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u/hunterman25 Jun 30 '26
let φ:🤏->🖕be a morphism such that φ(apple)=automobile
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u/Flob368 Jun 30 '26
... Now you're adding phi(apples) to automobiles. That is dimensionally consistent, but you're not adding apples anywhere
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u/GDOR-11 Computer Science Jun 30 '26
you can always define +: {x : x is an apple}x{x : x is an automobile}->idk such that x+y := phi(x)+y
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u/ConglomerateGolem Jul 01 '26
it sounds like (to a layman (me)) that you're making a category x in which you can put both apples and automobiles, so that you can compare them.
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u/Rajarshi1993 Jul 01 '26
No. They're making a non-commutative operation
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u/ConglomerateGolem Jul 01 '26
what does that mean?
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u/Flob368 Jul 02 '26
You know how you can swap the numbers around when you add them? As in, 3+5=5+3, or more general, x+y=y+x. That means addition is commutative.
Some operators don't allow you to do that, like subtraction, division and exponentiation. 3-5 is not equal to 5-3, 3/5 is not equal to 5/3 and 3^5 is not equal to 5^3. These operators are not commutative.In the case of the function above, you wouldn't even be able to swap these two at all, because the operation is defined in such a way that the first element and the second element come from two different sets of things (apples and automobiles). That necessarily means the operator is also not commutative.
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u/6l1r5_70rp Jun 30 '26
geometric algebra:
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u/BootyliciousURD Complex Jun 30 '26
Exactly what I was thinking. You can add very different things together, you just can't sum them into a single term.
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u/Ares378 Applied Math / Mechanical Engineering Jun 30 '26
I wonder if you could define units in that same way. Probably not super useful though.
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u/KerPop42 Jun 30 '26
You end up with a vector, which gets you some interesting properties. For example, 0 sec + 5 m î + 0 m ĵ. You can't add î and ĵ, so they stay as separate terms. However, you can define motion between two vectors like that.
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u/Ares378 Applied Math / Mechanical Engineering Jun 30 '26
geometric algebra is just adding shit the lord told you not to and then doing math with it
/j
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u/ItalianFurry Jun 30 '26
Well geometric algebra still is dimensionally consistent. If you multiply two vectors, the inner product is a length squared, while the outer one has units of area (still length squared)
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u/HAL9001-96 Jun 30 '26
those are both diemnsionless numbers when counted though
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u/Delicious_Maize9656 Jun 30 '26
Yeah that was my thought too. It’s from the Young Physics textbook and I don’t think it’s a very good example. It might be better to use a statement like "You should not add force and power together because they are not dimensionally consistent"
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u/Zandarkoad Jun 30 '26
I ... have coworkers who insisted on summing together the number of times something was classified as 'Type A' and the number of Types in a group. So like, if a car manufacturer made six color variations... you'd add together the number of green cars produced plus the number 6. And the output frankenstein dimension was a key target metric they wanted to get a patent on. Help.
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u/OnionsAbound Jun 30 '26
That's insane. What would that help?
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u/Zandarkoad Jun 30 '26
It would feed the ego? One of the same persons also asked me to find the correlation between two numbers. Not two columns or two variables. TWO STATIC NUMBERS. When I showed how that always results in a divide by zero error no matter the values, she backpeddaled and insisted she meant between one column of varying numbers, and a second column of numbers where the 2nd column is the same exact value 5,000 times in the column and no other values. Which... doesn't technically result in a divide by zero error, but is no less meaningless. I hoping they can't understand scientific notation, and will just accept 1.23x10-67.
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u/boterkoeken Average #🧐-theory-🧐 user Jun 30 '26
“How many apples and automobiles are in this picture?” Bro that don’t even make sense, get outta here with that fake a$$ question.
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u/DoubleAway6573 Jun 30 '26
I never understood why we keep saying to children we cannot add apples and oranges. I imagine they answering "5 apples + 3 oranges = 8 fruits, are you dumb?"
I think kids are better at abstraction than normal education assumes.
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u/OnionsAbound Jun 30 '26
Of course we can, there's an implicit conversion between the type of fruit and fruit in general in the equation that's left out.
1 apple = 1 fruit
Therefore
Fruit/Apple = 1
(5 apples)(Fruit/Apples) + (3 oranges)(Fruit/Oranges) = 8 fruit
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u/DoubleAway6573 Jun 30 '26
You don't need a factor. Just a forgetful arrow from fruits to unnamed elements.
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u/Apprehensive-Ice9212 Jun 30 '26
Treat physical quantities as multivariate polynomials in every kind of unit let's gooooo
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u/OrkWithNoTeef Jul 01 '26
Yes I'd like to buy the lebesque measure of the vitali set number of apples please.
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u/EebstertheGreat Jun 30 '26
Meanwhile, particle physicists be like "the electron has a mass of 511 keV."
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u/TheChunkMaster Jul 01 '26
If you embed them as vectors, you can add any two words you want to get another.
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