Ciro Santilli @cirosantilli 37

 Articles (11k) Discussions (26) Comments (64) Follows  Received likes Files

New Updated  Top  Announced  A-Z  Liked  Followed

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

 View more

Section type: sh_type == SHT_SYMTAB.

Common name: "symbol table".

First the we note that:

sh_link = 5
sh_info = 6

For SHT_SYMTAB sections, those numbers mean that:

strings that give symbol names are in section 5, .strtab
the relocation data is in section 6, .rela.text

A good high level tool to disassemble that section is:

nm hello_world.o

which gives:

0000000000000000 T _start
0000000000000000 d hello_world
000000000000000d a hello_world_len

This is however a high level view that omits some types of symbols and in which the symbol types . A more detailed disassembly can be obtained with:

readelf -s hello_world.o

which gives:

Symbol table '.symtab' contains 7 entries:
   Num:    Value          Size Type    Bind   Vis      Ndx Name
     0: 0000000000000000     0 NOTYPE  LOCAL  DEFAULT  UND
     1: 0000000000000000     0 FILE    LOCAL  DEFAULT  ABS hello_world.asm
     2: 0000000000000000     0 SECTION LOCAL  DEFAULT    1
     3: 0000000000000000     0 SECTION LOCAL  DEFAULT    2
     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

The binary format of the table is documented at www.sco.com/developers/gabi/2003-12-17/ch4.symtab.html

The data is:

readelf -x .symtab hello_world.o

which gives:

Hex dump of section '.symtab':
  0x00000000 00000000 00000000 00000000 00000000 ................
  0x00000010 00000000 00000000 01000000 0400f1ff ................
  0x00000020 00000000 00000000 00000000 00000000 ................
  0x00000030 00000000 03000100 00000000 00000000 ................
  0x00000040 00000000 00000000 00000000 03000200 ................
  0x00000050 00000000 00000000 00000000 00000000 ................
  0x00000060 11000000 00000100 00000000 00000000 ................
  0x00000070 00000000 00000000 1d000000 0000f1ff ................
  0x00000080 0d000000 00000000 00000000 00000000 ................
  0x00000090 2d000000 10000200 00000000 00000000 -...............
  0x000000a0 00000000 00000000                   ........

The entries are of type:

typedef struct {
    Elf64_Word  st_name;
    unsigned char   st_info;
    unsigned char   st_other;
    Elf64_Half  st_shndx;
    Elf64_Addr  st_value;
    Elf64_Xword st_size;
} Elf64_Sym;

Like in the section table, the first entry is magical and set to a fixed meaningless values.

 Read the full article

Elon Musk Updated 2025-07-16

 View more

Musk is a truly ambivalent personality. Some points are very good. Some are very bad.

Respect on the technical side by Ciro Santilli.

But the way he treated his first wife Justine Musk, is very very weird, incomprehensible: www.marieclaire.com/sex-love/a5380/millionaire-starter-wife/

Positive Cirocoins for possibly going to reverse Twitter's unfair Trump ban if his Twitter acquisition goes through:

twitter.com/elonmusk/status/1519036983137509376
By "free speech", I simply mean that which matches the law.
I am against censorship that goes far beyond the law.
If people want less free speech, they will ask government to pass laws to that effect.
Therefore, going beyond the law is contrary to the will of the people.
twitter.com/elonmusk/status/1507259709224632344

Negative Cirocoins for according to Wikipedia:

Within the merged company [Thiel's Confinity + Elon's X.com], Musk returned as CEO. Musk's preference for Microsoft software over Unix created a rift in the company and caused Thiel to resign.

Video 1.

The REAL Reason Why Tesla Made All Patents Open-Source by The not so boring Man (2021)

Source. Supercut from various interviews/presentations in which Elon saying that Tesla has open source patents and pro open source stuff. Can we trust it? Maybe.

 Read the full article

Engine Updated 2025-07-16

 Read the full article

Enthalpy Updated 2025-07-16

 View more

Adds up chemical energy and kinetic energy.

Wikipedia mentions however that the kinetic energy is often negligible, even for gases.

The sum is of interest when thinking about reactions because chemical reactions can change the number of molecules involved, and therefore the pressure.

To predict if a reaction is spontaneous or not, negative enthalpy is not enough, we must also consider entropy via Gibbs free energy.

Bibliography:

chemistry.stackexchange.com/questions/7696/how-do-i-distinguish-between-internal-energy-and-enthalpy

 Read the full article

Epic Rap Battles of History Updated 2025-07-16

 View more

www.youtube.com/EpicRapBattles

Most of the videos are crap, but the following ones almost killed Ciro Santilli of laughter:

Video "Bill Gates vs Steve Jobs by Epic Rap Battles of History (2012)"
Video 1. "Rasputin vs Stalin by Epic Rap Battles of History (2013)"

Video 1.

Rasputin vs Stalin by Epic Rap Battles of History (2013)

Monty Python has a few precursors to the "random famous people mixed together compting" format, although not in the rap fight format:

Video 2.

Communist Quiz by Monty Python (1970)

Source. Has a Wiki page: en.wikipedia.org/wiki/World_Forum/Communist_Quiz. Brings to mind: Video "Football, Football, Football by Mitchell and Webb".

Video 3.

Philosophers' Football Match by Monty Python (1972)

Source. If you can understand the jokes, your philosophy level is pretty good. Like more than zero. Wiki page: en.wikipedia.org/wiki/The_Philosophers%27_Football_Match. Ciro loves how that page currently uses a standard footbal match template to describe the match!

 Read the full article

Equation of state Updated 2025-07-16

 Read the full article

Ethernet cable Updated 2025-07-16

 View more

When non-specialists say "Ethernet cable", they usually mean twisted pair for Ethernet over twisted pair.

But of course, this term is much more generic to a more specialized person, since notably fiber optics are also extensively used in Ethernet over fiber.

en.wikipedia.org/wiki/Category:Ethernet_cables

 Read the full article

Universal asynchronous receiver-transmitter Updated 2025-07-16

 View more

A good project to see UARTs at work in all their beauty is to connect two Raspberry Pis via UART, and then:

type in one and see characters appear in the other: scribles.net/setting-up-uart-serial-communication-between-raspberry-pis/
send data via a script: raspberrypi.stackexchange.com/questions/29027/how-should-i-properly-communicate-2-raspberry-pi-via-uart

Part of the beauty of this is that you can just connect both boards directly manually with a few wire-to-wire connections with simple jump wire. Its simplicity is just quite refreshing. Sure, you could do something like that for any physical layer link presumably...

Remember that you can only have one GNU screen connected at a time or else they will mess each other up: unix.stackexchange.com/questions/93892/why-is-screen-is-terminating-without-root/367549#367549

On Ubuntu 22.04 you can screen without sudo by adding yourself to the dialout group with:

sudo usermod -a -G dialout $USER

 Read the full article

Existence of the matrix logarithm Updated 2025-07-16

 View more

en.wikipedia.org/wiki/Logarithm_of_a_matrix#Existence mentions it always exists for all invertible complex matrices. But the real condition is more complicated. Notable counter example: -1 cannot be reached by any real

e^{t k}

The Lie algebra exponential covering problem can be seen as a generalized version of this problem, because

Lie algebra of $G L (n)$ is just the entire $M_{n}$
we can immediately exclude non-invertible matrices from being the result of the exponential, because $e^{tM}$ has inverse $e^{- tM}$ , so we already know that non-invertible matrices are not reachable

 Read the full article

Existential risk of AGI Updated 2025-07-16

 View more

www.cam.ac.uk/research/news/the-best-or-worst-thing-to-happen-to-humanity-stephen-hawking-launches-centre-for-the-future-of

The rise of powerful AI will either be the best or the worst thing ever to happen to humanity. We do not yet know which.

 Read the full article

University Updated 2025-09-09

 View more

As of 2020, university has the following very important applications:

meet an intelligent sexual partner (see also: Section "Sexual selection", Section "The main function of university is sexual selection") and or have fun and or come out of the closet
get you in debt if you are from the United States

Notably, Education is an IQ test, not a way to learn useful and beautiful things.

One major issue is that teachers don't have the right incentive to, nor are selected to, teach well. Thus the existence of Rate My Professors! But we can do better...

Which is why Ciro Santilli wants to destroy its current format with OurBigBook.com. He believes that we can find a more efficient organization to achieve both the social and research functions of university, by first doing as much as possible online

Ciro's university experiences are mentioned at: Ciro Santilli's formal education.

 Read the full article

Fabless manufacturing Updated 2025-07-16

 View more

In the past, most computer designers would have their own fabs.

But once designs started getting very complicated, it started to make sense to separate concerns between designers and fabs.

What this means is that design companies would primarily write register transfer level, then use electronic design automation tools to get a final manufacturable chip, and then send that to the fab.

It is in this point of time that TSMC came along, and benefied and helped establish this trend.

The term "Fabless" could in theory refer to other areas of industry besides the semiconductor industry, but it is mostly used in that context.

 Read the full article

Fast Fourier transform Updated 2025-07-16

 View more

An efficient algorithm to calculate the discrete Fourier transform.

 Read the full article

FFmpeg Updated 2025-07-16

 View more

FFmpeg is the assembler of audio and video.

As a result, Ciro Santilli who likes "lower level stuff", has had many many hours if image manipulation fun with this software, see e.g.:

the "Media" section of the best articles by Ciro Articles.
Figure "Ciro knows how to convert videos to GIFs"

As older Ciro grows, the more he notices that FFmpeg can do basically any lower level audio video task. It is just an amazing piece of software, the immediate go-to for any low level operation.

FFmpeg was created by Fabrice Bellard, which Ciro deeply respects.

Resize a video: superuser.com/questions/624563/how-to-resize-a-video-to-make-it-smaller-with-ffmpeg:

ffmpeg -i input.avi -filter:v scale=720:-1 -c:a copy output.mkv

Unlike every other convention under the sun, the height in scale is the first number.

 Read the full article

Fiat currency Updated 2025-07-16

 View more

A useless piece of paper (or digital version of it) that you can pay taxes with :)

As opposed to:

2020 cryptocurrencies, while governments still don't accept them for taxes, as well as other assets that are also not accepted for taxes (i.e. most assets)
physical currencies that have intrinsic material value, e.g. gold coins

 Read the full article

Lie algebra of

S L (2)

Updated 2025-07-16

 View more

This is a good first concrete example of a Lie algebra. Shown at Lie Groups, Physics, and Geometry by Robert Gilmore (2008) Chapter 4.2 "How to linearize a Lie Group" has an example.

We can use use the following parametrization of the special linear group on variables

x

y

and

z

M = [1 + x z y (1 + yz) / (1 + x)]

(1)

Every element with this parametrization has determinant 1:

d e t (M) = (1 + x) (1 + yz) / (1 + x) - yz = 1

(2)

Furthermore, any element can be reached, because by independently settting

x

y

and

z

M_{00}

M_{01}

and

M_{10}

can have any value, and once those three are set,

M_{11}

is fixed by the determinant.

To find the elements of the Lie algebra, we evaluate the derivative on each parameter at 0:

M_{x} M_{y} M_{z} = \frac{d M}{d x}_{(x, y, z) = (0, 0, 0)} = \frac{d M}{d y}_{(x, y, z) = (0, 0, 0)} = \frac{d M}{d z}_{(x, y, z) = (0, 0, 0)} = [10 0 - (1 + yz) / (1 + x)^{2}]_{(x, y, z) = (0, 0, 0)} = [00 1 z / (1 + x)]_{(x, y, z) = (0, 0, 0)} = [01 0 y / (1 + x)]_{(x, y, z) = (0, 0, 0)} = [10 0 - 1] = [0010] = [0100]

(3)

Remembering that the Lie bracket of a matrix Lie group is really simple, we can then observe the following Lie bracket relations between them:

[M_{x}, M_{y}] [M_{x}, M_{z}] [M_{y}, M_{z}] = M_{x} M_{y} - M_{y} M_{x} = M_{x} M_{z} - M_{z} M_{x} = M_{y} M_{z} - M_{z} M_{y} = [0010] = [0 - 1 00] = [1000] - [00 - 1 0] - [0100] - [0001] = [0020] = [0 - 2 00] = [10 0 - 1] = 2 M_{y} = - 2 M_{z} = M_{x}

(4)

One key thing to note is that the specific matrices

M_{x}

M_{y}

and

M_{z}

are not really fundamental: we could easily have had different matrices if we had chosen any other parametrization of the group.

TODO confirm: however, no matter which parametrization we choose, the Lie bracket relations between the three elements would always be the same, since it is the number of elements, and the definition of the Lie bracket, that is truly fundamental.

Lie Groups, Physics, and Geometry by Robert Gilmore (2008) Chapter 4.2 "How to linearize a Lie Group" then calculates the exponential map of the vector

x M_{x} + y M_{y} + z M_{z}

as:

I cos h (θ) + M_{x} s inh (θ) / θ

(5)

with:

θ^{2} = x^{2} + b c

(6)

TODO now the natural question is: can we cover the entire Lie group with this exponential? Lie Groups, Physics, and Geometry by Robert Gilmore (2008) Chapter 7 "EXPonentiation" explains why not.

 Read the full article

Lie algebra of

SO (3)

Updated 2025-07-16

 View more

We can reach it by taking the rotations in three directions, e.g. a rotation around the z axis:

R_{z} (θ) = cos (θ) s in (θ) 0 - s in (θ) cos (θ) 0 001

(1)

then we derive and evaluate at 0:

L_{z} = \frac{d R _{z} ( θ )}{d θ}_{0} = - s in (θ) cos (θ) 0 - cos (θ) - s in (θ) 0 001_{0} = 010 - 1 00 000

(2)

L_{z}

therefore represents the infinitesimal rotation.

Note that the exponential map reverses this and gives a finite rotation around the Z axis back from the infinitesimal generator

L_{z}

e^{θ L_{z}} = R_{z} (θ)

(3)

Repeating the same process for the other directions gives:

L_{x} = TO D O L_{y} = TO D O

(4)

We have now found 3 linearly independent elements of the Lie algebra, and since

SO (3)

has dimension 3, we are done.

 Read the full article

Lie bracket of a matrix Lie group Updated 2025-07-16

 View more

[X, Y] = X Y - Y X

(1)

This makes it clear how the Lie bracket can be seen as a "measure of non-commutativity"

Because the Lie bracket has to be a bilinear map, all we need to do to specify it uniquely is to specify how it acts on every pair of some basis of the Lie algebra.

Then, together with the Baker-Campbell-Hausdorff formula and the Lie group-Lie algebra correspondence, this forms an exceptionally compact description of a Lie group.

 Read the full article

Lie group bibliography Updated 2025-07-16

 View more

Recommended from Physics from Symmetry by Jakob Schwichtenberg (2015) page 92:

 Read the full article

Lie Groups, Physics, and Geometry by Robert Gilmore (2008) Updated 2025-07-16

 View more

The author seems to have uploaded the entire book by chapters at: www.physics.drexel.edu/~bob/LieGroups.html

And the author is the cutest: www.physics.drexel.edu/~bob/Personal.html.

Overview:

Chapter 3: gives a bunch of examples of important matrix Lie groups. These are done by imposing certain types of constraints on the general linear group, to obtain subgroups of the general linear group. Feels like the start of a classification
Chapter 4: defines Lie algebra. Does some basic examples with them, but not much of deep interest, that is mostl left for Chapter 7
Chapter 5: calculates the Lie algebra for all examples from chapter 3
Chapter 6: don't know
Chapter 7: describes how the exponential map links Lie algebras to Lie groups

 Read the full article

 Unlisted articles are being shown, click here to show only listed articles.