones.

Sometimes it goes a little bit overboard, like defining what a function does several times.

But Ciro Santilli really prefers it when authors error on the side of obvious.

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Normal subgroup Updated 2025-07-16

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Ultimate explanation: math.stackexchange.com/questions/776039/intuition-behind-normal-subgroups/3732426#3732426

Only normal subgroups can be used to form quotient groups: their key definition is that they plus their cosets form a group.

Intuition:

One key intuition is that "a normal subgroup is the kernel" of a group homomorphism, and the normal subgroup plus cosets are isomorphic to the image of the isomorphism, which is what the fundamental theorem on homomorphisms says.

Therefore "there aren't that many group homomorphism", and a normal subgroup it is a concrete and natural way to uniquely represent that homomorphism.

The best way to think about the, is to always think first: what is the homomorphism? And then work out everything else from there.

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ELF Hello World Tutorial / .shstrtab Updated 2025-07-16

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Section type: sh_type == SHT_STRTAB.

Common name: "section header string table".

The section name .shstrtab is reserved. The standard says:

This section holds section names.

This section gets pointed to by the e_shstrnd field of the ELF header itself.

String indexes of this section are are pointed to by the sh_name field of section headers, which denote strings.

This section does not have SHF_ALLOC marked, so it will not appear on the executing program.

readelf -x .shstrtab hello_world.o

outputs:

Hex dump of section '.shstrtab':
  0x00000000 002e6461 7461002e 74657874 002e7368 ..data..text..sh
  0x00000010 73747274 6162002e 73796d74 6162002e strtab..symtab..
  0x00000020 73747274 6162002e 72656c61 2e746578 strtab..rela.tex
  0x00000030 7400                                t.

The data in this section has a fixed format: www.sco.com/developers/gabi/2003-12-17/ch4.strtab.html

If we look at the names of other sections, we see that they all contain numbers, e.g. the .text section is number 7.

Then each string ends when the first NUL character is found, e.g. character 12 is \0 just after .text\0.

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

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Sections with sh_type == SHT_STRTAB are called string tables.

They hold a null separated array of strings.

Such sections are used by other sections when string names are to be used. The using section says:

which string table they are using
what is the index on the target string table where the string starts

So for example, we could have a string table containing:

Data: \0 a b c \0 d e f \0
Index: 0 1 2 3  4 5 6 7  8

The first byte must be a 0. TODO rationale?

And if another section wants to use the string d e f, they have to point to index 5 of this section (letter d).

Notable string table sections:

.shstrtab
.strtab

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ELF Hello World Tutorial / SHT_SYMTAB on the executable Updated 2025-07-16

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By default, NASM places a .symtab on the executable as well.

This is only used for debugging. Without the symbols, we are completely blind, and must reverse engineer everything.

You can strip it with objcopy, and the executable will still run. Such executables are called "stripped executables".

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Nuclear magnetic resonance spectroscopy Updated 2025-07-16

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Used to identify organic compounds.

Seems to be based on the effects that electrons around the nuclei (shielding electrons) have on the outcome of NMR.

So it is a bit unlike MRI where you are interested in the position of certain nuclei in space (of course, these being atoms, you can't see their positions in space).

Video 1.

What's Nuclear Magnetic Resonance by Bruker Corporation (2020)

Source. Good 3D animations showing the structure of the NMR machine. We understand that it is very bulky largely due to the cryogenic system. It then talks a bit about organic compound identification by talking about ethanol, i.e. this is NMR spectroscopy, but it is a bit too much to follow closely. Basically the electron configuration alters the nuclear response somehow, and allows identifying functional groups.

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Nuclear weapon Updated 2025-07-16

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Ciro Santilli is mildly obsessed by nuclear reactions, because they are so quirky. How can a little ball destroy a city? How can putting too much of it together produce criticality and kill people like in the Slotin accident or the Tokaimura criticality accident. It is mind blowing really.

Uranium vs plutonium: Section "Uranium vs plutonium Quora answer by Ciro Santilli".

More fun nuclear stuff to watch:

Dr. Strangelove (1964)
en.wikipedia.org/wiki/Chernobyl_(miniseries)
The World Of Enrico Fermi by Harvard Project Physics (1970)
Fat Man and Little Boy (1987) shows a possibly reasonably realistic of the history of the development of the Trinity

Video 1.

Tour of a nuclear misile silo from the 60's by Arizona Highways TV (2019)

Source.

Video 2.

The Ultimate Guide to Nuclear Weapons by hypohystericalhistory (2022)

Source. Good overall summary. Some interesting points:

youtu.be/8uIPQBOCJ64?t=2946 talks about the difference between tactical and strategic nuclear weapons
youtu.be/8uIPQBOCJ64?t=3291 mentions variable yield devices, this is the main new thing Ciro Santilli learned from this video
youtu.be/8uIPQBOCJ64?t=3416 discusses if a strategic nuclear weapon usage would inevitably lead to tactical nuclear weapon escalation. It then mentions one case in which a possibly comparable escalation didn't happen: the abstinence of using chemical weapon during World War II.

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ELF Hello World Tutorial / .strtab Updated 2025-07-16

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Holds strings for the symbol table.

This section has sh_type == SHT_STRTAB.

It is pointed to by sh_link == 5 of the .symtab section.

readelf -x .strtab hello_world.o

outputs:

Hex dump of section '.strtab':
  0x00000000 0068656c 6c6f5f77 6f726c64 2e61736d .hello_world.asm
  0x00000010 0068656c 6c6f5f77 6f726c64 0068656c .hello_world.hel
  0x00000020 6c6f5f77 6f726c64 5f6c656e 005f7374 lo_world_len._st
  0x00000030 61727400                            art.

This implies that it is an ELF level limitation that global variables cannot contain NUL characters.

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

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Then come the most important symbols:

Num:    Value          Size Type    Bind   Vis      Ndx Name
  4: 0000000000000000     0 NOTYPE  LOCAL  DEFAULT    1 hello_world
  5: 000000000000000d     0 NOTYPE  LOCAL  DEFAULT  ABS hello_world_len
  6: 0000000000000000     0 NOTYPE  GLOBAL DEFAULT    2 _start

hello_world string is in the .data section (index 1). It's value is 0: it points to the first byte of that section.

_start is marked with GLOBAL visibility since we wrote:

global _start

in NASM. This is necessary since it must be seen as the entry point. Unlike in C, by default NASM labels are local.

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ELF Hello World Tutorial / .text section Updated 2025-07-16

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Now that we've done one section manually, let's graduate and use the readelf -S of the other sections:

  [Nr] Name              Type             Address           Offset
       Size              EntSize          Flags  Link  Info  Align
  [ 2] .text             PROGBITS         0000000000000000  00000210
       0000000000000027  0000000000000000  AX       0     0     16

.text is executable but not writable: if we try to write to it Linux segfaults. Let's see if we really have some code there:

objdump -d hello_world.o

gives:

hello_world.o:     file format elf64-x86-64


Disassembly of section .text:

0000000000000000 <_start>:
   0:       b8 01 00 00 00          mov    $0x1,%eax
   5:       bf 01 00 00 00          mov    $0x1,%edi
   a:       48 be 00 00 00 00 00    movabs $0x0,%rsi
  11:       00 00 00
  14:       ba 0d 00 00 00          mov    $0xd,%edx
  19:       0f 05                   syscall
  1b:       b8 3c 00 00 00          mov    $0x3c,%eax
  20:       bf 00 00 00 00          mov    $0x0,%edi
  25:       0f 05                   syscall

If we grep b8 01 00 00 on the hd, we see that this only occurs at 00000210, which is what the section says. And the Size is 27, which matches as well. So we must be talking about the right section.

This looks like the right code: a write followed by an exit.

The most interesting part is line a which does:

movabs $0x0,%rsi

to pass the address of the string to the system call. Currently, the 0x0 is just a placeholder. After linking happens, it will be modified to contain:

4000ba: 48 be d8 00 60 00 00    movabs $0x6000d8,%rsi

This modification is possible because of the data of the .rela.text section.

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Elliptic geometry Updated 2025-07-16

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Elliptic partial differential equation Updated 2025-07-16

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Emission theory (vision) Updated 2025-07-16

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It is so mind blowing that people believed in this theory. How can you think that, when you turn on a lamp and then you see? Obviously, the lamp must be emitting something!!!

Then comes along this epic 2002 paper: pubmed.ncbi.nlm.nih.gov/12094435/ "Fundamentally misunderstanding visual perception. Adults' belief in visual emissions". TODO review methods...

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Empty circle control qubit notation Updated 2025-07-16

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Some authors use the convention of:

filled black circle: conventional controlled quantum gate, i.e. operate if control qubit is active
empty (White) circle: operate if control qubit is inactive

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Endosymbiont Updated 2025-07-16

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EngineerGuy Updated 2025-07-16

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www.youtube.com/c/engineerguyvideo

en.wikipedia.org/wiki/William_S._Hammack

Does deliver good concise ideas. Now we need something on the less concise side of it.

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Epistle to the Romans Updated 2025-07-16

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Eppendorf tube Updated 2025-07-16