3180: Apples

Apples

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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.

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Explanation

This is one of 54 incomplete explanations: This page was created BY A CAR HEADING WEST AT 70MPH. Don't remove this notice too soon. If you can fix this issue, edit the page!

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.

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 the theories were sound.

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. 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.

This particular kind of abstraction sometimes fails in the real world when combining different things. For example, when measured volumes of two different substances are combined to make a solution, the volume of that solution is usually not exactly equal to the sum of the volumes of the original substances. Even in the case of combining equal volumes of nearly-freezing and nearly-boiling water, the result will not exactly equal the sum of the two volumes, since the density-vs.-temperature curve of water isn't a straight line (and the specific heat capacity of water varies with temperature).

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 null hypothesis in which it might not.

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, 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.

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 simultaneous equations in particular). These may take the analogous 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 acceptable 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.)

As every regular train calling at Chicago Union Station either originates or terminates there, a train has to accelerate first before reaching 45 mph. To leave the station at this speed at 9:00pm, the department has to rent a train using one of only two through tracks, and resolve possible conflicts with other scheduled trains.

A flaw in the system is that with irrational numbers and infinitesimals. Those cannot be represented with physical objects easily and will probably need very precise things or are just impossible.

Transcript

This is one of 29 incomplete transcripts: Don't remove this notice too soon. If you can fix this issue, edit the page!

[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!

Blondie: Incredible!

Blondie: Perfect agreement with the theory!

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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 guess this was the explanation at the time of this comment!? --Kynde (talk) 19:43, 14 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)

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)

As cardinal, ordinal or nominal numbers? Actually, more like "household numbers:, which includes named fractions like half, third, quarter but not 17/47, defined by tradition like the culinary definition of tomato as a vegetable. Lordpishky (talk) 17:35, 13 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)

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)
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