Ciro Santilli @cirosantilli 35

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Product definition of the exponential function  Updated 2024-12-23  +Created 1970-01-01

e^{x} = lim_{n \to \infty} (1 + \frac{x}{n})^{n}

The basic intuition for this is to start from the origin and make small changes to the function based on its known derivative at the origin.

More precisely, we know that for any base b, exponentiation satisfies:

$b^{x + y} = b^{x} b^{y}$ .
$b^{0} = 1$ .

And we also know that for

b = e

in particular that we satisfy the exponential function differential equation and so:

\frac{d e ^{x}}{d x} (0) = 1

One interesting fact is that the only thing we use from the exponential function differential equation is the value around

x = 0

, which is quite little information! This idea is basically what is behind the importance of the ralationship between Lie group-Lie algebra correspondence via the exponential map. In the more general settings of groups and manifolds, restricting ourselves to be near the origin is a huge advantage.

Now suppose that we want to calculate

e^{1}

. The idea is to start from

e^{0}

and then then to use the first order of the Taylor series to extend the known value of

e^{0}

to

e^{1}

.

E.g., if we split into 2 parts, we know that:

e^{1} = e^{1 / 2} e^{1 / 2}

or in three parts:

e^{1} = e^{1 / 3} e^{1 / 3} e^{1 / 3}

so we can just use arbitrarily many parts

e^{1 / n}

that are arbitrarily close to

x = 0

:

e^{1} = (e^{1 / n})^{n}

and more generally for any

x

we have:

e^{x} = (e^{x / n})^{n}

Let's see what happens with the Taylor series. We have near

y = 0

in little-o notation:

e^{y} = 1 + y + o (y)

Therefore, for

y = x / n

, which is near

y = 0

for any fixed

x

:

e^{x / n} = 1 + x / n + o (1 / n)

and therefore:

e^{x} = (e^{x / n})^{n} = (1 + x / n + o (1 / n))^{n}

which is basically the formula tha we wanted. We just have to convince ourselves that at

lim_{n \to \infty}

, the

o (1 / n)

disappears, i.e.:

(1 + x / n + o (1 / n))^{n} = (1 + x / n)^{n}

To do that, let's multiply

e^{y}

by itself once:

e^{y} e^{y} = (1 + y + o (y)) (1 + y + o (y)) = 1 + 2 y + o (y)

and multiplying a third time:

e^{y} e^{y} e^{y} = (1 + 2 y + o (y)) (1 + y + o (y)) = 1 + 3 y + o (y)

TODO conclude.

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Oh, but there are 2 trees: local and remote  Updated 2024-12-23  +Created 1970-01-01

Oh but there are usually 2 trees: local and remote.

So you also have to learn how to observe and modify and sync with the remote tree!

But basically:

git fetch

to update the remote tree. And then you can use it exactly like any other branch, except you prefix them with the remote (usually origin/*), e.g.:

origin/master is the latest fetch of the remote version of master
origin/my-feature is the latest fetch of the remote version of my-feature

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Early Google employee  Updated 2024-12-23  +Created 1970-01-01

Bibliography:

ChatGPT produces:

Heather Cairns (Employee #4) - Joined in 1998. She handled HR and was one of the earliest administrative hires.
Harry Cheung (Employee #5) - Joined in 1999. An early engineer.
Gerald Aigner (Employee #6) - Hired in 1999. Worked as a software engineer.
Susan Wojcicki (Employee #16) - Joined in 1999. She rented her garage to Larry and Sergey in 1998 and later became an integral part of Google's business and advertising teams.
Marissa Mayer (Employee #20) - Hired in 1999. Played a major role in Google Search and design.

Omid Kordestani - Joined in 1999 as Google’s first business hire, focusing on sales and revenue generation.

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How to learn  Updated 2024-12-23  +Created 1970-01-01

Spin like mad between:

standards
high level generators. We use the assembler as and linker ld.
hexdumps
file decompilers. We use readelf. It makes it faster to read the ELF file by turning it into human readable output. But you must have seen one byte-by-byte example first, and think how readelf output maps to the standard.
low-level generators: stand-alone libraries that let you control every field of the ELF files you generated. github.com/BR903/ELFkickers, github.com/sqall01/ZwoELF and many more on GitHub.
consumer: the exec system call of the Linux kernel can parse ELF files to starts processes: github.com/torvalds/linux/blob/v4.11/fs/binfmt_elf.c, stackoverflow.com/questions/8352535/how-does-kernel-get-an-executable-binary-file-running-under-linux/31394861#31394861

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Index 0 section  Updated 2024-12-23  +Created 1970-01-01

Contained in bytes 0x40 to 0x7F.

The first section is always magic: www.sco.com/developers/gabi/2003-12-17/ch4.sheader.html says:

If the number of sections is greater than or equal to SHN_LORESERVE (0xff00), e_shnum has the value SHN_UNDEF (0) and the actual number of section header table entries is contained in the sh_size field of the section header at index 0 (otherwise, the sh_size member of the initial entry contains 0).

There are also other magic sections detailed in Figure 4-7: Special Section Indexes.

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Thali  Updated 2024-12-23  +Created 1970-01-01

Indian vegetarian thali is the best thing ever! The Southern version in particular. Also do watch a video on how to eat it.

A good place to have it abroad is Saravana Bhavan. The founder killed a dude to marry his wife, but failed and was sentenced to life prison. But he died in 2019 so we're all fine eating there now.

Figure 1. Source. This Wikipedia image of Thali is fundamentally wrong: you have to have a banana leaf on the bottom of the tray!

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Suwu herding sheep  Updated 2024-12-23  +Created 1970-01-01

www.ibiblio.org/chinese-music/html/traditional.html contains an amazing orchestral version for di flute TODO identify! When attempting to upload to YouTube, it identifies as "Su Wu Tending the Sheep" and give a name "Chen Tao", but no further information. Chen Tao is presumably this dude: www.barduschinamusic.org/chen-tao-dizi | www.melodyofdragon.org/chentao.html 陈涛

baike.baidu.com/item/苏武牧羊/5532#11_2 mentions that it comes from an erhu concerto composed by Peng Xiuwen

The sadness of the erhu perfectly fits the role and mood of the story! Brilliant!

Suwu herding sheep played by Song Fei (2017)

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Nvidia  Updated 2024-12-23  +Created 1970-01-01

Open source driver/hardware interface specification??? E.g. on Ubuntu, a large part of the nastiest UI breaking bugs Ciro Santilli encountered over the years have been GPU related. Do you think that is a coincidence??? E.g. ubuntu 21.10 does not wake up from suspend.

Linus Torvalds saying "Nvidia Fuck You" (2012)

How Nvidia Won Graphics Cards by Asianometry (2021)

Doom was the first killer app of personal computer 3D graphics! As opposed to professional rendering e.g. for CAD as was supported by Silicon Graphics
youtu.be/TRZqE6H-dww?t=694 they bet on Direct3D
youtu.be/TRZqE6H-dww?t=749 they wrote their own drivers. At the time, most drivers were written by the computer manufacturers. That's insane!

How Nvidia Won AI by Asianometry (2022)

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Global file structure  Updated 2024-12-23  +Created 1970-01-01

An ELF file contains the following parts:

ELF header. Points to the position of the section header table and the program header table.
Section header table (optional on executable). Each has e_shnum section headers, each pointing to the position of a section.
N sections, with N <= e_shnum (optional on executable)
Program header table (only on executable). Each has e_phnum program headers, each pointing to the position of a segment.
N segments, with N <= e_phnum (only on executable)

The order of those parts is not fixed: the only fixed thing is the ELF header that must be the first thing on the file: Generic docs say:

Although the figure shows the program header table immediately after the ELF header, and the section header table following the sections, actual files may differ. Moreover, sections and segments have no specified order. Only the ELF header has a fixed position in the file.

In pictures: sample object file with three sections:

            +-------------------+
            | ELF header        |---+
+---------> +-------------------+   | e_shoff
|           |                   |<--+
| Section   | Section header 0  |
|           |                   |---+ sh_offset
| Header    +-------------------+   |
|           | Section header 1  |---|--+ sh_offset
| Table     +-------------------+   |  |
|           | Section header 2  |---|--|--+
+---------> +-------------------+   |  |  |
            | Section 0         |<--+  |  |
            +-------------------+      |  | sh_offset
            | Section 1         |<-----+  |
            +-------------------+         |
            | Section 2         |<--------+
            +-------------------+

But nothing (except sanity) prevents the following topology:

            +-------------------+
            | ELF header        |---+ e_shoff
            +-------------------+   |
            | Section 1         |<--|--+
+---------> +-------------------+   |  |
|           |                   |<--+  | sh_offset
| Section   | Section header 0  |      |
|           |                   |------|---------+
| Header    +-------------------+      |         |
|           | Section header 1  |------+         |
| Table     +-------------------+                |
|           | Section header 2  |---+            | sh_offset
+---------> +-------------------+   | sh_offset  |
            | Section 2         |<--+            |
            +-------------------+                |
            | Section 0         |<---------------+
            +-------------------+

But some newbies may prefer PNGs :-)

Figure 1.
ELF Executable and Linkable Format diagram by Ange Albertini
. Source.

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English as a universal language by Dan Dascalescu (2008)  Updated 2024-12-23  +Created 1970-01-01

wiki.dandascalescu.com/essays/english-universal-language

web.archive.org/web/20200317221752/https://wiki.dandascalescu.com/essays/english-universal-language

Dan Dascalescu's version of having more than one natural language is bad for the world.

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Obsidian (software)  Updated 2024-12-23  +Created 1970-01-01

Good:

WYSIWYG
Extended-Markdown-based

Bad:

no browser-only editor, it's just a local app apparently:
help.obsidian.md/Getting+started/Sync+your+notes+across+devices they do have a device sync mechanism

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Synchronous dynamic random-access memory  Updated 2024-12-23  +Created 1970-01-01

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The beauty of alebraic geometry  Updated 2024-12-23  +Created 1970-01-01

mathoverflow.net/questions/20112/interesting-results-in-algebraic-geometry-accessible-to-3rd-year-undergraduates Interesting results in algebraic geometry accessible to 3rd year undergraduates

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Lagrangian mechanics lectures by Michel van Biezen (2017)  Updated 2024-12-23  +Created 1970-01-01

www.youtube.com/playlist?list=PLX2gX-ftPVXWK0GOFDi7FcmIMMhY_7fU9

Original playlist name: "PHYSICS 68 ADVANCED MECHANICS: LAGRANGIAN MECHANICS"

Author: Michel van Biezen.

High school classical mechanics material, no mention of the key continuous symmetry part.

But does have a few classic pendulum/pulley/spring worked out examples that would be really wise to get under your belt first.

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TCP/IP  Updated 2024-12-23  +Created 1970-01-01

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Test driven development  Updated 2024-12-23  +Created 1970-01-01

This is a good approach. The downside is that while you are developing the implementation and testing interactively you might notice that the requirements are wrong, and then the tests have to change.

One intermediate approach Ciro Santilli likes is to do the implementation and be happy with interactive usage, then create the test, make it pass, then remove the code that would make it pass, and see it fail. This does have a risk that you will forget to test something, but Ciro finds it is a worth it generally. Unless it really is one of those features that you are unable to develop without an automated test, generally more "logical/mathematical" stuff. This is a sort of laziness Driven Development.

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Tetrapod  Updated 2024-12-23  +Created 1970-01-01

Includes:

amphibians
amniotes, which includes:
- sauropsida: reptiles and birds, which really are reptiles
- mammals

The exact relationships between those clades is not very clear as there's a bunch of extinct species in the middle we are not sure exactly where they go exactly, some hypothesis are listed at: en.wikipedia.org/w/index.php?title=Tetrapod&oldid=1053601110#Temnospondyl_hypothesis_(TH)

But at least it seems rock solid that those three are actually clades.

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Lagrangian vs Hamiltonian  Updated 2024-12-23  +Created 1970-01-01

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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WhatsApp  Updated 2024-12-23  +Created 1970-01-01

Claimed to remove metadata from servers unless legally obliged to collect it: www.quora.com/Does-WhatsApp-store-messages-on-its-servers-or-is-all-deleted-after-delivery-and-only-stored-on-recipients-phones/answer/Ciro-Santilli

They've had a few breaches: www.whatsapp.com/security/advisories/

They claim to delete metadata: www.quora.com/Does-WhatsApp-store-messages-on-its-servers-or-is-all-deleted-after-delivery-and-only-stored-on-recipients-phones/answer/Ciro-Santilli

WhatsApp founder Jan Koum talks about their Journey by Roots (2017)

Source. Good talk, explains how everything happened in the perfect location at the perfect time: unemployed people who knew how to code, bought an iPhone, the next big platform, at its very beginning, they had just release the required push notifications API, and he travelled a lot and knew how much SMS sucked, especially international.

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Carl Jung  Updated 2024-12-23  +Created 1970-01-01

Figure 1. Source.

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