3 ms·

I don't follow your line of reasoning. You can add speeds (vector space), you can't add temperatures (points in an affine space cannot be added), but you can ad

by qsort 6y ago

I don't follow your line of reasoning. You can add speeds (vector space), you can't add temperatures (points in an affine space cannot be added), but you can add temperatures and temperature differentials (points and vectors in an affine space). Speeds are vectors in the first place, that's why you get to add them, while "temperature" denotes, depending on context, either a point (not addable) or a vector (addable). This explains why you can't add temperatures, but the average temperature makes 100% sense and has a direct physical meaning.

ttoinou 6y ago
Speed and temperature are intensive properties, they don't add up. You can remove the unit and do whatever you want mathematically and add back the physical unit, but it's not physics. Average temperature has no meaning it's a common fallacy, the only reason I ever got for that meaning is "my teacher told me it was OK !"
- qsort 6y ago
  I'm not following your train of thought. > Speed and temperature are intensive properties, they don't add up. You can add speeds by their very definition. They are vectors in R^3 (or some other coordinate system, you get the point). The fact that addition of vectors is allowed is literally baked into the axioms of a vector space. > Average temperature has no meaning it's a common fallacy Yes, average temperature does have unambiguous meaning: https://en.wikipedia.org/wiki/Boltzmann_constant https://en.wikipedia.org/wiki/Boltzmann_constant > You can remove the unit and do whatever you want mathematically and add back the physical unit, but it's not physics. You do realize math can handle units of measurements/dimensions just fine, do you?
  - ttoinou 6y ago
    > You do realize math can handle units of measurements/dimensions just fine, do you? Yes that's exactly what I'm talking about. Kelvin don't support the addition operator. You can pretend it's not Kelvin/Celsius, do something with the number, and add back the unit if you like, but it won't have any physical meaning. > Yes, average temperature does have unambiguous meaning: https://en.wikipedia.org/wiki/Boltzmann_constant https://en.wikipedia.org/wiki/Boltzmann_constant ... in an ideal gas model you can have a meaning adding and averaging k*T with k a magical constant that transforms your intensive property into extensive (energy) > You can add speeds by their very definition Definition of time derivation of the position function ? Yeah well [length]/[time] don't add up that's it. You need to first give a meaning to the addition operator of [length]/[time]. I'm talking in one dimension, of course if you can prove this then going 2D or 3D is easy

by qsort 6y ago

ttoinou 6y ago

Speed and temperature are intensive properties, they don't add up. You can remove the unit and do whatever you want mathematically and add back the physical unit, but it's not physics. Average temperature has no meaning it's a common fallacy, the only reason I ever got for that meaning is "my teacher told me it was OK !"

qsort 6y ago
I'm not following your train of thought. > Speed and temperature are intensive properties, they don't add up. You can add speeds by their very definition. They are vectors in R^3 (or some other coordinate system, you get the point). The fact that addition of vectors is allowed is literally baked into the axioms of a vector space. > Average temperature has no meaning it's a common fallacy Yes, average temperature does have unambiguous meaning: https://en.wikipedia.org/wiki/Boltzmann_constant https://en.wikipedia.org/wiki/Boltzmann_constant > You can remove the unit and do whatever you want mathematically and add back the physical unit, but it's not physics. You do realize math can handle units of measurements/dimensions just fine, do you?
- ttoinou 6y ago
  > You do realize math can handle units of measurements/dimensions just fine, do you? Yes that's exactly what I'm talking about. Kelvin don't support the addition operator. You can pretend it's not Kelvin/Celsius, do something with the number, and add back the unit if you like, but it won't have any physical meaning. > Yes, average temperature does have unambiguous meaning: https://en.wikipedia.org/wiki/Boltzmann_constant https://en.wikipedia.org/wiki/Boltzmann_constant ... in an ideal gas model you can have a meaning adding and averaging k*T with k a magical constant that transforms your intensive property into extensive (energy) > You can add speeds by their very definition Definition of time derivation of the position function ? Yeah well [length]/[time] don't add up that's it. You need to first give a meaning to the addition operator of [length]/[time]. I'm talking in one dimension, of course if you can prove this then going 2D or 3D is easy