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mwengler comments on The Emergence of Math - Less Wrong
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Don't we have the same problem with complex numbers?
2 + 3j = 5 I end up with 5 because I ignored imaginary numbers?
I'm not sure what my point is, this is after all a question. I am wondering, does the fact the same error occurs from dropping physical units as from dropping the very non-physical, seemingly quite mathematical concept of the sqrt(-1)==j?
It's a different error, because quantities aren't inherently algebraic, even though they very often behave as though they were.
For example, arranging apples in a grid three wide and two apples deep requires 6 apples, not 6 apples^2, even though the area of a grid two inches wide and two inches deep is 6 in^2.