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What's the difference between multiplication and addiction conceptually ? It's one of my mystery in programming. The Tao has no answer for it.

chimpanzee 3y ago
> What's the difference between multiplication and addiction conceptually? Addiction is multiplication by infinity.
- liquidise 3y ago
  Possibly the most thoughtful and profound reply to a typo i've seen.
deleted 3y ago
[deleted]
KMag 3y ago
In any field, there's always an additive inverse, not so for multiplication.
- dhosek 3y ago
  Exactly. In fact, there will always be some element a in a field¹ for which there is no multiplicative inverse. This is why with boolean algebra, both ⋀ and ⋁ are multiplication operators (for ⋀, T has no inverse; for ⋁, F has no inverse). ⸻ 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.
gilcot 3y ago
foo times boo ...means you are adding foo, boo times... see[1]@[2] so it's a kinda shortcut. [1] https://wikimedia.org/api/rest_v1/media/math/render/svg/e12e0ec9572a5430da7af15b101284975d36f19c https://wikimedia.org/api/rest_v1/media/math/render/svg/e12e... [2] https://en.wikipedia.org/wiki/Multiplication 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/dcb8949e2c2dbe952c87d89e208b8018f107ad79 https://wikimedia.org/api/rest_v1/media/math/render/svg/dcb8... [4] https://en.wikipedia.org/wiki/Exponentiation https://en.wikipedia.org/wiki/Exponentiation
- pyinstallwoes 3y ago
  Given that multiplication is repeated addition, then division is repeated subtraction.
  - revskill 3y ago
    So x / 0 should be equal to x right ? Because you substract x zero time.
    - pyinstallwoes 3y ago
      I similarly went down that route and found the answer to be at least plausibly more definitive than undefined. 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.
  - gilcot 3y ago
    Ah ha... :) I wouldn't see division as exact opposite (or symmetrical inverse) of multiplication. Multiplication is both left-distributive and right-distributive, and thus distributive. Unlike multiplication and addition, division is not commutative, neither associative in general.
    - pyinstallwoes 3y ago
      It seems as my logic holds in the sense and case that it is “an inversion of meaning in some way” - whether that can be argued as an opposite, inversion, chiral disposition towards 0 or away from 0, who knows! 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.
bee_rider 3y ago
Since it is from the 80’s, maybe the Motorola 68000 can answer your question. Looks like… more than 60 clock cycles. Yikes! https://oldwww.nvg.ntnu.no/amiga/MC680x0_Sections/timstandard.HTML https://oldwww.nvg.ntnu.no/amiga/MC680x0_Sections/timstandar...

chimpanzee 3y ago

> What's the difference between multiplication and addiction conceptually? Addiction is multiplication by infinity.

liquidise 3y ago
Possibly the most thoughtful and profound reply to a typo i've seen.

deleted 3y ago

[deleted]

KMag 3y ago

In any field, there's always an additive inverse, not so for multiplication.

dhosek 3y ago
Exactly. In fact, there will always be some element a in a field¹ for which there is no multiplicative inverse. This is why with boolean algebra, both ⋀ and ⋁ are multiplication operators (for ⋀, T has no inverse; for ⋁, F has no inverse). ⸻ 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.

gilcot 3y ago

foo times boo ...means you are adding foo, boo times... see[1]@[2] so it's a kinda shortcut. [1] https://wikimedia.org/api/rest_v1/media/math/render/svg/e12e0ec9572a5430da7af15b101284975d36f19c https://wikimedia.org/api/rest_v1/media/math/render/svg/e12e... [2] https://en.wikipedia.org/wiki/Multiplication 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/dcb8949e2c2dbe952c87d89e208b8018f107ad79 https://wikimedia.org/api/rest_v1/media/math/render/svg/dcb8... [4] https://en.wikipedia.org/wiki/Exponentiation https://en.wikipedia.org/wiki/Exponentiation

pyinstallwoes 3y ago
Given that multiplication is repeated addition, then division is repeated subtraction.
- revskill 3y ago
  So x / 0 should be equal to x right ? Because you substract x zero time.
  - pyinstallwoes 3y ago
    I similarly went down that route and found the answer to be at least plausibly more definitive than undefined. 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.
- gilcot 3y ago
  Ah ha... :) I wouldn't see division as exact opposite (or symmetrical inverse) of multiplication. Multiplication is both left-distributive and right-distributive, and thus distributive. Unlike multiplication and addition, division is not commutative, neither associative in general.
  - pyinstallwoes 3y ago
    It seems as my logic holds in the sense and case that it is “an inversion of meaning in some way” - whether that can be argued as an opposite, inversion, chiral disposition towards 0 or away from 0, who knows! 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.

bee_rider 3y ago

Since it is from the 80’s, maybe the Motorola 68000 can answer your question. Looks like… more than 60 clock cycles. Yikes! https://oldwww.nvg.ntnu.no/amiga/MC680x0_Sections/timstandard.HTML https://oldwww.nvg.ntnu.no/amiga/MC680x0_Sections/timstandar...