Ciro Santilli @cirosantilli 37

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Hall effect Updated 2025-07-16

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The voltage changes perpendicular to the current when magnetic field is applied.

Figure 1.
Hall effect experimental diagram
. Source. The Hall effect refers to the produced voltage $V_{H}$ , AKA $V_{y}$ on this setup.

An intuitive video is:

Video 1. Source.

The key formula for it is:

V_{H} = \frac{I _{x} B _{z}}{n t e}

(1)

where:

$I_{x}$ : current on x direction, which we can control by changing the voltage $V_{x}$
$B_{z}$ : strength of transversal magnetic field applied
$n$ : charge carrier density, a property of the material used
$t$ : height of the plate
$e$ : electron charge

Applications:

the direction of the effect proves that electric currents in common electrical conductors are made up of negative charged particles
measure magnetic fields, TODO vs other methods

Other more precise non-classical versions:

quantum Hall effect

Bibliography:

hyperphysics.phy-astr.gsu.edu/hbase/magnetic/Hall.html

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Spin half Updated 2025-07-16

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Leads to the Dirac equation.

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Genome Project-Write Updated 2025-07-16

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Hash function Updated 2025-07-16

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Applications:

hash map which is a O(1) amortized implementation of a map
creating unbreakable chains of data, e.g. for Git commits or Bitcoin.
storing passwords on a server in a way that if the password database is stolen, attackers can't reuse them on other websites where the user used the same password: security.blogoverflow.com/2013/09/about-secure-password-hashing/

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How to teach / Projects must aim for novelty Updated 2025-07-16

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The projects you do must always aim to achieving some novel result.

You don't have to necessarily reach it. But you must aim for it.

Novel result can be taken broadly.

E.g., a new tutorial that explains something in a way never done before is novel.

But there must be something to your project that has never been done before.

You can start by reproducing other's work.

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Rydberg atom Updated 2025-07-16

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Spin 1 Updated 2025-07-16

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Leads to the Proca equation.

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

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Section type: sh_type == SHT_RELA.

Common name: "relocation section".

.rela.text holds relocation data which says how the address should be modified when the final executable is linked. This points to bytes of the text area that must be modified when linking happens to point to the correct memory locations.

Basically, it translates the object text containing the placeholder 0x0 address:

   a:       48 be 00 00 00 00 00    movabs $0x0,%rsi
  11:       00 00 00

to the actual executable code containing the final 0x6000d8:

4000ba: 48 be d8 00 60 00 00    movabs $0x6000d8,%rsi
4000c1: 00 00 00

It was pointed to by sh_info = 6 of the .symtab section.

readelf -r hello_world.o outputs:

Relocation section '.rela.text' at offset 0x3b0 contains 1 entries:
  Offset          Info           Type           Sym. Value    Sym. Name + Addend
00000000000c  000200000001 R_X86_64_64       0000000000000000 .data + 0

The section does not exist in the executable.

The actual bytes are:

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  |................|

The struct represented is:

typedef struct {
    Elf64_Addr  r_offset;
    Elf64_Xword r_info;
    Elf64_Sxword    r_addend;
} Elf64_Rela;

So:

370 0: r_offset = 0xC: address into the .text whose address this relocation will modify
370 8: r_info = 0x200000001. Contains 2 fields:
- ELF64_R_TYPE = 0x1: meaning depends on the exact architecture.
- ELF64_R_SYM = 0x2: index of the section to which the address points, so .data which is at index 2.
The AMD64 ABI says that type 1 is called R_X86_64_64 and that it represents the operation S + A where:
- S: the value of the symbol on the object file, here 0 because we point to the 00 00 00 00 00 00 00 00 of movabs $0x0,%rsi
- A: the addend, present in field r_added
This address is added to the section on which the relocation operates.
This relocation operation acts on a total 8 bytes.
380 0: r_addend = 0

So in our example we conclude that the new address will be: S + A = .data + 0, and thus the first thing in the data section.

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

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Besides sh_type == SHT_RELA, there also exists SHT_REL, which would have section name .text.rel (not present in this object file).

Those represent the same struct, but without the addend, e.g.:

typedef struct {
    Elf64_Addr  r_offset;
    Elf64_Xword r_info;
} Elf64_Rela;

The ELF standard says that in many cases the both can be used, and it is just a matter of convenience.

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State initialization (quantum computing) Updated 2025-07-16

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Switzerland Updated 2025-07-16

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Heat equation Updated 2025-07-16

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Besides being useful in engineering, it was very important historically from a "development of mathematics point of view", e.g. it was the initial motivation for the Fourier series.

Some interesting properties:

TODO confirm: for a fixed boundary condition that does not depend on time, the solutions always approaches one specific equilibrium function.
This is in contrast notably with the wave equation, which can oscillate forever.
TODO: for a given point, can the temperature go down and then up, or is it always monotonic with time?
information propagates instantly to infinitely far. Again in contrast to the wave equation, where information propagates at wave speed.

Sample numerical solutions:

with FreeFem:
- heat-dirichlet.1d.freefem
- heat-dirichlet-2d-freefem

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One-to-one (data-model) Updated 2025-07-16

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Subtitle editor Updated 2025-07-16

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ELF Hello World Tutorial / Section header table Updated 2025-07-16

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Array of Elf64_Shdr structs.

Each entry contains metadata about a given section.

e_shoff of the ELF header gives the starting position, 0x40 here.

e_shentsize and e_shnum from the ELF header say that we have 7 entries, each 0x40 bytes long.

So the table takes bytes from 0x40 to 0x40 + 7 + 0x40 - 1 = 0x1FF.

Some section names are reserved for certain section types: www.sco.com/developers/gabi/2003-12-17/ch4.sheader.html#special_sections e.g. .text requires a SHT_PROGBITS type and SHF_ALLOC + SHF_EXECINSTR

Running:

readelf -S hello_world.o

outputs:

There are 7 section headers, starting at offset 0x40:

Section Headers:
  [Nr] Name              Type             Address           Offset
       Size              EntSize          Flags  Link  Info  Align
  [ 0]                   NULL             0000000000000000  00000000
       0000000000000000  0000000000000000           0     0     0
  [ 1] .data             PROGBITS         0000000000000000  00000200
       000000000000000d  0000000000000000  WA       0     0     4
  [ 2] .text             PROGBITS         0000000000000000  00000210
       0000000000000027  0000000000000000  AX       0     0     16
  [ 3] .shstrtab         STRTAB           0000000000000000  00000240
       0000000000000032  0000000000000000           0     0     1
  [ 4] .symtab           SYMTAB           0000000000000000  00000280
       00000000000000a8  0000000000000018           5     6     4
  [ 5] .strtab           STRTAB           0000000000000000  00000330
       0000000000000034  0000000000000000           0     0     1
  [ 6] .rela.text        RELA             0000000000000000  00000370
       0000000000000018  0000000000000018           4     2     4
Key to Flags:
  W (write), A (alloc), X (execute), M (merge), S (strings), l (large)
  I (info), L (link order), G (group), T (TLS), E (exclude), x (unknown)
  O (extra OS processing required) o (OS specific), p (processor specific)

The struct represented by each entry is:

typedef struct {
    Elf64_Word  sh_name;
    Elf64_Word  sh_type;
    Elf64_Xword sh_flags;
    Elf64_Addr  sh_addr;
    Elf64_Off   sh_offset;
    Elf64_Xword sh_size;
    Elf64_Word  sh_link;
    Elf64_Word  sh_info;
    Elf64_Xword sh_addralign;
    Elf64_Xword sh_entsize;
} Elf64_Shdr;

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Quartz clock Updated 2025-07-16

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Video 1.

How a quartz watch works by Steve Mould (2017)

Source. Mentions feedback loop loop with the quartz tuning fork for the piezoelectricity and an amplifier. Also mentions the choice of 32768 Hertz (

2^{15}

) as the first power of 2 that is outside of the human hearing range, and then how a frequency divider is used to reduce the frequency to get the second counter.

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Animal-in-the-loop Updated 2025-07-16

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Ciro Santilli invented this term, it refers to mechanisms in which you put an animal in a virtual world that the animal can control, and where you can measure the animal's outputs.