Difference between revisions of "3180: Apples"

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==Explanation==
 
==Explanation==
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{{incomplete|This page was created BY 7+5=13 APPLES. Don't remove this notice too soon.}}
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{{incomplete|This page was created BY A CAR HEADING WEST AT 70MPH. Is there not way too much talk about math concepts that has nothing to do with the simple joke in this comic. Like three paragraphs too much (1+2)? Don't remove this notice too soon.}}
  
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In the comic, a group of three "experimental mathematicians" has experimentally confirmed the answer to a math story problem that might normally appear in elementary school: "If Cueball has seven apples and Hairbun has five, how many apples are there?" Cueball counts the two groups of apples and states that the total is twelve. Blondie agrees that this is noteworthy.  
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Three "experimental mathematicians" have experimentally confirmed the answer to a mathematical query that might normally {{w|word problem (mathematics education)|be described}} to an elementary school class: "If [[Cueball]] has seven apples and [[Hairbun]] has five, how many apples are there in total?" With everyone having literally brought together their stated number of apples, Cueball counts the two groups of apples and states that the total is twelve. [[Blondie]] is very excited that this real world demonstration has perfect agreement with some theory, presumably arithmetic.
  
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Most people with a basic level of math would represent this as 7+5=12 and be confident of the answer without needing to count groups of physical objects. However, the title text states that there is an entire experimental math department dedicated to testing out common story problems in the real world, as if there was some doubt that {{w|Number theory|the theories}} were sound.
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The root of the joke is the conflation of mathematics, an abstract framework, with sciences like physics or chemistry that describe real world phenomena and that require experimental confirmation. In the context of the comic, because most sciences have both theoretical and experimental wings, mathematics should as well, with a humorous example of what "experimental mathematics" would look like. In this case Cueball and Hairbun are literally "testing" the concept of addition by reenacting a word problem in a mathematics textbook. This physical experiment itself is humorous because there is no mathematical difference between adding groups of apples or groups of {{w|Number sign|hash marks}} on a piece of paper, but the characters would likely consider the latter to be "theoretical".  
  
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It may also be an allusion to the most basic step of human mathematics, that of realising that seven of ''any'' conceived item plus five more of it will be twelve such items in total, and that numbers alone can therefore represent items without there ''being'' actual items to prove their own totals. {{w|History of ancient numeral systems#Clay tokens|Early accounting methods}} initially used proxy representations of the items, in a form of hybrid literal/symbolic manner, which meant that the combining of numbers of apples and combining numbers of livestock could be considered almost as different concepts, even though they had the same total sum applied only to different products.
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A different take on the joke is that mathematics is inherently experimental, but the "experiments" take the form of rigorously proving concepts, including something as basic as addition, {{w|Foundations of mathematics|from first principles}}. From this angle one would find humor in the fact that the three characters are testing math with physical objects instead of referring to the established proofs.  
  
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It is possible that this Experimental Mathematics department has been working on this particular level of problem, as part of a mostly pre-mathematical culture. They are just now checking that 7 apples plus 5 apples equals 12 apples, after perhaps extrapolating from the recently confirmed fact that (e.g.) 7 sheep plus 5 sheep equals 12 sheep. Their theory that this extends to apples (and any other items they have tested before this point) has so far not managed to support the {{w|null hypothesis}} in which it might not.
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The irony is that some aspects of mathematics ''are'' experimental in the manner depicted in the cartoon. Children are often taught that the angles of a triangle sum to 180° by tearing off the points of a paper triangle and using them to construct a straight line. Some aspects of computer science can also be considered "experimental mathematics", especially at the circuit level where binary logic can be physically used to perform mathematical computation.  
  
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Many branches of science have a known division between the empirical approach (gathering direct evidence or practically demonstrating that something works) and the theoretical (developing abstract models that fit the available information without fully testing them). High-quality experiments tend to be difficult and expensive, so rigorous testing is normally reserved for problems that someone considers sufficiently important or interesting. Math often deals with numbers and situations that cannot be reliably reproduced. The department's focus on confirming what most people already know may face difficulties when applying for grant funding.  In reality, {{w|experimental mathematics}} is the branch of mathematics which uses computation as opposed to "pure" deductive proof methods. This does not involve "verifying" simple arithmetic, but could encompass e.g. calculating long runs of the digits of pi in search of patterns that may not be 'obvious' from known principles but which could be proven once identified as a candidate for proof.
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The title text confirms the comic's point of experimentally reenacting mathematics textbook word problems by reference to the "Two Trains Problem", a popular type of question to teach students how to solve {{w|System of linear equations|simultaneous linear equations}}. A [https://mathseasy.quora.com/If-a-train-leaves-station-A-at-9-00-am-and-travels-at-60-miles-per-hour-and-another-train-leaves-station-B-at-10-00-am typical question of this type] asks “If a train leaves station A at 9:00 am and travels at 60 miles per hour, and another train leaves station B at 10:00 am and travels at 80 miles per hour, where will the two trains meet if station A and B are 200 miles apart?” This type of problem is so common that it became a pre-internet meme with many references in popular culture, so Randall has to provide only the setup ("trains leaving Chicago at 9 pm traveling at 45 mph") to be reasonably sure that the reader will know what he's talking about.
  
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On top of the simple problem that requires simple addition (and possibly subtraction) to fully understand the answer of, the title text goes on to cover a slightly more complicated schoolroom mathematical problem, one which generally requires at least some understanding of multiplication and division (though more advanced problems of this type might require moving into the realms of algebra, and the nature of {{w|System of equations|simultaneous equations}} in particular). These may take the analagous form of a train (or other vehicle) setting off at a given time and constant speed along a given hypothetical route, and comparing that against other trips made to/from the same location. As with the hyper-practical experimentations with the number of apples, these more advanced queries are being investigated by directly examining the real-world incarnations of the terms of the problem. It seems that enough identical repetitions have been attempted, at least of a particular Chicago-departing rail service, to have worried those who oversee the financial accounts. (Presumably the accountants at least know enough about numbers to know that the acceptible number of purchased train tickets plus yet more purchased train tickets is adding up to more train tickets purchased than the accountants can consider to be justified.)
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Unlike apples, chartering real life trains to leave both Chicago and another city to test that class of word problem would present enormous expense to the experimental mathematics department. This expense again implies that the experimental mathematics department is not content with any abstraction, such as using model trains, and must test the word problems as written.
  
 
==Transcript==
 
==Transcript==
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{{incomplete transcript|Don't remove this notice too soon.}}
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:[Hairbun and Cueball stand at the left of the panel. Blondie stands at the right. Between them are two piles of apples, one of seven apples (stacked four on the bottom, two in the middle row, and one on top) and the other of five apples (stacked three on the bottom, and two on top).They are all looking at the apples but Blondie has her arms raised high above her head.]
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:[Hairbun and Cueball stand at the left of the panel. Blondie stands at the right. Between them are two piles of apples, one of seven apples (stacked four on the bottom, two in the middle row, and one on top) and the other of five apples (stacked three on the bottom, and two on top).]
 
 
:Cueball: Okay, with my seven apples added to your five, we have ... let's see ... twelve apples!
 
:Cueball: Okay, with my seven apples added to your five, we have ... let's see ... twelve apples!
 
:Blondie: Incredible!
 
:Blondie: Incredible!
 
:Blondie: Perfect agreement with the theory!
 
:Blondie: Perfect agreement with the theory!
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:[Caption below the panel:]
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:Experimental mathematicians
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{{comic discussion}}<noinclude>
 
{{comic discussion}}<noinclude>
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[[Category:Comics featuring Hairbun]]
 
[[Category:Comics featuring Cueball]]
 
[[Category:Comics featuring Cueball]]
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[[Category:Comics featuring Hairbun]]
 
 
[[Category:Comics featuring Blondie]]
 
[[Category:Comics featuring Blondie]]
 
[[Category:Math]]
 
[[Category:Math]]
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[[Category:Food]]

Latest revision as of 17:56, 15 December 2025

Apples
The experimental math department's budget is under scrutiny for how much they've been spending on trains leaving Chicago at 9:00pm traveling at 45 mph.
Title text: The experimental math department's budget is under scrutiny for how much they've been spending on trains leaving Chicago at 9:00pm traveling at 45 mph.

    Explanation[edit]

    Ambox warning blue construction.svg This is one of 53 incomplete explanations:
    This page was created BY A CAR HEADING WEST AT 70MPH. Is there not way too much talk about math concepts that has nothing to do with the simple joke in this comic. Like three paragraphs too much (1+2)? Don't remove this notice too soon. If you can fix this issue, edit the page!

    Three "experimental mathematicians" have experimentally confirmed the answer to a mathematical query that might normally be described to an elementary school class: "If Cueball has seven apples and Hairbun has five, how many apples are there in total?" With everyone having literally brought together their stated number of apples, Cueball counts the two groups of apples and states that the total is twelve. Blondie is very excited that this real world demonstration has perfect agreement with some theory, presumably arithmetic.

    The root of the joke is the conflation of mathematics, an abstract framework, with sciences like physics or chemistry that describe real world phenomena and that require experimental confirmation. In the context of the comic, because most sciences have both theoretical and experimental wings, mathematics should as well, with a humorous example of what "experimental mathematics" would look like. In this case Cueball and Hairbun are literally "testing" the concept of addition by reenacting a word problem in a mathematics textbook. This physical experiment itself is humorous because there is no mathematical difference between adding groups of apples or groups of hash marks on a piece of paper, but the characters would likely consider the latter to be "theoretical".

    A different take on the joke is that mathematics is inherently experimental, but the "experiments" take the form of rigorously proving concepts, including something as basic as addition, from first principles. From this angle one would find humor in the fact that the three characters are testing math with physical objects instead of referring to the established proofs.

    The irony is that some aspects of mathematics are experimental in the manner depicted in the cartoon. Children are often taught that the angles of a triangle sum to 180° by tearing off the points of a paper triangle and using them to construct a straight line. Some aspects of computer science can also be considered "experimental mathematics", especially at the circuit level where binary logic can be physically used to perform mathematical computation.

    The title text confirms the comic's point of experimentally reenacting mathematics textbook word problems by reference to the "Two Trains Problem", a popular type of question to teach students how to solve simultaneous linear equations. A typical question of this type asks “If a train leaves station A at 9:00 am and travels at 60 miles per hour, and another train leaves station B at 10:00 am and travels at 80 miles per hour, where will the two trains meet if station A and B are 200 miles apart?” This type of problem is so common that it became a pre-internet meme with many references in popular culture, so Randall has to provide only the setup ("trains leaving Chicago at 9 pm traveling at 45 mph") to be reasonably sure that the reader will know what he's talking about.

    Unlike apples, chartering real life trains to leave both Chicago and another city to test that class of word problem would present enormous expense to the experimental mathematics department. This expense again implies that the experimental mathematics department is not content with any abstraction, such as using model trains, and must test the word problems as written.

    Transcript[edit]

    [Hairbun and Cueball stand at the left of the panel. Blondie stands at the right. Between them are two piles of apples, one of seven apples (stacked four on the bottom, two in the middle row, and one on top) and the other of five apples (stacked three on the bottom, and two on top).They are all looking at the apples but Blondie has her arms raised high above her head.]
    Cueball: Okay, with my seven apples added to your five, we have ... let's see ... twelve apples!
    Blondie: Incredible!
    Blondie: Perfect agreement with the theory!
    [Caption below the panel:]
    Experimental mathematicians



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    Discussion

    As heretical as it is, I almost want to keep the explanation just like this KelOfTheStars! (talk) 00:09, 13 December 2025 (UTC)

    I wasnt going to ruin it, when I saw it like that. But now it's been expanded, I've added in my own thoughts on the subject. Namely elemental number-theory, i.e. the possibility of counting any item just like you count any other item, plus what's going on with the title text, including a slightly kludgy call-back to the fact that (to have a budget, that must have people succesfully counting expenditures and purchased values) the Exp. Maths Dept. has clearly trained people in the use of numbers enough for them to now be awkwardly snapping at the heels of the EMD querying the justifiability of at least one of their ongoing studies. (Not sure how long my thoughts will actually last, though, in the light of further editing. But I hope at least some of what I'm getting at will be successfully distilled into any more succinct version.) 78.144.255.82 01:05, 13 December 2025 (UTC)
    I guess this was the explanation at the time of this comment!? --Kynde (talk) 19:43, 14 December 2025 (UTC)

    Twelve apples! <*thunder rolls*> Ha! Ha! Ha! BunsenH (talk) 04:36, 13 December 2025 (UTC)

    Oh the irony! How did they count the twelve apples? 0,succ(0),succ(succ(0))..., I bet. This is already heavy math. (For example, what guarantees you that succ(0) exists and has exactly one value 1 and is the successor only of 0? Peano envy.) 2A02:2455:1960:4000:FD7E:5F02:5364:961 08:52, 13 December 2025 (UTC)

    Thank you for starting your counting at 0. I have espoused that zero IS a counting number, as you can't get to 1, unless you first arrive at 0. "Sherman, count how many unicorns there are in this field." "Um, there are zero, Mr. Peabody." SDSpivey (talk) 15:11, 13 December 2025 (UTC)
    How'd you "get to" zero? You have to start somewhere and it is arbitrary. You could start at 17, define succ^-1(x) and go back to 1 or 0. Clearly this is inconvenient but not wrong. If you need zero it may make sense to start at zero but if you need negatives it may not matter. If you are teaching you might want to deal with other concepts and not "we start at zero because". There is no one true set of axioms & definition. Usefulness of Non-Euclidian geometry does not make Euclidian geometry useless.Lordpishky (talk) 17:35, 13 December 2025 (UTC)

    In fact if you really want to nitpick, while most people would accept that 7+5=12 it is demonstrably false that my seven apples plus your 5 apples are equal to a pool of 12 apples. In fact it is demonstrably false that I even have 7 apples. Because no 2 apples are identical they can't be combined together. We may be willing to disregard such gross inaccuracies for the sake of, you know, being able to continue to survive for a little while longer, though. 176.138.186.7 11:10, 13 December 2025 (UTC)

    When you say "seven apples plus 5 apples is 12 apples" you are saying when a set of apples that can be put in a 1-to-1 correspondence with the set of the 1st seven cardinal numbers is combined with a set of apples that can be put in a 1-to-1 correspondence with the set of the 1st five cardinal numbers you get a set that can be put in a 1-to-1 correspondence with the set of the 1st twelve cardinal numbers". Like Cantor's proof that the cardinality of the unit interval is the same as the unit square. There is such a natural correspondence between (finite) cardinal numbers and strictly positive integers that it can be hard to keep in mind that, in a fussy sense, they are not the same things. Lordpishky (talk) 05:50, 15 December 2025 (UTC)
    The physicists have already shown that all apples are perfect spheres of uniform density and cannot be split into smaller apples. SDSpivey (talk) 15:11, 13 December 2025 (UTC)
    Are the perfect spheres bosons or fermions?76.180.39.133 15:38, 13 December 2025 (UTC)
    Not spinning? spin=0 => boson.Lordpishky (talk) 17:35, 13 December 2025 (UTC)

    This comic makes me wonder if Randall is aware of us, and if he might someday try to make a comic so bizarre, we become unable to "explain" it at all. Would such a thing be possible? Something so absurd, we're forced to shrug and say "I got nothing"? It's possible I've been awake too long.69.5.140.194 18:32, 13 December 2025 (UTC)

    Cranberry sauce.Lordpishky (talk) 05:17, 15 December 2025 (UTC)

    i think there's a direct connection between this and Ultrafinitism!! 129.64.0.34 04:56, 14 December 2025 (UTC)Bumpf

    "Okay, with my hrair apples added to your hrair, we have ... let's see ... hrair apples!" "Incredible! Perfect agreement with the theory!" It even works with multiple theories! --Divad27182 (talk) 19:22, 14 December 2025 (UTC)

    Holy overexplanation, Batman! Elektrizikekswerk (talk) 11:29, 15 December 2025 (UTC)

    And yet somehow still seeming to miss the heart of the joke, in that maths rests on proving generalizable rules, so that any specific instance of a rule doesn't have to be proven from first principles. 82.13.184.33 14:17, 15 December 2025 (UTC)

    AI bros must not have a sense of humor because LLM's clearly don't get jokes. Seriously, can we please stop accepting these auto-gen explanations as anything close to being sufficient and work to replace them ASAP? This site functioned fine for years getting well crafted hand written explanations up within 24 hours, but today it seems that editors see the walls of text and just declare mission accomplished.Sturmovik (talk) 17:12, 15 December 2025 (UTC)

    what the... what makes you think you are smarter than everyone???--Trimutius (talk) 17:29, 15 December 2025 (UTC)
    I don't know about any other edits, most of which actually just looked like honest hand-crafted attempts to me but I must admit that sometimes I feel that maybe 3126: Disclaimer needs applying to some of mine. (I know that my rushed "rejig", aiming to shave things down again, ended up with some typos. Though you'd be excused for thinking they were AI 'double-bluff' remnants, I suppose.) 78.144.255.82 17:37, 15 December 2025 (UTC)
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