explain xkcd - User contributions [en]

3108: Laser Danger

2025-07-03T16:43:44Z

Darkmatterisntsquirrels: Added reference to 1463.

{{comic
| number = 3108
| date = June 27, 2025
| title = Laser Danger
| image = laser_danger_2x.png
| imagesize = 684x272px
| noexpand = true
| titletext = To combat the threat, many airlines are installing wing-mounted spray bottles.
}}

==Explanation==
{{incomplete|This page was created by A GIANT KITTEN WITH GIANT FRICKIN LASERS. Don't remove this notice too soon.}}
Shining a laser at a plane is a federal crime in the United States, and similarly proscribed in many other locations. A sufficiently powerful laser can disorient, distract and/or blind the pilot operating the aircraft. This can prove particularly dangerous to the safety of the aircraft and its occupants during take-off and landing, when planes are likely to have altitudes and orientations particularly susceptible to laser interference, and are phases that are already hazardous periods of flight. This 'use' of lasers was previously discussed in [[3030: Lasering Incidents]] and [[2481: 1991 and 2021]].

Megan claims that there's another reason why lasering a plane is illegal: to avoid provoking cats into leaping at them. Cats are known to [[729: Laser Pointer|chase and jump onto]] the dots created by laser pointers. Cats also prey on birds, with estimates of 1.3 to 3.7 billion birds killed each year. Of course, a cat would be unable to jump to the height of a flying plane{{Citation needed}}. If the cat were able to reach the plane, it would find itself hilariously outsized, though colliding with the plane mid-air could cause damage akin to a bird strike (e.g. shattered windshield or engine failure). The cat in the image is similar in size to the plane and thus could do significant damage. It is unclear whether the cat is unusually large or the plane is a model aircraft. A similar joke was used in the title text of [[1463: Altitude]].

The laser is shown in green, which have become more popular in recent decades as they offer the highest power for the lowest cost and are most frequently the type used in aviation related incidents.

The title text alludes to the fact that many cats do not like getting wet, and one of the methods people use to discourage them from a place or activity that is unwanted is to use spray bottles to wet their fur. The spray bottle might also emit a hissing sound, which cats associate with other cats threatening them. The "wing mounted spray bottles" on aircraft could be a reference to fuel dump tubes, which spray out fuel to lighten the aircraft, commonly used before emergency landings (especially soon after take-off, when a nearly full load of fuel is now more trouble than it should have been). To combat against actual physical threats to aircraft in real life, El Al (the Israeli national airline) and government aircraft {{w|Air Force One|used by heads of state}} often have various {{w|Flare (countermeasure)|countermeasures}} installed.

==Transcript==
: Megan: Shining laser pointers at planes is a federal crime. It's incredibly dangerous.
: Cueball: Oh, because it can blind the pilot?
: Megan: That's one reason...

: [A plane is shown, with a green laser pointer aimed at it.]

: [The laser disappears. A cat, approximately the same size as the plane, pounces on the plane and sends it tumbling.]

{{comic discussion}}<noinclude>

[[Category:Comics featuring Cueball]]
[[Category:Comics featuring Megan]]
[[Category:Aviation]]
[[Category:Cats]]
[[Category:Comics with color]]

1972: Autogyros

2024-12-16T01:22:27Z

Darkmatterisntsquirrels: Added meaning of "Light sport rule".

{{comic
| number = 1972
| date = March 26, 2018
| title = Autogyros
| image = autogyros.png
| titletext = I understand modern autogyros are much more stable, so I've probably angered the autogyro people by impugning their safety. Once they finish building the autogyros they've been working on in their garages for 10 years, they'll come after me.
}}

==Explanation==
[[Randall]] has been looking at the facts about [[wikipedia:autogyro|autogyro]]s, hence the title of the comic. He has drawn [[Megan]] flying in such a vehicle with several statements of the facts he has unveiled.

Randall states that an autogyro is nothing like a [[wikipedia:helicopter|helicopter]] (which it looks like), nothing like a [[wikipedia:airplane|plane]] (but flies like one) and works like a [[wikipedia:paraplane|powered parachute or paraplane]] (which it might kind of look like except without a parachute). He continues to make a total of 12 [[#Statements|statements]] which will be explained individually below.

The final statement at the bottom right is the punch line of how strange these flying machines are, because they are safe, as long as you do not do what a pilot instinctively would do in a plane in case of a stall because if you do so the autogyros will crash immediately... See the [[#Extremely safe|explanation below]]. That sentence is almost rendered unnecessary by the one above it that states that autogyros [[#Never stalls|never stall]]!

Randall's conclusion is clear: Autogyros are '''''weird'''''.

In the title text Randall continues on the last statement by saying that today, autogyros are much more stable. Which, presumably, must refer to how this was not always the case. This new stability, then, probably means that a [[#Never stalls|stall situation]] is much less likely and the last statement is not really all that relevant.

Randall then goes on to suggest that ''the autogyro people'' will be angered by this comic, which attacks the safety of their beloved machines. But he keeps on mocking them, stating that they will come after him, once they have finished building the autogyros they have been working on in their garages for the last 10 years. By this, he implies that the people who work on them do this as a home garage project, so they will never really be able to finish or fly them.

===Statements===
*Below, each statement in the comic is explained.
**The optimal reading order is to read them in the four columns they are arranged in:
**The left with four, the two single in the middle, and the six on the right.

;"Looks like a helicopter, but is nothing like a helicopter"

It is like a helicopter in the sense that a horizontally spinning fan provides the lift. It is unlike a helicopter because A) the fan is not powered, B) the fan does not provide forward propulsion, C) it is incapable of hovering, or moving in any other direction than forward.

;"Flies like a plane but is nothing like a plane"

Its flight pattern resembles a plane in that it can only move forward, turns by banking, and needs to maintain forward velocity in order to climb. However, unlike a plane, it can only maintain control when the rotor is loaded in the normal direction. Airplanes are "ok" when upside down, or when there's no load on the lifting surfaces. Autogyros lose control, much like a parachute under those circumstances.

;"Sort of like a powered parachute"

A [[wikipedia:paraplane|powered parachute]], also referred to as a PPC or paraplane, is a similar design except instead of a freely-rotating blade they are attached to a large parachute that acts like an airplane wing. As long as there is thrust the parachute will fill with air and maintain its wing-like characteristics, with the advantage of acting like a real parachute in the event of a loss of thrust (i.e. engine dies) wherein they come floating down at a speed significantly slower and more survivable than freefall. A single-seater can often be flown without a license and can be as inexpensive as $5,000 USD in parts.

;"Rare in the US, usually homemade. Common in Europe."

Autogyros are uncommon in the US because the light sport rule (a rule allowing people to operate certain lightweight aircraft with less stringent licensing requirements), contains nothing on autogyros, while there is a detailed section in the European version of the light sport rule so they would obviously be more common in Europe.

;"Big blade on top is not powered and spins freely"

The blades rotate due to the wind. Some autogyros use power to rotate the blade to speed before take-off but the power is removed for flight.

;"Can often be flown without a license"

Autogyros are frequently built as [[wikipedia:Ultralight aviation|ultralight]]s, and that group of aircraft are a special case where licenses are not needed. ([[wikipedia:Ultralight aircraft (United States)|In the US]], ultralights are aircraft that weigh less than 254lbs, carry less than 5 gallons of fuel, stall at less than 24kts, have a maximum speed of less than 55kts, and carry only the pilot.)

;"Cheap"
Helicopters are notorious for being extremely expensive to operate. At a typical general aviation service in the US, a two-seat aircraft may rent for under $100/hr, while a helicopter runs over $200/hr. Similarly, a small used helicopter may cost almost $200,000 while a small new autogyro may cost under $25,000. Since many people home-build their autogyros, it would often be even cheaper.

;"Needs a runway to take off, but not a long one"

An autogyro must be moving forward relative to airspeed in order for the rotor to generate lift. It needs a runway to take off, but with the extra lift provided by the rotors, the runway can be much shorter than a regular one.

;"Can land vertically"
An autogyro can land vertically: for that matter, so can any airplane. What matters isn't ground speed but airspeed, and as long as there's as much headwind as the landing airspeed of the aircraft, it will land vertically. Now, with fixed-wing airplanes, the landing speed is at least 40-50 mph, and you don't often find headwinds like that. The much lower landing airspeed of an autogyro makes vertical landings feasible.

;"Cannot hover"
True hovering would require the rotor to be powered. However, an autogyro must be moving forward relative to airspeed in order for the rotor to generate lift.

;"Never stalls"
Most conditions that would cause a [[wikipedia:Stall (fluid mechanics)|stall]] in a fixed-wing airplane such as low speeds, high-G maneuvers, and gusty winds don't apply to autogyros.
The rotor in an autogyro is in equilibrium, the inner, slower part is stalled, the middle part makes it spin and the outer, faster part slows down the rotor and provides lift. As the angle of attack increases, a fixed-wing aircraft would stall, however, on an autogyro, it will just make the lift-generating area smaller, causing the rotor to automatically spin faster and the equilibrium is restored.

This is not entirely correct, however. If you reduce the forward speed of an autogyro, the rotor slows down, reducing lift so the autogyro will descend. Under most circumstances, this would lead to a controlled landing. However, if it happens at a high altitude, you can run out of lift completely while still high above the ground causing a stall. This is more likely to happen if there is a strong tailwind.

;"Extremely safe, unless you do the ''one'' thing you instinctively do to escape a stall in a normal airplane, in which case it will crash immediately."

Autogyros are considered safe due to their slow landing speed, which is important in emergency landings, their forgiving behavior in windy conditions, and the fact they are almost impossible to stall. This is thanks to the freely spinning rotor. Unfortunately, as soon as the rotor stops spinning, the whole aircraft falls like a brick and the rotor may be impossible to restart in flight. This is a situation that should be avoided at all costs.

Normally it is not a problem since the weight of the aircraft keeps the rotor spinning. However, if the weight becomes too low or even negative, the angle of attack will become negative, and the rotor will slow down and eventually stop. It can happen when the pilot "pushes on the stick" and dives.

Unfortunately, "pushing on the stick" is also how you escape a stall in a fixed-wing (normal) airplane as it is a way to regain airspeed. This is actually a counter-intuitive maneuver but because a stall is an emergency, pilots are trained to do it instinctively. It can trick a pilot trained in fixed-wing aircraft into doing the one thing that shouldn't be done on a gyro.

==Transcript==

:[A picture of Megan wearing aviator goggles, sitting in an autogyro and holding the control stick. The autogyro is surrounded by sentence fragments, explaining its characteristics. The one above the blade that concerns the blade has an arrow pointing from the text to the blade. The sentences in columns from the left (i.e. first four sentences to the left, then two above the autogyro's body, and finally six sentences to the right):]
:Looks like a helicopter, but is nothing like a helicopter
:Flies like a plane but is nothing like a plane
:Sort of like a powered parachute
:Rare in the US, usually homemade. Common in Europe.
:Big blade on top is not powered and spins freely
:Can often be flown without a license
:Cheap
:Needs a runway to take off, but not a long one
:Can land vertically
:Cannot hover
:Never stalls
:Extremely safe, unless you do the '''''one''''' thing you instinctively do to escape a stall in a normal airplane, in which case it will crash immediately.

:[Caption below the panel:]
:Autogyros are '''''weird'''''.

{{comic discussion}}

[[Category:Comics featuring Megan]]
[[Category:Aviation]]

2966: Exam Numbers

2024-12-16T01:02:34Z

Darkmatterisntsquirrels: 37 linked to disambiguation, fixed.

{{comic
| number = 2966
| date = July 31, 2024
| title = Exam Numbers
| image = exam_numbers_2x.png
| imagesize = 553x400px
| noexpand = true
| titletext = Calligraphy exam: Write down the number 37, spelled out, nicely.
}}

==Explanation==
The comic depicts various similarly formatted examination questions that might appear on test papers at various points in a student's potential academic career. While they all share a similar feel, they are asking for different things, some of which might be considered more serious and examinable proofs of study than others. The joke is that the first and last questions are the same, but have very different interpretations based on the context.
{| class="wikitable"
|+ Exam numbers
! Exam level !! Question !! Answer
|-
| {{w|Kindergarten}} math || Write down the biggest number you can think of || At a kindergarten-level education, it is assumed that an individual might write down a relatively small number like 300, depending upon whether they have encountered the concept of hundreds. It might also be interpreted as "what's the highest number that you (think you) can count up to". Given the nature of a child's exuberant glee at learning about ''really'' big (but otherwise normal) numbers, they may even try an answer something like "a million billion squillion gazillion... and seven!". However, a kindergarten student is not likely to be able to write small enough to fit that number in the space provided; the largest numeral that will fit in a box of arbitrary size is consists of repeated ones, which are narrower than other digits, thereby allowing more digits to fit. It is not certain what criteria would be used to mark this question correct or otherwise, it may actually be a stealth question in child psychology or a question that everybody "gets right" so long as they answer it.

Although an advanced concept taught years later, infinity is not out of the question here, as employing it is often the only way to explain a substantial number of very simple math questions.
|-
| Pre-{{w|algebra}} || Write down the value of x if x=3x-8 ||

''3x'' refers to the multiplication of 3 and the originally unknown number ''x'', as a convenient shorthand.

By subtracting ''3x'' from both sides, ''-2x = -8''. Divide both sides by -2 to find ''x''=4. Alternately, subtract ''x'' from both sides to give ''0 = 2x - 8'', and as taking 8 from two ''x''s makes it zero, one ''x'' is half that

(Verify by plugging ''x''=4 into the original equation. '''4''' = (3*'''4''') - 8 -> '''4''' = 12 - 8 -> '''4''' = 4.)

4 is also the subject of [[221: Random Number]].

|-
| {{w|Calculus}} || Write down the value of <pre style="line-height: initial;">⌠π
│ x sin²x dx
⌡0</pre>||
The integral can be solved using {{w|List_of_trigonometric_identities#Power-reduction_formulae|a trigonometric identity}} and [https://math.libretexts.org/Bookshelves/Calculus/Calculus_(OpenStax)/07%3A_Techniques_of_Integration/7.01%3A_Integration_by_Parts integration by parts]:

<pre style="line-height: initial;">⌠π
│ x sin²x dx
⌡0

⌠π
= │ x (1−cos 2x)÷2 dx
⌡0

⌠π ⌠π
= ½│ x dx − ½│ x cos 2x dx
⌡0 ⌡0

│π ⌠π
= ¼ x² │ -¼│ x (sin 2x)′ dx
│0 ⌡0

│π │π ⌠π
= ¼ x² │ -¼ x sin 2x │ +¼│ (x)′ sin 2x dx
│0 │0 ⌡0

│π │π ⌠π
= ¼ x² │ -¼ x sin 2x │ +¼│ sin 2x dx
│0 │0 ⌡0

│π │π │π
= ¼ x² │ -¼ x sin 2x │ +⅛ cos 2x │
│0 │0 │0

= ¼ π² = 2.4674…
</pre>

|-
| PhD {{w|Cosmology}} || Write down the Hubble constant to within 1% || The Hubble constant is a component of {{w|Hubble's law}}, which describes the relationship between the distance between galaxies and their speed of separation. Its exact value is not known to this level of precision; it is ''about'' 70 (km/s)/Mpc. Different methods of measuring it have come up with significantly different values, with their own error bars, generally of 2% to 5% (both plus and minus, or asymmetrically, but with a similar overall range) and resolving this difference (the {{w|Hubble's law#Hubble tension|Hubble tension}}) is one of the great challenges of modern cosmology. Getting a PhD involves advancing the field, so it seems this particular PhD student has completed a thesis solving this problem. This question might have a different acceptable answer if asked again of the student, depending upon further developments in cosmology, and the 'constant' itself is supposed to change over cosmological time (the nature of this change being yet another subject requiring further study, calculation and observation).

What would a correct answer look like? Because of how {{w|significant digits}} are interpreted, 69 (km/s)/Mpc could be correct to within 1% while 70 is not.
|-
| {{w|Game Theory}} || Write down 10 more than the average of the class's answers || Game Theory studies "games" (and 'game-like' situations) in which two or more participants take actions that will succeed or fail based on other participants' decisions. In this case, all students' answers will be averaged (likely a simple {{w|arithmetical mean}}), and the best answer would be one that is 10 more than that average. For instance, if the answers end up being 30, 40, 50, 60, and 70, the mean would be 50, making 60 the best possible answer. As an individual test taker who doesn't know what your classmates are going to write down, the objective is to answer 10 more than your estimate of the average including your own guess, ''knowing that everyone else will be doing the same.'' Attempts at numerical solutions, including {{w|Monte-Carlo method}}s, will not converge because the problem as stated is unstable. The best answer will always be ten more than what the other students think the best answer is, and they have the same information as everyone else, which results in a contradiction.

However, the average of any set of numbers that includes infinity is infinity, and ∞ + 10 is still ∞. Something similar to this question is found in the title text of [[2385: Final Exam]].
|-
| Postgraduate Math || Write down the biggest number you can think of || This question echoes the very first example, but would be expected to be answered very differently (unlike a revisiting of most of the others).
Postgraduate math students can probably think of ''very'' large numbers. While a tempting answer could be "{{w|infinity}}", most mathematicians do not consider infinity to be a number,{{acn}} but rather a class of numbers. (Writing down "Infinity" in this context would be as wrong as writing down "Primes" or "Positive integers"). Even if infinity is an acceptable answer, some infinities are bigger than others. Students familiar with the field of [https://googology.fandom.com/wiki/Googology#History Googology] or [https://sites.google.com/view/transcology/lists/numbers Transcology] may give an answer such as {{w|Rayo's number}}, which was the winning entry in the [https://googology.fandom.com/wiki/Big_Number_Duel Big Number Duel].

This might heavily depend upon the branch of mathematics you are studying. Named (finite) numbers, or ones with specific and useful notations, might satisfy some questioning contexts, whilst the existence of a whole further set of trans-finite numbers (i.e. increasingly large types of "infinity") would be important considerations in others. For those associated with more computational mathematics, any infinity would be {{w|NaN|Not a Number}}, and their answer might instead be the ceiling of some binary representation (typically ''28n-1'' for some value of ''n''), the largest unsigned value reliably storable in a given byte form for an integer (e.g. a {{w|Integer (computer science)|double quadword}}). On the other end of the spectrum, many abstract algebraists might answer with some variation of "What ring are we working in, and is it even well ordered?" It also might be a trick question: if you can envision a real number greater than one, are you even doing real math (in a given field)?

As with the kindergarten question, there may be no previously anticipated "correct" answer. It could be another "correct just so long as you answer it" (or perhaps "sensibly" so) or the mark goes only to those giving the greatest valid number across all submissions.
|-
| {{w|Calligraphy}} (title text) || Write down the number 37, spelled out, nicely || Calligraphy is the art of artistic writing. The title text expands the joke outside the realm of math and points out that since calligraphy does not require any math skills, the only way a calligraphy exam would even mention numbers is if one had to write them out in such a way as to showcase their calligraphic skill and aesthetic judgement (choosing a form and adornment of script that is "nice", which may be a highly subjective choice). In this case, it could be rendered as "thirty-seven" or "thirty seven", or possibly, "one score and seventeen" in old-fashioned writing. The subject may choose to render it in a language other than English — for example "dau ar bymtheg ar hugain" would provide significant scope to show off calligraphic skill. {{w|37_(number)|37}} is a number that some people believe [http://thirty-seven.org mysteriously appears more often than it should]; this was a subject of a [https://www.youtube.com/watch?v=d6iQrh2TK98 recent Veritasium video].
|}

Note that "PhD Cosmology" and "Postgraduate Math", unlike the other items, aren't specific courses but instead refer to areas of study, and as such wouldn't have a exam (unless a PhD thesis defense is considered an "exam").

This style of final exam question, un-numbered and therefore possibly the ''only'' question upon the whole of each final paper, in some ways (for some instances) echoes the question "What is your name?" that Randall will be aware was the sole question given to Discworld's {{w|List of Discworld characters#Victor Tugelbend|Victor Tugelbend}} in an attempt to ensure he comprehensively passed (or utterly failed) his final student-wizard's exam, after many prior times of deliberately not-quite-passing.

==Transcript==
{{incomplete transcript|Do NOT delete this tag too soon.}}
:[6 different math test questions.]

:[The first panel:]
:Kindergarten math final exam
:Q. Write down the biggest number you can think of
:A. [empty box]

:[The second panel:]
:Pre-algebra final exam
:Q. Write down the value of x if x=3x-8
:A. [empty box]

:[The third panel:]
:Calculus final exam
:Q. Write down the value of [integral sign, from 0 to pi] x sin^2 x dx
:A. [empty box]

:[The fourth panel:]
:PhD cosmology final exam
:Q. Write down the Hubble constant to within 1%
:A. [empty box]

:[The fifth panel:]
:Game theory final exam
:Q. Write down 10 more than the average of the class's answers
:A. [empty box]

:[The sixth panel:]
:Postgraduate math final exam
:Q. Write down the biggest number you can think of
:A. [empty box]

{{comic discussion}}

[[Category:Math]]
[[Category:Cosmology]]
[[Category:Comics with lowercase text]]

3015: D&D Combinatorics

2024-11-23T01:36:43Z

Darkmatterisntsquirrels: Fixed transcript and made several edits to the explanation.

{{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 would roll a dice 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 dice, 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]]).

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

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

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-poisoned arrows is 2/9.

The Dungeon Master in this case 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 dice), 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.

==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: 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}}

Talk:3015: D&D Combinatorics

2024-11-23T01:29:11Z

Darkmatterisntsquirrels:

The bot originally created this page as “D Combinatorics”. I renamed it to the correct title and tried to get as many of the references as possible (including a few redirects). [[User:JBYoshi|JBYoshi]] ([[User talk:JBYoshi|talk]]) 00:54, 23 November 2024 (UTC)

What are the odds of rolling 16 or higher on 3D6+D4? 3D6 average 10.5, D4 average is 2.5, total average should be 13. I do not know how to proceed from here.

It seems like we edited the transcript at the same time. The odds of rolling 16 or higher in this situation seem to be 2/9? [[User:Darkmatterisntsquirrels|Darkmatterisntsquirrels]] ([[User talk:Darkmatterisntsquirrels|talk]]) 01:29, 23 November 2024 (UTC)

3015: D&D Combinatorics

2024-11-23T01:18:04Z

Darkmatterisntsquirrels: Added transcript (probably needs review)