- This page refers to the comic named "2". For comic #2, see 2: Petit Trees (sketch).
Title text: It's like sigma summation notation, except instead of summing the argument over all values of i, you 2 the argument over all values of 2.
This demonstrates the different ways in which the number 2 can be typeset in various scientific fields. While these ways of typesetting are used with any number, using the number 2 in this instance provides a clear illustration how adding numbers can significantly alter a feature of a concept (such as the number of electrons in an atom) or perform a mathematical operation on it (such as raising a value to its second power).
The dotted box represents any character (a number, letter, or bigram of letters, as appropriate to the various signifiers). All the other notation consists only of the digit 2, with occasional additional punctuation, in various locations in relation to this character. Each of these is labelled as to what its 'purpose' might normally be with respect to the general term:
- Regular Math
- Precedes the term. "2x" indicates two times the value of x in normal algebraic use that should be familiar for many people.
- A preceding superscript. "2H" would indicate the particular isotope of hydrogen with the atomic weight of two, namely deuterium, which is most often encountered when working with the atomic level of matter where the total number of neutrons and protons in the atom is important. It can also represent tetration, which is iterated exponentiation.
- Chemical Physics
- A preceding subscript, as in "2He", indicates the atomic number of an atom, which is the number of protons it contains. It is thus a guide to the number of electrons its unionised form usually has and hence is meaningful for its potential chemical interactions with other atoms. This number of protons should be invariant for any particular named element, but is usually given simultaneously with the presuperscripted mass number for which it can indicate the applicable nuclear physics. Chemical physics is a subdiscipline of physics and chemistry. It can also represent pentation, which is iterated tetration.
- Regular Math or Footnotes
- A trailing superscript is typical of a power value; in this case "x²" would be x multiplied by itself - a common mathematical standard.
- Additionally, superscripted numbers are one common way to mark words in a line of text in a way to refer to a footnote, typically placed at the bottom of the page and containing additional information that would distract from the main text itself. The ambiguity between footnotes and exponents was used in 1184: Circumference Formula.
- A trailing subscript is used in chemistry to indicate a multiple of the element (or group of elements, in brackets) in a chemical formula. "H2O" indicates two hydrogen atoms bond with a single oxygen atom in a molecule of water.
- Matrices! ("2,2")
- Extending the trailing subscript with a comma-separated value usually indicates a multidimensional array (e.g., establishing a 2-by-2 square of numbers, or this particular position in such an array), which is in the realm of matrix mathematics. This is a little bit beyond 'everyday algebra' for many people, as seemingly indicated by the exclamation of the mere mention of matrices.
- The Physicists Are At It Again ("2;2")
- This label encompasses a mark that turns the prior comma into a semicolon, as part of the trailing subscript. This is a common notation for the Covariant derivative of a tensor field, which is commonly used in the mathematics of general relativity.
- Either High School Math Function or Incomprehensible Group Theory
- The number 2 in parentheses that follow a term would normally be the argument to a function. For example, "f(2)" means that you should take the value 2, and find the result if manipulated by the predefined function f. It is generally taught as part of algebraic mathematics in high school.
- In group theory, however, the number 2 in parentheses could indicate a special kind of group, such as an an element of a symmetry group that keeps 2 fixed, or some kind of group of 2x2 matrices. For instance, SU(2) is a 3-dimensional Lie group of unitary matrices. These concepts are taught in graduate or advanced undergraduate mathematics courses.
- Oh no. Whatever this is, it's cursed.
- A symbol centered underneath another larger symbol is normally reserved for doing summations or products, where the big symbol is Σ or Π, or some other operation applied to a sequence of numbers. It does not make sense to have a single number on top of a smaller one. As with other things where something appears to have gone wrong in Randall's comic universe, the explanation for this particular anomaly is that it is 'Cursed'.
- Two natural numbers may be stacked directly on top of one another in parentheses as binomial coefficients: (
), but those are always the same size, denoting a combination. In this case, 2 choose 2 is equal to one combination.
- The usage mentioned in the alt text is an operation (e.g. Σ for summation) over a variable, usually indicated by a letter such as i, where the operation is performed over all values of the variable (i.e., you Σ (sum) the argument over all values of i). In the "2" case, the alt text says "you 2 the argument over all values of 2" (i.e., the Σ operation has been replaced by the "2" operation and the i variable has been replaced by the "2" variable). 2 is usually not an operation, though the definition of 2 under Church encoding is a function that takes in and produces functions. 2 applied to 2 in Church encoding is 4. However, the title text implies that 2 is treated like a variable, which it is not (and it's definitely not a operator and variable at the same time).
- Things being cursed is a common trope within recent xkcd comics, which have mentioned items including Cursed chairs and cursed connectors. This notation is one of the few occasions where the supernatural has demonstrable implications for science and mathematics for those foolhardy enough to use it.
- [An apparent generalisation of a scientific expression consisting of a dotted rectangular 'box' outline, left empty, and various commonly-themed symbology around it:]
- [as normal text, to the left of all the rest:] 2
- [superscript to the immediate left of the box:] 2
- [subscript also to the immediate left of the box:] 2
- [superscript to the immediate right of the box:] 2
- [subscript also to the immediate right of the box:] 2;2 [i.e. separated by a semicolon]
- [as normal text, to the right of almost all the rest:] (2) [i.e. enclosed in standard parentheses]
- [smaller subscript, centered immediately beneath the 2 within the parentheses:] 2
- [Further details are drawn in grey tone, around or near various of the elements of the expression:]
- [Captions above the numbers]
- [with an arrow pointing to the leftmost 2:] Regular Math
- [with an arrow pointing to the leftwards superscript 2:] Physics
- [with an arrow pointing to the rightwards superscript 2:] Regular math or footnotes
- [with an arrow pointing to the parenthetical 2 at the right:] Either high school math functions or incomprehensible group theory
- [Captions below the numbers]
- [with an arrow pointing to the leftwards subscript 2:] Chemical Physics
- [with an arrow pointing to just the rightwards subscript 2:] Chemistry
- [with an arrow pointing to a distorted grey ring snaking around only the comma of the semicolon and the following 2 of the rightmost subscript:] Matrices!
- [with an arrow pointing to a larger grey ring that passes fully around the whole semicolon and final 2 of the rightmost subscript:] The physicists are at it again
- [with an arrow pointing to the small 2 placed below the parenthetical 2:] Oh no. Whatever this is, it's cursed.
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