Difference between revisions of "3180: Apples"

Explain xkcd: It's 'cause you're dumb.
Jump to: navigation, search
(→‎Transcript: fix)
(A mention of experimental statistics)
 
(20 intermediate revisions by 10 users not shown)
Line 10: Line 10:
  
 
==Explanation==
 
==Explanation==
−
{{incomplete|This page was created BY 7+5=13 APPLES. Don't remove this notice too soon.}}
+
{{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.}}
  
−
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.  
+
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 and is excited that this real world demonstration has perfect agreement with some presupposed theory.
  
−
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.
+
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 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.
+
It 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.
  
−
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.
+
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.
  
−
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.
+
(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 {{w|Properties of water#Density of water and ice|measureably different}} from the simple combination of the prior values.)
  
−
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.)
+
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 {{w|algebra}} and even {{w|System of equations|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, {{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. Also part of mathematics would be something like [https://nvlpubs.nist.gov/nistpubs/sp958-lide/132-134.pdf experimental statistics], though here usually it means analyzing statistically results of experiments rather than mathematics itself being experimental.
  
 
==Transcript==
 
==Transcript==
−
{{incomplete transcript|Don't remove this notice too soon.}}
+
:[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
 +
 
  
 
{{comic discussion}}<noinclude>
 
{{comic discussion}}<noinclude>
 +
[[Category:Comics featuring Hairbun]]
 
[[Category:Comics featuring Cueball]]
 
[[Category:Comics featuring Cueball]]
−
[[Category:Comics featuring Hairbun]]
 
 
[[Category:Comics featuring Blondie]]
 
[[Category:Comics featuring Blondie]]
 
[[Category:Math]]
 
[[Category:Math]]
 +
[[Category:Food]]

Latest revision as of 01:51, 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 54 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 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. Also part of mathematics would be something like experimental statistics, though here usually it means analyzing statistically results of experiments rather than mathematics itself being experimental.

    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



    comment.png  Add comment      new topic.png  Create topic (use sparingly)     refresh discuss.png  Refresh 

    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)
          comment.png  Add comment
    Retrieved from "https://www.explainxkcd.com/wiki/index.php?title=3180:_Apples&oldid=401487"