explain xkcd - User contributions [en]

Talk:2754: Relative Terms

2023-03-25T21:56:03Z

172.69.34.10:

Does this mean that the steam calliopes which are as loud as an airplane are LARGER than that airplane? I'm not finding any examples of such. [[User:Ikidre|Ikidre]] ([[User talk:Ikidre|talk]]) 01:31, 25 March 2023 (UTC)

Holy shit what a terrible comic [[Special:Contributions/172.68.58.130|172.68.58.130]] 02:24, 25 March 2023 (UTC)
:I've seen many a terrible comic and I personally don't consider this one to be terrible, but relative to other XKCD comics I would consider it one of the least interesting and entertaining, unfortunately. [[Special:Contributions/172.70.38.230|172.70.38.230]] 15:44, 25 March 2023 (UTC)

I'm somewhat terrified that "Statue" isn't considered *maximally* quiet. [[User:Trimeta|Trimeta]] ([[User talk:Trimeta|talk]]) 02:32, 25 March 2023 (UTC)
:I don't think the position in the quadrants is meant to indicate degree of loudness or size. [[User:Barmar|Barmar]] ([[User talk:Barmar|talk]]) 04:07, 25 March 2023 (UTC)
::Yes it is, that's how such graphs work. That's why sewing machine is in the middle, Randall is declaring that it's neither small nor big, and neither quiet nor loud, it's medium on both scales. Comics like this are roughly the standard X-Y graph but without numbered scales and having words instead of points. And I too noted that statues aren't maximum quiet, LOL! Maybe he's referring to the Doctor Who Weeping Angels? DO they make any sound? [[User:NiceGuy1|NiceGuy1]] ([[User talk:NiceGuy1|talk]]) 05:29, 25 March 2023 (UTC)
:::Well, that may be how such graphs sometimes work, but clearly not this one. The quadrants are positioned relative to the sewing machine, but that appears to be the only significance afforded to positioning in this layout - an item's position within its quadrant does not indicate the degree to which it qualifies as belonging there. Otherwise a firecracker and a blender would be quieter than a cricket. Unless Randall is referring to the crowd at a test match. But that seems pretty unlikely.[[User:Yorkshire Pudding|Yorkshire Pudding]] ([[User talk:Yorkshire Pudding|talk]]) 10:20, 25 March 2023 (UTC)
::::The fact that xkcd charts usually have arrows on the axes when the position within the quadrant does matter would support this claim. [[User:NcPenguin|NcPenguin]] ([[User talk:NcPenguin|talk]]) 16:45, 25 March 2023 (UTC)
:::::Came here to point out that I’ve heard a mouse that somehow got in scritch-scritching n something in my kitchen, and I’ve heard a butterfly that somehow got in battering against a window trying to get out, but I’ve never in my life heard an ant, nor even a hundred ants working together to wreck stuff. But as you pointed out, there are no arrows on the chart, so the positions in the quadrants probably aren’t intended to be meaningful.[[Special:Contributions/172.69.34.10|172.69.34.10]] 21:56, 25 March 2023 (UTC)

:::Gartner Magic Quadrants include arrows on the axes, e.g. "completeness of vision -->" and "ability to execute-->". This is not that. However it is '''mostly''' implied by the contents of each quadrant that the items are arranged smallest to biggest (top-down) and quietest to loudest (left-to-right). I think for those who study the items carefully, this then introduces some situational irony for comedic effect in the way of the unexpected placement of certain items like "statues" (louder than a Giraffe?), "baby" (smaller than a harmonica?), and "cannon" (quieter than a riding mower?). Additionally, having spent time in a quiet room with a cricket, I think the "maximally loud" position of the cricket here feels about right. [[Special:Contributions/172.70.179.61|172.70.179.61]] 16:44, 25 March 2023 (UTC)

I've always considered a microwave oven to be the central item
: I concur that microwave would be excellent in the center, and less ambiguous (I mean, I feel certain that Randall didn't think of industrial sewing machines, but this community loves being uncertain, LOL!) [[User:NiceGuy1|NiceGuy1]] ([[User talk:NiceGuy1|talk]]) 05:22, 25 March 2023 (UTC)

AFAIK, only Randall/xkcd uses the term "Bun" to mean bunnies... :) I feel like it should be worded that way. [[User:NiceGuy1|NiceGuy1]] ([[User talk:NiceGuy1|talk]]) 05:22, 25 March 2023 (UTC)
:No, it's very common in the furry community, and I swear I've heard it elsewhere as well. [[Special:Contributions/172.70.230.72|172.70.230.72]] 12:03, 25 March 2023 (UTC)

Is the breadbox no longer the standard item for size comparison? Because I still use it that way. [[User:Mathmannix|Mathmannix]] ([[User talk:Mathmannix|talk]]) 12:43, 25 March 2023 (UTC)

Is the moon really bigger than the northern lights? [[Special:Contributions/172.70.126.117|172.70.126.117]] 17:39, 25 March 2023 (UTC)
:Hmmmm... I wonder. Well, the Moon is a tad under 3,500km (diameter). Taking just a single pole's Aurora (combined, you could just say they are approx. Earth's diamater, which is bigger than the Moon,{{Citation needed}} going pole-to-pole) the height is the thickness of the (upper) atmosphere, very much of that below the altitude of satellites (e.g. ISS), which is mere hundreds of km at best. Or take its 3-6 degrees of 'band width', that is perhaps a tad over 300-600km thick. But if we go with its extent all the way round off the pole, it seems to get about the size of the Moon (linear distance, not 'over the pole') once it extends by 15-16 degrees of latitude (i.e. to less than 74 degrees N/S). It is generally accepted that it varies between 10 and 20 degrees from each geomagnetic pole (is seen at lower latitudes, but only above the horizon) so... it's a close thing. If I've done my calculations correctly. [[Special:Contributions/162.158.34.235|162.158.34.235]] 18:58, 25 March 2023 (UTC)

2719: Hydrogen Isotopes

2023-01-03T02:23:14Z

172.69.34.10: Copyedit

{{comic
| number = 2719
| date = January 2, 2023
| title = Hydrogen Isotopes
| image = hydrogen_isotopes_2x.png
| imagesize = 442x250px
| noexpand = true
| titletext = Oops, All Neutrons is also known as Neutral Quadrium, Nydnonen, and Goth Tritium.
}}

==Explanation==
{{incomplete|Created by a BREAK ROOM DE BROGLIE MICROWAVE USER. Do NOT delete this tag too soon.}}

{{W|Hydrogen}} is the simplest of the chemical atoms, usually consisting of a single electron orbiting a single proton. , for This comic imagines other humorous fictional forms of hydrogen.

'''Hydrogen'''
This is the most common isotope of hydrogen, with one proton and one electron, shown with the electron "orbiting" the proton.

'''Deuterium'''
This is the second most common isotope of hydrogen, with one electron, and both a neutron and proton in it's nucleus. About five hundredths of the hydrogen in water on Earth is deuterium.

'''Tritium'''
This is the third most common isotope of hydrogen, with one electron, and a nucleus of one proton and two neutrons, for an atomic mass of three {{w|Dalton}}s.. It is radioactive with a half-life of about twelve years. It is quite rare.

'''Ium'''
This is not an actual isotope of hydrogen (as are the rest of them, excluding maximum strength hydrogen), and is one imagined by Randall. It consists of one electron orbiting around nothing. The name likely relates to the fact that the past two isotopes consist of a suffix and "ium". Thus, hydrogen with only and electron in it would be called ium.

'''Wheelium'''
This isotope consists of a proton, electron, and neutron orbiting around nothing. It is likely called wheelium as it is shaped similarly to a wheel.

'''Instant Hydrogen (ready in 15 minutes)'''
This isotope consists of a single neutron. The title likely refers to how neutrons will on average take fifteen minutes to decay into a proton, an electron, and a neutrino, which would then form a hydrogen atom.

'''Hydrogen (Maximum Strength)'''
This isotope consists of a proton, an electron, and at least 13 neutrons. This isotope would decay quite quickly. The title likely refers to the fact that it is filled with neutrons, and is thus "Maximum Strength".

'''Oops, all neutrons'''
This isotope consists of four neutrons, with one orbiting around a group of three. It is likely to be a joke about an error, where, the creator (of these atoms) made an atom entirely out of neutrons.

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

{{comic discussion}}

Talk:1447: Meta-Analysis

2022-09-14T20:34:38Z

172.69.34.10: /* How much paper is there? */ reply

What is this "Medline, Embase and Cochrane" ? Thanks. Dams. {{unsigned ip|108.162.254.30}}
:Databases of Medical Publications [[Special:Contributions/108.162.254.30|108.162.254.30]] 08:19, 14 November 2014 (UTC)
:Medline[http://www.medline.com/], Embase[http://www.elsevier.com/online-tools/embase/about] and Cochrane[http://www.cochrane.org/] are medical research databases. You can find there studies on various drug uses or treatment plans. A useful information source if you want to compare studies on use of Allopurinol for chronic gout or else. [[User:Jkotek|Jkotek]] ([[User talk:Jkotek|talk]]) 08:28, 14 November 2014 (UTC)
::Seems to me that should be in the explanation, no? -- [[User:Brettpeirce|Brettpeirce]] ([[User talk:Brettpeirce|talk]]) 15:03, 14 November 2014 (UTC)
Would it be helpful to include a breakdown of the terms?
*Meta-Analysis = "We searched M, E, & C for [keyword]"
*Meta-Meta-Analysis = "We searched M, E, & C for 'We searched M, E, & C for [keyword]'"
*Meta-Meta-Meta-Analysis = "We searched M, E, & C for 'We searched M, E, & C for 'We searched M, E, & C for [keyword]""
[[User:Smperron|Smperron]] ([[User talk:Smperron|talk]]) 08:46, 14 November 2014 (UTC)

Your paper is rejected. //"TOO META"--[[User:Theme|Theme]] ([[User talk:Theme|talk]]) 08:49, 14 November 2014 (UTC)

IMHO a better would be this:
*Meta-Analysis = "We searched M, E, & C for [keyword] and compared results between each other"
*Meta-Meta-Analysis = "We analyzed how others 'search the M, E, & C for for [keyword] and compare the results'"
*Meta-Meta-Meta-Analysis = "We analyzed how other 'analyze how others search the M, E, & C for for [keyword] and compare the results'"
too meta [[User:Jkotek|Jkotek]] ([[User talk:Jkotek|talk]]) 15:22, 14 November 2014 (UTC)

I don't understand this explanation! Why isn't there an "Explain Explain XKCD" site? --[[User:RenniePet|RenniePet]] ([[User talk:RenniePet|talk]]) 23:43, 15 November 2014 (UTC)
:I don't understand this comment! We need a Explain XKCD comment comments section!--[[Special:Contributions/108.162.231.199|108.162.231.199]] 09:51, 19 November 2014 (UTC)

It seems that Randall actually enjoys rejections. [[Special:Contributions/173.245.50.139|173.245.50.139]] 03:18, 18 November 2014 (UTC)

The term "too meta" means that something is too self referential. Not "so abstract that they can't be easily interpreted." {{unsigned ip|108.162.254.88}}
:Actually, if we stick to the greek root, "meta" simply signifies "beyond", or "after". So, by adding level after level of analysis, by going beyond single studies, and single studies of single studies, it is truly becoming "too meta", too grand. [[Special:Contributions/108.162.229.207|108.162.229.207]] 21:17, 31 March 2015 (UTC)
:My interpretation is that it could mean both. For example, "too meta" = "the strenght of meta is too high" for being too self referential or "too meta" = "there's too many metas" for the excess or abstraction. I'm now experiencing {{w|Semantic satiation}}. [[Special:Contributions/188.114.99.189|188.114.99.189]] 18:43, 1 December 2015 (UTC)

== How much paper is there? ==

If the paper is a meta-meta-meta-analysis, then the paper is discussing the paper is discussing the paper? Is the Methods section (near-)infinite? How much paper does Randall have? [[Special:Contributions/108.162.246.164|108.162.246.164]] 17:22, 14 September 2022 (UTC)
:Papers are mostly paperless these days. [[Special:Contributions/172.69.34.10|172.69.34.10]] 20:34, 14 September 2022 (UTC)

2658: Coffee Cup Holes

2022-08-13T16:55:42Z

172.69.34.10: /* Explanation */ no question, because practical reality is always geometric (maybe some information theoretical exceptions exist)

{{comic
| number = 2658
| date = August 12, 2022
| title = Coffee Cup Holes
| image = coffee_cup_holes.png
| titletext = Theoretical physicist: At the Planck length, uncountably many.
}}

==Explanation==
{{incomplete|Created by a CAFFEINE MOLECULE WITH A HOLE DRILLED IN ITS SIDE. Do NOT delete this tag too soon.}}

This comic depicts people in different fields of study answering the question, "How many holes are there in a coffee cup?" This question can have multiple interpretations, in particular concerning the definition of a hole.

[[File:Mug and Torus morph.gif|thumb|150px|The coffee mug and donut shown in this animation both have topological genus one.]]

[[Ponytail]], a {{w|topology|topologist}}, states the coffee cup belongs in the {{w|Genus (mathematics)#Topology|genus}} of one hole. A common joke is that topologists can't tell the difference between a coffee cup and a donut since they're homeomorphic to each other — they have the same genus. From the topologist's point of view, the coffee cup definitely has one hole. See [[2625: Field Topology]] for more information about topology.

[[Hairy]], a normal person, is not sure (the acronym "IDK" stands for "I don't know") and asks for clarification about whether the opening at the top counts as a hole. This shows flaws in the question, which suffers from the mathematically imprecise, ambiguous common usage of the word hole. Topologists would refer to the opening as a concavity, not a hole, and while they consider such geometrical properties generally outside their field, most practical applications of topology do involve geometric components.

[[File:Double torus illustration.png|thumb|left|150px|A genus two surface]]

[[Hairbun]], a philosopher, answers the question with an elucidating counter-question, considering a hypothetical scenario. Drilling a new hole should increase the number of holes by one, and after the hole has been drilled, a common teacup or mug has two holes according to topologists. Since drilling a hole increases the number of holes by one,{{cn}} the philosopher's question requires the original questioner to reveal the answer to their own question. Also, she asks how many holes there are ''now'' rather than ''after we do that'', an ambiguity.

[[Image:Point cloud torus.gif|thumb|150px|A point cloud of a genus one surface]]

[[Cueball]], a chemist, looks at the coffee in the cup on a molecular level, which means it has very many holes: 1,000,000,000,000,000,000,000 (1021 or 1 sextillion) “in the [https://chemapps.stolaf.edu/jmol/jmol.php?model=CN1C%3DNC2%3DC1C%28%3DO%29N%28C%28%3DO%29N2C%29C caffeine] alone.” The implication is that there are more in the cup itself, depending on what material it’s made out of. Also, the coffee itself could have other holes, depending on the type of coffee. For example, espresso contains significant amounts of niacin and riboflavin, each of which has at least one hole in its chemical structure. However, this ignores the fact that bonds are not discrete sticks as portrayed in many molecular models. The "holes" in the middle of a caffeine molecule are not completely empty but instead merely have lower electron densities/probabilities. So the point-cloud duality of {{w|Bonding molecular orbital|electron orbitals and bonds}} might not satisfy a topologist's, normal person's, or philosopher's criteria for a connected substrate in which holes may be formed.

[[Image:World lines and world sheet.svg|left|thumb|150px|{{w|String theory}} describes the {{w|worldline}}s of point-like particles as {{w|worldsheet}}s of "closed strings," forming topological holes.]]

In the title text, a theoretical physicist looks even deeper, at the subatomic scale of {{w|Planck units}}. Since fundamental particle interaction is governed by fundamental forces and collision (per the {{w|Pauli exclusion principle}}) instead of tensile or ductile solid connectedness, the theoretical physicist posits that any definition providing for a single hole would also describe a number of holes akin to the factorial of the number of particles in the universe, or at least within the cup's {{w|light cone}}, which is a number impractical to accurately count, but not uncountable in a mathematical sense.

Part of the joke could be that all five methods of inquiry don't discern between a {{w|cup}} (as described) and a {{w|mug}} (as depicted), the cliché being that topologists are unusual because they don't. Or, as many people use the terms interchangeably, [[Randall]] may too.

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

:[The first panel has text only. The "Q:" below is a large letter Q representing a question, not a character name.]
:Q:
:How many holes are there in a coffee cup?

:[Each of the next four panels has a caption at the top to indicate the kind of person answering the question.]
:Caption: Topologist
:[Ponytail stands holding a coffee mug.]
:Ponytail: One.

:Caption: Normal person
:[Hairy stands to the right of Ponytail, holding a coffee mug at an angle to look into it.]
:Hairy: IDK, does the opening count as a hole?

:Caption: Philosopher
:[Hairbun is shown in closeup, with two drawings of coffee mugs to her left.]
:Hairbun: To answer that question, consider another: If we drill a hole in the side, how many holes are there now?

:Caption: Chemist
:[Cueball stands with a drawing of a caffeine molecule above him and to the right.]
:Cueball: 1021 in the caffeine alone

{{comic discussion}}
[[Category:Comics featuring Ponytail]]
[[Category:Comics featuring Hairy]]
[[Category:Comics featuring Hairbun]]
[[Category:Comics featuring Cueball]]
[[Category:Math]]
[[Category:Food]]
[[Category:Science]]
[[Category:Chemistry]]
[[Category:Philosophy]]

Talk:2657: Complex Vowels

2022-08-11T07:57:12Z

172.69.34.10: reply

Spoken symbol bears resemblance to 🜏, https://en.wiktionary.org/wiki/%F0%9F%9C%8F
:Not really, it's closer to 'əG.' [[Special:Contributions/172.69.33.25|172.69.33.25]] 01:15, 11 August 2022 (UTC)
::Looks like ꬱ to me. Plus some diacritics sprinkled over it, of course. It does look ''similar'' to 🜏 when you include the zalgo. [[Special:Contributions/172.71.98.99|172.71.98.99]] 06:53, 11 August 2022 (UTC)

sscchhwwaa is easy, say it like the x in "fire" and the silent p in "bath"[[Special:Contributions/172.70.85.13|172.70.85.13]] 21:42, 10 August 2022 (UTC)
:What? There is no 'x' in "fire." [[Special:Contributions/172.69.33.25|172.69.33.25]] 01:17, 11 August 2022 (UTC)

Ideas: bellows-, reed-, and lucite-based voiced phone production tracts typical in science museums; {{w|diphone}}s as an alternative to phomemes (a diphone is the second half of one phoneme followed by the first half of the next -- NOT two adjacent phomemes as the Wikipedia article claims. Two adjacent phomemes are a biphone, not a diphone); the relationship of the position of the tongue in two dimensional place × closedeness space to the fundamental and second {{w|formant}} frequencies of speech audio; {{w|diphthong}}s; {{w|Mel-frequency cepstrum|cepstral}} representation such as {{w|MFCC|mel-frequency ceptstral coefficients}}; and {{w|Zalgo text}} IPA. [[Special:Contributions/172.70.206.213|172.70.206.213]] 22:41, 10 August 2022 (UTC)
: Roger. [[Special:Contributions/172.69.33.149|172.69.33.149]] 03:25, 11 August 2022 (UTC)

The vowelspace is depicted in two dimensions for convenience, but it has at least three dimensions. Look at the IPA vowel diagram (already added to this page). The third dimension is roundedness.
:Yes, of the lips; apart from the two dimensions (out: place, and up: closedeness) of the tongue. [[Special:Contributions/172.70.206.95|172.70.206.95]] 22:59, 10 August 2022 (UTC)
::Does roundedness also involve the tongue and cheeks to any extent? [[Special:Contributions/172.69.33.199|172.69.33.199]] 23:36, 10 August 2022 (UTC)

This linguist character has appeared 3 times now. Will there be a new character page dedicated to Gretchen or "The Linguist"? [[Special:Contributions/172.69.33.225|172.69.33.225]] 00:21, 11 August 2022 (UTC)

Can someone please create and paste in a zalgostring for the fancy 'əG' ligature shown twice in the comic? [[Special:Contributions/172.70.211.134|172.70.211.134]] 01:10, 11 August 2022 (UTC)
:Is this another example of Randall trolling Explainxkcd as in [[2619: Crêpe]]? [[Special:Contributions/172.69.33.37|172.69.33.37]] 01:45, 11 August 2022 (UTC)

Someone please remind me how to Zalgo a top horizontal bar over √-1. [[Special:Contributions/172.70.211.134|172.70.211.134]] 02:34, 11 August 2022 (UTC)
: Slow way = Windows Character Map --> Group by: unicode subrange... Group By: Combining Diacritical Marks. 6th character from the top left (U+0305:Overline) yields √-̅1̅.
:Fast way = HTML character entities, ''{character it combines with}&#{character number code};'' (773:Overline) yields √-̅1̅
:Ignore other codes as they are either non-combining or have height relative to combining character (ie Macron) -- [[Special:Contributions/172.69.70.201|172.69.70.201]] 04:35, 11 August 2022 (UTC)
::Are you sure? Those aren't wide enough to connect along the top for me. [[Special:Contributions/172.69.34.10|172.69.34.10]] 07:57, 11 August 2022 (UTC)

I don’t think what Randall is trying to do is provide a “roundness” dimension, but that’s how the explanation reads to me right now (“such” a dimension, e.g.) [[User:Szeth Pancakes|Szeth Pancakes]] ([[User talk:Szeth Pancakes|talk]]) 05:13, 11 August 2022 (UTC)

2657: Complex Vowels

2022-08-11T02:25:59Z

172.69.34.10: /* Explanation */ √-1

{{comic
| number = 2657
| date = August 10, 2022
| title = Complex Vowels
| image = complex_vowels.png
| titletext = Pronouncing [ṡṡċċḣḣẇẇȧȧ] is easy; you just say it like the 'x' in 'fire'.
}}

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

[[File:Ipa-chart-vowels.png|thumb|200px|The IPA vowel chart]]

In phonetics based on the {{w|International Phonetic Alphabet}} (IPA), the space of {{w|vocal tract}} articulators determining {{w|vowel}}s  is represented as two-dimensional, from the position of the tongue. The vertical axis represents vowel height or ''closedness'' (i.e. how close or far the tongue is from the top of the mouth), and the horizontal axis represents front-to-back ''place'' (i.e., how close or far the top of tongue is from the teeth.) The position of the tongue, along with the frequency of the {{w|vocal cords}} vibrating in the larynx from air being exhaled by the diaphragm, are the primary determinants of the fundamental and second {{w|formant}}s of vowel sounds.

A third dimension of vowel sounds is the "roundedness" of the lips, and to a much lesser extent the tongue and cheeks, which is not represented on the IPA vowel chart to the right. [[Randall]] thus suggests using complex notation to indicate such a third dimension. Other higher-dimensional vowel representations include {{w|diphthong}}s, which are simply two different sequential vowels slurred together; diphones, which represent the last half of one phoneme followed by the first half of the next; the {{w|vowel shift}} mappings delineating different accents[https://core.ac.uk/download/pdf/47086396.pdf][https://www.sciencedirect.com/science/article/abs/pii/S0095447010000562] and long-term evolution of voiced phone sounds; and {{w|cepstrum|ceptstral}} representations such as {{w|Mel-frequency cepstrum|mel-frequency ceptstral coefficients}}.

In mathematics, {{w|complex number}}s are numbers including both real numbers and {{w|imaginary number}}s. A complex number can be expressed as, "''a'' + ''b''i," where ''a'' and ''b'' are real numbers, but the latter imaginary part is combined with 'i,' the square root of negative one, as depicted in the central expression in the comic by √-1, presumably indicating the coordinates of the complex vowel. When expanding the one-dimensional number line with an imaginary axis, it becomes two-dimensional with any "''b''i" component being represented perpendicularly away from the original 'real' line. Linguists never use the {{w|complex plane}} to represent vowel roundedness, or any other higher-dimensional features of phonemes.{{cn}}

This comic conflates complex numbers in mathematics with "complex vowels" in linguistics. Such complex vowels are implied to create sounds which cannot be properly processed by the human brain, represented graphically as {{w|Zalgo text}} IPA, similarly to the cliché of "black speech" in {{w|Lovecraftian horror}}, a language created by alien beings with different vocal patterns than humans. In reality, people find Zalgo text amusing, thus the humor of the comic, but not particularly insanity-inducing or even more than mildly confusing.{{cn}} This is also funny because unadorned IPA shares some characteristics with Zalgo text, such as extremely uncommon {{w|glyph}}s and weird {{w|diaeresis}}.

In linguistics, 'ə' is the {{w|schwa}} symbol, referred to in the title text as well as the depiction of complex phonemes, the most common vowel sound in English polysyllabic words (the 'a' in "comma" or the second 'e' in "letter"). Production of the schwa sound takes place with the tongue, jaw, and lips all in a relaxed, central position; and certainly sounds nothing like the 'x' in "fire," because it has no 'x.'

The linguist in the comic appears to be {{w|Gretchen McCulloch}}, as previously depicted in [[2421: Tower of Babel]] and [[2381: The True Name of the Bear]].

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

:[A diagram shows the extrusion of the trapezoidal IPA vowel chart upwards into three dimensions. A point near the center is labeled with an equation that shows "ə + 1/2 * sqrt(-1)" as being equivalent to a made-up symbol that looks like two schwas mirroring each other with other markings above and below.]

:[Below the diagram, a character with shoulder-length dark wavy hair pronounces the new vowel in a speech bubble with unstable lines surrounding it. Two bystanders to her right are bent over slightly, clutching their heads in apparent anguish.]

:[Caption below the panel:]
:Linguistics tip: Extend the IPA vowel plane along the imaginary axis to produce ''complex vowels'', cursed sounds which the human mind cannot comprehend.

{{comic discussion}}
[[Category:Tips]]
[[Category:Language]]

1963: Namespace Land Rush

2022-06-11T20:24:57Z

172.69.34.10:

{{comic
| number = 1963
| date = March 5, 2018
| title = Namespace Land Rush
| image = namespace_land_rush.png
| titletext = You can also just mash the keyboard at random, but you might end up with a gibberish name no one can pronounce.
}}

==Explanation==

When a new web service starts, such as a forum, a social media server or an email portal, the people who sign up get to choose their username on the service, which, in most cases, blocks future users from using those usernames. Common names such as "john" are likely to be taken quickly. This is analogous to the way that land was distributed in America, with the first to claim able to choose the best land.

This comic is a list of usernames [[Randall]] suggests should be used if they are available.

The title text is a self-reference to "xkcd"; the name of the comic is a purposefully unpronounceable phrase created by Randall. The fact that an unpronounceable name is portrayed as a disadvantageous outcome is also humorous because the comic has a section dedicated to unpronounceable usernames.

(Note: for a more serious list of problematic user names to block from a service provider’s point of view, see [https://ldpreload.com/blog/names-to-reserve Hostnames and usernames to reserve] as well as [https://tools.ietf.org/html/rfc2142 RFC 2142].)

==Table==
{| class="wikitable"
!style="width:30%"|Entry
!style="width:70%"|Explanation
|-
!colspan=2|Straightforward (Usernames that a person would use under typical circumstances)
|-
|<Your usual username, if any>
|Most internet users will have settled on some unique handle that they try to use across all platforms. Even if this wasn't a new service, most people would try this first.
|-
|<Your given name>
|More rare is using one's nickname or first name as their username, since the amount of common names will mean many users share a name. Thus, if you can get your given name, you will have a simple username that many others wanted, and without resorting to prefixes or numbers (i.e. Xx_MyName00_xX)
|-
|<Your full name>
|Similar to your given name, but slightly more unique since a last name and/or middle name is added.
|-
|<Initial><Surname>
|A common second choice if a given or full name is already in use.
|-
|<Surname>
|Possibly available if your last name is more uncommon; names like "Smith" or "Kim" will probably be taken faster than even given names.
|-
!colspan=2|Recognizable (Usernames that would make it look like the email came from an official source within the organization named)
|-
|Google
|Registering the name "Google" would allow for communicating on the site (or even outside of it) with a name that appears to be an official Google account. For any of the examples in this section, you would select the names for the same reason. This has been done in the past with both [https://twitter.com/BiIIMurray humorous] and [http://www.chicagotribune.com/bluesky/technology/ct-russian-twitter-account-tennessee-gop-20171018-story.html nefarious] results.
|-
|iPhone
|Many services would mark messages sent from an iOS client on iPhone as "sent from iPhone".
This could make people believe that your messages are sent from an iPhone even if you don't own one.
|-
|Facebook
|Similiar to Google above.
|-
|Bitcoin
|One could pose as the Bitcoin Core development group by using this handle and/or scam uninformed users interested in cryptocurrencies.
|-
|Obama
|Impersonating a president, supposedly to send messages as them to make them seem bad (or not).
|-
|Canada
|Impersonating a whole country might get you in trouble.{{Citation needed}}
|-
|NFL
|The American "National Football League".
|-
|Garfield
|In the original "GMail" service on the Internet, the G stood for "Garfield".
|-
|<Your city>
|Impersonating the official account for your place of residence.
|-
|NASA
|The American "National Aeronautics and Space Administration". Randall worked there as a contract programmer and roboticist.
|-
|<Name of person who runs the service>
|Impersonating the site owner can get you the trust of users.
|-
!colspan=3|Causing Trouble (Usernames that might cause errors when mixed with the service's back-end code)
|-
|User
|This is usually the default username for a non-administrative account. This may trick a user that this is owned by the operator of the service.
|-
|Username
|See above.
|-
|Name
|See above.
|-
|You
|Many services display "You" as the signed-on user, so naming oneself "You" makes users think that they are you/they are signed on when they aren't.
|-
|Guest
|Attempts to fool users into thinking that they have a guest account.
|-
|Account
|The opposite of "Guest" (someone without an account). However, for someone with an account, their username will usually be displayed.
|-
!colspan=2|Causing More Trouble
|-
|Admin
|Impersonating to be a system administrator will let someone fool people and cause a lot of trouble. In particular, it could be used to obtain SSL certificates by demonstrating ownership of a supposedly internal address.
|-
|Administrator
|See above.
|-
|System
|Pretending to be a system-controlled account - might give permissions if the server checks by name.
|-
|<Name of service>
|Pretending to be the official account of the service.
|-
|Help
|Pretending to be the help account. This could led to many questions from new users.
|-
|Error
|This may trick users to do what the user says as they could claim that it was a legitimate error.
|-
!colspan=2|Impossible to Say
|-
|Hyphen-Emdash
|Could be read "Hyphen hyphen Em dash" or "Hyphen dash em dash".
|-
|Dash-8hyphen-8
|Could be read "Dash dash eight hyphen dash eight" or "Dash hyphen eight hyphen hyphen eight". "Hyphen eight" sounds like "hyphenate".
|-
|Zero0ne2numeral2
|Could be read "Zero zero one two numeral two" or "Zero zero ne two numeral two" or "Zero oh ne two numeral two".
|-
|KrisasinHemsworth
|This would be confusing to say out loud, as it would sound like the user was saying that their username was "Chris," spelled the same way that famous actor {{w|Chris Hemsworth}} spells his name. However, the actual username uses the name "Kris," spelled a completely different way than Chris Hemsworth's name, and the phrase "as in Hemsworth" being also part of the username, rather than a clarification of the spelling of "Kris" as would be assumed.
|-
|TheWord&Ampersand
|This would also be confusing and difficult to communicate, as anyone trying to read the username to someone else would say "The word ampersand ampersand" which could be interpreted as "ampersand&" or "ampersand ampersand". Having the phrase "the word" in front of a symbol makes it quite difficult to communicate which variation of ampersand (word or symbol) is actually being referred to.
|-
|ZettaWith3Teees 
|Read aloud, this would lead the listener to expect a username of 'Zettta'. Clarifying that "with three tees" is text and not description would in turn make it difficult to explain the spelling of 'Zetta' with two 't's, and 'Teees' with three 'e's.
|-
!colspan=2|Misc
|-
|<Single Letters> and <Single Numbers>
|These are highly valuable. The Twitter handle "@n" for example is constantly bombarded with offers and hacking attempts.
|-
|<Common Words>
|Also highly valuable; overlaps with "Recognizable" and "Causing (more) Trouble".
|-
|<SQL/JS Injection>
|Codes such as "Drop Table" intended to cause errors or even damage the service's back-end code. (See [[327|Comic 327]])
|-
|ASDF and QWERTY
|Since those keys are right next to each other (on English language layouts), they are often typed as placeholders.
|-
|Yes
|This might be a [[Beret Guy]]-esque misunderstanding when filling out the sign up form. When encountering the form field "Username:" someone may type "Yes" (as in "yes, I want a username") instead of specifying it.
|-
|Bot and Computer
|Pretending to be a bot.
|-
|Blocked
|When users get banned or blocked, their name is often replaced by a string like this.
|-
|Deleted
|Some services like Reddit keep up user posts and data after account deletion, marking the content as submitted by the user "[Deleted]" or "Deleted".
|-
|Jeeves
|Might refer to {{w|Ask Jeeves}} (now Ask.com), a Internet Search Engine.
|-
|Narrator
|In books, radio plays and movies it is quite common to have a narrator explain parts of the story. In an online forum however, it is not.{{Citation needed}}
|-
|Internet
|"The Internet" sometimes refers to a large group of users, the collective hive-mind if you will. However, there cannot be a single user account speaking on behalf of them, as they aren't a single entity.
|-
|NPC
|Stands for Non-player character.
|-
|Password
|If the user accidentally typed their password into the username field, this would be the result.
|-
!colspan=2|Permissive Character Sets
|-
|<Space>
|Usernames containing only whitespace can not only be confusing for other people, but often systems 'trim' (remove whitespace at the beginning and end) user input. If the username was only made of spaces, after trimming it would be completely empty, which can cause a whole slew of other problems.
|-
|<nowiki>@ é |</nowiki>
|The @ separates the local part from the domain part of email addresses. If a service decides to create email addresses for their users, they will have a hard time if they allowed the "at" character as part of a username.
é is encoded in many character sets, like Latin-1 and Unicode. In Unicode, it can even be described either "U+00E9 LATIN SMALL LETTER E WITH ACUTE" or as the sequence "U+0065 LATIN SMALL LETTER E" and "U+0301 COMBINING ACUTE ACCENT". If a system uses {{w|Unicode normalization}} after the check if the username is available, this might allow someone to take over someone else's account.
|-
|<nowiki>“ ” " ‘ ’ ' `</nowiki>
|Various quotation marks.
“, ”,‘ and ’ (Unicode quotes): can expose a system's inability to handle multi-byte-encodings. If they are converted to their ASCII counterparts, they might cause code injections.
' and " (ASCII single and double quotes): often used as string delimeter (causing the rest of the name to be interpreted as HTML, or worse, code.
` (ASCII grave / backtick): Sometimes used as string delimeter; Perl (which some websites are still programmed in) executes commands ("shell code") when between backticks.
|-
|<NBSP>
|Unicode character "U+00A0 NO-BREAK SPACE". Similar attack vector as <Space>, but some programming languages will not strip non-ASCII whitespace (therefore the validation will pass).
|-
|<nowiki>\ . #</nowiki>
|The backslash is very often used for "escape sequences", that get expanded to other characters. (\n -> newline, \t -> tab character, \b -> backspace character (deletes the character to its left), etc.)
The period can be problematic in emails. RFC 2822 forbids periods at the beginning or end of the local part or more than one period in a row.
In URLs, the Octothorpe (#) is used as the 'anchor'. Anything following a # will not be transmitted to the server. If a user is named 'logout#blahblah' (which might be a valid username) and the user profile is located at http://example.com/<the_username>, the server might generate the URL http://example.com/logout#blahblah. Since the URL will be truncated at the '#', any user attempting to view this profile will be logged out of the service.
|-
|<RTL override>
|The right to left override is an Unicode character which forces text after it to be laid out right to left. Thus, in left-to-right locales, it flips everything after it. This can be rather amusing if permitted. (See [[1137|Comic 1137]])
|-
|<nowiki>– - _ /</nowiki>
|Includes both the em-dash and the hyphen, which are easily confused and are highly unusual for user names. The forward slash is also the path delimeter for URLs; if user profiles are located at e.g. http://example.com/user/the_username, this can cause obvious issues.
|-
|<Any emoji>
|Current databases are not set up to store emojis as characters.
|-
|","
|In CSV files this separates one column or data item from another. This could cause bugs if the usernames are used as part of a CSV file since the next column on the row could be left blank filled with other data.
|-
|<nowiki>&NBSP</nowiki>;
|The special entity in HTML (web page language) for a non-breaking space, or a space that prevents an automatic line-break at its position. When rendered as part of an HTML page without sanitization, this would only display a space.
|-
|<nowiki></HTML></nowiki>
|This is trying to inject code for the web page using the user name. If the user name is not sanitized and does not have special characters encoded, this HTML end tag could end the HTML document, leading to page errors.
|-
|&LT;/HTML&GT;
|&LT; and &GT; are special character entities in HTML that represent < and >, repectively. So all together, when rendered as part of an HTML document, this would print "<nowiki></HTML></nowiki>" Although this would look similar to the previous <nowiki></HTML></nowiki> entry, it would be unlikely to cause problems as the symbols are not interpreted if encoded as special entities.
|-
|OkThisIsKindOfConfusingButIt's <LessThan\ForwardSlashHTML GreaterThanActualGreaterThan Symbol>Yes,ThatWasAllPartOfThe Name,ButSoIs...Ok,LetMeStartOver”
|The abundance of symbols and symbol related worlds and phrases such as ActualGreaterThanSymbol would make this extremely difficult to vocally communicate to another person. This difficulty is further compounded by the parts at the beginning and end, which sound like they are part of the explanation despite being part of the name itself.
|-
|}

==Transcript==
{{incomplete transcript|Layout not standard (eg. indentation) and a short description at the beginning about what is shown should be given.}}
'''Namespace Land Rush Cheat Sheet'''
(Note: if an item is "quoted", it is meant literally, otherwise the reader is supposed to substitute their own information for words in <angle brackets>)

When a new service appears that lets you register a name, here are some you may want to try and get first:

* Straightforward
** <Your usual username, if any>
** <Your given name>
** <Your full name>
** <Initial><Surname>
** <Surname> (Bold & Slightly Unconventional)

* Recognizable
** "Google"
** "iPhone"
** "Facebook"
** "BitCoin"
** "Obama"
** "Canada"
** "NFL"
** "Garfield"
** <Your city>
** "NASA"
** <Name of person who runs the service>

* Causing Trouble
** "User"
** "Username"
** "Name"
** "You"
** "Guest"
** "Account"

* Causing More Trouble
** "Admin"
** "Administrator"
** "System"
** <Name of service>
** "Help"
** "Error"

* Impossible to Say
** "Hyphen-Emdash"
** "Dash-8hyphen-8"
** "Zero0ne2numeral2"
** "KrisasinHemsworth"
** "TheWord&Ampersand"
** "ZettaWith3Teees" 

* Misc
** <Single Letters>
** <Single Numbers>
** <Common Words>
** <SQL/JS Injection>
** "ASDF"
** "QWERTY"
** "Yes"
** "Bot"
** "Computer"
** "Blocked"
** "Deleted"
** "Jeeves"
** "Narrator"
** "Internet"
** "NPC"
** "Password"

* Permissive Character Sets
** <Space>
** <NBSP>
** <RTL override>
** <Any emoji>
** "<nowiki>&NBSP</nowiki>;"
** "<nowiki></HTML></nowiki>"
** "&LT;/HTML&GT;"
** one or more of the following symbols: <nowiki>@ é | “ ” \ . # " ‘ – - _ / ’ ' `</nowiki>
** "," (including quote marks)
** "OkThisIsKindOfConfusingButIt's<LessThan\ForwardSlashHTMLGreaterThanActualGreaterThanSymbol>Yes,ThatWasAllPartOfTheName,ButSoIs...Ok,LetMeStartOver”"

{{comic discussion}}
[[Category:iOS]]

2630: Shuttle Skeleton

2022-06-11T02:00:04Z

172.69.34.10: /* Explanation */ provide citation

{{comic
| number = 2630
| date = June 8, 2022
| title = Shuttle Skeleton
| image = shuttle_skeleton.png
| titletext = It's believed to be related to the Stellar Sea Cow.
}}

==Explanation==
{{incomplete|Created by a NEBULA DESERT HORSE - Please change this comment when editing this page. Do NOT delete this tag too soon.}}
The Space Shuttle was a reusable spacecraft system used by {{w|NASA}} from 1981 to 2011, after which it was decommissioned. In this comic, Randall suggests that the nature of the shuttle was in doubt or misunderstood until either an intact 'specimen' (of which there are four) had been dissected, or possibly the remains were reassembled from the two that were [https://www.youtube.com/watch?v=yibNEcn-4yQ lost in accidents].

With its shape, shown in the small image, and the tail fin, it looks a bit like a {{w|Osteichthyes|bony fish}} or {{w|Batoidea|ray}}. The joke is that after the shuttle was taken out of use, its skeleton was analyzed, and as shown in the comic, was found to have a skeleton typical of a mammal, with details such as the pentadactyl quadripedal bodyform hidden beneath its aerodynamic sweep, as well as having bones (i.e., not primarily cartilage). This morphology is similar to that possessed by a whale. Of course, the skeleton of a spacecraft is not made of bones, but rather of [https://www.nytimes.com/2003/04/22/science/inquiry-focuses-on-skeletons-of-space-shuttles.html metal] and other manufactured materials.

As the understanding of the natural world developed, many taxonomic misconceptions were overturned, or at least the scientific terminology was tightened. For instance, it was found that dolphins and whales were mammals, not fish.[''{{what if|156|cetacean needed}}''] Because of convergent evolution – the tendency for distantly-related species to adapt similarly to a given environment – it is often not easy to properly classify organisms merely by observing their exterior. For example, whales and fish have very similar body shapes, as did the extinct plesiosaurs, because life as a swimming vertebrate favors the same adaptations. In lieu of genetic analysis, or even of sufficient observation of them in the wild, the main progress in understanding differences among marine animals was often in dissecting the corpses of creatures found stranded or caught in nets, or reconstructing them from skeletal remains. Together with fossil evidence, insights were developed about their origins and differences from others' origins.

The title text conflates the now-extinct {{w|Steller's sea cow}}, an aquatic mammal related to manatees and named after explorer/zoologist Georg Steller (also extinct) {{Citation needed}}, with the adjective "stellar", which means being of a star or stars, such as inter-stellar space or stellar masses. While this conflation is often done accidentally, due to the name Steller being much rarer than the adjective "stellar," in this case it is probably an intentional pun.

One might expect that the idea for this comic may have come from the recent California Supreme Court ruling that [https://www.wsj.com/articles/when-is-a-bumblebee-a-fish-when-a-california-court-says-so-11654611927?st=umo4uckleempt0e&reflink=desktopwebshare_permalink bumblebees are considered fish] under a law which categorized several other invertebrates as part of a broad colloquial category of fish (as in "Fish and Game Department" designations.) However, given the short time between the ruling and the comic's release, it is likely that this was a coincidence.

The comic also prominently conflates biology with artifice, a budding and controversial concept in these times of rapid AI use and research.

==Transcript==
:[In the upper right part of the panel there is a small drawing of the Space Shuttle as seen from above. Beneath it, and to its left, is a much larger drawing with the same outline as the Shuttle. But this time the outer layers have been removed to reveal the inside. This has revealed a skeleton taking up the entire space inside. The head is in the front, and legs and tail at the rear, with arms and fingers in the wings, looking somewhat like a bat's "hand/wings". The bones are white with the frame of the shuttle gray or black. Some of the lines outlining the design of the shuttle are both on the small and the large drawing, along the wings and rear engines. Both feet and arms have five fingers/toes. There seem to be 24 ribs in the very long rib-cage.]

:[Caption beneath the panel:]
:The Space Shuttle was long assumed to be a type of fish or shark, but after it was decommissioned in 2011, analysis of its skeleton determined that it was actually a mammal.

{{comic discussion}}

[[Category:Animals]]
[[Category:Space]]

2627: Types of Scopes

2022-06-01T20:47:57Z

172.69.34.10: Undo revision 285426 by 172.70.126.87 (talk)

{{comic
| number = 2627
| date = June 1, 2022
| title = Types of Scopes
| image = types_of_scopes.png
| titletext = An x-ray gyroscope is used to determine exactly which toppings they included in the pita.
}}

==Explanation==
{{incomplete|Created by a BOTOSCOPE - Please change this comment when editing this page. Do NOT delete this tag too soon.}}
''{{w|Electron microscopes}}'', ''{{w|Calorimetric Electron Telescope|electron telescopes}}'' and ''{{w|radio telescopes}}'' are special forms of {{w|microscopes}} and {{w|telescopes}}, respectively. This comic explores what you could do with a hypothetical "electron ___-scope" and "radio ___-scope" for other "regular" items whose name also ends in -scope (namely: {{w|periscope}}, {{w|stethoscope}}, {{w|kaleidoscope}}, {{w|gyroscope}} and {{w|horoscope}}).

The third column with "radio" often plays on different meanings of the word ''radio:'' 1) related to radiation and 2) a device for receiving radio communication or broadcasts.

The title text makes a pun on "gyroscope" and the Greek foods {{w|gyros}} which are typically served in {{w|pita}} bread.

===Table with scopes===
{| class="wikitable"
|+ What the words could mean according to the comic
|-
! Word !! Regular ___ !! Electron ___ !! Radio ___
|-
| Microscope || A laboratory instrument used for magnifying small objects. || ''Really exists:'' A microscope that uses a beam of accelerated electrons as a source of illumination, has a higher resolution than a conventional microscope. || Simply a microscope that one would use when repairing a radio.
|-
| Telescope || An optical instrument used for observing distant objects. || ''{{w|Calorimetric Electron Telescope|''Really exists''}}'': A type of telescope used to detect electrons and other high-energy particles, such as cosmic rays. || ''Really exists:'' A directional antenna used to detect radio waves from astronomical radio sources in the sky.
|-
| Periscope || Periscopes allow submarine crews to watch what happens above the water surface, without exposing the submarine to enemy observers, or enemy radars. In practice, periscope use is minimized because periscopes are still observable, but to a lesser degree. || An electron microscope seemingly mounted on a periscope. Examining enemy boats like a periscope, with the detail of an electron microsope. This would not be useful in combat. || In principle, the German navy has invented radio periscopes during World War 2. The {{w|Metox radar detector}}'s early antenna had to be built up after surfacing, and dismantled before diving. Later, the fixed ''Bali'' antenna could act like a true periscope, in order to detect aircraft and ships that were using radar to hunt submarines.

Radio signals do not propagate well in water, so raising a radio receiver above the water would be necessary for listening to NPR or any radio station which is not in the {{w|extremely low frequency}} band.
|-
| Stethoscope
|| A medical device for listening to sounds made by a patient's body, for example the heart. Has a disc-shaped resonator that is placed against the patient's skin.
|| If the resonator is emitting electromagnetic radiation, it could burn the skin due to its close proximity.
|| Normally, the sounds are transmitted to an earpiece that the examiner wears. There are also recording stethoscopes. A radio stethoscope would transmit the sound either directly via radio waves, or send it to a radio station such as NPR where it could then be broadcasted.
|-
| Kaleidoscope || A optical instrument which uses two or more tilted reflectors to show a regular symmetrical pattern || Seemingly a pun of electron "collide"-oscope, as electron collisions generate {{w|Bremsstrahlung}}. || The scan button on a radio scans through many frequencies, and the radio station changes a lot, depending on the frequency. The rapid change is remisiscent of a normal Kaleidoscope.
|-
| Gyroscope || Gyroscopes are used for {{w|inertial navigation}}, for example. || Gyroscopes make stuff point in certain directions by spinning. An {{w|Electromagnet}} uses sometimes-spinning electric fields to induce a magnetic field, moving magnetic stuff and, in some instances, making it point in a certain direction. || A music turntable spins a vinyl record to stimulate an electromagnetic needle, which plays music. Such devices are common in radio stations.

In theory, radio waves could be sent around in a triangular pattern, thus replicating the existing {{w|ring laser gyroscope}}.
|-
| Horoscope
|| In common usage, predictions or advice given based on the position of stars and planets. Proven to be unscientific junk.
|| Predicting the position of a particle, such as an electron (possibly based on the position of stars and planets). In a funny twist, the exact location of an electron cannot be determined, due to Heisenberg's uncertainty principle.
|| Predictions or advice given based on the radiation emitted by exploding stars or galaxies.
|}

==Transcript==
{{incomplete transcript|Do NOT delete this tag too soon.}}
Content is a table, with column headings "Regular ''Blank'' Scope", "Electron ''Blank'' Scope", and "Radio ''Blank'' Scope". Row headings are "Micro", "Tele", "Peri", "Stetho", "Kaleido", "Gyro", and "Horo".

;Regular Microscope
:Look at small stuff
;Electron Microscope
:Look at ''really'' small stuff
;Radio Microscope
:Figure out why your radio broke
;Regular Telescope
:Look at stuff that's far away
;Electron Telescope
:Detect cosmic rays
;Radio Telescope
:Look at distant high-energy stuff
;Regular Periscope
:Look for enemy ships
;Electron Periscope
:Examine the hull of an enemy ship for structural flaws
;Radio Periscope
:Let the crew of your submarine listen to NPR
;Regular Stethoscope
:Listen to a patient's chest
;Electron Stethoscope
:Burn a patient's skin
;Radio Stethoscope
:Play the noises from a patient's chest on NPR
;Regular Kaleidoscope
:See cool shapes and colors
;Electron Kaleidoscope
:See cool Bremsstrahlung
;Radio Kaleidoscope
:Another word for the "Scan" button
;Regular Gyroscope
:Balance by spinning
;Electron Gyroscope
:Another word for electromagnet
;Radio Gyroscope
:Another word for turntable
;Regular Horoscope
:Get random life advice
;Electron Horoscope
:Predict a particle's quantum state
;Radio Horoscope
:Get random life advice from exploding galaxies

{{comic discussion}}

[[Category:Charts]]
[[Category:Food]]
[[Category:Science]]
[[Category:Space]]

Talk:2622: Angular Diameter Turnaround

2022-05-20T20:24:43Z

172.69.34.10:

Slightly creepy, NGL[[Special:Contributions/172.69.34.10|172.69.34.10]]

1331: Frequency

2022-05-04T21:21:39Z

172.69.34.10: /* Events */ Fixed link to Old Faithful. Can't find a replacement link for the "Feb 16 2014 eruption"

{{comic
| number = 1331
| date = February 17, 2014
| title = Frequency
| custom = <center><table title="This comic shows estimated average frequency. I wanted to include the pitch drop experiment, but it turns out the gif format has some issues with decade-long loops."><tr>
<td>[[File:heartbeat.gif]]</td>
<td>[[File:birth.gif]]</td>
<td>[[File:death.gif]]</td>
<td>[[File:wikipedia.gif]]</td>
<td>[[File:vibrator.gif]]</td>
</tr><tr>
<td>[[File:car china.gif]]</td>
<td>[[File:car japan.gif]]</td>
<td>[[File:car germany.gif]]</td>
<td>[[File:car us.gif]]</td>
<td>[[File:car elsewhere.gif]]</td>
</tr><tr>
<td>[[File:kiss.gif]]</td>
<td>[[File:fire dept.gif]]</td>
<td>[[File:holeinone.gif]]</td>
<td>[[File:turnsignal1.gif]]</td>
<td>[[File:turnsignal2.gif]]</td>
</tr><tr>
<td>[[File:earthquake1.gif]]</td>
<td>[[File:earthquake2.gif]]</td>
<td>[[File:earthquake3.gif]]</td>
<td>[[File:earthquake4.gif]]</td>
<td>[[File:parliament toilet.gif]]</td>
</tr><tr>
<td>[[File:flight.gif]]</td>
<td>[[File:book mockingbird.gif]]</td>
<td>[[File:cat mockingbird.gif]]</td>
<td>[[File:phoenixshoes.gif]]</td>
<td>[[File:phoenix.gif]]</td>
</tr><tr>
<td>[[File:keys.gif]]</td>
<td>[[File:amelia.gif]]</td>
<td>[[File:dogbite.gif]]</td>
<td>[[File:bike.gif]]</td>
<td>[[File:eagle.gif]]</td>
</tr><tr>
<td>[[File:bottles.gif]]</td>
<td>[[File:recycled.gif]]</td>
<td>[[File:meteor.gif]]</td>
<td>[[File:oldfaithful.gif]]</td>
<td>[[File:shark.gif]]</td>
</tr><tr>
<td>[[File:us cancer.gif]]</td>
<td>[[File:us cancer death.gif]]</td>
<td>[[File:dog.gif]]</td>
<td>[[File:cat.gif]]</td>
<td>[[File:wedding.gif]]</td>
</tr><tr>
<td>[[File:domain.gif]]</td>
<td>[[File:house.gif]]</td>
<td>[[File:tattoo.gif]]</td>
<td>[[File:pulsar.gif]]</td>
<td>[[File:facebook.gif]]</td>
</tr><tr>
<td>[[File:iphone.gif]]</td>
<td>[[File:littleleague.gif]]</td>
<td>[[File:ndsex.gif]]</td>
<td>[[File:bieber.gif]]</td>
<td>[[File:denverpizza.gif]]</td>
</tr></table></center>
| titletext = This comic shows estimated average frequency. I wanted to include the pitch drop experiment, but it turns out the gif format has some issues with decade-long loops.
}}

==Explanation==
This comic shows a number of common events, arranged in a grid. Each of the events flashes with its average frequency.

For example, statistically a child is born somewhere on the world approximately every 0.24 seconds, or four times per second. Therefore, the tile "One birth" blinks about 4 times per second.

The title text refers to the {{w|Pitch drop experiment}} which measures the flow of a piece of pitch over many years. At room temperature, tar pitch flows at a very slow rate, taking several years to form a single drop. The title text jokes that Randall tried to include a tile that flashes about once every {{w|decade|ten years}}, but the tiles are all {{w|Animated GIF|animated GIFs}} and while the file format supports animations of any length, the resulting file would be too big (at least 10 megabytes).

A thorough analysis of the frequencies present in this comic and how they relate to the underlying technology (the GIF format) was published as [http://notebooks.jsvine.com/reverse-engineering-xkcd-frequency/ Reverse Engineering xkcd's 'Frequency'].

The table below lists all the events and their duration / frequency. Some events make reference to other comics.

===Events===
{| class="wikitable sortable"
!class="unsortable"|Picture
!class="unsortable"|Text
!Period (seconds)
!Frequency (per minute)
!Frequency (per year)
!class="unsortable"|Explanation and/or references to other comics.
|-
|[[File:heartbeat.gif]]
|Heartbeat||style="text-align:right;"|0.86||style="text-align:right;"|70||style="text-align:right;"|33,000,000||The typical resting {{w|heart rate}} in adults is 60–80 beats per minute (bpm).
|-
|[[File:birth.gif]]
|One birth||style="text-align:right;"|0.24||style="text-align:right;"|250||style="text-align:right;"|131,490,000||The {{w|Birth rate|birth rate}} that occurs on Earth.
|-
|[[File:death.gif]]
|One death||style="text-align:right;"|0.56||style="text-align:right;"|107||style="text-align:right;"|56,360,000||The {{w|Mortality rate|Mortality rate}} is much lower than the birth rate shown above; thus, the world's population continues to increase. (Mass deaths not included.)
|-
|[[File:wikipedia.gif]]
|Someone edits Wikipedia||style="text-align:right;"|0.67||style="text-align:right;"|90||style="text-align:right;"|47,100,000||{{w|Wikipedia}} is an online, freely editable encyclopedia. A table recording the time between completion of each block of 10 million edits can be found [http://en.wikipedia.org/wiki/User:Katalaveno/TBE here], which suggests that the value 0.67 Sec/Edit is a little high, with the average being closer to 0.63 Sec/Edit.
|-
|[[File:vibrator.gif]]
|Someone buys a vibrator||style="text-align:right;"|2.99||style="text-align:right;"|20||style="text-align:right;"|10,550,000 || This is just a joke; there are no reliable statistics on worldwide vibrator productions or sales.
|-
|[[File:car china.gif]]
|China builds a car||style="text-align:right;"|1.89||style="text-align:right;"|32||style="text-align:right;"|16,700,000|| According to the International Organization of Motor Vehicle Manufacturers, China is the world's most prolific car manufacturer, producing just over [http://www.oica.net/category/production-statistics/2013-statistics/ 18 million cars in 2013].
|-
|[[File:car japan.gif]]
|Japan builds a car||style="text-align:right;"|4.01||style="text-align:right;"|15||style="text-align:right;"|7,870,000|| According to the International Organization of Motor Vehicle Manufacturers, Japan is the second most prolific car manufacturing country, producing just over [http://www.oica.net/category/production-statistics/2013-statistics/ 8 million cars in 2013].
|-
|[[File:car germany.gif]]
|Germany builds a car||style="text-align:right;"|5.8||style="text-align:right;"|10||style="text-align:right;"|5,440,000|| According to the International Organization of Motor Vehicle Manufacturers, Germany is the third most prolific car manufacturing country, producing nearly [http://www.oica.net/category/production-statistics/2013-statistics/ 5.5 million cars in 2013].
|-
|[[File:car us.gif]]
|The US builds a car||style="text-align:right;"|6.95||style="text-align:right;"|8.6||style="text-align:right;"|4,540,000|| According to the International Organization of Motor Vehicle Manufacturers, the US is the fourth most prolific car manufacturing country, producing just under [http://www.oica.net/category/production-statistics/2013-statistics/ 4.4 million cars in 2013].
|-
|[[File:car elsewhere.gif]]
|Someone else builds a car||style="text-align:right;"|1.03||style="text-align:right;"|58||style="text-align:right;"|30,640,000|| This relates to car manufacture in countries other than those four listed above. According to the International Organization of Motor Vehicle Manufacturers, this total is just under [http://www.oica.net/category/production-statistics/2013-statistics/ 29.4 million cars in 2013].
|-
|[[File:kiss.gif]]
|A European Union resident has their first kiss||style="text-align:right;"|5.53||style="text-align:right;"|11||style="text-align:right;"|5,700,000|| Given that each person can only have their first kiss once, this statistic is tied to the EU birth rate. This [http://epp.eurostat.ec.europa.eu/statistics_explained/index.php/File:Number_of_live_births,_EU-28,_1961%E2%80%932012_(1)_(million)_YB14.png eurostat graph] shows the birth rate in the EU, and if we assume that the majority of people experience their first 'real' kiss at around age 12-16, then the years 1998-2002 are of interest, where the birth rate is fairly stable at just over 5.5 million.
|-
|[[File:fire dept.gif]]
|A US fire department puts out a fire||style="text-align:right;"|23||style="text-align:right;"|2.6||style="text-align:right;"|1,370,000|| The latest available statistics from the US Fire Administration show that in 2011 there were [http://www.usfa.fema.gov/data/statistics/ roughly 1.39 million] reported fires.
|-
|[[File:holeinone.gif]]
|Someone hits a hole-in-one||style="text-align:right;"|180 (3 minutes)||style="text-align:right;"|⅓ (20 per hour)||style="text-align:right;"|175,320||A {{w|hole in one}} is a feat in {{w|golf}} in which the player hits the ball directly from the tee into the cup with one shot. This does not account for the possibility of [https://what-if.xkcd.com/85/ Rocket Golf].
|-
|[[File:turnsignal1.gif]]
|My turn signal blinks||style="text-align:right;"|0.94||style="text-align:right;"|64||style="text-align:right;"|33,638,400||This, together with "The turn signal of the car in front of me blinks", forms a reference to [[165: Turn Signals]].
|-
|[[File:turnsignal2.gif]]
|The turn signal of the car in front of me blinks||style="text-align:right;"|0.9||style="text-align:right;"|67||style="text-align:right;"|35,215,200||This, together with "My turn signal blinks", forms a reference to [[165: Turn Signals]].
|-
|[[File:earthquake1.gif]]
|Earthquake (magnitude 1)||style="text-align:right;"|2.43||style="text-align:right;"|25||style="text-align:right;"|13,000,000||These are continually happening, and not felt by humans. The [http://earthquake.usgs.gov/earthquakes/map/#%7B%22feed%22%3A%221419026358584%22%2C%22sort%22%3A%22newest%22%2C%22mapposition%22%3A%5B%5B-85%2C0%5D%2C%5B85%2C360%5D%5D%2C%22viewModes%22%3A%7B%22help%22%3Afalse%2C%22list%22%3Atrue%2C%22map%22%3Atrue%2C%22settings%22%3Afalse%7D%2C%22autoUpdate%22%3Afalse%2C%22search%22%3A%7B%22id%22%3A%221419026358584%22%2C%22name%22%3A%22Search%20Results%22%2C%22isSearch%22%3Atrue%2C%22params%22%3A%7B%22starttime%22%3A%222014-12-12%2000%3A00%3A00%22%2C%22minmagnitude%22%3A-1%2C%22eventtype%22%3A%22earthquake%22%2C%22endtime%22%3A%222014-12-19%2023%3A59%3A59%22%2C%22maxmagnitude%22%3A1.9%2C%22orderby%22%3A%22time%22%7D%7D%7D USGS does report them], but the link provided was produced at the time this description was written. It can however be updated by the user.
|-
|[[File:earthquake2.gif]]
|Earthquake (magnitude 2)||style="text-align:right;"|24.26||style="text-align:right;"|2.5||style="text-align:right;"|1,300,000|| The US Geological Survey estimates that [http://earthquake.usgs.gov/earthquakes/eqarchives/year/eqstats.php 1.3 million] earthquakes of magnitude 2.0-2.9 occur worldwide each year.
|-
|[[File:earthquake3.gif]]
|Earthquake (magnitude 3)||style="text-align:right;"|242.6 (~4 minutes)||style="text-align:right;"|¼ (15 per hour)||style="text-align:right;"|130,000|| The US Geological Survey estimates that [http://earthquake.usgs.gov/earthquakes/eqarchives/year/eqstats.php 130 thousand] earthquakes of magnitude 3.0-3.9 occur worldwide each year.
Earthquakes below this magnitude pass by largely unnoticed by most people (or [[723|tweeters]]).
|-
|[[File:earthquake4.gif]]
|Earthquake (magnitude 4)||style="text-align:right;"|2426 (40.4 minutes)||style="text-align:right;"|0.025 (1.5 per hour)||style="text-align:right;"|13,000|| The US Geological Survey estimates that [http://earthquake.usgs.gov/earthquakes/eqarchives/year/eqstats.php 13 thousand] earthquakes of magnitude 4.0-4.9 occur worldwide each year.
|-
|[[File:parliament toilet.gif]]
|A member of the UK parliament flushes a toilet||style="text-align:right;"|10.06||style="text-align:right;"|6||style="text-align:right;"|3,140,000||At the time of this comic, there were 650 elected MPs and in the UK parliament, resulting in an average of 13.2 flushes per MP per day, which would mean that supposing that MPs get up to go to the toilet once between midnight and 6am, that means that during the rest of the day they are averaging a trip to the toilet every hour and a half. It appears that Randall included the unelected Lords in the upper house of Parliament (not technically called Members of Parliament), which numbered around 780 at the time of the comic. In that case, that averages a slightly more reasonable 6 flushes per Parlimentarian per day.
|-
|[[File:flight.gif]]
|An airline flight takes off||style="text-align:right;"|0.93||style="text-align:right;"|65||style="text-align:right;"|34,000,000|| Research conducted in 2008 by Thomas Ruosch and Dr Karl Rege at [http://www.init.zhaw.ch/index.php?id=9&L=1 Zurich University of Applied Science] plotted the [https://www.youtube.com/watch?v=oR00_uLfGVE 93,000 daily worldwide airline flights].
|-
|[[File:book mockingbird.gif]]
|Someone buys ''To Kill a Mockingbird''||style="text-align:right;"|42.05||style="text-align:right;"|1.4||style="text-align:right;"|750,000||"{{w|To Kill a Mockingbird}}" is a novel by {{w|Harper Lee}}, often an assigned reading in high school. Since 1960 it has sold in the region of [http://www.theguardian.com/books/2010/jul/09/harper-lee-to-kill-a-mockingbird 40 million copies], an average of 740,000 a year.
|-
|[[File:cat mockingbird.gif]]
|Someone's pet cat kills a mockingbird||style="text-align:right;"|1.82||style="text-align:right;"|33||style="text-align:right;"|17,340,000||Whereas the previous item references the well-known book "To Kill a Mockingbird", this one talks about {{w|Mockingbird|mockingbirds}} being literally killed (in this case, by cats). [http://animaldiversity.ummz.umich.edu/accounts/Mimus_polyglottos/ There are 45 million mockingbirds in the world;] this means that according to Randall, cats kill 39% of mockingbirds in one year, i.e. in 2.5 years they are able to kill all mockingbirds (excluding the ones that are born in the meantime).
|-
|[[File:phoenixshoes.gif]]
|Someone in Phoenix buys new shoes||style="text-align:right;"|1.08||style="text-align:right;"|56||style="text-align:right;"|29,200,000||Since {{w|Phoenix metropolitan area|metro Phoenix}} has 4,200,000 inhabitants, according to Randall people in Phoenix buy 7 pairs of shoes per capita per year.
|-
|[[File:phoenix.gif]]
|Someone in Phoenix puts on a condom||style="text-align:right;"|2.05||style="text-align:right;"|29||style="text-align:right;"|15,390,000||Randall probably found the number of Condoms sold in Phoenix and estimated that most of those would be used. Estimates directly from the frequency of intercourse and contraceptive uses would be wildly inaccurate, especially as those statistics count encounters that might need multiple condoms as one instance of intercourse. There are [https://www.birthcontrol.com/condom-use-statistics 450,000,000 Condoms sold in the US each Year.]
|-
|[[File:keys.gif]]
|Someone locks their keys in their car||style="text-align:right;"|2.43||style="text-align:right;"|25||style="text-align:right;"|13,000,000||There does not appear to be any data on this mishap, but a [https://twitter.com/search?q=locked%20keys%20in%20car&src=typd Twitter search] reveals this happens, or people discuss it happening at a high frequency.
|-
|[[File:amelia.gif]]
|A Sagittarius named Amelia drinks a soda||style="text-align:right;"|7.79||style="text-align:right;"|7.7||style="text-align:right;"|4,000,000||Randall Munroe is a [http://blog.xkcd.com/2014/01/31/the-baby-name-wizard/ fan of The Baby Name Wizard] blog and its [http://www.babynamewizard.com Name Voyager] tool which shows that "[http://www.babynamewizard.com/baby-name/girl/amelia Amelia]" has recently exploded in popularity. 
This particular frequency is taken from:
* The number of persons called {{w|Amelia (given name)|Amelia}} ([http://howmanyofme.com/ est. 82,572 people in the U.S.])
* The number of persons born between November 22 and December 22 under the astrological sign of {{w|Sagittarius (astrology)|Sagittarius}} (~1/12th of the population, i.e. approximately 6881 Amelias in the U.S.)
* The frequency of soda (soft drinks) being drunk ([http://www.nationmaster.com/graph/foo_sof_dri_con-food-soft-drink-consumption 216 liters per person per year in the U.S.]).
According to our figures, 6881 Amelias drink 1.44 million liters of soft drinks per year in the United States alone, which means that Randall's figures only account for American Amelias (drinking 355 mL or 12 fl. oz. of soda in each drink).
|-
|[[File:dogbite.gif]]
|A dog bites someone in the US||style="text-align:right;"|7.01||style="text-align:right;"|8.6||style="text-align:right;"|4,500,000|| A [http://www.ncbi.nlm.nih.gov/pubmed/18836045 2008 report] by the Centers for Disease Control concluded that 4.5 million people are bitten by dogs each year.
|-
|[[File:bike.gif]]
|Someone steals a bicycle||style="text-align:right;"|24.93||style="text-align:right;"|2.4||style="text-align:right;"|1,265,000||About half of all people who cycle infrequently have their bikes stolen at some time, but people who cycle every day have a 90% higher chance of bike theft, all according to [http://www.citylab.com/commute/2014/04/these-8-depressing-bike-theft-statistics-show-just-how-bad-problem/8890/ this report] of cyclists in Montreal.
|-
|[[File:eagle.gif]]
|A bald eagle catches a fish||style="text-align:right;"|2.69||style="text-align:right;"|22||style="text-align:right;"|11,700,000||It is estimated that there are 70,000 bald eagles in the world and they eat up to [http://www.hancockwildlife.org/forum/viewtopic.php?showtopic=949 a pound-and-a-half of fish] every day.
|-
|[[File:bottles.gif]]
|50,000 plastic bottles are produced||style="text-align:right;"|1.27||style="text-align:right;"|47||style="text-align:right;"|1.24 trillion||This fact speaks for itself, but here are some [http://www.banthebottle.net/bottled-water-facts/ alarming facts] about plastic bottle production and usage.
|-
|[[File:recycled.gif]]
|50,000 plastic bottles are recycled||style="text-align:right;"|4.64||style="text-align:right;"|13||style="text-align:right;"|340 billion||27% of the plastic bottles manufactured get [[885: Recycling|recycled]]
|-
|[[File:meteor.gif]]
|A bright meteor is visible somewhere||style="text-align:right;"|1.15||style="text-align:right;"|52||style="text-align:right;"|27,400,000||This varies based on location, time of day, time of year, weather, personal perception and a number of other factors, but according to [http://www.amsmeteors.org/meteor-showers/meteor-faq/#4 The American Meteor Society], between 2-16 can be seen during the hours before daylight where it would be too bright to see them.
|-
|[[File:oldfaithful.gif]]
|Old Faithful erupts||style="text-align:right;"|5640 (94 minutes)||style="text-align:right;"|0.011 (15 per day)||style="text-align:right;"|5,595||{{w|Old Faithful}} is a geyser in {{w|Yellowstone National Park}} in the US, that tends to erupt every 65 or 91 minutes. XKCD's period of 1h 34m falls between the [https://geysertimes.org/geyser.php?id=Old%20Faithful mean and median of recent Old Faithful eruptions] and corresponds to a [http://geysertimes.org/getSingleEruption.php?id=645135 February 16, 2014 eruption].
|-
|[[File:shark.gif]]
|A fishing boat catches a shark||style="text-align:right;"|0.83||style="text-align:right;"|72||style="text-align:right;"|38,000,000|| [[1326: Sharks]]; Shark populations have experienced severe declines due to fishing impacts both of {{w|shark finning|finning}} and by-catch.
|-
|[[File:us cancer.gif]]
|Someone in the US is diagnosed with cancer||style="text-align:right;"|18.99||style="text-align:right;"|3.2||style="text-align:right;"|1,660,000|| According to the [http://www.cancer.org American Cancer Society], there will be an estimated 1,665,540 new cancer cases diagnosed in the US in 2014.
|-
|[[File:us cancer death.gif]]
|Someone in the US dies from cancer||style="text-align:right;"|54.34||style="text-align:right;"|1.1||style="text-align:right;"|580,000|| According to the [http://www.cancer.org American Cancer Society], in 2014 there will be an estimated 585,720 cancer deaths in the US.
|-
|[[File:dog.gif]]
|Someone adopts a dog from a shelter||style="text-align:right;"|15.6||style="text-align:right;"|3.8||style="text-align:right;"|2,000,000||[http://www.statisticbrain.com/pet-owner-industry-stats/ 10%] of owned dogs were adopted from shelters
|-
|[[File:cat.gif]]
|Someone adopts a cat from a shelter||style="text-align:right;"|21.3||style="text-align:right;"|2.8||style="text-align:right;"|1,500,000||[http://www.statisticbrain.com/pet-owner-industry-stats/ 18%] of owned cats were adopted from shelters
|-
|[[File:wedding.gif]]
|Someone gets married||style="text-align:right;"|0.75||style="text-align:right;"|80||style="text-align:right;"|42,000,000||According to [http://www.statisticbrain.com/marriage-statistics/ this study], there are 2,077,000 marriages in the US every year.
|-
|[[File:domain.gif]]
|Someone registers a domain||style="text-align:right;"|0.64||style="text-align:right;"|94||style="text-align:right;"|49,300,000 ||According to [http://www.dailychanges.com/ Dailychanges.com], about 135,000 domains are registered every day, but this figure fluctuates.
|-
|[[File:house.gif]]
|Someone in the US buys a house||style="text-align:right;"|6.22||style="text-align:right;"|9.6||style="text-align:right;"|5,000,000||According to [http://www.census.gov/construction/nrs/pdf/newressales.pdf The Census Bureau], on average there are 400,000 home purchases in the US each month.
|-
|[[File:tattoo.gif]]
|Someone in the US gets a tattoo||style="text-align:right;"|2.06||style="text-align:right;"|29||style="text-align:right;"|15,300,000||This estimate is probably based on the percentage of people who are tattooed, and not how frequently they purchase one, but the figures [http://theweek.com/article/index/233633/the-tattoo-economy-by-the-numbers here], [http://www.vanishingtattoo.com/tattoo_facts.htm here], and [http://www.statisticbrain.com/tattoo-statistics/ here] add to the credibility of the claim.
|-
|[[File:pulsar.gif]]
|The star PSR J1748-2446AD rotates 1,000 times||style="text-align:right;"|1.4||style="text-align:right;"|42.9||style="text-align:right;"|22,548,240, which means 22.5 billion times per year||{{w|PSR J1748-2446ad}} is the fastest spinning {{w|pulsar}} known.
|-
|[[File:facebook.gif]]
|Someone lies about their age to sign up for Facebook||style="text-align:right;"|4.32||style="text-align:right;"|14||style="text-align:right;"|7,300,000||To sign up for Facebook, [https://www.facebook.com/help/210644045634222 the user must claim to be at least 13 years old]. This is a reflection of the U.S. {{w|Children's Online Privacy Protection Act}}.
|-
|[[File:iphone.gif]]
|Someone breaks an iPhone screen||style="text-align:right;"|0.93||style="text-align:right;"|65||style="text-align:right;"|34,000,000||According to a [http://www.cnet.com/news/quarter-of-iphones-have-a-broken-screen-says-new-poll/ CNET report], up to a quarter of iPhones have a broken screen.
|-
|[[File:littleleague.gif]]
|A Little League player strikes out||style="text-align:right;"|1.23||style="text-align:right;"|49||style="text-align:right;"|25,754,400||{{w|Little League Baseball|Little League}} is a system of local youth baseball and softball competitions. A {{w|strikeout}} is a situation in baseball and softball. This figure will be inconsistent throughout the year as baseball is normally not played in the winter.
|-
|[[File:ndsex.gif]]
|Someone has sex in North Dakota||style="text-align:right;"|1.38||style="text-align:right;"|43||style="text-align:right;"|22,900,000||Since {{w|North Dakota}} has 723,000 inhabitants (ranked the 48th state), and if we estimate the sexually active population as 80% (and if ''someone'' means ''a couple)'' this means that people in North Dakota have sex 79.1 times a year. It is estimated that [http://geography.about.com/od/culturalgeography/a/geographyofsex.htm 3.93% of the world population has sex on a given day;] Randall's rate for North Dakota is 17.3% which is not low.
|-
|[[File:bieber.gif]]
|Justin Bieber gains a follower on Twitter||style="text-align:right;"|4.73||style="text-align:right;"|13||style="text-align:right;"|6,670,000|| [[802: Online Communities 2#Twitter Region|802: Online Communities 2]]; {{w|Justin Bieber}} is a Canadian pop music singer whose [https://twitter.com/justinbieber Twitter account] is extremely popular.
|-
|[[File:denverpizza.gif]]
|Someone in Denver orders a pizza||style="text-align:right;"|1.27||style="text-align:right;"|47||style="text-align:right;"|24,800,000|| In 2013, an estimated [http://www.statisticbrain.com/pizza-statistics/ 3 billion] pizzas were sold in the US. With a population of approximately 320 million, this is an average of just over 9 pizzas per person per year. According to the [http://quickfacts.census.gov/qfd/states/08/08031.html 2010 Census], the population of Denver was, rounded, 650,000. The frequency shown equates to over 38 pizzas per person per year, four times the national average. But counting the larger {{w|Denver metropolitan area}}, with a population of 2,890,000, the frequency shown equates to a much more reasonable 8.5 pizzas per person per year
|}

==Transcript==
:[Repetitive events are written in grey and arranged in a grid. Each statement pulses to black and then returns to grey at an interval characteristic of the named event.]

{| style="text-align:center;"
|- style="vertical-align: top; background-color:#eeeeee;"
|Heartbeat (0.86 sec)
|One birth (0.24 sec)
|One death (0.56 sec)
|Someone edits Wikipedia (0.67 sec)
|Someone buys a vibrator (2.99 sec)
|- style="vertical-align: top;"
|China builds a car (1.89 sec)
|Japan builds a car (4.01 sec)
|Germany builds a car (5.8 sec)
|The US builds a car (6.95 sec)
|Someone else builds a car (1.03 sec)
|- style="vertical-align: top; background-color:#eeeeee;"
|A European Union resident has their first kiss (5.53 sec)
|A US fire department puts out a fire (23 sec)
|Someone hits a hole-in-one (180 sec)
|My turn signal blinks (0.94 sec)
|The turn signal of the car in front of me blinks (0.9 sec)
|- style="vertical-align: top;"
|Earthquake (magnitude 1) (2.43 sec)
|Earthquake (magnitude 2) (24.26 sec)
|Earthquake (magnitude 3) (242.6 sec)
|Earthquake (magnitude 4) (2426 sec, 42 min)
|Member of the UK Parliament flushes a toilet (10.06 sec)
|- style="vertical-align: top; background-color:#eeeeee;"
|An airline flight takes off (0.93 sec)
|Someone buys ''To Kill a Mockingbird'' (42.05 sec)
|Someone's pet cat kills a mockingbird (1.82 sec)
|Someone in Phoenix buys new shoes (1.08 sec)
|Someone in Phoenix puts on a condom (2.05 sec)
|- style="vertical-align: top;"
|Someone locks their keys in their car (2.43 sec)
|A Sagittarius named Amelia drinks a soda (7.79 sec)
|A dog bites someone in the US (7.01 sec)
|Someone steals a bicycle (24.93 sec)
|A bald eagle catches a fish (2.69 sec)
|- style="vertical-align: top; background-color:#eeeeee;"
|50,000 plastic bottles are produced (1.27 sec)
|50,000 plastic bottles are recycled (4.64 sec)
|A bright meteor is visible somewhere (1.15 sec)
|Old Faithful erupts (5640 sec, 94 min)
|A fishing boat catches a shark (0.83 sec)
|- style="vertical-align: top;"
|Someone in the US is diagnosed with cancer (18.99 sec)
|Someone in the US dies from cancer (54.34 sec)
|Someone adopts a dog from a shelter (15.6 sec)
|Someone adopts a cat from a shelter (21.3 sec)
|Someone gets married (0.75 sec)
|- style="vertical-align: top; background-color:#eeeeee;"
|Someone registers a domain (0.64 sec)
|Someone in the US buys a house (6.22 sec)
|Someone in the US gets a tattoo (2.06 sec)
|The star ''PSR J1748-2446ad'' rotates 1,000 times (1.4 sec)
|Someone lies about their age to sign up for Facebook (4.32 sec)
|- style="vertical-align: top;"
|Someone breaks an iPhone screen (0.93 sec)
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2613: Bad Map Projection: Madagascator

2022-04-29T23:07:49Z

172.69.34.10: aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa

2613: Bad Map Projection: Madagascator

2022-04-29T22:40:48Z

172.69.34.10: will this work?

{{comic
| number = 2613
| date = April 29, 2022
| title = Bad Map Projection: Madagascator
| image = bad_map_projection_madagascator.png
| titletext = The projection's north pole is in a small lake on the island of Mahé in the Seychelles, which is off the top of the map and larger than the rest of the Earth's land area combined.
}}

==Explanation==
{{incomplete|Created by MADAGASCAR (2005) - Please change this comment when editing this page. Do NOT delete this tag too soon.}}

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣯⡿⠷⠾⠿⠛⠋⠉⠁⠀⠀⠀⠀⢀⣀⣀⣀⣈⣉⣙⡻⢿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣯⡿⠿⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠉⠉⠀⠈⠉⠉⠉⠉⠀⠈⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠤⠤⠤⠴⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⣤⣀⣀⣈⡛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⠞⠋⠁⠀⠀⠀⠀⠈⠉⠙⠛⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣸⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠛⠉⠁⠀⠈⢿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠃⠀⠀⠀⠀⠀⠀⠘⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⣀⣀⣀⣠⣤⣤⣤⣤⣤⣤⣤⣄⣀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃⠀⠀⠀⠀⠀⠀⠀⠀⢻⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠚⠛⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠶⢤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣶⣶⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠳⣤⠀⢀⣀⡀⠀⠀⠀⠀⠀⣠⡴⠖⠚⠛⠛⠛⠛⠛⠛⢻⣿⣿⣯⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⣠⣿⡿⠃⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠉⠉⠙⠛⠛⠳⠶⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⢿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⢀⣼⣿⠟⠁⠀⠀⠘⣧⠀⠀⠀⠀⠀⣀⣠⣤⡴⠶⠶⠶⢤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠸⢦⣄⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⣠⣾⡟⠁⠀⠀⠀⠀⠀⢸⡆⠀⠀⣼⠋⠉⣠⣤⣶⣶⣦⡀⠀⠀⠉⠙⢳⡆⠀⠀⠀⠀⢠⡟⣸⡇⠀⠀⠀⠀⠈⠛⢿⣆⣠⣤⣤⣶⣒⡒⠒⠒⠲⣄⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⢠⣼⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⢳⣄⠀⣏⣀⣸⣿⣿⣿⣿⣿⣇⣀⣤⣤⠶⠟⠁⠀⠀⠀⢠⡞⠰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣾⣿⣿⣷⡄⠀⠀⣿⠀⠀⠘⣷⣿⣿⣿⣿⣯⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⢰⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⠿⢿⣭⣭⣭⣭⣉⣉⣁⣀⣀⣀⣀⣀⣀⣀⣴⠛⠁⠀⣀⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠉⠛⠳⠶⠶⠟⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⡇⠀⠀⠀⠀⣴⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⢩⡭⠥⠶⠶⠞⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣤⣤⣤⣤⣄⣀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⢀⣀⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣦⡀⠈⠉⠉⠉⠉⠙⢿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣰⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⣴⣿⣿⣿⣿⡿⠀⠀⠀⠀⣠⣶⣶⣤⣄⠀⠈⢳⣄⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢀⣴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⠀⠀⢸⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠻⣿⣿⣿⡿⠀⣠⠶⠋⠀⠀⠀⠀⠀⠀⠀⠈⢿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠶⠶⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣤⣤⣤⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠞⢿⡉⠉⢹⡆⠀⠀⠀⣿⠀⠀⠀⣿⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⢿⡅⠀⠀⠘⡇⢀⣠⣷⣤⣤⣤⣿⣀⡀⢸⡇⠀⣼⠿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⣏⠀⠈⢷⣄⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡻⢿⣇⣠⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠏⠀⢙⣦⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠷⠶⢻⡄⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣧⠀⠀⠀⠀⠀⠀⠀⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⣼⢳⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣀⣠⣼⠟⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⠀⠀⠀⢠⣤⣼⠶⠛⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠏⠀⠀⠀⠀⢰⡇⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣤⣶⣾⣶⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⠂⢀⠀⠀⢀⡼⢀⣠⡴⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣠⣿⣶⡾⠿⢿⠋⠁⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣁⣴⡶⠾⠿⠏⣀⣠⡤⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⢀⣀⢶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⢀⣾⣧⣠⡴⠟⢂⡴⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⣙⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⡟⠋⢹⣇⣦⣶⠟⣀⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢀⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣿⣿⣟⣻⠛⠉⢀⣠⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠃⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠐⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣿⠏⠉⠁⢀⡘⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⢨⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣾⣿⣿⡀⠀⣼⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⢰⠏⠀⠀⠀⠀⢀⣾⣿⣻⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡞⢃⣶⡿⠶⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢀⡿⠀⠀⠀⠀⢀⣾⢿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣫⣿⣿⣄⠈⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⢸⠁⠀⠀⠀⠀⣼⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣼⣿⣿⡷⠦⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠚⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⣿⣷⡾⠿⣋⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣴⣶⣿⣿⣶⠚⢋⢠⡾⣱⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡞⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠐⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⡇⢹⣤⣿⠟⢛⡵⠂⠀⠀⠀⠀⠀⢰⣆⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡞⠋⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣻⡟⣹⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⣿⣽⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡾⢿⡁⣠⠞⢡⣖⡀⠀⠀⢀⣠⣤⣿⡏⣩⠍⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣦⡞⠁⣹⣟⢿⣿⣿⣿⣿⣿⠟⣿⣩⠿⣿⠁⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⠿⢻⡅⣀⡾⢃⠉⠉⠉⢉⣉⣽⣯⣿⣇⣀⣠⣤⠤⠄⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣞⡁⠈⣻⠿⢶⡷⠶⢿⠚⠻⡇⣀⣽⣾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣯⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⠟⠛⠁⠀⣿⠈⠉⢻⣿⠃⢸⣤⣄⠀⣰⣟⣁⣈⣉⣹⣿⡷⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣷⣤⣼⣧⣤⣾⣷⣾⠿⠟⠋⠀⠀⠀⠀⠀⢀⡠⣤⡀⠀⠈⢷⣿⣿⣤⣤⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋⠁⠀⠀⠀⠀⣿⢀⣴⠟⠻⡄⢸⣿⣿⠛⠁⠉⠉⠉⠉⣩⠿⢿⣤⠤⠤⠤⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠸⣷⡏⠙⠓⠀⣾⢿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⢠⣤⣼⠿⠋⠁⢠⣤⣿⣿⣿⣸⣀⠀⠛⣦⣤⣾⣥⣤⣤⠿⢶⣛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣷⣿⣏⠻⠄⠀⣿⡧⠘⢿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⡿⠛⠁⠀⠀⠀⠀⠀⠀⠛⠛⠁⠀⠠⠼⠟⢛⣫⠟⢛⣿⣿⣟⣻⡷⠟⣼⣶⣦⣤⠐⠒⠛⢿⡄⣠⣇⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⡜⣿⣿⡏⠙⢧⡀⣿⢿⡟⠛⠿⠿⠯⠉⠙⢿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣴⣯⣥⣶⣛⣡⠟⢿⣜⣧⣾⡽⠋⣹⣟⠻⠿⠟⢻⣟⣿⡿⠁⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⡀⣴⣿⡿⣿⡟⠛⠛⣿⡟⠛⣿⣶⣀⡀⠀⠀⠀⠀⠀⠉⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠋⠉⠀⠀⠉⠉⢁⣤⢴⣿⣿⡟⠐⣶⣿⠋⠀⠀⠀⢸⡏⠉⠳⣤⣤⡾⣿⠀⠀⠀⣤⠀⠀⠀⢀⡀⣧⡀⡄⠀⠀⣀⣸⣿⣿⡉⠈⡇⠀⠁⢀⣰⣿⡛⠶⠭⠭⠿⠶⠶⠃⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⢿⣽⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠶⠶⠶⠶⠛⠋⢁⣙⣿⣾⣿⣧⡤⠴⠖⢠⣼⠛⠛⠛⠛⠛⣶⣿⣤⣴⣞⣿⣀⣆⣀⣸⣧⣿⣿⡷⢶⣾⣉⣀⣨⡿⣿⣄⢲⣆⠀⣼⡟⠈⠙⠛⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠛⠿⠿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⡶⠾⣿⢿⡿⣿⣿⣥⣤⣴⡿⣿⠈⠉⣉⠉⠙⠛⠛⠛⠛⠻⣿⣬⡏⢈⣏⣰⡇⠸⣧⠀⠀⠀⢹⡇⠀⠀⠙⢻⡿⢳⣿⣿⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠴⠞⠁⢸⡷⠿⠟⣿⣿⣾⣟⠁⠀⠀⣿⠀⡀⠀⢶⣀⣶⣀⣿⣀⣠⡿⠿⠛⠀⠀⠀⠀⠀⠀⠈⠁⠀⠠⠤⠬⣷⣿⠬⣿⣿⣆⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢉⣉⡼⠿⣍⠛⠂⠀⣿⣼⣇⡼⠀⠉⠉⠉⠁⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣸⣂⣠⣾⡯⠟⠙⠛⠛⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠶⠋⢁⡾⠂⠈⣳⣶⣷⣿⣿⡿⠃⠀⢠⡄⢰⡆⡀⠀⣀⠀⣀⣀⠀⡀⠲⣦⣴⣾⣿⣟⣽⣋⣉⣉⣉⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣄⣀⣤⠟⠉⠉⠉⠭⠽⣿⣿⢿⣧⡀⢀⣼⠃⡾⣁⠙⣶⡇⠀⢈⣹⣿⣿⣾⣿⣿⡛⠋⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠠⣬⡿⠉⢸⣿⣿⣿⣿⣿⣻⣿⣷⣾⣿⣟⣛⢻⡟⠛⠚⠋⢹⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠶⠾⠿⣏⡉⠉⠙⣿⡯⠍⡽⠉⠛⠻⢿⡷⢦⠄⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠆⠀⠀⠀⠀⠈⠓⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

==Transcript==
{{incomplete transcript|Do NOT delete this tag too soon.}}
Bad map projection #248: Madagascar

Mercator projection but with the North Pole in the Indian Ocean so it exaggerates the size of Madagascar instead of Greenland

{{comic discussion}}

[[Category:Bad Map Projections]]

Talk:2610: Assigning Numbers

2022-04-27T20:01:53Z

172.69.34.10: /* Paradoxicality argument */

Does this imply that [https://en.wikipedia.org/wiki/G%C3%B6del%27s_incompleteness_theorems Gödel's Incompleteness Theorem] isn't correct? And that it's method is bunk? Please help! -Seer [[Special:Contributions/162.158.107.230|162.158.107.230]] 02:08, 23 April 2022 (UTC)
I believe the intention is that the theorem is not part of the set of bad data science, just that they share this one feature.

Isn't the Gödel number for a theorem calculated by multiplying the numbers of the components together, so complicated theorems would have larger numbers? If so, the current explanation that this isn't a good way to judge fields is wrong. I'm not too sure though. [[User:MrCandela|MrCandela]] ([[User talk:MrCandela|talk]]) 05:52, 23 April 2022 (UTC)

:I do not believe that the title suggests renumbering theorems with Gödel numbers, but averaging the existing theorem numbers. Or otherwise, MrCandela's suggestion would be the way to go: Complicated Theorems have larger numbers. Sebastian --[[Special:Contributions/172.68.110.133|172.68.110.133]] 08:10, 23 April 2022 (UTC)

:Yeah a quick look at some magazines like [https://www.quantamagazine.org/how-godels-incompleteness-theorems-work-20200714/#jump2/ this one] and I think Randall has a point [[User:MrCandela|MrCandela]] ([[User talk:MrCandela|talk]]) 09:48, 23 April 2022 (UTC)

I wish I'd started the explanation off when I first saw it (somone posted the first Transcript whilst I was pondering, so I left off). I think there's some serious re-editing to be done, but basically it points to someone (Cueball, a dabbling armchair mathematician faced with some not directly mathematically-based problem) thinking that 'all' it takes is to encode the whatever-it-is, arbitrarily, and then with a few easy equations something useful cannbe derived. When, in reality, even if this is possible (ignoring the "takes the age of the universe to permute things to find the right answer" sort of sticking-block) it depends upon a ''good'' numerical encoding (enough attention to detail, but not too much, and in the right sort of way) and possibly quite a lot of data-demunging and filtration (again, just the right amount and in the correct manner) to pop out the "answer" being looked for. For some things, this can be easy, though there are always statistical pitfalls/etc. For others ("life, the universe and everything", say) the task is far more complex and the result ("42"?) might not seem to be a very useful result for various reasons. And, on top this, there's Gödel. But that's an additional punchline, not the whole scope of the original joke. ...Anyway, this long comment is why I held back from writing the original Explanation, but I might yet wrangle my thoughts into what's since been put there. While trying not to tread upon too many toes and alternate explanations. Which is the hardest bit, I think... [[Special:Contributions/172.70.86.64|172.70.86.64]] 15:48, 23 April 2022 (UTC)

Just a comment about the technicalities of Gödel's First Incompleteness Theorem: The 'third' possibility presented [http://dstoner.net/Math_Science/godel.html here] misunderstands the term 'true but unprovable'. When mathematicians say 'true but unprovable' in the context of Gödel's Incompleteness Theorems, what they mean is 'true in the standard model but unprovable in the formal system'. The Gödel sentence is certainly true for the standard natural numbers, by contradiction: assume that the Gödel sentence is false for the standard naturals, which means that there exists a standard natural number which is the Gödel number for the proof of the Gödel sentence. Then we could decode the Gödel number into a proof (of the formal system) proving the Gödel sentence true; a contradiction. (Note that the preceding proof by contradiction can be formalised in ZFC, but not in the formal system under study.) The reason why the Gödel sentence is unprovable in the formal system is because, from the point of view of the formal system, there might be a non-standard natural number which is the Gödel number for the proof of the Gödel sentence (and non-standard numbers cannot be decoded into a proof); or there might not be. --[[User:Underbase|Underbase]] ([[User talk:Underbase|talk]]) 04:56, 24 April 2022 (UTC)

:Regarding this, I know that the policy on this site is to include every possible interpretation, but the page mentioned is an html page (and not a [https://xkcd.com/2304/ pdf]) that was not [https://xkcd.com/1847/ peer reviewed] (thus not recognized by the community), and as mentioned by the user above it fails understand the concepts it is talking about. I do not think this site should be spreading this kind of idea. I believe Randall Monroe himself would be against this.

::I also believe the current explanation is both incorrect about explaining the seeming paradox of the Gödel conjecture, & therefore somewhat incorrect about this joke. It is surely the transition from abstract to quantized - the act of applying limited formal numbering to potentially unbounded or otherwise non-standard terms - which incurs incompleteness? Within the constraints of a formal system of standard natural numbers, true≠provable, & therein lies the internal (but not total) contradiction. ''That's'' the contradiction, right? & the joke is that numbering theorems by their complexity, is not generally a productive approach for 'doing math' on them, in any sense but an abstract analytical one?
::[[User:ProphetZarquon|ProphetZarquon]] ([[User talk:ProphetZarquon|talk]]) 17:54, 24 April 2022 (UTC)

:I do not believe the Title Text calls for "calculating the average of all the fields' theorems' Gödel numbers". It asks for 'the lowest average theorem number'. The average of all, is not the average of each. The Title Text wants the average of ''each of'' the fields' theorems' Gödel numbers.
:[[User:ProphetZarquon|ProphetZarquon]] ([[User talk:ProphetZarquon|talk]]) 17:54, 24 April 2022 (UTC)

Today's [https://www.smbc-comics.com/comic/derivative Saturday Morning Breakfast Cereal] is slightly related.

== Paradoxicality argument ==

I think that revision [https://www.explainxkcd.com/wiki/index.php?title=2610:_Assigning_Numbers&oldid=231000 231000] should be removed. My explanation of what's wrong with the linked site is as follows:

Up until the section "Gödel's String", nothing is incorrect. Furthermore, the first wrong line is numbered (49), and says that Gödel's statement is equivalent to "This statement is not a theorem (of any formal system)." This is where he goes wrong, for writing down a formula for "n proves m" requires inclusion of the formal system in which this proof happens. As such, the correct translation of Gödel's statement is "This statement is not a theorem of [system]", which it indeed is not. Then he says that "We have decided that Gödel's string cannot be a theorem and neither can its negation" (true, after Rosser's trick) and therefore that this gives us "~<G∨~G>" (which is false). He has commited the sin of confusing truth and provability here.

His discussion of the Epimenides string ("This statement is not true") is accurate, except for the claim that the truth predicate is "as valid an extension to [PA] as [the provability and quining] extensions were". This is false. The provability and quining predicates can be constructed in PA and thus are not "extensions" so much as "shorthand"; this was Gödel's contribution: to see that PA can talk about provability of statements in any fixed formal system. The truth predicate is not definable in PA, as he quite ably proves (suppose it was definable, then you could write down the Epimenides sentence in PA, and thereby prove false).

The section "Gödel's Error" is just plain silly.[[Special:Contributions/172.70.114.147|172.70.114.147]] 19:28, 24 April 2022 (UTC)

What if we just change it to say something along the lines of "Certain logical systems allow values to be 'not false' without being necessarily 'true'; Godel's theorem is based on an axiomatic assumption that every statement is either true or false."?[[Special:Contributions/108.162.221.163|108.162.221.163]] 06:06, 25 April 2022 (UTC)

Is it just me, or is the given argument gibberish? Replacing the terms with more graspable ones, it seems to be saying: "1. Assume that bananas can be grown from banana-trees (why is this a reasonable assumption? Is it also a reasonable assumption to make about pear trees?). 2. Banana-trees exist. 3. Therefore, the statement that bananas cannot be grown from the trees is true (HOW is this a reasonable conclusion to leap to from the preceding points? By what bizarre leap of elided logic?). 4. This is a contradiction, therefore our initial assumption must be wrong (No, clearly the conclusion in 3 is wrong). Therefore, the statement is true (which statement are you even talking about here?)." Any chance someone could clarify that passage by including the missing steps in the logic? --[[Special:Contributions/172.69.70.159|172.69.70.159]] 19:02, 25 April 2022 (UTC)

:It's not missing any steps. The argument really is that simple. Maybe I didn't write it clearly enough... Anyway to address your specific points, I would first recommend you read {{w|Reductio ad absurdum}}, but if you don't have time (Because let's be real, nobody has enough time for reading Wikipedia articles), I'll break it down. 1. Assume the opposite of the statement (This is not a reasonable assumption almost by definition; the whole point is to disprove it, after all) using the Law of Assumption, which states that we can assume absolutely anything we want in a logical proof, so long as we keep track of what's been derived from it. 2 Assume anything else relevant 3. Follow the assumptions through to their conclusions, and find that the valid reasoning has led to an unsound result, such as a statement directly contradicting the assumption in 1. 4. One of the assumptions must be wrong in order to maintain consistency. Choose the assumption which was made for the purpose of disproving it to be the one we deem untrue, which means its opposite is true. Unfortunately these sorts of arguments don't really lend themselves to analogies with 'more graspable' statements.[[Special:Contributions/108.162.221.193|108.162.221.193]] 02:30, 26 April 2022 (UTC)

Hello,
1) Why couldn't Gödel's string be paradoxical? It is certainly A) self-referencing and B) Self-negating. Even "This Statement is True" causes trouble.
2) Where did Gödel even consider paradox to be a possibility? If he didn't, his argument is "incomplete" (just like its conclusion implies it might very well be anyway).
3) Has anyone here bothered to prove that his string is not actually paradoxical?
- Don Stoner (nobody in particular -- just a senile wimpy old nerd)

Hi again,
Here's a fun one:
"This statement is paradoxical"
1) It certainly is paradoxical (provably so)
2) It even says it's paradoxical (echoing Gödel)
3) Therefore, it must be "true" (echoing Gödel)
4) But (this time) this means it's simply "false"
5) Etc.
- Don (nobody in particular)

:1) I'm not sure what you mean by "paradoxical". If you mean something like "true and false" or "neither true nor false", that fails classical logic. Gödel (with a bit of help from Rosser) proved that we can write down a sentence G of Peano arithmetic, then prove (in PA) that G is equivalent to "no integer encodes a proof in PA of G unless a smaller one encodes a proof in PA of not G". He then pointed out that if G was provable in PA, there was also a proof of not G (basically, work out what integer encodes that proof of G, then for each smaller integer, try to decode it into a proof of not G; if you succeed, you have a proof of not G; if you fail for all, you have proved by exhaustion that your integer encodes a proof of G and no smaller integer encodes a proof of not G; all this is a proof of not G). Thus, if PA is consistent, there is no proof in PA of G. Now assume there is a proof in PA of not G. Encode this proof into an integer N. We shall now prove either G or "every integer less than N does not encode a proof in PA of G". We thus work through every integer less than N, checking to see if it encodes a proof in PA of G. If it does we have proved G; if no integers less than N encode a proof of G then we have proved "for all n < N, n does not encode a proof in PA of G". In the latter case, we have proved that every integer encoding a proof in PA of G is greater than N, which is an integer encoding a proof in PA of not G; this implies G! As such, we started with a proof in PA of not G (NOTE: THIS IS DIFFERENT FROM MERELY ASSUMING not G), and produced a proof in PA of G. So if PA is consistent, there is no proof in PA of not G either. Hence PA is either inconsistent (as if PA proves either G or not G, it proves the other and hence false) or incomplete (proving neither).

:2) He proved that either PA proves false, or there is a statement such that PA proves neither the statement nor its negation. The first includes paradoxicality. (His second incompleteness theorem was essentially: "By the argument above, PA proves that if PA is consistent then G has no proof in PA, which easily implies that PA proves "If PA is consistent, then G". Now suppose PA proves that PA is consistent. Then by modus ponens, PA proves G, and therefore PA is inconsistent. So if PA proves that PA is consistent, then PA is inconsistent.") (It ''is'' possible for a consistent system to prove its own inconsistency.)

:3) Most mathematicians assume that ZFC is consistent, even augmented by some pretty strong large cardinal hypotheses. [[Special:Contributions/172.70.35.72|172.70.35.72]] 17:11, 27 April 2022 (UTC)

:The short answer to your questions is that Godel's method was rigorous. Godel numbering is much more precise than natural language ever could be. The longer answer is that there's a reason Godel's theorem is considered a work of genius; though the overall concept is fairly easy to grasp intuitively, making it into an actual theorem takes a lot of work and cleverness. There are multiple long Wikipedia pages about it just outlining the generals. The proof itself is rock solid, but far beyond the scope of this page. And the pithy answer is "Do you really think you're the first person to think of that? Mathematicians spent decades analyzing the theorems with uncharitable eyes."[[Special:Contributions/108.162.221.119|108.162.221.119]] 04:12, 27 April 2022 (UTC)

:: I am certain I am not the only person to notice his error because I have been contacted by others who noticed it independently. (None of us were sufficiently arrogant to presume we were first.) Further, we have all spent a great deal more time investigating this than you presume. Gödel's numbering was indeed rigorous and precise, but in spite of his genius, he simply failed to consider the possibility of paradox (incompleteness). If I am wrong about this, it would be would be a simple matter to show me where he addressed this. - Don Stoner (n.i.p.)

I'm going to remove the section stating that Godel's theorem is self-negating (it's not) and that his methodology was incomplete. And before anyone re-adds it, I simply ask that you please please PLEASE actually read up on the subject (and I don't mean from random html pages). Mathematicians have been actively trying to find a flaw in Godel's proof since before it was published; I promise you that whatever clever paradoxicality argument you've come up with has already been considered and eliminated by the professionals.

: Your parting shot kind of reminds me of Junior high school. Specifically, I was one nerd being confronted by a few dozen "normal" kids. I was outnumbered, but there was really only room for one kid to get in my face at a time. As I told each of those kids (one at a time), "Your buddies aren't here right now. It's just you and me." So, unless you can talk one of those "professionals" (who actually understands Gödel's proof) into joining us here, you need to explain to me where Gödel addressed the possibility of paradox (he didn't). His methodology was incomplete. You also need to explain to me why you assert that "This statement cannot..." is not self-negating (it is). Further, since "the policy on this site is to include every possible interpretation" you also need to explain to me why you have taken it upon yourself to override Randal's authority. - Don Stoner (n.i.p.)
:: I can't even be bothered to work out who is saying what. Don, if you're interested in site policy, use the proper <nowiki>~~~~</nowiki> signature (get an account in your name, if you want to be named), and possibly chill out a bit too. If someone is arguing (can't be bothered to check the edit history/diffs) then they need to use a .sig too. And colon-indents per level of reply is useful. But don't mind me, it looks like you're having fun either on your own or as a pair (or more). Just sayin'... [[Special:Contributions/162.158.159.71|162.158.159.71]] 17:54, 27 April 2022 (UTC)
::: Thanks! (I'm a retired robotics-embedded-system programmer, but I'm not much of an end used. I need help to use my cellphone.) - Don --[[Special:Contributions/172.69.34.10|172.69.34.10]] 19:55, 27 April 2022 (UTC)

Talk:2610: Assigning Numbers

2022-04-27T20:00:14Z

172.69.34.10: /* Paradoxicality argument */

Does this imply that [https://en.wikipedia.org/wiki/G%C3%B6del%27s_incompleteness_theorems Gödel's Incompleteness Theorem] isn't correct? And that it's method is bunk? Please help! -Seer [[Special:Contributions/162.158.107.230|162.158.107.230]] 02:08, 23 April 2022 (UTC)
I believe the intention is that the theorem is not part of the set of bad data science, just that they share this one feature.

Isn't the Gödel number for a theorem calculated by multiplying the numbers of the components together, so complicated theorems would have larger numbers? If so, the current explanation that this isn't a good way to judge fields is wrong. I'm not too sure though. [[User:MrCandela|MrCandela]] ([[User talk:MrCandela|talk]]) 05:52, 23 April 2022 (UTC)

:I do not believe that the title suggests renumbering theorems with Gödel numbers, but averaging the existing theorem numbers. Or otherwise, MrCandela's suggestion would be the way to go: Complicated Theorems have larger numbers. Sebastian --[[Special:Contributions/172.68.110.133|172.68.110.133]] 08:10, 23 April 2022 (UTC)

:Yeah a quick look at some magazines like [https://www.quantamagazine.org/how-godels-incompleteness-theorems-work-20200714/#jump2/ this one] and I think Randall has a point [[User:MrCandela|MrCandela]] ([[User talk:MrCandela|talk]]) 09:48, 23 April 2022 (UTC)

I wish I'd started the explanation off when I first saw it (somone posted the first Transcript whilst I was pondering, so I left off). I think there's some serious re-editing to be done, but basically it points to someone (Cueball, a dabbling armchair mathematician faced with some not directly mathematically-based problem) thinking that 'all' it takes is to encode the whatever-it-is, arbitrarily, and then with a few easy equations something useful cannbe derived. When, in reality, even if this is possible (ignoring the "takes the age of the universe to permute things to find the right answer" sort of sticking-block) it depends upon a ''good'' numerical encoding (enough attention to detail, but not too much, and in the right sort of way) and possibly quite a lot of data-demunging and filtration (again, just the right amount and in the correct manner) to pop out the "answer" being looked for. For some things, this can be easy, though there are always statistical pitfalls/etc. For others ("life, the universe and everything", say) the task is far more complex and the result ("42"?) might not seem to be a very useful result for various reasons. And, on top this, there's Gödel. But that's an additional punchline, not the whole scope of the original joke. ...Anyway, this long comment is why I held back from writing the original Explanation, but I might yet wrangle my thoughts into what's since been put there. While trying not to tread upon too many toes and alternate explanations. Which is the hardest bit, I think... [[Special:Contributions/172.70.86.64|172.70.86.64]] 15:48, 23 April 2022 (UTC)

Just a comment about the technicalities of Gödel's First Incompleteness Theorem: The 'third' possibility presented [http://dstoner.net/Math_Science/godel.html here] misunderstands the term 'true but unprovable'. When mathematicians say 'true but unprovable' in the context of Gödel's Incompleteness Theorems, what they mean is 'true in the standard model but unprovable in the formal system'. The Gödel sentence is certainly true for the standard natural numbers, by contradiction: assume that the Gödel sentence is false for the standard naturals, which means that there exists a standard natural number which is the Gödel number for the proof of the Gödel sentence. Then we could decode the Gödel number into a proof (of the formal system) proving the Gödel sentence true; a contradiction. (Note that the preceding proof by contradiction can be formalised in ZFC, but not in the formal system under study.) The reason why the Gödel sentence is unprovable in the formal system is because, from the point of view of the formal system, there might be a non-standard natural number which is the Gödel number for the proof of the Gödel sentence (and non-standard numbers cannot be decoded into a proof); or there might not be. --[[User:Underbase|Underbase]] ([[User talk:Underbase|talk]]) 04:56, 24 April 2022 (UTC)

:Regarding this, I know that the policy on this site is to include every possible interpretation, but the page mentioned is an html page (and not a [https://xkcd.com/2304/ pdf]) that was not [https://xkcd.com/1847/ peer reviewed] (thus not recognized by the community), and as mentioned by the user above it fails understand the concepts it is talking about. I do not think this site should be spreading this kind of idea. I believe Randall Monroe himself would be against this.

::I also believe the current explanation is both incorrect about explaining the seeming paradox of the Gödel conjecture, & therefore somewhat incorrect about this joke. It is surely the transition from abstract to quantized - the act of applying limited formal numbering to potentially unbounded or otherwise non-standard terms - which incurs incompleteness? Within the constraints of a formal system of standard natural numbers, true≠provable, & therein lies the internal (but not total) contradiction. ''That's'' the contradiction, right? & the joke is that numbering theorems by their complexity, is not generally a productive approach for 'doing math' on them, in any sense but an abstract analytical one?
::[[User:ProphetZarquon|ProphetZarquon]] ([[User talk:ProphetZarquon|talk]]) 17:54, 24 April 2022 (UTC)

:I do not believe the Title Text calls for "calculating the average of all the fields' theorems' Gödel numbers". It asks for 'the lowest average theorem number'. The average of all, is not the average of each. The Title Text wants the average of ''each of'' the fields' theorems' Gödel numbers.
:[[User:ProphetZarquon|ProphetZarquon]] ([[User talk:ProphetZarquon|talk]]) 17:54, 24 April 2022 (UTC)

Today's [https://www.smbc-comics.com/comic/derivative Saturday Morning Breakfast Cereal] is slightly related.

== Paradoxicality argument ==

I think that revision [https://www.explainxkcd.com/wiki/index.php?title=2610:_Assigning_Numbers&oldid=231000 231000] should be removed. My explanation of what's wrong with the linked site is as follows:

Up until the section "Gödel's String", nothing is incorrect. Furthermore, the first wrong line is numbered (49), and says that Gödel's statement is equivalent to "This statement is not a theorem (of any formal system)." This is where he goes wrong, for writing down a formula for "n proves m" requires inclusion of the formal system in which this proof happens. As such, the correct translation of Gödel's statement is "This statement is not a theorem of [system]", which it indeed is not. Then he says that "We have decided that Gödel's string cannot be a theorem and neither can its negation" (true, after Rosser's trick) and therefore that this gives us "~<G∨~G>" (which is false). He has commited the sin of confusing truth and provability here.

His discussion of the Epimenides string ("This statement is not true") is accurate, except for the claim that the truth predicate is "as valid an extension to [PA] as [the provability and quining] extensions were". This is false. The provability and quining predicates can be constructed in PA and thus are not "extensions" so much as "shorthand"; this was Gödel's contribution: to see that PA can talk about provability of statements in any fixed formal system. The truth predicate is not definable in PA, as he quite ably proves (suppose it was definable, then you could write down the Epimenides sentence in PA, and thereby prove false).

The section "Gödel's Error" is just plain silly.[[Special:Contributions/172.70.114.147|172.70.114.147]] 19:28, 24 April 2022 (UTC)

What if we just change it to say something along the lines of "Certain logical systems allow values to be 'not false' without being necessarily 'true'; Godel's theorem is based on an axiomatic assumption that every statement is either true or false."?[[Special:Contributions/108.162.221.163|108.162.221.163]] 06:06, 25 April 2022 (UTC)

Is it just me, or is the given argument gibberish? Replacing the terms with more graspable ones, it seems to be saying: "1. Assume that bananas can be grown from banana-trees (why is this a reasonable assumption? Is it also a reasonable assumption to make about pear trees?). 2. Banana-trees exist. 3. Therefore, the statement that bananas cannot be grown from the trees is true (HOW is this a reasonable conclusion to leap to from the preceding points? By what bizarre leap of elided logic?). 4. This is a contradiction, therefore our initial assumption must be wrong (No, clearly the conclusion in 3 is wrong). Therefore, the statement is true (which statement are you even talking about here?)." Any chance someone could clarify that passage by including the missing steps in the logic? --[[Special:Contributions/172.69.70.159|172.69.70.159]] 19:02, 25 April 2022 (UTC)

:It's not missing any steps. The argument really is that simple. Maybe I didn't write it clearly enough... Anyway to address your specific points, I would first recommend you read {{w|Reductio ad absurdum}}, but if you don't have time (Because let's be real, nobody has enough time for reading Wikipedia articles), I'll break it down. 1. Assume the opposite of the statement (This is not a reasonable assumption almost by definition; the whole point is to disprove it, after all) using the Law of Assumption, which states that we can assume absolutely anything we want in a logical proof, so long as we keep track of what's been derived from it. 2 Assume anything else relevant 3. Follow the assumptions through to their conclusions, and find that the valid reasoning has led to an unsound result, such as a statement directly contradicting the assumption in 1. 4. One of the assumptions must be wrong in order to maintain consistency. Choose the assumption which was made for the purpose of disproving it to be the one we deem untrue, which means its opposite is true. Unfortunately these sorts of arguments don't really lend themselves to analogies with 'more graspable' statements.[[Special:Contributions/108.162.221.193|108.162.221.193]] 02:30, 26 April 2022 (UTC)

Hello,
1) Why couldn't Gödel's string be paradoxical? It is certainly A) self-referencing and B) Self-negating. Even "This Statement is True" causes trouble.
2) Where did Gödel even consider paradox to be a possibility? If he didn't, his argument is "incomplete" (just like its conclusion implies it might very well be anyway).
3) Has anyone here bothered to prove that his string is not actually paradoxical?
- Don Stoner (nobody in particular -- just a senile wimpy old nerd)

Hi again,
Here's a fun one:
"This statement is paradoxical"
1) It certainly is paradoxical (provably so)
2) It even says it's paradoxical (echoing Gödel)
3) Therefore, it must be "true" (echoing Gödel)
4) But (this time) this means it's simply "false"
5) Etc.
- Don (nobody in particular)

:1) I'm not sure what you mean by "paradoxical". If you mean something like "true and false" or "neither true nor false", that fails classical logic. Gödel (with a bit of help from Rosser) proved that we can write down a sentence G of Peano arithmetic, then prove (in PA) that G is equivalent to "no integer encodes a proof in PA of G unless a smaller one encodes a proof in PA of not G". He then pointed out that if G was provable in PA, there was also a proof of not G (basically, work out what integer encodes that proof of G, then for each smaller integer, try to decode it into a proof of not G; if you succeed, you have a proof of not G; if you fail for all, you have proved by exhaustion that your integer encodes a proof of G and no smaller integer encodes a proof of not G; all this is a proof of not G). Thus, if PA is consistent, there is no proof in PA of G. Now assume there is a proof in PA of not G. Encode this proof into an integer N. We shall now prove either G or "every integer less than N does not encode a proof in PA of G". We thus work through every integer less than N, checking to see if it encodes a proof in PA of G. If it does we have proved G; if no integers less than N encode a proof of G then we have proved "for all n < N, n does not encode a proof in PA of G". In the latter case, we have proved that every integer encoding a proof in PA of G is greater than N, which is an integer encoding a proof in PA of not G; this implies G! As such, we started with a proof in PA of not G (NOTE: THIS IS DIFFERENT FROM MERELY ASSUMING not G), and produced a proof in PA of G. So if PA is consistent, there is no proof in PA of not G either. Hence PA is either inconsistent (as if PA proves either G or not G, it proves the other and hence false) or incomplete (proving neither).

:2) He proved that either PA proves false, or there is a statement such that PA proves neither the statement nor its negation. The first includes paradoxicality. (His second incompleteness theorem was essentially: "By the argument above, PA proves that if PA is consistent then G has no proof in PA, which easily implies that PA proves "If PA is consistent, then G". Now suppose PA proves that PA is consistent. Then by modus ponens, PA proves G, and therefore PA is inconsistent. So if PA proves that PA is consistent, then PA is inconsistent.") (It ''is'' possible for a consistent system to prove its own inconsistency.)

:3) Most mathematicians assume that ZFC is consistent, even augmented by some pretty strong large cardinal hypotheses. [[Special:Contributions/172.70.35.72|172.70.35.72]] 17:11, 27 April 2022 (UTC)

:The short answer to your questions is that Godel's method was rigorous. Godel numbering is much more precise than natural language ever could be. The longer answer is that there's a reason Godel's theorem is considered a work of genius; though the overall concept is fairly easy to grasp intuitively, making it into an actual theorem takes a lot of work and cleverness. There are multiple long Wikipedia pages about it just outlining the generals. The proof itself is rock solid, but far beyond the scope of this page. And the pithy answer is "Do you really think you're the first person to think of that? Mathematicians spent decades analyzing the theorems with uncharitable eyes."[[Special:Contributions/108.162.221.119|108.162.221.119]] 04:12, 27 April 2022 (UTC)

: I am certain I am not the only person to notice his error because I have been contacted by others who noticed it independently. (None of us were sufficiently arrogant to presume we were first.) Further, we have all spent a great deal more time investigating this than you presume. Gödel's numbering was indeed rigorous and precise, but in spite of his genius, he simply failed to consider the possibility of paradox (incompleteness). If I am wrong about this, it would be would be a simple matter to show me where he addressed this. - Don Stoner (n.i.p.)

I'm going to remove the section stating that Godel's theorem is self-negating (it's not) and that his methodology was incomplete. And before anyone re-adds it, I simply ask that you please please PLEASE actually read up on the subject (and I don't mean from random html pages). Mathematicians have been actively trying to find a flaw in Godel's proof since before it was published; I promise you that whatever clever paradoxicality argument you've come up with has already been considered and eliminated by the professionals.

: Your parting shot kind of reminds me of Junior high school. Specifically, I was one nerd being confronted by a few dozen "normal" kids. I was outnumbered, but there was really only room for one kid to get in my face at a time. As I told each of those kids (one at a time), "Your buddies aren't here right now. It's just you and me." So, unless you can talk one of those "professionals" (who actually understands Gödel's proof) into joining us here, you need to explain to me where Gödel addressed the possibility of paradox (he didn't). His methodology was incomplete. You also need to explain to me why you assert that "This statement cannot..." is not self-negating (it is). Further, since "the policy on this site is to include every possible interpretation" you also need to explain to me why you have taken it upon yourself to override Randal's authority. - Don Stoner (n.i.p.)
: I can't even be bothered to work out who is saying what. Don, if you're interested in site policy, use the proper <nowiki>~~~~</nowiki> signature (get an account in your name, if you want to be named), and possibly chill out a bit too. If someone is arguing (can't be bothered to check the edit history/diffs) then they need to use a .sig too. And colon-indents per level of reply is useful. But don't mind me, it looks like you're having fun either on your own or as a pair (or more). Just sayin'... [[Special:Contributions/162.158.159.71|162.158.159.71]] 17:54, 27 April 2022 (UTC)
:: Thanks! (I'm a retired robotics-embedded-system programmer, but I'm not much of an end used. I need help to use my cellphone.) - Don --[[Special:Contributions/172.69.34.10|172.69.34.10]] 19:55, 27 April 2022 (UTC)

Talk:2610: Assigning Numbers

2022-04-27T19:57:23Z

172.69.34.10: /* Paradoxicality argument */

Does this imply that [https://en.wikipedia.org/wiki/G%C3%B6del%27s_incompleteness_theorems Gödel's Incompleteness Theorem] isn't correct? And that it's method is bunk? Please help! -Seer [[Special:Contributions/162.158.107.230|162.158.107.230]] 02:08, 23 April 2022 (UTC)
I believe the intention is that the theorem is not part of the set of bad data science, just that they share this one feature.

Isn't the Gödel number for a theorem calculated by multiplying the numbers of the components together, so complicated theorems would have larger numbers? If so, the current explanation that this isn't a good way to judge fields is wrong. I'm not too sure though. [[User:MrCandela|MrCandela]] ([[User talk:MrCandela|talk]]) 05:52, 23 April 2022 (UTC)

:I do not believe that the title suggests renumbering theorems with Gödel numbers, but averaging the existing theorem numbers. Or otherwise, MrCandela's suggestion would be the way to go: Complicated Theorems have larger numbers. Sebastian --[[Special:Contributions/172.68.110.133|172.68.110.133]] 08:10, 23 April 2022 (UTC)

:Yeah a quick look at some magazines like [https://www.quantamagazine.org/how-godels-incompleteness-theorems-work-20200714/#jump2/ this one] and I think Randall has a point [[User:MrCandela|MrCandela]] ([[User talk:MrCandela|talk]]) 09:48, 23 April 2022 (UTC)

I wish I'd started the explanation off when I first saw it (somone posted the first Transcript whilst I was pondering, so I left off). I think there's some serious re-editing to be done, but basically it points to someone (Cueball, a dabbling armchair mathematician faced with some not directly mathematically-based problem) thinking that 'all' it takes is to encode the whatever-it-is, arbitrarily, and then with a few easy equations something useful cannbe derived. When, in reality, even if this is possible (ignoring the "takes the age of the universe to permute things to find the right answer" sort of sticking-block) it depends upon a ''good'' numerical encoding (enough attention to detail, but not too much, and in the right sort of way) and possibly quite a lot of data-demunging and filtration (again, just the right amount and in the correct manner) to pop out the "answer" being looked for. For some things, this can be easy, though there are always statistical pitfalls/etc. For others ("life, the universe and everything", say) the task is far more complex and the result ("42"?) might not seem to be a very useful result for various reasons. And, on top this, there's Gödel. But that's an additional punchline, not the whole scope of the original joke. ...Anyway, this long comment is why I held back from writing the original Explanation, but I might yet wrangle my thoughts into what's since been put there. While trying not to tread upon too many toes and alternate explanations. Which is the hardest bit, I think... [[Special:Contributions/172.70.86.64|172.70.86.64]] 15:48, 23 April 2022 (UTC)

Just a comment about the technicalities of Gödel's First Incompleteness Theorem: The 'third' possibility presented [http://dstoner.net/Math_Science/godel.html here] misunderstands the term 'true but unprovable'. When mathematicians say 'true but unprovable' in the context of Gödel's Incompleteness Theorems, what they mean is 'true in the standard model but unprovable in the formal system'. The Gödel sentence is certainly true for the standard natural numbers, by contradiction: assume that the Gödel sentence is false for the standard naturals, which means that there exists a standard natural number which is the Gödel number for the proof of the Gödel sentence. Then we could decode the Gödel number into a proof (of the formal system) proving the Gödel sentence true; a contradiction. (Note that the preceding proof by contradiction can be formalised in ZFC, but not in the formal system under study.) The reason why the Gödel sentence is unprovable in the formal system is because, from the point of view of the formal system, there might be a non-standard natural number which is the Gödel number for the proof of the Gödel sentence (and non-standard numbers cannot be decoded into a proof); or there might not be. --[[User:Underbase|Underbase]] ([[User talk:Underbase|talk]]) 04:56, 24 April 2022 (UTC)

:Regarding this, I know that the policy on this site is to include every possible interpretation, but the page mentioned is an html page (and not a [https://xkcd.com/2304/ pdf]) that was not [https://xkcd.com/1847/ peer reviewed] (thus not recognized by the community), and as mentioned by the user above it fails understand the concepts it is talking about. I do not think this site should be spreading this kind of idea. I believe Randall Monroe himself would be against this.

::I also believe the current explanation is both incorrect about explaining the seeming paradox of the Gödel conjecture, & therefore somewhat incorrect about this joke. It is surely the transition from abstract to quantized - the act of applying limited formal numbering to potentially unbounded or otherwise non-standard terms - which incurs incompleteness? Within the constraints of a formal system of standard natural numbers, true≠provable, & therein lies the internal (but not total) contradiction. ''That's'' the contradiction, right? & the joke is that numbering theorems by their complexity, is not generally a productive approach for 'doing math' on them, in any sense but an abstract analytical one?
::[[User:ProphetZarquon|ProphetZarquon]] ([[User talk:ProphetZarquon|talk]]) 17:54, 24 April 2022 (UTC)

:I do not believe the Title Text calls for "calculating the average of all the fields' theorems' Gödel numbers". It asks for 'the lowest average theorem number'. The average of all, is not the average of each. The Title Text wants the average of ''each of'' the fields' theorems' Gödel numbers.
:[[User:ProphetZarquon|ProphetZarquon]] ([[User talk:ProphetZarquon|talk]]) 17:54, 24 April 2022 (UTC)

Today's [https://www.smbc-comics.com/comic/derivative Saturday Morning Breakfast Cereal] is slightly related.

== Paradoxicality argument ==

I think that revision [https://www.explainxkcd.com/wiki/index.php?title=2610:_Assigning_Numbers&oldid=231000 231000] should be removed. My explanation of what's wrong with the linked site is as follows:

Up until the section "Gödel's String", nothing is incorrect. Furthermore, the first wrong line is numbered (49), and says that Gödel's statement is equivalent to "This statement is not a theorem (of any formal system)." This is where he goes wrong, for writing down a formula for "n proves m" requires inclusion of the formal system in which this proof happens. As such, the correct translation of Gödel's statement is "This statement is not a theorem of [system]", which it indeed is not. Then he says that "We have decided that Gödel's string cannot be a theorem and neither can its negation" (true, after Rosser's trick) and therefore that this gives us "~<G∨~G>" (which is false). He has commited the sin of confusing truth and provability here.

His discussion of the Epimenides string ("This statement is not true") is accurate, except for the claim that the truth predicate is "as valid an extension to [PA] as [the provability and quining] extensions were". This is false. The provability and quining predicates can be constructed in PA and thus are not "extensions" so much as "shorthand"; this was Gödel's contribution: to see that PA can talk about provability of statements in any fixed formal system. The truth predicate is not definable in PA, as he quite ably proves (suppose it was definable, then you could write down the Epimenides sentence in PA, and thereby prove false).

The section "Gödel's Error" is just plain silly.[[Special:Contributions/172.70.114.147|172.70.114.147]] 19:28, 24 April 2022 (UTC)

What if we just change it to say something along the lines of "Certain logical systems allow values to be 'not false' without being necessarily 'true'; Godel's theorem is based on an axiomatic assumption that every statement is either true or false."?[[Special:Contributions/108.162.221.163|108.162.221.163]] 06:06, 25 April 2022 (UTC)

Is it just me, or is the given argument gibberish? Replacing the terms with more graspable ones, it seems to be saying: "1. Assume that bananas can be grown from banana-trees (why is this a reasonable assumption? Is it also a reasonable assumption to make about pear trees?). 2. Banana-trees exist. 3. Therefore, the statement that bananas cannot be grown from the trees is true (HOW is this a reasonable conclusion to leap to from the preceding points? By what bizarre leap of elided logic?). 4. This is a contradiction, therefore our initial assumption must be wrong (No, clearly the conclusion in 3 is wrong). Therefore, the statement is true (which statement are you even talking about here?)." Any chance someone could clarify that passage by including the missing steps in the logic? --[[Special:Contributions/172.69.70.159|172.69.70.159]] 19:02, 25 April 2022 (UTC)

:It's not missing any steps. The argument really is that simple. Maybe I didn't write it clearly enough... Anyway to address your specific points, I would first recommend you read {{w|Reductio ad absurdum}}, but if you don't have time (Because let's be real, nobody has enough time for reading Wikipedia articles), I'll break it down. 1. Assume the opposite of the statement (This is not a reasonable assumption almost by definition; the whole point is to disprove it, after all) using the Law of Assumption, which states that we can assume absolutely anything we want in a logical proof, so long as we keep track of what's been derived from it. 2 Assume anything else relevant 3. Follow the assumptions through to their conclusions, and find that the valid reasoning has led to an unsound result, such as a statement directly contradicting the assumption in 1. 4. One of the assumptions must be wrong in order to maintain consistency. Choose the assumption which was made for the purpose of disproving it to be the one we deem untrue, which means its opposite is true. Unfortunately these sorts of arguments don't really lend themselves to analogies with 'more graspable' statements.[[Special:Contributions/108.162.221.193|108.162.221.193]] 02:30, 26 April 2022 (UTC)

Hello,
1) Why couldn't Gödel's string be paradoxical? It is certainly A) self-referencing and B) Self-negating. Even "This Statement is True" causes trouble.
2) Where did Gödel even consider paradox to be a possibility? If he didn't, his argument is "incomplete" (just like its conclusion implies it might very well be anyway).
3) Has anyone here bothered to prove that his string is not actually paradoxical?
- Don Stoner (nobody in particular -- just a senile wimpy old nerd)

Hi again,
Here's a fun one:
"This statement is paradoxical"
1) It certainly is paradoxical (provably so)
2) It even says it's paradoxical (echoing Gödel)
3) Therefore, it must be "true" (echoing Gödel)
4) But (this time) this means it's simply "false"
5) Etc.
- Don (nobody in particular)

:1) I'm not sure what you mean by "paradoxical". If you mean something like "true and false" or "neither true nor false", that fails classical logic. Gödel (with a bit of help from Rosser) proved that we can write down a sentence G of Peano arithmetic, then prove (in PA) that G is equivalent to "no integer encodes a proof in PA of G unless a smaller one encodes a proof in PA of not G". He then pointed out that if G was provable in PA, there was also a proof of not G (basically, work out what integer encodes that proof of G, then for each smaller integer, try to decode it into a proof of not G; if you succeed, you have a proof of not G; if you fail for all, you have proved by exhaustion that your integer encodes a proof of G and no smaller integer encodes a proof of not G; all this is a proof of not G). Thus, if PA is consistent, there is no proof in PA of G. Now assume there is a proof in PA of not G. Encode this proof into an integer N. We shall now prove either G or "every integer less than N does not encode a proof in PA of G". We thus work through every integer less than N, checking to see if it encodes a proof in PA of G. If it does we have proved G; if no integers less than N encode a proof of G then we have proved "for all n < N, n does not encode a proof in PA of G". In the latter case, we have proved that every integer encoding a proof in PA of G is greater than N, which is an integer encoding a proof in PA of not G; this implies G! As such, we started with a proof in PA of not G (NOTE: THIS IS DIFFERENT FROM MERELY ASSUMING not G), and produced a proof in PA of G. So if PA is consistent, there is no proof in PA of not G either. Hence PA is either inconsistent (as if PA proves either G or not G, it proves the other and hence false) or incomplete (proving neither).

:2) He proved that either PA proves false, or there is a statement such that PA proves neither the statement nor its negation. The first includes paradoxicality. (His second incompleteness theorem was essentially: "By the argument above, PA proves that if PA is consistent then G has no proof in PA, which easily implies that PA proves "If PA is consistent, then G". Now suppose PA proves that PA is consistent. Then by modus ponens, PA proves G, and therefore PA is inconsistent. So if PA proves that PA is consistent, then PA is inconsistent.") (It ''is'' possible for a consistent system to prove its own inconsistency.)

:3) Most mathematicians assume that ZFC is consistent, even augmented by some pretty strong large cardinal hypotheses. [[Special:Contributions/172.70.35.72|172.70.35.72]] 17:11, 27 April 2022 (UTC)

:The short answer to your questions is that Godel's method was rigorous. Godel numbering is much more precise than natural language ever could be. The longer answer is that there's a reason Godel's theorem is considered a work of genius; though the overall concept is fairly easy to grasp intuitively, making it into an actual theorem takes a lot of work and cleverness. There are multiple long Wikipedia pages about it just outlining the generals. The proof itself is rock solid, but far beyond the scope of this page. And the pithy answer is "Do you really think you're the first person to think of that? Mathematicians spent decades analyzing the theorems with uncharitable eyes."[[Special:Contributions/108.162.221.119|108.162.221.119]] 04:12, 27 April 2022 (UTC)

I am certain I am not the only person to notice his error because I have been contacted by others who noticed it independently. (None of us were sufficiently arrogant to presume we were first.) Further, we have all spent a great deal more time investigating this than you presume. Gödel's numbering was indeed rigorous and precise, but in spite of his genius, he simply failed to consider the possibility of paradox (incompleteness). If I am wrong about this, it would be would be a simple matter to show me where he addressed this. - Don Stoner (n.i.p.)

I'm going to remove the section stating that Godel's theorem is self-negating (it's not) and that his methodology was incomplete. And before anyone re-adds it, I simply ask that you please please PLEASE actually read up on the subject (and I don't mean from random html pages). Mathematicians have been actively trying to find a flaw in Godel's proof since before it was published; I promise you that whatever clever paradoxicality argument you've come up with has already been considered and eliminated by the professionals.

Your parting shot kind of reminds me of Junior high school. Specifically, I was one nerd being confronted by a few dozen "normal" kids. I was outnumbered, but there was really only room for one kid to get in my face at a time. As I told each of those kids (one at a time), "Your buddies aren't here right now. It's just you and me." So, unless you can talk one of those "professionals" (who actually understands Gödel's proof) into joining us here, you need to explain to me where Gödel addressed the possibility of paradox (he didn't). His methodology was incomplete. You also need to explain to me why you assert that "This statement cannot..." is not self-negating (it is). Further, since "the policy on this site is to include every possible interpretation" you also need to explain to me why you have taken it upon yourself to override Randal's authority. - Don Stoner (n.i.p.)
: I can't even be bothered to work out who is saying what. Don, if you're interested in site policy, use the proper <nowiki>~~~~</nowiki> signature (get an account in your name, if you want to be named), and possibly chill out a bit too. If someone is arguing (can't be bothered to check the edit history/diffs) then they need to use a .sig too. And colon-indents per level of reply is useful. But don't mind me, it looks like you're having fun either on your own or as a pair (or more). Just sayin'... [[Special:Contributions/162.158.159.71|162.158.159.71]] 17:54, 27 April 2022 (UTC)
:: Thanks! (I'm a retired robotics-embedded-system programmer, but I'm not much of an end used. I need help to use my cellphone.) - Don --[[Special:Contributions/172.69.34.10|172.69.34.10]] 19:55, 27 April 2022 (UTC)

Talk:2610: Assigning Numbers

2022-04-27T19:55:57Z

172.69.34.10: /* Paradoxicality argument */

Does this imply that [https://en.wikipedia.org/wiki/G%C3%B6del%27s_incompleteness_theorems Gödel's Incompleteness Theorem] isn't correct? And that it's method is bunk? Please help! -Seer [[Special:Contributions/162.158.107.230|162.158.107.230]] 02:08, 23 April 2022 (UTC)
I believe the intention is that the theorem is not part of the set of bad data science, just that they share this one feature.

Isn't the Gödel number for a theorem calculated by multiplying the numbers of the components together, so complicated theorems would have larger numbers? If so, the current explanation that this isn't a good way to judge fields is wrong. I'm not too sure though. [[User:MrCandela|MrCandela]] ([[User talk:MrCandela|talk]]) 05:52, 23 April 2022 (UTC)

:I do not believe that the title suggests renumbering theorems with Gödel numbers, but averaging the existing theorem numbers. Or otherwise, MrCandela's suggestion would be the way to go: Complicated Theorems have larger numbers. Sebastian --[[Special:Contributions/172.68.110.133|172.68.110.133]] 08:10, 23 April 2022 (UTC)

:Yeah a quick look at some magazines like [https://www.quantamagazine.org/how-godels-incompleteness-theorems-work-20200714/#jump2/ this one] and I think Randall has a point [[User:MrCandela|MrCandela]] ([[User talk:MrCandela|talk]]) 09:48, 23 April 2022 (UTC)

I wish I'd started the explanation off when I first saw it (somone posted the first Transcript whilst I was pondering, so I left off). I think there's some serious re-editing to be done, but basically it points to someone (Cueball, a dabbling armchair mathematician faced with some not directly mathematically-based problem) thinking that 'all' it takes is to encode the whatever-it-is, arbitrarily, and then with a few easy equations something useful cannbe derived. When, in reality, even if this is possible (ignoring the "takes the age of the universe to permute things to find the right answer" sort of sticking-block) it depends upon a ''good'' numerical encoding (enough attention to detail, but not too much, and in the right sort of way) and possibly quite a lot of data-demunging and filtration (again, just the right amount and in the correct manner) to pop out the "answer" being looked for. For some things, this can be easy, though there are always statistical pitfalls/etc. For others ("life, the universe and everything", say) the task is far more complex and the result ("42"?) might not seem to be a very useful result for various reasons. And, on top this, there's Gödel. But that's an additional punchline, not the whole scope of the original joke. ...Anyway, this long comment is why I held back from writing the original Explanation, but I might yet wrangle my thoughts into what's since been put there. While trying not to tread upon too many toes and alternate explanations. Which is the hardest bit, I think... [[Special:Contributions/172.70.86.64|172.70.86.64]] 15:48, 23 April 2022 (UTC)

Just a comment about the technicalities of Gödel's First Incompleteness Theorem: The 'third' possibility presented [http://dstoner.net/Math_Science/godel.html here] misunderstands the term 'true but unprovable'. When mathematicians say 'true but unprovable' in the context of Gödel's Incompleteness Theorems, what they mean is 'true in the standard model but unprovable in the formal system'. The Gödel sentence is certainly true for the standard natural numbers, by contradiction: assume that the Gödel sentence is false for the standard naturals, which means that there exists a standard natural number which is the Gödel number for the proof of the Gödel sentence. Then we could decode the Gödel number into a proof (of the formal system) proving the Gödel sentence true; a contradiction. (Note that the preceding proof by contradiction can be formalised in ZFC, but not in the formal system under study.) The reason why the Gödel sentence is unprovable in the formal system is because, from the point of view of the formal system, there might be a non-standard natural number which is the Gödel number for the proof of the Gödel sentence (and non-standard numbers cannot be decoded into a proof); or there might not be. --[[User:Underbase|Underbase]] ([[User talk:Underbase|talk]]) 04:56, 24 April 2022 (UTC)

:Regarding this, I know that the policy on this site is to include every possible interpretation, but the page mentioned is an html page (and not a [https://xkcd.com/2304/ pdf]) that was not [https://xkcd.com/1847/ peer reviewed] (thus not recognized by the community), and as mentioned by the user above it fails understand the concepts it is talking about. I do not think this site should be spreading this kind of idea. I believe Randall Monroe himself would be against this.

::I also believe the current explanation is both incorrect about explaining the seeming paradox of the Gödel conjecture, & therefore somewhat incorrect about this joke. It is surely the transition from abstract to quantized - the act of applying limited formal numbering to potentially unbounded or otherwise non-standard terms - which incurs incompleteness? Within the constraints of a formal system of standard natural numbers, true≠provable, & therein lies the internal (but not total) contradiction. ''That's'' the contradiction, right? & the joke is that numbering theorems by their complexity, is not generally a productive approach for 'doing math' on them, in any sense but an abstract analytical one?
::[[User:ProphetZarquon|ProphetZarquon]] ([[User talk:ProphetZarquon|talk]]) 17:54, 24 April 2022 (UTC)

:I do not believe the Title Text calls for "calculating the average of all the fields' theorems' Gödel numbers". It asks for 'the lowest average theorem number'. The average of all, is not the average of each. The Title Text wants the average of ''each of'' the fields' theorems' Gödel numbers.
:[[User:ProphetZarquon|ProphetZarquon]] ([[User talk:ProphetZarquon|talk]]) 17:54, 24 April 2022 (UTC)

Today's [https://www.smbc-comics.com/comic/derivative Saturday Morning Breakfast Cereal] is slightly related.

== Paradoxicality argument ==

I think that revision [https://www.explainxkcd.com/wiki/index.php?title=2610:_Assigning_Numbers&oldid=231000 231000] should be removed. My explanation of what's wrong with the linked site is as follows:

Up until the section "Gödel's String", nothing is incorrect. Furthermore, the first wrong line is numbered (49), and says that Gödel's statement is equivalent to "This statement is not a theorem (of any formal system)." This is where he goes wrong, for writing down a formula for "n proves m" requires inclusion of the formal system in which this proof happens. As such, the correct translation of Gödel's statement is "This statement is not a theorem of [system]", which it indeed is not. Then he says that "We have decided that Gödel's string cannot be a theorem and neither can its negation" (true, after Rosser's trick) and therefore that this gives us "~<G∨~G>" (which is false). He has commited the sin of confusing truth and provability here.

His discussion of the Epimenides string ("This statement is not true") is accurate, except for the claim that the truth predicate is "as valid an extension to [PA] as [the provability and quining] extensions were". This is false. The provability and quining predicates can be constructed in PA and thus are not "extensions" so much as "shorthand"; this was Gödel's contribution: to see that PA can talk about provability of statements in any fixed formal system. The truth predicate is not definable in PA, as he quite ably proves (suppose it was definable, then you could write down the Epimenides sentence in PA, and thereby prove false).

The section "Gödel's Error" is just plain silly.[[Special:Contributions/172.70.114.147|172.70.114.147]] 19:28, 24 April 2022 (UTC)

What if we just change it to say something along the lines of "Certain logical systems allow values to be 'not false' without being necessarily 'true'; Godel's theorem is based on an axiomatic assumption that every statement is either true or false."?[[Special:Contributions/108.162.221.163|108.162.221.163]] 06:06, 25 April 2022 (UTC)

Is it just me, or is the given argument gibberish? Replacing the terms with more graspable ones, it seems to be saying: "1. Assume that bananas can be grown from banana-trees (why is this a reasonable assumption? Is it also a reasonable assumption to make about pear trees?). 2. Banana-trees exist. 3. Therefore, the statement that bananas cannot be grown from the trees is true (HOW is this a reasonable conclusion to leap to from the preceding points? By what bizarre leap of elided logic?). 4. This is a contradiction, therefore our initial assumption must be wrong (No, clearly the conclusion in 3 is wrong). Therefore, the statement is true (which statement are you even talking about here?)." Any chance someone could clarify that passage by including the missing steps in the logic? --[[Special:Contributions/172.69.70.159|172.69.70.159]] 19:02, 25 April 2022 (UTC)

:It's not missing any steps. The argument really is that simple. Maybe I didn't write it clearly enough... Anyway to address your specific points, I would first recommend you read {{w|Reductio ad absurdum}}, but if you don't have time (Because let's be real, nobody has enough time for reading Wikipedia articles), I'll break it down. 1. Assume the opposite of the statement (This is not a reasonable assumption almost by definition; the whole point is to disprove it, after all) using the Law of Assumption, which states that we can assume absolutely anything we want in a logical proof, so long as we keep track of what's been derived from it. 2 Assume anything else relevant 3. Follow the assumptions through to their conclusions, and find that the valid reasoning has led to an unsound result, such as a statement directly contradicting the assumption in 1. 4. One of the assumptions must be wrong in order to maintain consistency. Choose the assumption which was made for the purpose of disproving it to be the one we deem untrue, which means its opposite is true. Unfortunately these sorts of arguments don't really lend themselves to analogies with 'more graspable' statements.[[Special:Contributions/108.162.221.193|108.162.221.193]] 02:30, 26 April 2022 (UTC)

Hello,
1) Why couldn't Gödel's string be paradoxical? It is certainly A) self-referencing and B) Self-negating. Even "This Statement is True" causes trouble.
2) Where did Gödel even consider paradox to be a possibility? If he didn't, his argument is "incomplete" (just like its conclusion implies it might very well be anyway).
3) Has anyone here bothered to prove that his string is not actually paradoxical?
- Don Stoner (nobody in particular -- just a senile wimpy old nerd)

Hi again,
Here's a fun one:
"This statement is paradoxical"
1) It certainly is paradoxical (provably so)
2) It even says it's paradoxical (echoing Gödel)
3) Therefore, it must be "true" (echoing Gödel)
4) But (this time) this means it's simply "false"
5) Etc.
- Don (nobody in particular)

:1) I'm not sure what you mean by "paradoxical". If you mean something like "true and false" or "neither true nor false", that fails classical logic. Gödel (with a bit of help from Rosser) proved that we can write down a sentence G of Peano arithmetic, then prove (in PA) that G is equivalent to "no integer encodes a proof in PA of G unless a smaller one encodes a proof in PA of not G". He then pointed out that if G was provable in PA, there was also a proof of not G (basically, work out what integer encodes that proof of G, then for each smaller integer, try to decode it into a proof of not G; if you succeed, you have a proof of not G; if you fail for all, you have proved by exhaustion that your integer encodes a proof of G and no smaller integer encodes a proof of not G; all this is a proof of not G). Thus, if PA is consistent, there is no proof in PA of G. Now assume there is a proof in PA of not G. Encode this proof into an integer N. We shall now prove either G or "every integer less than N does not encode a proof in PA of G". We thus work through every integer less than N, checking to see if it encodes a proof in PA of G. If it does we have proved G; if no integers less than N encode a proof of G then we have proved "for all n < N, n does not encode a proof in PA of G". In the latter case, we have proved that every integer encoding a proof in PA of G is greater than N, which is an integer encoding a proof in PA of not G; this implies G! As such, we started with a proof in PA of not G (NOTE: THIS IS DIFFERENT FROM MERELY ASSUMING not G), and produced a proof in PA of G. So if PA is consistent, there is no proof in PA of not G either. Hence PA is either inconsistent (as if PA proves either G or not G, it proves the other and hence false) or incomplete (proving neither).

:2) He proved that either PA proves false, or there is a statement such that PA proves neither the statement nor its negation. The first includes paradoxicality. (His second incompleteness theorem was essentially: "By the argument above, PA proves that if PA is consistent then G has no proof in PA, which easily implies that PA proves "If PA is consistent, then G". Now suppose PA proves that PA is consistent. Then by modus ponens, PA proves G, and therefore PA is inconsistent. So if PA proves that PA is consistent, then PA is inconsistent.") (It ''is'' possible for a consistent system to prove its own inconsistency.)

:3) Most mathematicians assume that ZFC is consistent, even augmented by some pretty strong large cardinal hypotheses. [[Special:Contributions/172.70.35.72|172.70.35.72]] 17:11, 27 April 2022 (UTC)

:The short answer to your questions is that Godel's method was rigorous. Godel numbering is much more precise than natural language ever could be. The longer answer is that there's a reason Godel's theorem is considered a work of genius; though the overall concept is fairly easy to grasp intuitively, making it into an actual theorem takes a lot of work and cleverness. There are multiple long Wikipedia pages about it just outlining the generals. The proof itself is rock solid, but far beyond the scope of this page. And the pithy answer is "Do you really think you're the first person to think of that? Mathematicians spent decades analyzing the theorems with uncharitable eyes."[[Special:Contributions/108.162.221.119|108.162.221.119]] 04:12, 27 April 2022 (UTC)

I am certain I am not the only person to notice his error because I have been contacted by others who noticed it independently. (None of us were sufficiently arrogant to presume we were first.) Further, we have all spent a great deal more time investigating this than you presume. Gödel's numbering was indeed rigorous and precise, but in spite of his genius, he simply failed to consider the possibility of paradox (incompleteness). If I am wrong about this, it would be would be a simple matter to show me where he addressed this. - Don Stoner (n.i.p.)

I'm going to remove the section stating that Godel's theorem is self-negating (it's not) and that his methodology was incomplete. And before anyone re-adds it, I simply ask that you please please PLEASE actually read up on the subject (and I don't mean from random html pages). Mathematicians have been actively trying to find a flaw in Godel's proof since before it was published; I promise you that whatever clever paradoxicality argument you've come up with has already been considered and eliminated by the professionals.

Your parting shot kind of reminds me of Junior high school. Specifically, I was one nerd being confronted by a few dozen "normal" kids. I was outnumbered, but there was really only room for one kid to get in my face at a time. As I told each of those kids (one at a time), "Your buddies aren't here right now. It's just you and me." So, unless you can talk one of those "professionals" (who actually understands Gödel's proof) into joining us here, you need to explain to me where Gödel addressed the possibility of paradox (he didn't). His methodology was incomplete. You also need to explain to me why you assert that "This statement cannot..." is not self-negating (it is). Further, since "the policy on this site is to include every possible interpretation" you also need to explain to me why you have taken it upon yourself to override Randal's authority. - Don Stoner (n.i.p.)
: I can't even be bothered to work out who is saying what. Don, if you're interested in site policy, use the proper <nowiki>~~~~</nowiki> signature (get an account in your name, if you want to be named), and possibly chill out a bit too. If someone is arguing (can't be bothered to check the edit history/diffs) then they need to use a .sig too. And colon-indents per level of reply is useful. But don't mind me, it looks like you're having fun either on your own or as a pair (or more). Just sayin'... [[Special:Contributions/162.158.159.71|162.158.159.71]] 17:54, 27 April 2022 (UTC)
:: Thanks! (I'm a retired robotics-embedded-system programmer, but I'm not much of an end used. I need help to use my cellphone.)--[[Special:Contributions/172.69.34.10|172.69.34.10]] 19:55, 27 April 2022 (UTC)

Talk:2610: Assigning Numbers

2022-04-27T19:54:02Z

172.69.34.10:

Does this imply that [https://en.wikipedia.org/wiki/G%C3%B6del%27s_incompleteness_theorems Gödel's Incompleteness Theorem] isn't correct? And that it's method is bunk? Please help! -Seer [[Special:Contributions/162.158.107.230|162.158.107.230]] 02:08, 23 April 2022 (UTC)
I believe the intention is that the theorem is not part of the set of bad data science, just that they share this one feature.

Isn't the Gödel number for a theorem calculated by multiplying the numbers of the components together, so complicated theorems would have larger numbers? If so, the current explanation that this isn't a good way to judge fields is wrong. I'm not too sure though. [[User:MrCandela|MrCandela]] ([[User talk:MrCandela|talk]]) 05:52, 23 April 2022 (UTC)

:I do not believe that the title suggests renumbering theorems with Gödel numbers, but averaging the existing theorem numbers. Or otherwise, MrCandela's suggestion would be the way to go: Complicated Theorems have larger numbers. Sebastian --[[Special:Contributions/172.68.110.133|172.68.110.133]] 08:10, 23 April 2022 (UTC)

:Yeah a quick look at some magazines like [https://www.quantamagazine.org/how-godels-incompleteness-theorems-work-20200714/#jump2/ this one] and I think Randall has a point [[User:MrCandela|MrCandela]] ([[User talk:MrCandela|talk]]) 09:48, 23 April 2022 (UTC)

I wish I'd started the explanation off when I first saw it (somone posted the first Transcript whilst I was pondering, so I left off). I think there's some serious re-editing to be done, but basically it points to someone (Cueball, a dabbling armchair mathematician faced with some not directly mathematically-based problem) thinking that 'all' it takes is to encode the whatever-it-is, arbitrarily, and then with a few easy equations something useful cannbe derived. When, in reality, even if this is possible (ignoring the "takes the age of the universe to permute things to find the right answer" sort of sticking-block) it depends upon a ''good'' numerical encoding (enough attention to detail, but not too much, and in the right sort of way) and possibly quite a lot of data-demunging and filtration (again, just the right amount and in the correct manner) to pop out the "answer" being looked for. For some things, this can be easy, though there are always statistical pitfalls/etc. For others ("life, the universe and everything", say) the task is far more complex and the result ("42"?) might not seem to be a very useful result for various reasons. And, on top this, there's Gödel. But that's an additional punchline, not the whole scope of the original joke. ...Anyway, this long comment is why I held back from writing the original Explanation, but I might yet wrangle my thoughts into what's since been put there. While trying not to tread upon too many toes and alternate explanations. Which is the hardest bit, I think... [[Special:Contributions/172.70.86.64|172.70.86.64]] 15:48, 23 April 2022 (UTC)

Just a comment about the technicalities of Gödel's First Incompleteness Theorem: The 'third' possibility presented [http://dstoner.net/Math_Science/godel.html here] misunderstands the term 'true but unprovable'. When mathematicians say 'true but unprovable' in the context of Gödel's Incompleteness Theorems, what they mean is 'true in the standard model but unprovable in the formal system'. The Gödel sentence is certainly true for the standard natural numbers, by contradiction: assume that the Gödel sentence is false for the standard naturals, which means that there exists a standard natural number which is the Gödel number for the proof of the Gödel sentence. Then we could decode the Gödel number into a proof (of the formal system) proving the Gödel sentence true; a contradiction. (Note that the preceding proof by contradiction can be formalised in ZFC, but not in the formal system under study.) The reason why the Gödel sentence is unprovable in the formal system is because, from the point of view of the formal system, there might be a non-standard natural number which is the Gödel number for the proof of the Gödel sentence (and non-standard numbers cannot be decoded into a proof); or there might not be. --[[User:Underbase|Underbase]] ([[User talk:Underbase|talk]]) 04:56, 24 April 2022 (UTC)

:Regarding this, I know that the policy on this site is to include every possible interpretation, but the page mentioned is an html page (and not a [https://xkcd.com/2304/ pdf]) that was not [https://xkcd.com/1847/ peer reviewed] (thus not recognized by the community), and as mentioned by the user above it fails understand the concepts it is talking about. I do not think this site should be spreading this kind of idea. I believe Randall Monroe himself would be against this.

::I also believe the current explanation is both incorrect about explaining the seeming paradox of the Gödel conjecture, & therefore somewhat incorrect about this joke. It is surely the transition from abstract to quantized - the act of applying limited formal numbering to potentially unbounded or otherwise non-standard terms - which incurs incompleteness? Within the constraints of a formal system of standard natural numbers, true≠provable, & therein lies the internal (but not total) contradiction. ''That's'' the contradiction, right? & the joke is that numbering theorems by their complexity, is not generally a productive approach for 'doing math' on them, in any sense but an abstract analytical one?
::[[User:ProphetZarquon|ProphetZarquon]] ([[User talk:ProphetZarquon|talk]]) 17:54, 24 April 2022 (UTC)

:I do not believe the Title Text calls for "calculating the average of all the fields' theorems' Gödel numbers". It asks for 'the lowest average theorem number'. The average of all, is not the average of each. The Title Text wants the average of ''each of'' the fields' theorems' Gödel numbers.
:[[User:ProphetZarquon|ProphetZarquon]] ([[User talk:ProphetZarquon|talk]]) 17:54, 24 April 2022 (UTC)

Today's [https://www.smbc-comics.com/comic/derivative Saturday Morning Breakfast Cereal] is slightly related.

== Paradoxicality argument ==

I think that revision [https://www.explainxkcd.com/wiki/index.php?title=2610:_Assigning_Numbers&oldid=231000 231000] should be removed. My explanation of what's wrong with the linked site is as follows:

Up until the section "Gödel's String", nothing is incorrect. Furthermore, the first wrong line is numbered (49), and says that Gödel's statement is equivalent to "This statement is not a theorem (of any formal system)." This is where he goes wrong, for writing down a formula for "n proves m" requires inclusion of the formal system in which this proof happens. As such, the correct translation of Gödel's statement is "This statement is not a theorem of [system]", which it indeed is not. Then he says that "We have decided that Gödel's string cannot be a theorem and neither can its negation" (true, after Rosser's trick) and therefore that this gives us "~<G∨~G>" (which is false). He has commited the sin of confusing truth and provability here.

His discussion of the Epimenides string ("This statement is not true") is accurate, except for the claim that the truth predicate is "as valid an extension to [PA] as [the provability and quining] extensions were". This is false. The provability and quining predicates can be constructed in PA and thus are not "extensions" so much as "shorthand"; this was Gödel's contribution: to see that PA can talk about provability of statements in any fixed formal system. The truth predicate is not definable in PA, as he quite ably proves (suppose it was definable, then you could write down the Epimenides sentence in PA, and thereby prove false).

The section "Gödel's Error" is just plain silly.[[Special:Contributions/172.70.114.147|172.70.114.147]] 19:28, 24 April 2022 (UTC)

What if we just change it to say something along the lines of "Certain logical systems allow values to be 'not false' without being necessarily 'true'; Godel's theorem is based on an axiomatic assumption that every statement is either true or false."?[[Special:Contributions/108.162.221.163|108.162.221.163]] 06:06, 25 April 2022 (UTC)

Is it just me, or is the given argument gibberish? Replacing the terms with more graspable ones, it seems to be saying: "1. Assume that bananas can be grown from banana-trees (why is this a reasonable assumption? Is it also a reasonable assumption to make about pear trees?). 2. Banana-trees exist. 3. Therefore, the statement that bananas cannot be grown from the trees is true (HOW is this a reasonable conclusion to leap to from the preceding points? By what bizarre leap of elided logic?). 4. This is a contradiction, therefore our initial assumption must be wrong (No, clearly the conclusion in 3 is wrong). Therefore, the statement is true (which statement are you even talking about here?)." Any chance someone could clarify that passage by including the missing steps in the logic? --[[Special:Contributions/172.69.70.159|172.69.70.159]] 19:02, 25 April 2022 (UTC)

:It's not missing any steps. The argument really is that simple. Maybe I didn't write it clearly enough... Anyway to address your specific points, I would first recommend you read {{w|Reductio ad absurdum}}, but if you don't have time (Because let's be real, nobody has enough time for reading Wikipedia articles), I'll break it down. 1. Assume the opposite of the statement (This is not a reasonable assumption almost by definition; the whole point is to disprove it, after all) using the Law of Assumption, which states that we can assume absolutely anything we want in a logical proof, so long as we keep track of what's been derived from it. 2 Assume anything else relevant 3. Follow the assumptions through to their conclusions, and find that the valid reasoning has led to an unsound result, such as a statement directly contradicting the assumption in 1. 4. One of the assumptions must be wrong in order to maintain consistency. Choose the assumption which was made for the purpose of disproving it to be the one we deem untrue, which means its opposite is true. Unfortunately these sorts of arguments don't really lend themselves to analogies with 'more graspable' statements.[[Special:Contributions/108.162.221.193|108.162.221.193]] 02:30, 26 April 2022 (UTC)

Hello,
1) Why couldn't Gödel's string be paradoxical? It is certainly A) self-referencing and B) Self-negating. Even "This Statement is True" causes trouble.
2) Where did Gödel even consider paradox to be a possibility? If he didn't, his argument is "incomplete" (just like its conclusion implies it might very well be anyway).
3) Has anyone here bothered to prove that his string is not actually paradoxical?
- Don Stoner (nobody in particular -- just a senile wimpy old nerd)

Hi again,
Here's a fun one:
"This statement is paradoxical"
1) It certainly is paradoxical (provably so)
2) It even says it's paradoxical (echoing Gödel)
3) Therefore, it must be "true" (echoing Gödel)
4) But (this time) this means it's simply "false"
5) Etc.
- Don (nobody in particular)

:1) I'm not sure what you mean by "paradoxical". If you mean something like "true and false" or "neither true nor false", that fails classical logic. Gödel (with a bit of help from Rosser) proved that we can write down a sentence G of Peano arithmetic, then prove (in PA) that G is equivalent to "no integer encodes a proof in PA of G unless a smaller one encodes a proof in PA of not G". He then pointed out that if G was provable in PA, there was also a proof of not G (basically, work out what integer encodes that proof of G, then for each smaller integer, try to decode it into a proof of not G; if you succeed, you have a proof of not G; if you fail for all, you have proved by exhaustion that your integer encodes a proof of G and no smaller integer encodes a proof of not G; all this is a proof of not G). Thus, if PA is consistent, there is no proof in PA of G. Now assume there is a proof in PA of not G. Encode this proof into an integer N. We shall now prove either G or "every integer less than N does not encode a proof in PA of G". We thus work through every integer less than N, checking to see if it encodes a proof in PA of G. If it does we have proved G; if no integers less than N encode a proof of G then we have proved "for all n < N, n does not encode a proof in PA of G". In the latter case, we have proved that every integer encoding a proof in PA of G is greater than N, which is an integer encoding a proof in PA of not G; this implies G! As such, we started with a proof in PA of not G (NOTE: THIS IS DIFFERENT FROM MERELY ASSUMING not G), and produced a proof in PA of G. So if PA is consistent, there is no proof in PA of not G either. Hence PA is either inconsistent (as if PA proves either G or not G, it proves the other and hence false) or incomplete (proving neither).

:2) He proved that either PA proves false, or there is a statement such that PA proves neither the statement nor its negation. The first includes paradoxicality. (His second incompleteness theorem was essentially: "By the argument above, PA proves that if PA is consistent then G has no proof in PA, which easily implies that PA proves "If PA is consistent, then G". Now suppose PA proves that PA is consistent. Then by modus ponens, PA proves G, and therefore PA is inconsistent. So if PA proves that PA is consistent, then PA is inconsistent.") (It ''is'' possible for a consistent system to prove its own inconsistency.)

:3) Most mathematicians assume that ZFC is consistent, even augmented by some pretty strong large cardinal hypotheses. [[Special:Contributions/172.70.35.72|172.70.35.72]] 17:11, 27 April 2022 (UTC)

:The short answer to your questions is that Godel's method was rigorous. Godel numbering is much more precise than natural language ever could be. The longer answer is that there's a reason Godel's theorem is considered a work of genius; though the overall concept is fairly easy to grasp intuitively, making it into an actual theorem takes a lot of work and cleverness. There are multiple long Wikipedia pages about it just outlining the generals. The proof itself is rock solid, but far beyond the scope of this page. And the pithy answer is "Do you really think you're the first person to think of that? Mathematicians spent decades analyzing the theorems with uncharitable eyes."[[Special:Contributions/108.162.221.119|108.162.221.119]] 04:12, 27 April 2022 (UTC)

I am certain I am not the only person to notice his error because I have been contacted by others who noticed it independently. (None of us were sufficiently arrogant to presume we were first.) Further, we have all spent a great deal more time investigating this than you presume. Gödel's numbering was indeed rigorous and precise, but in spite of his genius, he simply failed to consider the possibility of paradox (incompleteness). If I am wrong about this, it would be would be a simple matter to show me where he addressed this. - Don Stoner (n.i.p.)

I'm going to remove the section stating that Godel's theorem is self-negating (it's not) and that his methodology was incomplete. And before anyone re-adds it, I simply ask that you please please PLEASE actually read up on the subject (and I don't mean from random html pages). Mathematicians have been actively trying to find a flaw in Godel's proof since before it was published; I promise you that whatever clever paradoxicality argument you've come up with has already been considered and eliminated by the professionals.

Your parting shot kind of reminds me of Junior high school. Specifically, I was one nerd being confronted by a few dozen "normal" kids. I was outnumbered, but there was really only room for one kid to get in my face at a time. As I told each of those kids (one at a time), "Your buddies aren't here right now. It's just you and me." So, unless you can talk one of those "professionals" (who actually understands Gödel's proof) into joining us here, you need to explain to me where Gödel addressed the possibility of paradox (he didn't). His methodology was incomplete. You also need to explain to me why you assert that "This statement cannot..." is not self-negating (it is). Further, since "the policy on this site is to include every possible interpretation" you also need to explain to me why you have taken it upon yourself to override Randal's authority. - Don Stoner (n.i.p.)
: I can't even be bothered to work out who is saying what. Don, if you're interested in site policy, use the proper <nowiki>~~~~</nowiki> signature (get an account in your name, if you want to be named), and possibly chill out a bit too. If someone is arguing (can't be bothered to check the edit history/diffs) then they need to use a .sig too. And colon-indents per level of reply is useful. But don't mind me, it looks like you're having fun either on your own or as a pair (or more). Just sayin'... [[Special:Contributions/162.158.159.71|162.158.159.71]] 17:54, 27 April 2022 (UTC)
:: Thanks! (I'm a retired robotics-embedded-system programmer, but I'm not much of an end used. I need help to use my cellphone.)

Talk:2610: Assigning Numbers

2022-04-26T22:07:57Z

172.69.34.10: