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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

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 and is excited that this real world demonstration has perfect agreement with some presupposed theory.

Most people with a basic level of math would be confident that 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.

It may be reflecting the most basic step of 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. 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.

This Experimental Mathematics department may have been working on this type of problem, as part of a mostly pre-mathematical culture. They checking that 7 apples plus 5 apples equals 12 apples after some prior work, perhaps having counted that 7 sheep plus 5 sheep equals 12 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.

(There are cases where this might not occur, when combining certain items that aren't uniform and discrete. Measuring volumes of two different substances, combined to make a solution, can result in wildly different volumes of the end solution; both greater and lesser. Combining measured volumes of nearly-freezing and nearly-boiling water, the resulting liquid, eventually at an intermediate temperature, can be measureably different from the simple combination of the prior values.)

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.

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 arithmatic, a more advanced problem for older students may require a knowledge of algebra and even simultaneous equations to calculate the interesection of values that a described using multple shared variables. A common conceit is to describe it 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 passengets upon a particular Chicago-departing rail service. With, in all likelihood, observers 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.

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.

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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