Arrow types are a concept in programming, particularly in functional programming and type theory. They can be thought of as a way to generalize functions and represent computations. An arrow is often used to describe computations that have an input-output relation but can also include additional structure, such as the ability to combine or sequence computations.

The 179th meridian west is a line of longitude that is located 179 degrees west of the Prime Meridian, which is defined as 0 degrees longitude. It is one of the meridians in the geographic coordinate system and is part of the International Date Line (IDL). The 179th meridian west closely follows the 180th meridian but deviates slightly in places to accommodate political and geographic considerations.

DNA sequencing is a laboratory technique used to determine the precise order of nucleotides in a DNA molecule. Nucleotides are the building blocks of DNA and consist of four types: adenine (A), thymine (T), cytosine (C), and guanine (G). The sequence of these nucleotides encodes genetic information and plays a crucial role in various biological functions.

HaeIII is a restriction enzyme, also known as a restriction endonuclease, which is derived from the bacterium *Haemophilus aphrophilus*. It recognizes and cleaves specific sequences of DNA, typically at the sequence "GG|CC" (where the vertical bar indicates the cut point). Restriction enzymes like HaeIII are crucial tools in molecular biology and biotechnology for various applications, including DNA cloning, genetic engineering, and analysis of DNA fragments.

Elfatih Eltahir is a prominent Sudanese-American hydrologist and climate scientist known for his research on hydroclimatology, water resources, and the impacts of climate change on water systems. He is a faculty member at the Massachusetts Institute of Technology (MIT), where he conducts research and teaches in areas related to hydrology and climate.

Russian cryptographers are individuals from Russia who specialize in the study and practice of cryptography, which is the science of securing communication and information by transforming it into a secure format. This field encompasses a variety of techniques and methodologies for encoding messages, ensuring confidentiality, integrity, authentication, and non-repudiation. Historically, Russia has a prominent role in the development of cryptographic techniques and cryptographic theory, especially during the Cold War era, when secure communication was vital for national security.

Siarnaq is a celestial body, specifically a moon of the planet Saturn. It is one of the smaller moons of Saturn and is classified as a member of the irregular moons, which tend to have eccentric and inclined orbits. Siarnaq was discovered in 2000, and it is named after a figure in Inuit mythology. The moon is characterized by its distinctive features, including a relatively dark surface and a composition thought to be primarily composed of ice and rock.

The 60th meridian west is a line of longitude that is 60 degrees west of the Prime Meridian, which is located at 0 degrees longitude. This meridian runs from the North Pole to the South Pole and passes through several countries in North America and South America, including parts of Canada, the United States, and countries in the Caribbean and South America, such as Colombia.

Lists of asteroids typically refer to the various catalogs and databases that document the asteroids discovered in our solar system. These lists can include a wide range of information about each asteroid, such as its designation number, name, size, orbital characteristics, and sometimes other data such as composition and surface features. Some of the notable lists and catalogs include: 1. **Main Belt Asteroids**: A list of asteroids primarily located in the asteroid belt between Mars and Jupiter.

Full set of all possible special relativity symmetries:

In simple and concrete terms. Suppose you observe N particles following different trajectories in Spacetime.

There are two observers traveling at constant speed relative to each other, and so they see different trajectories for those particles:Note that the first two types of transformation are exactly the non-relativistic Galilean transformations.

The Poincare group is the set of all matrices such that such a relationship like this exists between two frames of reference.

Subset of Galilean transformation with speed equals 0.

This is a good and simple first example of Lie algebra to look into.

Take the group of all Translation in ${\mathbb{R}}^1$.

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

The way to think about this is:

So let's take the exponential map: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 $x_0$:

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

Physics from Symmetry by Jakob Schwichtenberg (2015) page 66 shows one in terms of 4x4 complex matrices.

More importantly though, are the representations of the Lie algebra of the Lorentz group, which are generally also just also called "Representation of the Lorentz group" since you can reach the representation from the algebra via the exponential map.

Bibliography:

One of the representations of the Lorentz group that show up in the Representation theory of the Lorentz group.

This was getting very hot as of 2022 for some reason. Would be good to understand why besides the awesome name.

TODO understand a bit more intuitively.