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Iran by

Ciro Santilli 37 Updated 2025-07-16

Turkey by

Ciro Santilli 37 Updated 2025-07-16

The derivative is the generator of the translation group by

Ciro Santilli 37 Updated 2025-07-16

Take the group of all Translation in

R^{1}

Let's see how the generator of this group is the derivative operator:

\frac{\partial}{\partial x}

(1)

The way to think about this is:

the translation group operates on the argument of a function $f (x)$
the generator is an operator that operates on $f$ itself

So let's take the exponential map:

e^{x_{0} \frac{\partial}{\partial x}} f (x) = (1 + x_{0} \frac{\partial}{\partial x} + x_{0}^{2} \frac{\partial ^{2}}{\partial x ^{2}} + \dots) f (x)

(2)

and we notice that this is exactly the Taylor series of

f (x)

around the identity element of the translation group, which is 0! Therefore, if

f (x)

behaves nicely enough, within some radius of convergence around the origin we have for finite

x_{0}

e^{x_{0} \frac{\partial}{\partial x}} f (x) = f (x + x_{0})

(3)

This example shows clearly how the exponential map applied to a (differential) operator can generate finite (non-infinitesimal) Translation!

Measurement and circuit based quantum computers by

Ciro Santilli 37 Updated 2025-07-16

Tesselation by

Ciro Santilli 37 Updated 2025-07-16

Aperiodic monotile by

Ciro Santilli 37 Updated 2025-07-16

Graph representation by

Ciro Santilli 37 Updated 2025-07-16

Weighted graph by

Ciro Santilli 37 Updated 2025-07-16

Read-modify-write by

Ciro Santilli 37 Updated 2025-07-16

That's what usually fucks up parallel programs.

GNU Compiler Collection by

Ciro Santilli 37 Updated 2025-07-16

LLVM IR hello world by

Ciro Santilli 37 Updated 2025-07-16

Example: llvm/hello.ll adapted from: llvm.org/docs/LangRef.html#module-structure but without double newline.

To execute it as mentioned at github.com/dfellis/llvm-hello-world we can either use their crazy assembly interpreter, tested on Ubuntu 22.10:

sudo apt install llvm-runtime
lli hello.ll

This seems to use puts from the C standard library.

Or we can Lower it to assembly of the local machine:

sudo apt install llvm
llc hello.ll

which produces:

hello.s

and then we can assemble link and run with gcc:

gcc -o hello.out hello.s -no-pie
./hello.out

or with clang:

clang -o hello.out hello.s -no-pie
./hello.out

hello.s uses the GNU GAS format, which clang is highly compatible with, so both should work in general.

Mathematics illustration software by

Ciro Santilli 37 Updated 2025-07-16

Survey by Ciro Santilli: math.stackexchange.com/questions/1985/software-for-drawing-geometry-diagrams/3938216#3938216

Many plotting software can be used to create mathematics illustrations. They just tend to have more data-oriented rather than explanatory-oriented output.

Computer security researcher by

Ciro Santilli 37 Updated 2025-07-16

Ciro Santilli found out that he likes computer security researchers and vice versa.

It's a bit the same reason why he likes physicists: you can't bullshit with security.

You can't just talk nice and hope for people to belive you.

You can't not try to break things and just keep everyone happy in their false illusion of safety.

You can't do a half job.

If you do any of that, you will get your ass handed to you in a little gift bag.

All of this is closely linked to Ciro Santilli's self perceived creative personality and being naughty and creative are correlated.

Outermorphism by

Outermorphism is a concept in the field of mathematics, specifically in category theory, which deals with the structure and relationships between different mathematical objects. While "outermorphism" is not a standard term widely recognized in mathematics, it may refer to a specific type of morphism that relates to certain structures or transformations in a broader context. In general, the term "morphism" in category theory refers to a structural-preserving map between two objects.

Prime ideals by

In abstract algebra, particularly in the context of ring theory, a **prime ideal** is a special type of ideal that has important properties related to the structure of rings.

Krull's theorem by

Krull's theorem is a result in commutative algebra that pertains to the structure of integral domains, specifically regarding the heights of prime ideals in a Noetherian ring. The theorem states: In a Noetherian ring (or integral domain), the height of a prime ideal $ P $ is less than or equal to the number of elements in any generating set of the ideal $ P $.

Peter Wyder by

As of my last knowledge update in October 2021, there isn't a widely recognized figure or entity known as "Peter Wyder." It's possible that he could be a person of interest in more recent news or events. If you have specific context or details about who Peter Wyder might be, I could provide more relevant information or insight. You may want to check current news sources for the latest information.

Deck-building card games by

Deck-building card games are a genre of tabletop games in which players start with a small, predetermined set of cards and gradually build a larger deck throughout the game. The primary mechanic involves acquiring new cards to add to one's deck, which enhances gameplay options and strategies as the game progresses. ### Key Features of Deck-Building Games: 1. **Starting Deck**: All players begin with the same or a similar set of basic cards that dictate their initial capabilities.

Digital collectible card games by

Digital collectible card games (CCGs) are a genre of digital games that combine elements of traditional collectible card games with digital gameplay mechanics. In these games, players build their decks by acquiring cards, which can represent characters, abilities, items, or spells, and use these decks to compete against other players or challenges in the game.