explain xkcd - User contributions [en]

3015: D&D Combinatorics

2024-11-23T13:27:55Z

Leduyquang753: Added additional explanation about the overkillness of the solution.

{{comic
| number = 3015
| date = November 22, 2024
| title = D&D Combinatorics
| image = dnd_combinatorics_2x.png
| imagesize = 328x446px
| noexpand = true
| titletext = Look, you can't complain about this after giving us so many scenarios involving N locked chests and M unlabeled keys.
}}

==Explanation==
{{incomplete|Created by a BOT THAT GRABBED A CURSED ARROW - Please change this comment when editing this page. Do NOT delete this tag too soon.}}

Dungeons and Dragons (D&D) is a role-playing game that usually has a "Dungeon Master" (narrator) that takes a team of players through scenarios where they attack monsters and go on quests.

Often, there will be semi-random events: e.g., when attacking a monster, often, a player will roll a die and deal damage based on what that die returns. D&D also uses a variety of dice, from regular d6 (6-sided, cubic dice) to other polyhedral dice, with the number of faces denoted by dX (e.g., d10 is a 10-sided die, with numbers from 1 to 10 on it). Common sets include: d4, d6, d8, d10, d12, d20, and occasionally d100 (typically not, however, the [[2626:_d65536|d65536]]).{{cn}}

With these, you can simulate events with a wide variety of denominators. In this case, Cueball gives a {{w|combinatorics|combinatorial}} problem:

* There are 10 arrows.
* 5 arrows are cursed.
* You randomly take two.
* What are the odds that neither of them are cursed?

Calculating using {{w|binomial coefficients}}, there are “10 choose 2” (45) ways to choose two arrows, of which there are “5 choose 2” (10) ways to choose 2 arrows that are non-cursed. As a result, the odds of taking all non-cursed arrows is 2/9.

The Dungeon Master in this case [[356: Nerd Sniping|has to]] map that probability into rolling multiple dice, whose sums are also not evenly distributed: i.e. if rolling 3d6 (3 six-sided dice) and a d4 (1 four-sided die), the sums can range from 4 to 22. It's pretty hard to do this in one's head, but it does happen that the odds of rolling 16 or more with this combination is 2/9, matching the probability that we want to simulate.

However, there is a much easier way of implementing the operation, that is, to literally present 10 similar-looking arrows, or other objects that are taken to represent arrows (cards, for example), with the assigned information of whether each one is cursed hidden away from Cueball, and then let Cueball pick any two. It may be inferred that as the DM's mind is too occupied with advanced, high-level knowledge, she is no longer capable of considering straightforward solutions to the problem.

The title text claims that Randall only started doing this to the DM after she herself insisted on forcing another combinatorial puzzle on the players several times, involving a bunch of locked treasure chests and a multitude of keys to unlock them with. This might be a reference to an M-of-N encryption system, where a system has ''n'' valid passwords (instead of just one) but requires ''m'' of those passwords to be given before it will open; it is assumed m is greater than 1 but less than n. While this is easy enough to implement in a computer system, it would be extremely cumbersome to build for a physical lock with keys, and spreading the mechanism across multiple separate treasure chests would be impossible without literal magic (luckily, magic is in plentiful supply in a typical Dungeons and Dragons game).

==Transcript==
{{incomplete transcript|Do NOT delete this tag too soon.}}
:[Cueball, Megan, Ponytail, White Hat, and Knit Cap are sitting at a table. Everyone is looking at Cueball. Ponytail is facepalming. The table is covered in sheets of paper and assorted dice.] 
:Cueball: I grab 2 of the 10 arrows without looking and fire them, hoping I didn't grab one of the 5 cursed ones. Did I?
:Ponytail: Sigh. Umm. Okay.
:Ponytail: Roll... Uh... Hang on...
:Ponytail: Roll 3d6 and a d4. You need... 16 or better to avoid the cursed arrows.

:[Caption below the panel:]
:I got '''''way''''' more annoying to play D&D with once I learned that our DM has a combinatorics degree and can't resist puzzles.

{{comic discussion}}

[[Category:Comics featuring Cueball]]
[[Category:Comics featuring Megan]]
[[Category:Comics featuring Ponytail]]
[[Category:Comics featuring White Hat]]
[[Category:Comics featuring Knit Cap]]
[[Category:Games]]
[[Category:Math]]

3013: Kedging Cannon

2024-11-19T15:35:52Z

Leduyquang753: Nicely reformatted the analysis section.

{{comic
| number = 3013
| date = November 18, 2024
| title = Kedging Cannon
| image = kedging_cannon_2x.png
| imagesize = 740x259px
| noexpand = true
| titletext = The real key was inventing the windmill-powered winch.
}}

==Explanation==
{{incomplete|Created by a HEADCANNON. Do NOT delete this tag too soon.}}

Sailing vessels can navigate upwind through a technique called {{w|Tacking_(sailing)|tacking}} (or "tacking against the wind") which involves zigzagging across the wind's direction. However, this comic describes a fictional scenario where a ship's captain, unfamiliar with tacking, has developed an alternative method based on {{w|kedging}}.

The basics of kedging are not dissimilar to the comic: a boat affixes a rope or chain to an anchor point (such as a literal anchor) and winches itself closer. Traditional kedging involves deploying an anchor from the vessel, either manually or via a smaller boat, and then {{w|winch|winching}} the ship toward the anchor point using ropes or chains. The anchor points often utilize natural features such as trees or reefs. Kedging is a real historical technique, but has definite limitations compared to tacking, typically reserved for specific situations where conventional sailing methods are impractical, such as in calm waters, during precise maneuvering, or against strong opposing winds or currents. In this comic, the captain has modified this technique by inventing a specialized "kedging cannon" to project the anchor greater distances.

In places with a large depth, an anchor cannot be used, but a so-called {{w|sea anchor}} could solve the problem... somewhat.

The title text indicates that the captain's system has evolved to incorporate a windmill mechanism that harnesses wind power to draw in the kedging rope, which might be intentionally ironic -- given that the captain knows that windmills work, they could presumably have used that knowledge to reinvent tacking. Additionally, this makes the solution even less efficient, given that wind could be used for tacking.

{{cot|Speed and economic analysis of dual wind-winched kedging cannons compared to tacking}}
A dual-anchor kedging cannon system for sailing upwind, consisting of:
* Two kedging cannons firing 16 kg anchors
* 6-meter diameter windmill powering winch system
* Dual-winch setup for continuous operation
* Operating in 15 knot headwind conditions

Vessel specifications:
* Length: 30 feet (9.1 meters)
* Displacement: 10,000 lbs (4536 kg)
* Sail area: 600 sq ft (55.7 m²)
* Wetted surface: 40 m²
* Frontal area: 8 m²

;Wind power generation
Available wind power is given by:
''P'' = ½''ρAv''³''η''
where:
* ''ρ'' = 1.225 kg/m³ (air density)
* ''A'' = ''π''(''D''/2)² = 28.3 m² (windmill area)
* ''v'' = 7.72 m/s (wind speed)
* ''η'' = 0.245 (combined efficiency)

This yields 1.95 kW of usable power.

;Drag forces
Total drag combines water and air resistance:
''F''drag = ''F''water + ''F''wind
where:
* ''F''water = ½''ρ''w''C''d''A''w''v''²
* ''F''wind = ½''ρ''a''C''a''A''f''v''²

Using:
* Water density (''ρ''w) = 1025 kg/m³
* Hull drag coefficient (''C''d) = 0.04
* Wetted area (''A''w) = 40 m²
* Air density (''ρ''a) = 1.225 kg/m³
* Air drag coefficient (''C''a) = 0.8
* Frontal area (''A''f) = 8 m²

Total drag force = 1053.4 N

;Anchor ballistics
For 300 m range with 45° launch angle:
* Required velocity = 54.7 m/s
* Launch energy = 23.7 kJ
* Black powder energy per shot = 680.4 kJ
* Launch efficiency = 3.5%

;System performance
* Winch speed = 3.60 knots
* Cycle time = 194.7 seconds
* Effective speed = 3.04 knots
* Compared to tacking speed = 4.95 knots
* Speed ratio (kedging/tacking) = 0.61

;Economic analysis
* Shots needed per nautical mile: 6.1
* Black powder cost per shot: $10 (0.5 lbs @ $20/lb)
* Cost per nautical mile: $60.76
* Powder consumption: 9.2 lbs/hour
* Operating cost: $184.90/hour

Example 100 nmi journey:
* Total powder cost: $6,076.12
* Journey time: 32.9 hours

;Conclusion
The dual-anchor kedging cannon system is both slower and significantly more expensive than traditional tacking:

Speed disadvantage:
* Achieves only 61% of tacking speed
* 100 nmi journey takes 32.9 hours vs 20.2 hours tacking

Economic disadvantage:
* High powder costs ($60.76 per nautical mile)
* Requires significant powder storage (303 lbs for 100 nmi journey)
* Additional wear and tear on mechanical systems

Key limiting factors:
* Limited wind power available (1.95 kW from 6 m windmill)
* High drag forces (1053.4 N total)
* Poor ballistic efficiency (3.5% of powder energy converts to useful launch)
* Long cycle times due to realistic winching speeds

The system could potentially be improved by:
* Larger windmill (though practical size limits on boats)
* More aerodynamic anchor design
* More efficient powder-to-launch energy conversion
* Reduced transfer time between anchors

Therefore, given both the energy constraints and economic factors, traditional tacking remains far more practical for upwind progress. The key insight is that while the kedging cannon seems to "cheat" the wind by going straight upwind, it actually requires converting wind energy to mechanical work less efficiently than a well-designed sail plan, while also consuming expensive gunpowder. The indirect path of tacking makes better use of the available wind force with no consumable costs.
{{cob}}

==Transcript==
:[A two-masted sailing ship with its sails up is floating on a calm sea with tiny waves. Two tiny figures can be seen at the ship's bow. One of them is speaking. In the next panel it becomes clear this is the captain.]
:Captain: I hope someday someone invents a way to sail upwind.
:Captain: Using the kedging cannon just wastes so much gunpowder.

:[Close-up on the deck of the ship, showing two persons behind the taffrail. Cueball is standing behind the ship's captain and talking to him. The captain is wearing a black bicorne navy hat and aiming a cannon containing an anchor forward. Chains are draped from the cannon.]
:Cueball: The '''''what?'''''
:Cueball: Wait, do you not know how to sail upwind? Is that why your ship takes forever to--
:Captain: Stand by...'''''Fire!'''''

:[Distant shot showing the anchor and its chain being launched out in front of the ship, towards the right of the panel. Cueball and the Captain can still be seen behind the cannon. The cannon has exhaust fumes coming out in front and the sound it makes is indicated:]
:Cannon: ''Boom''

:[Same setting but the anchor is now under water and the chain has become taut as the ship is dragged forward to the right. Movement lines behind the ship indicated its progress and it is also further into the frame than the previous panel. The movement is caused by pulling the chain back in on the ship. This produces a series of sounds:]
:Dragging chain: ''Click click click''

{{comic discussion}}

[[Category:Comics featuring Cueball]]
[[Category:Characters with hats]]

2748: Radians Are Cursed

2023-03-13T07:26:17Z

Leduyquang753: /* Transcript */ Added explicit descriptions of the colored texts.

{{comic
| number = 2748
| date = March 10, 2023
| title = Radians Are Cursed
| image = radians_are_cursed_2x.png
| imagesize = 394x437px
| noexpand = true
| titletext = Phil Plait once pointed out that you can calculate the total angular area of the sky this way. If the sky is a sphere with radius 57.3 degrees, then its area is 4*pi*r^2=41,253 square degrees. This makes dimensional analysts SO mad, but you can't argue with results.
}}

==Explanation==
{{incomplete|Created by a DIAMETER OF 114.6 DEGREES - Please change this comment when editing this page. Do NOT delete this tag too soon.}}

This comic presents a series of Math Facts, appearing to be in a sequential order.

The first fact states that the {{w|unit circle}} has a radius of one, which is precisely its definition. Randall labels this fact as being "normal," complete with a large green checkmark to verify this. The unit circle is typically used in abstract contexts rather than applications with a specific length unit (such as meters). For example, the trigonometric functions cosine and sine can be define the x and y coordinates of a point on the unit circle without any additional factor.

The second fact states that one {{w|radian}} is equal to the length of a circle's radius. This isn't actually the way that the unit is defined. Instead, radians are usually defined as the angle encompassing an arc of a circle equal in length to its radius. This comic's logic is thus somewhat erroneous. However, this fact is still labeled as also being "normal." Also, while Randall again uses the unit circle in the fact's associated diagram, any circle could theoretically be used to show the conventional definition. Under the standard definition of an {{w|angle}} as the ratio of the length of a circular arc to its radius, the radian is a dimensionless unit equal to 1.

A correct version of the second fact would be that a radian has the same value (1) as the radius of the unit circle.

The third fact states that one radian is equal to 57.3 degrees. This is indeed true (albeit rounded). The circumference of a circle is 2pi radius-lengths, so the angle of a complete circle is both 2pi radians and 360 degrees. Thus 1 radian equals 180/pi degrees. This fact is again labeled "normal."

The fourth and final fact states that because it was determined in earlier facts that a radian is equal to the radius of the unit circle as well as 57.3 degrees, then the radius of the unit circle must be equal to 57.3 degrees. This is usually not how degrees are supposed to work, because they are a measure of angle, not length. Hence, this fact is labeled "cursed" by Randall, leading to the comic's title. (However, since the radian is also an angular measure, the second fact could be viewed as equally cursed.)

The title text is referring to {{w|Phil Plait}}'s claim about the size of the sky, which was published on his blog: http://www.badastronomy.com/bitesize/bigsky.html. Dimensional analysis utilizes the rationale that both sides of an equation need to have the same unit. Radius typically refers to a length, which has SI units of meters. The surface area has SI units of square meters. The units of Phil Plait's "angular area" is as the title text mentions, {{w|square degrees}}. Thus the comic's {{w|dimensional analysis|dimensional analysts}} (not a profession, but instead the adherents of the mathematical technique) are said to be angered by this argument.

Randall has alluded to Plait's angular area tip previously [https://what-if.xkcd.com/109/ in his own blog What If?], in a post that examined the chances of hitting various celestial objects with a laser blast aimed at random from Earth's surface.

==Transcript==
{{incomplete transcript|Do NOT delete this tag too soon.}}

:[Title:]
:Math facts

:[A diagram of a circle is shown with radius labeled as “1”]
:The unit circle has a radius of one [In green] ✓ Normal
:[The diagram now has another (unlabeled and lighter) radius at a 57.3 degree angle. The arc between the points where the radii intersect the circle is labeled as “1”]
:One radian equals the length of a circle’s radius [In green] ✓ Normal
:[The diagram now is completely unlabeled except for the arc, which is labeled as “57.3°”]
:One radian is 57.3 degrees [In green] ✓ Normal
:[The first diagram is shown; however, the radius is labeled as “57.3°”]
:The unit circle has a radius of 57.3 degrees [In red] X Cursed

{{comic discussion}}

[[Category:Math]]
[[Category:Geometry]]
[[Category:Facts]]
[[Category:Comics featuring real people]] 
[[Category:Comics featuring cursed items]]

2740: Square Packing

2023-02-21T01:33:01Z

Leduyquang753: Fixed the last word of the paper name that I forgot to bring to lowercase.

{{comic
| number = 2740
| date = February 20, 2023
| title = Square Packing
| image = square_packing_2x.png
| imagesize = 326x295px
| noexpand = true
| titletext = I also managed to improve the solution for n=1 to s<0.97, and with some upgrades I think I can hit 0.96.
}}

==Explanation==
{{incomplete|Created by a HYDRAULIC PRESSED SQUARE - This appears to be referring to a specific puzzle that merits explanation before going into description of the comic. Do NOT delete this tag too soon.}}
A few days before this comic's post, a web page [https://erich-friedman.github.io/packing/squinsqu/ ''Squares in squares''] gained interest on social media platforms such as [https://twitter.com/KangarooPhysics/status/1625436240412540928 Twitter] and [https://news.ycombinator.com/item?id=34809023 Hacker News]. The page depicts the optimal, or at least the best known, solutions for the {{w|square packing in a square}} problem, where one attempts to arrange a provided number of non-overlapping unit squares such that the smallest square enclosing them is itself the smallest possible.

Herein, Randall claims to have found a more efficient solution for the case of 11 unit squares, by physically deforming the squares involved in the optimal solution (found by Walter Trump in 1979 and proved by Thierry Gensane et al. in 2004<ref>Gensane, T., Ryckelynck, P. – ''Improved dense packings of congruent squares in a square''. Discrete Comput Geom 34, pages 97–109 (2005). https://doi.org/10.1007/s00454-004-1129-z</ref>) with a hydraulic press. The size of the resulting bounding square is indeed smaller, but one may claim the solution doesn't look as elegant as the original solution, due to the countless wrinkles on every "square". Geometrical shapes in packing problems are not conventionally assumed to be deformable in this manner.{{citation needed}}

The title text mentions the same approach applied to the solution for 1 unit square, whose original optimal solution is obviously that unit square itself. Randall remarks that if he had "some upgrades", namely a more powerful hydraulic press, he could get the resulting square to be even smaller.

==Transcript==
{{incomplete transcript|Do NOT delete this tag too soon.}}
:[11 squares optimally packed inside a square arrangement]
:Previous best
:s<3.877084
:(Gensane, 2004)

:[11 deformed squares crushed together to pack them into a smaller square arrangement]
:New record
:s<3.40

:[Caption below the panel:]
:I've significantly improved on the solution to the n=11 square packing problem by using a hydraulic press.

{{comic discussion}}
[[Category:Math]]
[[Category:Geometry]]

2740: Square Packing

2023-02-21T01:31:55Z

Leduyquang753: Added a "pages" specifier to the reference and a missing closing parenthesis.

{{comic
| number = 2740
| date = February 20, 2023
| title = Square Packing
| image = square_packing_2x.png
| imagesize = 326x295px
| noexpand = true
| titletext = I also managed to improve the solution for n=1 to s<0.97, and with some upgrades I think I can hit 0.96.
}}

==Explanation==
{{incomplete|Created by a HYDRAULIC PRESSED SQUARE - This appears to be referring to a specific puzzle that merits explanation before going into description of the comic. Do NOT delete this tag too soon.}}
A few days before this comic's post, a web page [https://erich-friedman.github.io/packing/squinsqu/ ''Squares in squares''] gained interest on social media platforms such as [https://twitter.com/KangarooPhysics/status/1625436240412540928 Twitter] and [https://news.ycombinator.com/item?id=34809023 Hacker News]. The page depicts the optimal, or at least the best known, solutions for the {{w|square packing in a square}} problem, where one attempts to arrange a provided number of non-overlapping unit squares such that the smallest square enclosing them is itself the smallest possible.

Herein, Randall claims to have found a more efficient solution for the case of 11 unit squares, by physically deforming the squares involved in the optimal solution (found by Walter Trump in 1979 and proved by Thierry Gensane et al. in 2004<ref>Gensane, T., Ryckelynck, P. – ''Improved dense packings of congruent squares in a Square''. Discrete Comput Geom 34, pages 97–109 (2005). https://doi.org/10.1007/s00454-004-1129-z</ref>) with a hydraulic press. The size of the resulting bounding square is indeed smaller, but one may claim the solution doesn't look as elegant as the original solution, due to the countless wrinkles on every "square". Geometrical shapes in packing problems are not conventionally assumed to be deformable in this manner.{{citation needed}}

The title text mentions the same approach applied to the solution for 1 unit square, whose original optimal solution is obviously that unit square itself. Randall remarks that if he had "some upgrades", namely a more powerful hydraulic press, he could get the resulting square to be even smaller.

==Transcript==
{{incomplete transcript|Do NOT delete this tag too soon.}}
:[11 squares optimally packed inside a square arrangement]
:Previous best
:s<3.877084
:(Gensane, 2004)

:[11 deformed squares crushed together to pack them into a smaller square arrangement]
:New record
:s<3.40

:[Caption below the panel:]
:I've significantly improved on the solution to the n=11 square packing problem by using a hydraulic press.

{{comic discussion}}
[[Category:Math]]
[[Category:Geometry]]

2740: Square Packing

2023-02-21T01:28:28Z

Leduyquang753: Added more information to the explanation.

{{comic
| number = 2740
| date = February 20, 2023
| title = Square Packing
| image = square_packing_2x.png
| imagesize = 326x295px
| noexpand = true
| titletext = I also managed to improve the solution for n=1 to s<0.97, and with some upgrades I think I can hit 0.96.
}}

==Explanation==
{{incomplete|Created by a HYDRAULIC PRESSED SQUARE - This appears to be referring to a specific puzzle that merits explanation before going into description of the comic. Do NOT delete this tag too soon.}}
A few days before this comic's post, a web page [https://erich-friedman.github.io/packing/squinsqu/ ''Squares in squares''] gained interest on social media platforms such as [https://twitter.com/KangarooPhysics/status/1625436240412540928 Twitter] and [https://news.ycombinator.com/item?id=34809023 Hacker News]. The page depicts the optimal, or at least the best known, solutions for the {{w|square packing in a square}} problem, where one attempts to arrange a provided number of non-overlapping unit squares such that the smallest square enclosing them is itself the smallest possible.

Herein, Randall claims to have found a more efficient solution for the case of 11 unit squares, by physically deforming the squares involved in the optimal solution (found by Walter Trump in 1979 and proved by Thierry Gensane et al. in 2004<ref>Gensane, T., Ryckelynck, P. – ''Improved dense packings of congruent squares in a Square''. Discrete Comput Geom 34, 97–109 (2005). https://doi.org/10.1007/s00454-004-1129-z</ref> with a hydraulic press. The size of the resulting bounding square is indeed smaller, but one may claim the solution doesn't look as elegant as the original solution, due to the countless wrinkles on every "square". Geometrical shapes in packing problems are not conventionally assumed to be deformable in this manner.{{citation needed}}

The title text mentions the same approach applied to the solution for 1 unit square, whose original optimal solution is obviously that unit square itself. Randall remarks that if he had "some upgrades", namely a more powerful hydraulic press, he could get the resulting square to be even smaller.

==Transcript==
{{incomplete transcript|Do NOT delete this tag too soon.}}
:[11 squares optimally packed inside a square arrangement]
:Previous best
:s<3.877084
:(Gensane, 2004)

:[11 deformed squares crushed together to pack them into a smaller square arrangement]
:New record
:s<3.40

:[Caption below the panel:]
:I've significantly improved on the solution to the n=11 square packing problem by using a hydraulic press.

{{comic discussion}}
[[Category:Math]]
[[Category:Geometry]]

2586: Greek Letters

2022-02-26T01:58:26Z

Leduyquang753: /* Explanation */ Fixed formatting issues.

{{comic
| number = 2586
| date = February 25, 2022
| title = Greek Letters
| image = greek_letters.png
| titletext = If you ever see someone using a capital xi in an equation, just observe them quietly to learn as much as you can before they return to their home planet.
}}

==Explanation==
{{incomplete|Created by '''''O R B S''''' PRO®- Please change this comment when editing this page. Do NOT delete this tag too soon.}}

Mathematics uses lots of Greek letters, [https://en.wikipedia.org/wiki/Greek_letters_used_in_mathematics,_science,_and_engineering typically using the same letter consistently to represent a particular constant or type of variable].
This comic gives a (non-)explanation of what they typically mean.

The letters are:

- lower-case pi

- capital delta

Typically used to refer to a change in quantity.

- lower-case delta

Also typically used to refer to a change in quantity, but unlike the capital delta, this is only for infinitesimal changes and is used in derivative and integration expressions in mathematics hence the text's reference to "a mathematician's fault".

- lower-case theta

Typically used to refer to an angle, and is notably used in the polar coordinate system. The text refers to its close relationship with circles, on which the polar coordinate system is based on.

- lower-case phi

Typically used to refer to another angle other than one referred to by theta. It's used in spherical coordinates, and the text refers to how spheres, or orbs, are important in spherical coordinates.

- lower-case epsilon

- lower-case upsilon and lower-case nu

- lower-case mu

The SI prefix for "micro" = 10-6, representing very small quantities: a micrometer (μm) is tens of times smaller than the width of a human hair, a microgram (μg) is one single fine speck of flour, both of which are barely visible with the bare human eye nor feelable through the skin.

- capital sigma

Typically used as a symbol for summation of a series of numbers.

- capital pi

Typically used as a symbol for multiplication of a series of numbers.

- lower-case zeta

- lower-case beta

- lower-case alpha

- capital omega

- lower-case omega

- lower-case sigma

- lower-case ksi

- lower-case gamma

Gamma ray is the most powerful classification of electromagnetic radiation AKA "light", and powerful lights are frequently associated with high-tech, futuristic devices and weapons, hence "space noises".

- lower-care rho

- capital ksi

- lower-case psi

...

==Transcript==
{{incomplete transcript|Do NOT delete this tag too soon.}}

:What Greek letters mean in equations

:π This math is either very simple or impossible.
:Δ Something has changed.
:δ Something has changed and it's a mathematician's fault.
:θ Circles!
:Φ '''''O R B S'''''
:ϵ Not important, don't worry about it.
:υ,ν Is that a V or a U? Or...oh no, it's one of ''those''.
:μ This math is cool but it's not about anything that you will ever see or touch, so whatever.
:Σ Thank you for purchasing ''Addition Pro''®!
:Π ...and the ''Multiplication''® expansion pack!
:ζ This math will only lead to more math.
:β There are just too many coefficients.
:α Oh boy, now '''''this''''' is math about something real. This is math that could '''''kill''''' someone.
:Ω Oooh, ''some'' mathematician thinks their function is cool and important.
:ω A lot of work went into these equations and you are going to die here among them.
:σ Some poor soul is trying to apply this math to real life and it's not working.
:ξ Either this is terrifying mathematics or there was a hair on the scanned page.
:γ ''Zoom'' pew pew pew [space noises] ''zoooom!''
:ρ Unfortunately, the test vehicle suffered an unexpected wing separation event.
:Ξ Greetings! We hope to learn a great deal by exchanging knowledge with your Earth mathematicians.
:ψ You have entered the domain of King Trition, ruler of the waves.

{{comic discussion}}

2586: Greek Letters

2022-02-26T01:56:03Z

Leduyquang753: /* Explanation */ Fixed a misspelling in the previous edit.

{{comic
| number = 2586
| date = February 25, 2022
| title = Greek Letters
| image = greek_letters.png
| titletext = If you ever see someone using a capital xi in an equation, just observe them quietly to learn as much as you can before they return to their home planet.
}}

==Explanation==
{{incomplete|Created by '''''O R B S''''' PRO®- Please change this comment when editing this page. Do NOT delete this tag too soon.}}

Mathematics uses lots of Greek letters, [typically using the same letter consistently to represent a particular constant or type of variable](https://en.wikipedia.org/wiki/Greek_letters_used_in_mathematics,_science,_and_engineering).
This comic gives a (non-)explanation of what they typically mean.

The letters are:

- lower-case pi

- capital delta

Typically used to refer to a change in quantity.

- lower-case delta

Also typically used to refer to a change in quantity, but unlike the capital delta, this is only for infinitesimal changes and is used in derivative and integration expressions in mathematics hence the text's reference to "a mathematician's fault".

- lower-case theta

Typically used to refer to an angle, and is notably used in the polar coordinate system. The text refers to its close relationship with circles, on which the polar coordinate system is based on.

- lower-case phi

Typically used to refer to another angle other than one referred to by theta. It's used in spherical coordinates, and the text refers to how spheres, or orbs, are important in spherical coordinates.

- lower-case epsilon

- lower-case upsilon and lower-case nu

- lower-case mu

The SI prefix for "micro" = 10-6, representing very small quantities: a micrometer (μm) is tens of times smaller than the width of a human hair, a microgram (μg) is one single fine speck of flour, both of which are barely visible with the bare human eye nor feelable through the skin.

- capital sigma

Typically used as a symbol for summation of a series of numbers.

- capital pi

Typically used as a symbol for multiplication of a series of numbers.

- lower-case zeta

- lower-case beta

- lower-case alpha

- capital omega

- lower-case omega

- lower-case sigma

- lower-case ksi

- lower-case gamma

Gamma ray is the most powerful classification of electromagnetic radiation AKA "light", and powerful lights are frequently associated with high-tech, futuristic devices and weapons, hence "space noises".

- lower-care rho

- capital ksi

- lower-case psi

...

==Transcript==
{{incomplete transcript|Do NOT delete this tag too soon.}}

:What Greek letters mean in equations

:π This math is either very simple or impossible.
:Δ Something has changed.
:δ Something has changed and it's a mathematician's fault.
:θ Circles!
:Φ '''''O R B S'''''
:ϵ Not important, don't worry about it.
:υ,ν Is that a V or a U? Or...oh no, it's one of ''those''.
:μ This math is cool but it's not about anything that you will ever see or touch, so whatever.
:Σ Thank you for purchasing ''Addition Pro''®!
:Π ...and the ''Multiplication''® expansion pack!
:ζ This math will only lead to more math.
:β There are just too many coefficients.
:α Oh boy, now '''''this''''' is math about something real. This is math that could '''''kill''''' someone.
:Ω Oooh, ''some'' mathematician thinks their function is cool and important.
:ω A lot of work went into these equations and you are going to die here among them.
:σ Some poor soul is trying to apply this math to real life and it's not working.
:ξ Either this is terrifying mathematics or there was a hair on the scanned page.
:γ ''Zoom'' pew pew pew [space noises] ''zoooom!''
:ρ Unfortunately, the test vehicle suffered an unexpected wing separation event.
:Ξ Greetings! We hope to learn a great deal by exchanging knowledge with your Earth mathematicians.
:ψ You have entered the domain of King Trition, ruler of the waves.

{{comic discussion}}

2586: Greek Letters

2022-02-26T01:53:53Z

Leduyquang753: Added some more explanations.

{{comic
| number = 2586
| date = February 25, 2022
| title = Greek Letters
| image = greek_letters.png
| titletext = If you ever see someone using a capital xi in an equation, just observe them quietly to learn as much as you can before they return to their home planet.
}}

==Explanation==
{{incomplete|Created by '''''O R B S''''' PRO®- Please change this comment when editing this page. Do NOT delete this tag too soon.}}

Mathematics uses lots of Greek letters, [typically using the same letter consistently to represent a particular constant or type of variable](https://en.wikipedia.org/wiki/Greek_letters_used_in_mathematics,_science,_and_engineering).
This comic gives a (non-)explanation of what they typically mean.

The letters are:

- lower-case pi

- capital delta

Typically used to refer to a change in quantity.

- lower-case delta

Also typically used to refer to a change in quantity, but unlike the capital delta, this is only for infinitestimal changes and is used in derivative and integration expressions in mathematics hence the text's reference to "a mathematician's fault".

- lower-case theta

Typically used to refer to an angle, and is notably used in the polar coordinate system. The text refers to its close relationship with circles, on which the polar coordinate system is based on.

- lower-case phi

Typically used to refer to another angle other than one referred to by theta. It's used in spherical coordinates, and the text refers to how spheres, or orbs, are important in spherical coordinates.

- lower-case epsilon

- lower-case upsilon and lower-case nu

- lower-case mu

The SI prefix for "micro" = 10-6, representing very small quantities: a micrometer (μm) is tens of times smaller than the width of a human hair, a microgram (μg) is one single fine speck of flour, both of which are barely visible with the bare human eye nor feelable through the skin.

- capital sigma

Typically used as a symbol for summation of a series of numbers.

- capital pi

Typically used as a symbol for multiplication of a series of numbers.

- lower-case zeta

- lower-case beta

- lower-case alpha

- capital omega

- lower-case omega

- lower-case sigma

- lower-case ksi

- lower-case gamma

Gamma ray is the most powerful classification of electromagnetic radiation AKA "light", and powerful lights are frequently associated with high-tech, futuristic devices and weapons, hence "space noises".

- lower-care rho

- capital ksi

- lower-case psi

...

==Transcript==
{{incomplete transcript|Do NOT delete this tag too soon.}}

:What Greek letters mean in equations

:π This math is either very simple or impossible.
:Δ Something has changed.
:δ Something has changed and it's a mathematician's fault.
:θ Circles!
:Φ '''''O R B S'''''
:ϵ Not important, don't worry about it.
:υ,ν Is that a V or a U? Or...oh no, it's one of ''those''.
:μ This math is cool but it's not about anything that you will ever see or touch, so whatever.
:Σ Thank you for purchasing ''Addition Pro''®!
:Π ...and the ''Multiplication''® expansion pack!
:ζ This math will only lead to more math.
:β There are just too many coefficients.
:α Oh boy, now '''''this''''' is math about something real. This is math that could '''''kill''''' someone.
:Ω Oooh, ''some'' mathematician thinks their function is cool and important.
:ω A lot of work went into these equations and you are going to die here among them.
:σ Some poor soul is trying to apply this math to real life and it's not working.
:ξ Either this is terrifying mathematics or there was a hair on the scanned page.
:γ ''Zoom'' pew pew pew [space noises] ''zoooom!''
:ρ Unfortunately, the test vehicle suffered an unexpected wing separation event.
:Ξ Greetings! We hope to learn a great deal by exchanging knowledge with your Earth mathematicians.
:ψ You have entered the domain of King Trition, ruler of the waves.

{{comic discussion}}

2552: The Last Molecule

2021-12-09T06:08:13Z

Leduyquang753: /* Transcript */ Added transcript.

{{comic
| number = 2552
| date = December 8, 2021
| title = The Last Molecule
| image = the_last_molecule.png
| titletext = Biology is really struggling; they're barely at 93% and they keep finding more ants.
}}

==Explanation==
{{incomplete|Created by a FRUSTRATED BIOLOGIST - Please change this comment when editing this page. Do NOT delete this tag too soon.}}

There are an infinite number of ways to arrange atoms into molecules, and chemistry is the study of the interaction of subatomic particles, atoms, and molecules, not simply the cataloging of all specimens of molecule.

This is reminiscent of biology's focus on previous centuries on simply cataloging the species on Earth.

Further, the goal of science is not to "complete" a field, but to understand it better and better. No scientific field, with the possible exception of optics, is considered fully understood.

Putting Biology at 93% and Physics at 98% is patently absurd. As mentioned in the comic, we don't even know how many kinds of ants there are yet. When J.B.S Haldane, founder of the field of population genetics, was asked what could be inferred about the creator from the creation, he reportedly said, "He has an inordinate fondness for beetles". Insects aside, fundamental and important problems such as what genes promote which traits, the nature of cognition, and the mechanism behind several diseases remain complete mysteries. We know less about our own ocean floor than we do about the surface of Mars. Needless to say, Biology is nowhere close to 93% solved. As for Physics, questions such as "what the actual hell is dark matter?" and "how do we unify the four fundamental forces?" and "how do we make nuclear fusion possible on earth?" and "how fast does light travel in one direction?" make it clear that the field still has a long, long way to go.

==Transcript==
{{incomplete transcript|Do NOT delete this tag too soon.}}

[Ponytail is presenting on a stage. To the top-center of the slide displays "Chemistry" at a circled "100% complete", then to the left is "Biology" at "93% complete" and to the right is "Physics" at "98% complete". The bottom of the slide shows the [[Wikipedia:structural formula|structural formula]] of a molecule captioned "The last one", along with a few smaller captions around it drawn as squiggles.]

Ponytail:

:With the discovery of the last molecule, I'm pleased to announce that chemistry is finally complete.

:Best of luck to our competitors in their race for second place.

{{comic discussion}}

2496: Mine Captcha

2021-07-30T14:45:37Z

Leduyquang753: Added transcription.

{{comic
| number = 2496
| date = July 30, 2021
| title = Mine Captcha
| image = mine_captcha.png
| titletext = This data is actually going into improving our self-driving car project, so hurry up--it's almost at the minefield.
}}

==Explanation==
{{incomplete|Created by a LIVE MINEFIELD. Please mention here why this explanation isn't complete. Do NOT delete this tag too soon.}}

This comic expects users click on the mines in a minesweeper puzzle to proceed with their task. Traditionally, the goal in minesweeper is to click on boxes where there are NOT mines, so the puzzle would be especially difficult for anyone used to playing minesweeper.

The comic shows a 4x4 grid with mostly grey squares, and a few tiles showing colored numbers. The setup and colors suggest a gaming board of the popular minesweeper game, with a few tiles uncovered. Numbers would then show the number of mines in adjacent squares. Given the current board configuration, one can deduce that there are four mines (in squares A2, B2, B3 and D3, where letters (numbers) mark columns (rows)). For example, there are two mines within the squares A2,B1,B2, as signified by the 2 in A1, but only one of those can be in B1 or B2 (because of the 1 in C1). Therefore, A2 has to be a mine. The title suggests this as a CAPTCHA, where proving to be human involves first recognizing this as a minesweeper simile, and then solving for those squares with mines.

Traditionally, the goal in minesweeper is to click on boxes where there are NOT mines, so the puzzle would be especially difficult for anyone used to playing minesweeper.

==Transcript==
{{incomplete transcript|Do NOT delete this tag too soon.}}

[A "CAPTCHA" box.]

To proceed, click all the pictures of MINES

[A 4 by 4 ''Minesweeper'' field, with some cells revealed with numbers.]

<pre>
2 . 1 .
. . 3 .
3 . . .
. 1 . 1
</pre>

{{comic discussion}}

2089: Christmas Eve Eve

2018-12-24T14:59:11Z

Leduyquang753: /* Transcript */ Removed redundant "for".

{{comic
| number = 2089
| date = December 24, 2018
| title = Christmas Eve Eve
| image = christmas_eve_eve.png
| titletext = It turns out that saying "Oh, so THAT'S why they call it Boxing Day" is a good way to get punched a second time.
}}

==Explanation==
{{incomplete|Created by SANTA. There appears to be no explanation. Do NOT delete this tag too soon.}}

This comic was posted on December 24, 2018.

The day before a holiday, is often referred to as the "eve" of the holiday. Thus December 24 is Christmas Eve.
Some people (presumably including Randall) extend this and call December 23 "Christmas Eve Eve". We add one "eve" for each night before Christmas morning.

Cueball notes this, and Megan acknowledges this. Cueball follows by naming December 24 as Christmas Eve, December 25 as Christmas, and then mentions that the following day is his favorite.
Megan's "Oh no" implies that she knows what Cueball will say next.

Since December 26 is the 364th day before Christmas, it follows that December 26 is "Christmas eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve".

Cueball's friend Megan finds this fact unacceptable; as such, she announces that she will not give Cueball gifts.

The title text refers to the [[wikipedia:Boxing Day|Boxing Day]] holiday celebrated the day after Christmas in the UK and many parts of the former British Empire. In this title text we can presume Cueball was punched (or ''boxed'') after his litany of 364 “eves”, to which he replies “Oh, so that's why they call it Boxing Day” only to be boxed again.

==Transcript==
{{incomplete transcript|Do NOT delete this tag too soon. I demand a recount!}}

[Cueball, White Hat, and Megan stand in frame.]

Cueball: Today is Christmas Eve. Yesterday was Christmas eve eve.

Megan: Uh huh...

Cuball: Of course, tomorrow is Christmas. And then, my favourite...

Megan: Oh no.

Cueball: ...Christmas eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve eve!

[The "eve"s get smaller over time.]

Megan: I'm returning the presents I got you.

{{comic discussion}}