Connotations of Letter 'X'
In the English language, the letter X has a connotation of mystery, intrigue, or excitement.
Examples:
- Planet X: A theoretical planet of mysterious origin, or an unknown planet. [Edit: Bad example, the X here refers to Roman numeral 10.]
- Mr. X: A person remaining intentionally anonymous
- X-Factor: What makes something unique or exciting.
- Xylophone: Possibly the most exciting of all instruments, begins with X. [Author's note: Meant to be humorous, but apparently only to me]
How did this come about? What made X the grapheme of choice, instantly recognizable as carrying this meaning?
As a linguist, I could see it being how the grapheme X is the only reverse digraph in the English language, but I'm pretty sure that doesn't apply to the general populace. Another idea is that there are some cool sounding Latin phrases with the preposition Ex, e.g. Ex nihil nihil fit, "from nothing comes nothing", or Deus ex machina, "God from the Machine" (a literary device). I recognize, however, that the popularity of these could be a byproduct of the connotation of X and not the other way around.
Planet X: A theoretical planet of mysterious origin, or an unknown planet. [Edit: Bad example, the X here refers to Roman numeral 10.]
Or just more interesting example, as it contains the "unknown" element and the Roman numeral for 10.
Xylophone: Possibly the most exciting of all instruments, begins with X. [Author's note: Meant to be humorous, but apparently only to me]
Let's get this one out of the way; a xylophone is a wooden thing that makes sounds; ξύλον (xylon) "wood" + φωνή (phonē) "sound", along with the common change in pronunciation that ξ has when borrowed into English at the start of a word, where we pronounce it /ˈzaɪ/ or /ˈsaɪ/ rather than /ksi/, because we don't pronounce anything as starting with /ksi/. (See Why are there so few English words that begin with the letter X?).
Well, x is commonly used to represent an unknown thing in algebra. More to the point, it is often used to mean a currently-unknown but sought thing in algebra, in those cases where we can "solve for x".
And as a rule, the figurative uses are not just for things that are unknown, but for things that are unknown, that we want to make known.
From this use in algebra, we have figurative use of both "X" and "XYZ" for unknown or undetermined things not sensibly describable through algebra:
The black porker's killed—weighed x stone. —Thackeray, Vanity Fair, 1847
I use it rather as an X Y Z, an unknown quantity. — S. T. Coleridge "Lett. to J. P. Estlin", 1884
And from there we have the X-Factor and X-Rays (Röntgen was quite explicit in his naming after the unknown) and so on.
But why X in algebra?
Reason one:
Descartes used a, b, c,… for known quantities, and x, y, z (giving three quantities and then working backwards from w if necessary) for unknown, because they were far away from each other. He also used p, q, r, s… in yet other contexts, O for a chart origin and n was already in heavy use in mathematics. In all, he was picking his choice of letters so as to give himself space in the alphabet and avoid collisions between different uses.
Reason two:
X doesn't stand for very much (See again Why are there so few English words that begin with the letter X? and note that it applies to many other languages too), so x doesn't become the abbreviation of anything, so x as used by Descartes is "safe", in that it can go a good 350 years without causing confusion with a use of X as an abbreviation.
Reason three (doubtful, often stated but without much supporting evidence):
X can be press-ganged into all sorts of jobs because it's a bit superfluous in most languages' use of the Latin alphabet. In translating الشيء ("thing" and used by the Arabs when they invented algebra for unknown qualities, much as x is now) into Spanish, scribes used x to represent the ﺶ of الشيء, which doesn't have an equivalent sound in Spanish.
Reason four (even more doubtful):
A symbol that looks a bit like x was used as an abbreviation of res (thing) or radix (root) in Latin, much as & and ⁊ were used as an abbreviation of et, % for per 100, vi⁊ or viȜ for videlicet (itself short for videre licet) and so on. It then mutated further to become identical with the letter x much as vi⁊ or viȜ mutated to become viz.
These reasons are not mutually exclusive. We can be sure that the first and second were definitely influences on how we got to the current state. If there is truth to the story behind the third and fourth then they are also reasons, rather than "the real reason".
The relevant definition in OED is...
X - in Algebra and Higher Mathematics used as the symbol for an unknown or variable quantity (or for the first of such quantities, the others being denoted by y, z, etc.)
First citation 1660.Hence used attrib. as an indeterminate numeral adj. = ‘an unknown number of..’ Chiefly humorous.
First citation 1847
Note that there are various other senses for "attributive" X besides OP's "unknown". For example, x-rated ("adult-only" films), triple-x (strong beer), the X chromosome, etc.
Also note that in common parlance today we usually use n rather than x for the variable quantity sense referred to above (where the value isn't so much "unknown" as any value, not a "fixed" one).
I'm not sure this question is completely answerable -- or if it is, it would probably take too long to answer appropriately here -- but the following few suggestions are a good starting point to understanding why "X" is used as it is.
The most straightforward answer is that "X" is frequently used as the example variable in algebra and an extension of that usage is to use "Mr. X" to refer to someone whose identity is still a mystery. I have always assumed that "X" was used so the two subsequent letters can take the place of more variables (e.g., y = x * z).
Likewise, "X" is an extremely easy mark to make and "x marks the spot" is often associated with hidden treasure.
The American science fiction show "X-Files" noted that "X" never had anything filed under it so they started filing anything without an appropriate category under "X". The explanation is a bit tongue-in-cheek but the fact that very few words start with the letter "X" helps make it feel rare or exciting.
That being said, some of your examples don't fit. Planet X refers to the phantom tenth planet which is a reference to the Roman numeral X. "Xylophone" has nothing to do with your other examples. "X-Factor" is an term that most likely banks to the algebraic explanation above.
x factor — a circumstance, quality, or person that has a strong but unpredictable influence
The link notes the first known usage is from 1930.