Or, I could apply a constant force of 5 newtons to an object massing 25 kg for a duration of 8 seconds. I change it’s velocity by 5N8S(1MKG/(NSEC^2))/25KG 1.6 M/S. By conserving units on all quantities, I convert force-time against a mass into acceleration.
Those units can be preserved through all mathematical operations, including exponentiation and definite integration.
Hmm… Another good argument. This one is harder. But that’s just making this more fun, and getting me closer to giving in.
If I abstract a whole bunch of details about apples away, except the number and the fact that it’s an apple, I get math with units. So if I have a bag of 3 apples, I can abstract this to 3apples. I can add 1apple to this, and get 4apples. Why? Some ancient mathematicians have shown that when you retain this extra bit of information, the abstraction “math with units” is formed, which is pretty much exactly like normal math, except that numbers are multiplied by their units. “math with units” and plain old math are very similar because they are both numbers, but “math with units” happens to retain a few extra details about what the numbers are talking about.
1apple 1apple=1apple^2 is true, but it doesn’t make sense. You can’t add in details to turn this into apples because of physical limitations, so 1apple 1apple does not emerge from apples. But it is consistent with the rules of mathematics, which you obtain when you remove the complex details of what an apple is, so this is considered true.
1m * 1m=1m^2, however, does make sense, and we can add in details to transform this into an area. m/s can be transformed into the speed of an object by adding in details. m/s^2 can be transformed into an actual acceleration. kgm/s^2 can be transformed into an actual force by adding in details. I think this is true of all useful units, but if you can think of one for which this is not true, please share, because that will be a big blow to my theory. If this theory survives all the other arguments, I will still need to prove that this is true, and until I prove it, my theory is weak. Thank you for showing me this.
Anyway, a summary of this comment: math with units is an abstraction, one level below plain math, and it mostly follows the rules of math because it’s just math+(some simple other thing). Units which don’t make sense cannot be un-abstracted into things in the world, but because math is consistent, we can still manipulate them like anything else because we have abstracted the details which makes it not make sense away.
So I needed to extend my theory for this, but thankfully not by making it more complex at the base. This is all just emergent stuff in the universe. So if my theory holds up, I expect Occam’s Razor will be in favor of it.
Quantities can be converted to and from numbers: (32 ft lbf / (lbm sec^2))=1 (64 ft lbf / (lbm sec^2))=2
It is true, but not useful, to say that the area of a circle with radius R is equal to piR{frac{64ftlbf}{lbmsec2}}
or equivalently,
Taking the sec^2lbf root does not have an analogue in reality, but the units output from taking the time^2*Force root of a distance raised to the power of scalar*distance*mass is area in this specific case.
Hmm… Another good argument. This one is harder. But that’s just making this more fun, and getting me closer to giving in.
If I abstract a whole bunch of details about apples away, except the number and the fact that it’s an apple, I get math with units. So if I have a bag of 3 apples, I can abstract this to 3apples. I can add 1apple to this, and get 4apples. Why? Some ancient mathematicians have shown that when you retain this extra bit of information, the abstraction “math with units” is formed, which is pretty much exactly like normal math, except that numbers are multiplied by their units. “math with units” and plain old math are very similar because they are both numbers, but “math with units” happens to retain a few extra details about what the numbers are talking about.
1apple 1apple=1apple^2 is true, but it doesn’t make sense. You can’t add in details to turn this into apples because of physical limitations, so 1apple 1apple does not emerge from apples. But it is consistent with the rules of mathematics, which you obtain when you remove the complex details of what an apple is, so this is considered true.
1m * 1m=1m^2, however, does make sense, and we can add in details to transform this into an area. m/s can be transformed into the speed of an object by adding in details. m/s^2 can be transformed into an actual acceleration. kgm/s^2 can be transformed into an actual force by adding in details. I think this is true of all useful units, but if you can think of one for which this is not true, please share, because that will be a big blow to my theory. If this theory survives all the other arguments, I will still need to prove that this is true, and until I prove it, my theory is weak. Thank you for showing me this.
Anyway, a summary of this comment: math with units is an abstraction, one level below plain math, and it mostly follows the rules of math because it’s just math+(some simple other thing). Units which don’t make sense cannot be un-abstracted into things in the world, but because math is consistent, we can still manipulate them like anything else because we have abstracted the details which makes it not make sense away.
So I needed to extend my theory for this, but thankfully not by making it more complex at the base. This is all just emergent stuff in the universe. So if my theory holds up, I expect Occam’s Razor will be in favor of it.
Quantities can be converted to and from numbers:
(32 ft lbf / (lbm sec^2))=1
(64 ft lbf / (lbm sec^2))=2
It is true, but not useful, to say that the area of a circle with radius R is equal to piR{frac{64ftlbf}{lbmsec2}}
or equivalently,
Taking the sec^2lbf root does not have an analogue in reality, but the units output from taking the time^2*Force root of a distance raised to the power of scalar*distance*mass is area in this specific case.