Difference between revisions of "3180: Apples"

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(reword the stuff about solutions)
(Performed a complete re-write. Less is more, which is something the automated systems don't seem to get (in addition to the joke).)
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==Explanation==
 
==Explanation==
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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.}}
 
  
 
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 presupposed theory.
 
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 presupposed theory.
  
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Most people with a basic level of math would be confident to represent this as 7 + 5 = 12, without needing to count groups of physical objects. However, the title text indicates that there is an entire experimental mathematics department.
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The root of the joke is the conflation of mathematics (or "maths" in the UK), an abstract framework, with sciences like physics or chemistry that describe real world phenomena. In the context of the comic, because most sciences have both theoretical 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 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".  
  
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This may be reflecting the most basic step of {{w|Number theory|human mathematics}}: realising that having seven of ''any'' discrete item and combining with five more results in twelve items in total. Numbers alone can therefore be freely used without there ''being'' actual items to prove. {{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 a collection of apples and a collection of animals could be considered almost as conceptually different, even though the same initial numbers would result in identical end-totals.
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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 Cueball et al are testing math with physical objects instead of referring to the established proofs.  
  
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This Experimental Mathematics department may have been working on this type of problem, as part of a mostly pre-mathematical culture. They are checking that seven apples plus five apples equals twelve apples after some prior work, perhaps having counted that seven sheep plus five sheep equals twelve sheep (if not several other experimentally-proven summations). Prior to checking the apples, they postulated a theory that extends to other items, such as these apples, but only by using actual apples have they confirmed the continuing truth of it.
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The irony is that many branches of mathematics '''are''' experimental in the manner depicted in the cartoon. Children are often taught that the angles of a triangle sum to 180 degrees by tearing off the points of a paper triangle and using them to construct a straight line. 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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(There are cases where this might not occur, when combining certain items that aren't uniform and discrete. Measured volumes of two different substances, combined to make a solution, usually results in a volume of the end solution that differs from the sum of the original volumes. When measured volumes of nearly-freezing and nearly-boiling water are combined, the resulting liquid, at an intermediate temperature, will almost always be {{w|Properties of water#Density of water and ice|measurably different}} from the sum of the prior values.)
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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 question to teach students how to solve {{w|System of equations|simultaneous equations}}. The setup involves two trains, some distance apart, each leaving their origin at a specific time and moving towards each other at a specific speed. The question posed to the reader is something like what time the two trains will meet. This problem is so common that it became a pre-internet meme, with many references in popular culture so Randall only has to provide the setup ("a train departs Chicago at 9pm traveling at 45mph") to be reasonably sure that the reader will get what he's talking about. (Note, the motion of trains would normally be a physics problem, but the Two Trains word problem is devoid of details that would make it applicable to the field of classical mechanics, either classroom or practical.)  
  
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Branches of science may have a 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 through the use of abstract models). In some cases, advances in theory greatly outpace any direct physical evidence, and may deal with numbers and situations that cannot be readily reproduced or observed. For example, if straying into the territory of irrational or infinitesimal numbers, the usefulness of manifesting with physical objects may be less useful.
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Unlike apples, hiring 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.  
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The title text states that, more complicated schoolroom mathematical problems are also pursued. Where the question of how many apples there are in total is simple additive arithmetic, a more advanced problem for older students may require a knowledge of {{w|algebra}} and even {{w|System of equations|simultaneous equations}} to calculate the intersection of values that a described using multiple shared variables. A common conceit is to describe journeys by train (in which a position is directly dependant upon a given time). As with the physically performed experimentations with the number of apples, it is alluded to that these more advanced queries are investigated by members of the department becoming repeat passengers upon a particular Chicago-departing rail service. In all likelihood, observers are also being assigned to various Chicago-bound services that match the initial problems' various other stipulations. (In reality, physical trains are probably less reliable incarnations of pure mathematical problems. They are potentially subject to all kinds of delays, even 'non-stop' services may change speed for various reasons and there is no indication that the pure mathematical model being enacted takes account of the train needing to take time to reach even its idealised velocity.) Whatever the test(s) using trains might be, however, the cost of either boarding or outright ''commissioning'' the train journeys is of concern to the department's accountants/auditors, who seem to have number problems of their own (i.e. the depletion of the departmental operating budget).
 
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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, for example, 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. Also part of mathematics would be something like [https://nvlpubs.nist.gov/nistpubs/sp958-lide/132-134.pdf experimental statistics], though here it usually means statistically analyzing results of experiments, rather than mathematics itself being experimental.
 
  
 
==Transcript==
 
==Transcript==

Revision as of 17:05, 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

    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 presupposed theory.

    The root of the joke is the conflation of mathematics (or "maths" in the UK), an abstract framework, with sciences like physics or chemistry that describe real world phenomena. In the context of the comic, because most sciences have both theoretical 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 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 Cueball et al are testing math with physical objects instead of referring to the established proofs.

    The irony is that many branches of mathematics are experimental in the manner depicted in the cartoon. Children are often taught that the angles of a triangle sum to 180 degrees by tearing off the points of a paper triangle and using them to construct a straight line. 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 question to teach students how to solve simultaneous equations. The setup involves two trains, some distance apart, each leaving their origin at a specific time and moving towards each other at a specific speed. The question posed to the reader is something like what time the two trains will meet. This problem is so common that it became a pre-internet meme, with many references in popular culture so Randall only has to provide the setup ("a train departs Chicago at 9pm traveling at 45mph") to be reasonably sure that the reader will get what he's talking about. (Note, the motion of trains would normally be a physics problem, but the Two Trains word problem is devoid of details that would make it applicable to the field of classical mechanics, either classroom or practical.)

    Unlike apples, hiring 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

    [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)
    Oh, that's a good one :) Elektrizikekswerk (talk) 08:53, 16 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)
    I agree this explanation is way tooo long. I even added this to the incomplete reason, but that has been removed. I still think we at this moment would be better of with the original explanation mentioned in the top post 5+7=12! --Kynde (talk) 07:41, 16 December 2025 (UTC)
    And then there's the disappearing leprechaun [1]Lordpishky (talk) 20:04, 15 December 2025 (UTC)
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