2343: Mathematical Symbol Fight
|Mathematical Symbol Fight|
Title text: Oh no, a musician just burst in through the door confidently twirling a treble clef.
This comic imagines which mathematical symbols would be good in a fight if they were made corporeal in two (or three) dimensions.
Generally, objects with longer reach and pointier ends wound up on the right ("more useful") side of the scale, and symbols with less reach and more curves wound towards the left ("less useful") side. A straight line is farthest to the "more dangerous" side; however, the straight line does not appear to be any thicker or thinner, or pointier, than any of the other lines that would make it more "useful" (It should be noted that this chart seems to fall afoul of what Eliezer Yudkowsky (who also wrote HPMoR) calls the intent to kill: that humans tend to define "winning a fight" and "useful" as causing some form of bodily harm on their opponent despite survival and purely defensive strategies being an equally valid goals.).
Below the chart, with the symbols listed in order of usefulness, eight characters wield eight of the symbols. See the table below for the meaning of each symbol.
The comic invokes surreal humour by suggesting that mathematical symbols could be handled as physical objects in the real world. Another component of the humor is the implication that it is useful to prepare to use mathematical symbols in a fight, even though mathematicians, who use mathematical symbols, usually do not conduct their debates violently (though some stories suggest that Hippasus was killed by his fellow Pythagoreans for his proof that irrational numbers exist), and even if they did, they wouldn't use large reproductions of their symbols as weapons.
The title text refers to a Treble clef, which is not a mathematical symbol but rather a musical symbol. The note of concern in the text suggests musical symbols may be viewed in such fights as exotic or especially dangerous. See also the last entry in the table below.
Table of symbols
|Symbol||Meaning||Notes on using in a fight|
|ℝ||The set of real numbers||Megan seems to be struggling with a giant version of this symbol because of its weight. A very strong person might find it slightly more useful as a bludgeon.|
|θ||Theta||This symbol is not very sharp, and White Hat is unable to use it in combat. It would not work as a good shield due to the hole in the symbol, but it possibly could be thrown. (The later version of Xena's chakram had a bar in the middle.)|
|∅||Empty set||Similarly shaped to theta, but identified as being slightly more useful, presumably because the parts of the bar that extend beyond the circle can be used as thrusting weapons. Alternatively, the round nature of the symbol makes it easier to handle for defense, by holding on to the line and using the edge of the circular part to block.|
|∞||infinity||Could be gripped between the rings and used as a blunt instrument.|
|>||Greater than||Could be used to thrust with the point, but lacks a grip by which to do so. If held by one leg, the angle and balance is wrong to use it as a pick. Could also be used as a boomerang.|
|∝||Direct Proportionality (not to be confused with lowercase alpha)||Could be brandished by the ring and used to thrust with the prongs, but the two prongs extending at 90-degree angles make thrusting motions awkward.|
|∪||union (set theory)||Could be used as a boomerang, which is notoriously less practical in real life than in fiction|
|∈/ϵ||member of (set theory) or the "lunate" lowercase epsilon||Cueball is holding this in the manner of a Klingon "Bat'leth" from the Star Trek franchise. The Bat'leth is infamous among swordfighters for being rather impractical, and that the Klingon warrior race would have been better suited using swords like humans. It seems Randall agrees, as the ∈ is quite far on the left of the chart.|
|π||pi||Could be used as a hammer, but the two handles would make doing so impractical.|
|∀||"for all"||Could be held by the crossbar clenched in a fist, and then used as a push dagger, with the legs acting as a guard. Or could be held by the legs.
Compared to the similar Δ (delta) the point is sharper, the grip is closer to the point so it would be easier to control (keep the weapon from twisting). It is unclear why it is listed as much less effective than the delta. Perhaps the guard legs are too long?
|∂||∂ (partial derivative or boundary operator)||It's not clear why Randall ranks this symbol as so much less effective than the similarly-shaped 𝜌, but the curl in the "tail" of the ∂ would give it a shorter lever arm when swung and would disrupt the balance.|
|+||Plus||Maybe thrown like a shuriken? It could also be used like Kylo Ren's lightsaber.|
|Ψ||Psi||It could be used as a slightly-less-functional trident or pitchfork, with a shorter handle. More particularly, it resembles a sai (which, funnily enough, is how "Psi" is pronounced).|
|≠||not equal sign||Could be gripped by the crossbar, using the lengths to puncture. Notably, the equal sign (=) is absent from the chart, likely because the lengths are separate and would not be used as a single entity.|
|~||tilde, meaning "approximately", equivalent, or several transforms of a function||A potentially dangerous throwing weapon. Could also be similar to a wavy bladed dagger (Kris) or a sword (Flame-bladed sword).|
|#||Cardinality, connected sum (knot theory), or primorial.||Blondie uses this symbol, gripping it by two of the prongs on one side. The other three prongs could thus be swung at opponents, but being sharp on all sides would pose a threat to the user as well as the opponent.|
|Δ||Delta||Could be held with one bar clenched in a fist, and then used as a push dagger. It is unclear why listed as much more effective than ∀. Also, delta could be thrown like a star.|
|⇒||Material consequence or Logical consequence, meaning "implies"||The point is nice, but having two poles (or one board-like thick handle, if the shape is drawn "closed" at the back) would be difficult to wield. A collection of them might make a nice defensive pike line.|
|⋅||decimal point (or multiplication sign)||Functionally a ball, and could therefore be thrown as a projectile weapon, or scattered on the ground as a trip hazard.|
|ζ||Zeta||Could be sharpened into a scythe or curved saber, depending on the curvature and length of the 'tail' at the bottom.|
|ℵ||Aleph number||The irregular shape of the symbol leads to edges and points on all sides; thus it could be brandished or thrown in the manner of a shuriken.|
|Γ||uppercase Greek letter Gamma||If this letter is formed with serifs, it could be used as an axe or hook, and if it is made sans-serif, it would make a powerful pick or war hammer.|
|√||Radical symbol||Randall has drawn this sign with a long overbar, which makes it useful like a pole arm. Black Hat has chosen this symbol in his fight against Hairy.|
|ρ||italic rho||Ponytail is brandishing this symbol against Danish, apparently using it like a club or hammer and striking with the curve.|
|∮||contour integral||This symbol is drawn with a very tight center, giving it an almost identical figure to the regular integral symbol. Presumably, the added bulk for marginal additional use earns it a rating of 'less effective'.|
|∫||integral||Could be used in the manner of a shepherd's crook, or as a billhook. Could be used as a spear thrower, combined with ⋅ or ⇀.|
|→||Implies; X→Y means that if X is true, then Y is also true||Danish is brandishing this symbol against Ponytail, apparently using it like a spear.|
|⊥||up tack or falsum, indicating a false proposition in logic, perpendicular lines in geometry, or the bottom element in a partial order||Used as a war hammer (held by the long stem), the opponent would be struck with either leg of the top of the T. Held by the short legs (like a wishbone), could be used as a two handed sword.
(If tipped with a knapped stone head, it could become a falsum point.)
|⇀||Vector notation||Could be used as a single-barbed spear or, if held by the other end, similarly to a sabre. The multi-functionality is probably why it is listed as more useful than the 'implies' arrow.|
|––||Fraction bar (division) or overline (complex conjugate or mean) or minus sign.||Hairy is brandishing this symbol against Black Hat. The single shaft would allow it to be used in the manner of a quarterstaff, bō, or other stick-fighting weapon. Of the symbols shown in the comic, Randall considers this one the most useful in a fight, presumably because of its greater reach than the vector arrow and its simplicity compared to the radix root symbol. Alternatively, could be handled like a pike, with a reach greater than that of an implication or vector arrow.|
|𝄞||Treble clef||Mentioned in the title text; this is not a mathematical symbol, but a musical symbol. The treble clef is a much more complicated symbol than those used in mathematics, hence the musician's "confidence" in his weapon. The curve at the bottom could be used as a hook, the upper curl could be used as a blunt weapon, and the tight curl of the center would serve as a better defensive shield than theta.|
- [A chart is shown with 30 different symbols arranged above a line with arrows in both ends and with 17 ticks between the arrow heads. The symbols are mostly in two rows, but the first two symbols from the left do not have another symbol above them, and towards the right there are a segment with three rows of symbols. Above the symbols there is a heading and a subheading. And beneath those there is a long arrow pointing right with a label above it.]
- Mathematical Symbols
- By how useful they would be in a fight
- More useful
- ℝ ∅ > ∝ π + Ψ ~ ⇒ ⋅ Γ √ ∮ ∫ ⇀
- θ ∞ ∪ ∈ ∀ ∂ ≠ # Δ ζ ℵ ρ → ⊥ ––
- [Below the double arrow line are eight characters that fight each other in groups of two by using some of the symbols shown above them as weapons. They have chosen symbols that are almost above them in the chart.]
- [Megan is awkwardly handling a giant "ℝ" holding it up against White Hat who is holding a "θ" (or "∅"?) with both hands, as a shield.]
- [Cueball is holding an "∈" in both hands, with its "tines" pointed towards Blondie, who is swatting at him with a "#".]
- [Ponytail is leaping at Danish, swinging a "ρ" like an axe, while Danish is leaning back and thrusting a "→" back at her.]
- [Black Hat is swinging a long "√" like a polearm at Hairy, who is holding a long "⎯" defensively.]
- Here is a list of symbols from left to right (by rightmost edge):
- ℝ θ ∅ ∞ > ∪ ∝ ∈ ∀ π ∂ + ≠ Ψ # ~ △ ζ ⇒ ⋅ ℵ Γ ρ √ → ∮ ∫ ⊥ ⇀ ––
- Note: Where two symbols had similar right-most edges, the overlay grid on an ASUS pro-art display was used to decide which one went further right.
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