explain xkcd - User contributions [en]

2768: Definition of e

2023-05-07T14:59:54Z

Quark: /* Explanation */ italic for n, leap years, increased accuracy for "less than one part per million", below 1‰ error for thirty years.

{{comic
| number = 2768
| date = April 26, 2023
| title = Definition of e
| image = definition_of_e_2x.png
| imagesize = 571x186px
| noexpand = true
| titletext = Yeah, my math teacher back in high school set up the system to try to teach us something or other, but the 100% rate was unbelievably good, so I engineered a hostile takeover of his bank and now use it to make extra cash on the side.
}}

==Explanation==
{{incomplete|Created by 2.718 BANKERS - Please change this comment when editing this page. Do NOT delete this tag too soon.}}
In this comic the teacher [[Miss Lenhart]] is asked by the student [[Hairy]] to explain what the constant ''e'' actually means.

The mathematical constant ''{{w|e (mathematical constant)|e}}'' is known as Euler's number. It is typically demonstrated in terms of compound interest. Here, Miss Lenhart seems to be setting up such an example, but in a typical Lenhart style she is actually asking her student to give her money.

The constant ''e'' can be described {{w|E (mathematical constant)#Compound interest|in the context of compound interest}}. For a bank account that pays interest at a rate of 100% per year, and that interest is paid ''n'' times a year and compounded, then a $1 deposit will grow to $1 * (1 + 100%''/n'')^''n'' after a year. As ''n'' approaches infinity (continuous compounding), the amount approaches ''e'' dollars. In the comic, minutely compounding is used as an approximation of continuous compounding; here ''n'' = 365 * 24 * 60 = 525,600 (527,040 for leap years with 366 days), and the resulting amount would be $2.7182792…, less than one part per million different from that of a straight multiplication by ''e'' (which is 2.7182818…).

As such, one would expect Miss Lenhart to say in the last panel something like "you'll have ''e'' dollars in a year". It is not clear if Miss Lenhart sees the growth of the deposited amount as answer enough to explain ''e'' or if she's just charging $1 for answering the question of what ''e'' is. The supposed interest rate the teacher can earn off this deposit, alone, is so high that the $1 principal will grow to over $22,000 in ten years, $485 million in twenty years, or $10.68 trillion in thirty years.

In the title text, a {{w|Takeover#Hostile|hostile takeover}} is an acquisition of a company against its management's wishes, by simply buying up its shares from its shareholders. A bank offering accounts with an {{w|APY}} of 172% is certain to go bankrupt almost immediately, making it a very bad investment. Banks earn money by lending at a higher rate than they pay on deposits, but it is illegal in some jurisdictions to charge such high interest rates on loans, and no one would take them anyway. Therefore the bank will lose huge amounts of money on deposits while earning essentially no revenue. The off-comic speaker is effectively buying out the bank in order to drain it of its own funds, which is financially pointless, and may also be illegal. Alternatively, their plan may be to buy 51% of the stock, then attempt to extract a majority of the bank's reserve funds through huge high-interest deposits, which is still not profitable, since banks hold only a small fraction of deposits in reserve, and their market capitalizations (the cost of buying all the stock) are much higher than their total reserves. Even if for some reason this bank had a very high reserve ratio, and this tactic could somehow be profitable, it would usually still be illegal, effectively robbing the other 49% ownership of its equity through deliberately bad management.

In the title text, Randall may have also just confused a couple concepts. A bank offering a 100% rate (assuming somehow sustainably) would be an incredibly good place to open a checking or savings account, and a rational actor would shovel as much money as possible into such an account at this bank. Randall may have simply misused the term "hostile takeover," which would not yield any of the benefits of the 100% rate, as mentioned above, when he really meant to colloquially describe a scenario in which one would aggressively exploit the bank's 100% rate for one's own benefit. (A perhaps unintuitive aspect about banks that might have tripped up Randall is that "assets" in other contexts become liabilities for banks and vice versa. So customer deposits become liabilities upon which a bank would have to pay such an incredibly high rate, and loans, which are traditionally considered liabilities, are assets from which banks derive income.)

The teacher who inadvertently sparked this action, male, was clearly not Miss Lenhart, who may be better at providing more memorable (if somewhat non-standard) lessons. And, as the speaker cannot even recall what the point was of the original mathematical example, it is possible that they have insufficient understanding of the numbers involved and why their attempt to profit will turn out to be ultimately illusory. A similar lack of successful education in the subjects of business and/or law could also likely come back to bite them, sooner or later.

==Transcript==
:[Hairy is seated behind a classroom desk with his hand raised asking the teacher Miss Lenhart a question. She is standing in front of him with a board behind her. Beneath the board there are ledge with writing tools on it (markers or chalk).]
:Hairy: Can you explain what the constant ''e'' actually ''means?''
:Miss Lenhart: Sure.

:[Zoom in on Miss Lenhart's upper half, as she raises one hand palm up.]
:Miss Lenhart: I have a bank account that pays 100% annual interest, compounded every minute.

:[In a frame-less, and very slim panel, Miss Lenhart is shown holding a hand up in a fist.]
:Miss Lenhart: If you deposit $1 now,

:[Miss Lenhart now has both arms down as she continues to address the off-panel Hairy.]
:Miss Lenhart: I will answer your question.

{{comic discussion}}

[[Category:Comics with lowercase text]]
[[Category:Comics featuring Hairy]]
[[Category:Comics featuring Miss Lenhart]]
[[Category:Math]]

2007: Brookhaven RHIC

2018-06-17T10:27:44Z

Quark: /* Explanation */ fix direction

{{comic
| number = 2007
| date = June 15, 2018
| title = Brookhaven RHIC
| image = brookhaven_rhic.png
| titletext = "Buddy, you trying to pull something? I can't buy this gold--all the electrons are missing. I could face serious charges!"
}}

==Explanation==
{{incomplete|Someone could probably calculate the revenue of this proposed project... And I think we need to mention a few other comics involving absurd research proposals. Do NOT delete this tag too soon.}}
The {{w|Relativistic Heavy Ion Collider}} is a particle accelerator designed to collide gold ions together at incredibly high speeds. This is normally done to study particle physics - the high-energy collisions allow us to learn more about how subatomic particles behave.

[[Randall]] proposes that, instead of using the beam of gold ions for particle collisions, it should be diverted and sold at cash-for-gold stores to make money. He proposed damaging part of the circular particle accelerator to add a diverter, so he can direct the gold ion beam to the three stores. It is unclear, however, how he would manage to transport the gold to the stores, as once it leaves the circular particle accelerator, parts of the beam are not in an enclosed space, and would likely collide with something. It would also cause problems once it reached the stores.

The joke is that because they are traveling at relativistic speeds, the mass of the particles being sold will be much more than the mass of the ions being supplied to the collider's input. However, it would be very difficult to sell a beam of charged particles{{Citation needed}}, and the amount of gold involved is below microscopic scales. That, and the fact that he is trying to misuse the particle accelerator for his own profit, is the reason why Brookhaven rejected Randall's proposal. Also, the energy used by the particle accelerator would cost more than the revenue from selling the gold.

Randall has done many comics describing impractical research proposals in the past.

The title text imagines the owner of the stores complaining about the sale, not because of impracticality, but because Randall tries to sell gold ions with the entire positively-charged nucleus of the gold atom with all 79 electrons stripped from it instead of normal, electrically neutral gold atoms. This is also a pun on the word "charges", which could refer to {{w|electric charge}} or to {{w|criminal charge|criminal charges}}.

This is an actual map of the area around {{w|Brookhaven National Laboratory}}, with east at the top. The cash for gold stores depicted in the comic are, from left to right:

* New York Gold Center, 451 Glen Dr Ste D, Shirley NY 11967-1100
* Cash for Gold, 969 Montauk Hwy, Shirley NY 11967-2111
* Enrico's Jewelry Exchange, 442 William Floyd Pkwy, Shirley NY 11967-3454

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

:[A single panel contains a simplified overhead map view of the Brookhaven Relativistic Heavy Ion Collider and some of the surrounding area. The map is rotated 90°; north is to the left. The collider is located on the left hand side of the image as a yellow beam (representing the Gold ions) outlined in black. Parts of the collider are are labeled and there are light gray arrows indicating the direction of travel for the ions. At the bottom of the main accelerator ring there is a diverter that splits the ion beam and directs it towards a set of three Cash for Gold stores, passing through a more diverters along the way. Each Cash for Gold store is represented with a yellow burst and is marked with a Google maps style "store" locator pin. The following labels are written on the map.]

:Brookhaven Relativistic Heavy Ion Collider
:Gold Ion Source
:Accelerator Ring
:Diverter
:Gold Ion Beam

:[There are arrows coming from this label pointing at each store]
:Cash for Gold Stores

:[Caption below the panel:]
:Sadly, Brookhaven rejected my proposed experiment

{{comic discussion}}

[[Category:Physics]]
[[Category:Science]]
[[Category:Comics with color]]

388: Fuck Grapefruit

2016-07-03T11:59:00Z

Quark: /* Table */

{{comic
| number = 388
| date = February 25, 2008
| title = Fuck Grapefruit
| image = fuck_grapefruit.png
| titletext = Coconuts are so far down to the left they couldn't be fit on the chart. Ever spent half an hour trying to open a coconut with a rock? Fuck coconuts.
}}

==Explanation==
This comic consists of a chart where [[Randall]] has plotted {{w|fruits}} according to two criteria: ease/difficulty to eat on the horizontal axis, and tastiness on the vertical axis. The Y-axis goes from "tasty" at the top, to "untasty" at the bottom. The X-axis goes from "easy" on the right to "difficult" on the left.

For instance, {{w|pineapples}} are deemed fairly tasty but very difficult to eat, whereas (seeded) {{w|grapes}} are very tasty and somewhat easy, and logically {{w|Grape#Seedless_grapes|seedless grapes}} are roughly equally tasty but easier to eat.

Obviously being easy to eat is preferable to being difficult, and being tasty is preferable to being untasty, so the "best" fruits (regarding these two aspects only) are in the top-right corner, and the worst in the bottom-left; additionally, in the top-left corner are the "difficult-but-worthy" fruits, and in the bottom-right one, the "not-so-tasty-but-easy-anyway" ones.

The individual ratings of each fruit are subjective; very obviously in the case of tastiness, and more subtly for difficulty. Randall does not explain his criteria for ranking the difficulty of each fruit, and it is likely based on simply personal experiences. Someone who has grown up in an area where pineapples are plentiful is likely to be more adept at skillfully preparing them. The discrepancies between how Randall has rated certain fruits and how others believe they should have been rated caused a [[#Controversy|surprising level of controversy]].

According to the chart, {{w|Grapefruit}} is the third hardest fruit to eat as well as the second least tasty fruit (from the ones listed at least). Eating one of them is like spending too much of one's time and energy without much reward. Hence Randall's quip in the title: "Fuck grapefruit".

In the title text Randall mentions {{w|coconuts}}. Randall mentions that he would have to put them so far down to the left on the chart (not far down, just far down towards the left), that they would not fit in this chart. He thus states that it is so much more difficult to eat (especially to open) coconuts than the usual mainstream fruits such as the ones plotted here. If he did include coconuts in the chart the rest of the fruits would all be pushed to the right side of the chart. He does not say that he does not like to eat the fruit. (Although it has "{{w|nut}}" in its name, the coconut is actually a {{w|Drupe|stone fruit}} and thus belongs on a chart of fruit.) Having spent half an hour trying (in vain?) to open a coconut, Randall also only has one thing to say about them: "Fuck coconuts".

In [[1701: Speed and Danger]] another scatter plot shows exactly what happens when one point is inserted into such a plot if it is far removed from all the other points, in this case even on both axis.

===Table===
The table below lists approximate coordinates for each fruit using a scale of -100% (untasty/difficult) to 100% (tasty/easy). The coordinates are based on the included fruits, any new items added outside the current range (e.g. Coconuts) would cause the scales to be reassigned, and thus change the coordinate values of existing items.

The coordinates have been found by measuring each fruit from the center of the drawing (not center of mass, but center from left to right/top to bottom) to the two axes. The axes are hand drawn which is clearly visible. The numbers have been obtained be measuring to the nearest point of each axis, not taking into account that the axes are not perfect straight perpendicular lines.

{| class="wikitable sortable"
! Tastiness !! Easiness !! Fruit !! Comments
|-
| 100% || 68% || {{w|Peaches}} || Among Randall's favorite fruits, as it is the one deemed most tasty and it is far more tasty than the four fruits that are deemed easier to eat. While it does contain a stone/pit which may be annoying due to disposal of the sticky remains, it's large enough to eat around and Randall apparently sees it not to be that big a problem in the long run.
|-
| 85% || 13% || {{w|Grape|Seeded grapes}} || It is unclear why seeded grapes are shown as tastier.
|-
| 75% || 75% || {{w|Strawberries}} || Actually not a berry but an {{w|accessory fruit}}, like many of the other fruits on the chart
|-
| 72% || 100% || {{w|Grape#Seedless_grapes|Seedless grapes}} || It is unclear why seeded grapes are shown as tastier.
|-
| 68% || -100% || {{w|Pineapples}} || Requires a knife to prepare, and can be tricky to dissect without wasting a lot of the fruit.
|-
| 58% || 87% || {{w|Blueberries}} || Usually not listed as a fruit but as a {{w|berry}} although this is still a type of fruit.
|-
| 38% || 42% || {{w|Cherries}} || Containing a stone/pit which may be annoying due to disposal of the sticky remains and taking care not to swallow them.
|-
| 37% || 66% || {{w|Pear}}s || Most people will not eat the core of the pear and is thus left with some sticky part that need to be disposed.
|-
| 22% || 79% || {{w|Green apples}} || Most people will not eat the apple core and is thus left with some sticky part that need to be disposed. It is unclear why green apples are shown as tastier than red.
|-
| 17% || 59% || {{w|Plums}} || Containing a stone/pit which may be annoying due to disposal of the sticky remains and taking care not to swallow them.
|-
| 15% || -20% || {{w|Watermelons}} || Surprisingly considered by Randall to be easier than oranges, which are fairly easy to peel. A watermelon is larger, so the effort to reward ratio is better, but this should't affect its 'ease of eating' position. On the other hand, it is easy to cut a watermelon into edible pieces. You cannot cut an orange like this and they can sometimes be very difficult to peel and you will get very sticky when trying. This can be avoided with the watermelon.
|-
| -12% || 79% || {{w|Apple|Red apples}} || Most people will not eat the apple core and is thus left with some sticky part that need to be disposed. It is unclear why green apples are shown as tastier than red; in his "What If?" book, Randall mentions a specific dislike of "red delicious" apples.
|-
| -18% || 16% || {{w|Bananas}} || Shown in the chart as difficult to eat, even though they are among the most easily peeled fruit. This could be because of the skin which must be disposed of, or the stringy pith which some people refuse to eat and thus have to pick off. Also you do have to peel it, which is not the case for the easier fruits.
|-
| -20% || -85% || {{w|Pomegranates}} || Pomegranates have a very large number of inedible seeds.
|-
| -46% || -49% || {{w|Oranges}} || Considered more difficult than lemons, perhaps due to the layer of pith which is rarely encountered when preparing lemons.
|-
| -74% || 26% || {{w|Tomatoes}} || The culinary arts, nutritional sciences, and United States tax and customs regulations all treat tomatoes as a {{w|vegetable}}, mostly due to its taste. In the botanical sense however, it is actually a fruit (specifically, a {{w|berry}}).
|-
| -86% || -75% || {{w|Grapefruit}} || A very difficult fruit to peel, and thus eat, and also deemed very untasty.
|-
| -100% || -15% || {{w|Lemons}} || Considered easier than oranges, perhaps due to the layer of pith which is rarely encountered when preparing lemons.
|}

===Controversy===
As evident from the above section, and according to [http://blog.xkcd.com/2008/02/25/fruit-opinions/ FRUIT OPINIONS!] on the [http://blog.xkcd.com/ Blag], this was the most controversial comic written to this point, ''beating out comics about cunnilingus, the Obama endorsement, and my making 4chan tiny on the map of the internet''.
*{{w|Cunnilingus}} see [[136: Science Fair]].
*{{w|List of Barack Obama presidential campaign endorsements, 2008|The Obama endorsement}} See [http://blog.xkcd.com/2008/01/28/obama/ Politics] also from the Blag.
**The only comic mentioning {{w|Obama}} before this comic was [[360: Writers Strike]].
*{{w|4chan}} is tiny on the map of the internet called [[256: Online Communities]]. (See the small island to the far right - left of "dragons" in the sentence ''Here there be anthromorphic dragons''.)
**Not to be confused with the comic that is actually named [[195: Map of the Internet]].

==Transcript==
:[An X-Y scatter plot of fruit where both axes have arrows in both ends. At the end of each arrow is a label.]
:[The X-axis from left to right:]
:Difficult
:Easy
:[The Y-axis from top to bottom:]
:Tasty
:Untasty

:[The fruit names are listed here below from top to bottom according to the how tasty the fruit is, not necessarily in the same order that the names are written if one fruit is tall/large and the other low:]
:Peaches
:Seeded grapes
:Strawberries
:Seedless grapes
:Pineapples
:Blueberries
:Cherries
:Pears
:Green apples
:Plums
:Watermelons
:Red apples
:Bananas
:Pomegranates
:Oranges
:Tomatoes
:Grapefruit
:Lemons

{{comic discussion}}

[[Category:Comics with color]]
[[Category:Scatter plots]]
[[Category:Rankings]]
[[Category:Food]]