What's the difference between multiplication and addiction conceptually ? It's one of my mystery in programming. The Tao has no answer for it.
Addiction is multiplication by infinity.
[1] https://wikimedia.org/api/rest_v1/media/math/render/svg/e12e... [2] https://en.wikipedia.org/wiki/Multiplication
Similar relation between exponentiation (power) and multiplication... see[3]@[4]
[3] https://wikimedia.org/api/rest_v1/media/math/render/svg/dcb8... [4] https://en.wikipedia.org/wiki/Exponentiation
It also still reaches an intuition on what dividing by zero means, and it is not that it equals zero, but that the amount of cycles to do are 0. As in index is still 0 in the array.
But most intriguingly it applies that subtraction and division don’t have the properties you mention which is a symmetric “anti” feature of these operators and seemingly can be reduced to the primitive function of addition or subtraction as multiplication and division are just meta operators acting as a loop.
At least this is how I’m viewing it.
There’s an intuitive sense that symmetry breaks when you take away (reduce) compared to add which is in parts of a whole.
And then to realize you can use addition to implement subtraction is where my brain starts to melt even though it’s relatively straight forward. Everything is just addition, the holy monad, the primordial dimensionless unit.
Looks like… more than 60 clock cycles. Yikes!
https://oldwww.nvg.ntnu.no/amiga/MC680x0_Sections/timstandar...
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1. To be clear for readers, when KMag and I say, “field,” we’re referring to a specific mathematical construct in which there are + and × operators and symbols 0 and 1, the former being the additive identity and the latter the multiplicative identity.