A for alpha

What are transformers? The answer to this question would depend upon the qualifications of the respondent. A sci-fi movie buff would say that transformers are autobots that can change into different mechanical objects (Transformers timeline). A physicist would mention that these are electronic devices used for changing the voltage of alternating current (details). Those into artificial intelligence research would be quick to assert that these are deep learning language models (tutorial).

It is not uncommon for different disciplines to have different meanings for the same thing - be it words or symbols. The first letter of the Greek alphabet $\alpha$ (pronounced al-faa ) is derived from the Phoenician and Hebrew letter, Aleph ($\mathrm{\aleph }$), which means a leader or an ox. Therefore it is no surprise that $\alpha$ is generally used to denote the first in position or order. However, across different academic disciplines, $\alpha$ is associated with an assortment of concepts and meanings. Let’s look at some of the meanings of $\alpha$ across different academic disciplines.

Physics

Particle physics

$\alpha$ particles refers to the nucleus of the Helium atom i.e. a particle having two protons and two neutrons. These particles are emitted by the decay of radioactive elements like uranium, thorium, radium, etc. E.g., the $\alpha$ decay of U-238 is shown below (details). Click Th-234 to see the alpha decay of its isotope Th-230

${}_{92}^{238}\text{U}\to \underset{\alpha \text{-particle}}{\underbrace{{}_2^4\text{He}}}+$

${}_{90}^{230}\text{Th}\to \underset{\alpha \text{-particle}}{\underbrace{{}_2^4\text{He}}}+{}_{88}^{226}\text{Ra}$

Astro Physics

Alpha is used as a prefix in names of different stars. The nearest sun-like star to us is $\alpha$-centauri (about 4.367 light years from earth; details). It is the third brightest star in the night sky - after Sirius and Canopus (aka $\alpha$-Carinae). $\alpha$-centauri, in fact, is composed of two stars - Rigil Kentaurus and Toliman. Also, the brightest star in the Orion constellation is $\alpha$ Orionis (aka Betelgeuse).

Classical mechanics

Angular acceleration ($\alpha$) is defined as the rate of change of angular velocity (i.e. how fast an object is rotating around another point; denoted by $\omega$). $$\alpha =\frac{\mathrm{\Delta }\omega }{\mathrm{\Delta }t}$$

Electromagnetism

Arnold Sommerfeld introduced a constant ($\alpha$) which determines the strength of electromagnetic interaction.
$$\alpha =\frac{e^2/\hslash }{4\pi {ϵ}_0}=\frac{\mu {}_{0}c{e}^2}{2h}\approx \frac{1}{137}$$

This was named fine structure constant and could account for the relativistic splitting of atomic spectral lines. If the previous statement doesn’t make much sense to you, then you are in good company. This article has a quote from the Nobel laureate Wolfgang Pauli — “When I die, my first question to the devil will be: What is the meaning of the fine structure constant?”

Chemistry

Solid-state chemistry

Crystalline solids have atoms packed in a regular arrangement. The simplest repeating pattern within this arrangement is referred to as its unit cell and the location of atoms in a unit cell are lattice points. There are 7 groups of unit cells - cubic, tetragonal, orthorhombic, hexagonal, rhombohedral, monoclinic, and triclinic. The edges of these unit cells are denoted as a, b, c and the angles are $\alpha$, $\beta$, $\gamma$. The angle formed between the edges b and c is $\alpha$.

In a cubic unit cell, a = b = c and $\alpha$ = $\beta$ = $\gamma$ = 90°.

Thermodynamics

Objects expand on heating. The coefficient of thermal expansion ($\alpha$) relates the change in the size of an object with change in temperature.

$$\frac{\mathrm{\Delta }L}{L_0}=\alpha \mathrm{\Delta }T$$

Arts

In digital graphics, $\alpha$ is used to control the opacity of an object from being fully transparent ($\alpha$ = 0) to fully opaque ($\alpha$ = 1). Move the slider below to see this in action.

$\alpha$ = 0.5

Finance

For an investment, alpha is a performance metric that relates the actual return to the benchmark return (when adjusted for risk). In case an investement gives excess return than expected then it means a positive alpha. A common phrase amongst investment strategists is — How to generate alpha.

Psychology

In behavioral psychology, an individual having natural leadership abilities is referred to as an alpha. As mentioned here, “alphas’ quintessential strengths are also what make them so challenging, and often frustrating, to work with”.

Social Science

In demography parlance, there is a fashion of, unofficially, naming generations. Generation $\alpha$ represents the cohort born after 2010. Apparently, this kind of naming of generation started with X and then Y and then Z; and after Z, well… Greek.

Statistics

If a null hypothesis is rejected when it is actually true it is called a type I error (or false positive). The probability of committing a type I error, denoted by $\alpha$, is equal to the significance level in hypothesis testing. An $\alpha$ of 0.05 indicates a 5% chance of incorrectly rejecting a null hypothesis if it is true.

Communication

The NATO phonetic alphabets are a set of codes for clear and precise communication of English alphabets. This system is not only important for military communications but is also helpful in day to day communications (e.g. when spelling your name). In this system, to refer to ‘A’ the code is $\alpha$ (full list). Interestingly, the code for ‘I’ is India.

Biology

Biochemistry

Many proteins and enzymes name have $\alpha$ as prefices or suffices e.g. $\alpha$-keratin, $\alpha$-synuclein, TNF-$\alpha$ (Tumor Necrosis Factor - $\alpha$) etc. Some protein have multiple subunits that are designated with greek prefices, for instance, the pharmacuetically important protein family of G-protein coupled receptors, which are heterotrimers, have an $\alpha$-subunit.

Ecology

Alpha diversity is a measure of species richness within a particular area or ecosystem e.g. number of fishes in a pond or number of insect species in a patch of forest. Variations in the $\alpha$ diversity of the human gut microbiome have been shown to play a role in health and diseases.

Structural Biology

In the structure of amino acids, the carbon atom which is bonded to the amino and carboxyl groups is labeled as C${}_{\alpha }$. Also, the most common secondary structure element in proteins is an $\alpha$-helix. As the story goes, these secondary structure elements were initially called a spiral; later with inputs from Jack Dunitz, Pauling corrected it to helix.

Cell biology

Certain types of cells have $\alpha$ as a prefix to their names. A notable one is the $\alpha$-cells in the pancreas that produce the hormone Glucagon. A subtype of T-cells, which are critical component of the immune system, is referred as $\alpha \beta$ T-cells (denoting the presence of a particular cell-surface receptors).

Neuroscience

Our brain has neural oscillations (aka brainwaves) which are evolutionarily conserved indicating their important (and arguable) functional role(s). Amongst these osciallations, $\alpha$-waves having a frequency range of 8-12 Hz are the most predominant. An alpha state of mind is relaxed yet alert and boosts creativity. This article mentions that you can increase $\alpha$ by closing your eyes or deep breathing or decrease $\alpha$ by thinking or calculating.