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I think it would have to play well with Taylor series -- for example e^s would be 1 + s + s^2/2 + s^3/6 + s^4/24 + ... -- and that would be mixing units. That'
by kmill 6y ago
I think it would have to play well with Taylor series -- for example e^s would be 1 + s + s^2/2 + s^3/6 + s^4/24 + ... -- and that would be mixing units. That's not to say it's meaningless, but rather you'd have to accept measurements like 4s + 5s^2, with incompatible units hanging around. (There's something similar in geometric algebra, I think, where expressions contain terms of different dimensions added together.)
- amelius 6y agoInteresting point. But I think that the Taylor series is just a mathematical tool, and as such it hides the units that exist in these expressions. From a physics point of view, every term in the Taylor series needs to be augmented with a unit that follows from the definition of the Taylor series.