4 ms·

Yeah—technically, a scalar is just whatever type can be used to multiplicatively scale a vector in some given vector space but, at least in computing, it’s pret

by burke 7y ago

Yeah—technically, a scalar is just whatever type can be used to multiplicatively scale a vector in some given vector space but, at least in computing, it’s pretty clear that people just mean “some kind of integer or real number, definitely not a collection/enumerator type”

r-w 7y ago
Wasn’t clear to me at all. A scalar is any kind of singleton number, but it doesn’t exist in contrast to boolean values; rather, it includes them. “Exists on a spectrum/scale” or “is a real number” would be universally understood ways of communicating that particular meaning. The notion of “fuzzy logic” is especially relevant: https://en.wikipedia.org/wiki/Fuzzy_logic https://en.wikipedia.org/wiki/Fuzzy_logic
- JadeNB 7y ago
  > A scalar is any kind of singleton number, but it doesn’t exist in contrast to boolean values; rather, it includes them. But this was exactly my point: scalars, regarded as 'singleton number's, don't include Booleans, because Booleans aren't numbers, singleton or otherwise. (Unless, again, you wish to regard them as belonging to the field with two elements.) Booleans can be coerced to numbers, but the way to do so, even if we agree that the two numbers are 0 and 1, is arbitrary—unless we require that certain algebraic identities hold, identities that indicate that the (usual) algebra of Booleans is not the (usual) algebra of real numbers. It is a nitpick, to be sure; but (a) part of the point of types is to facilitate, and even automate, exactly this sort of nitpicking, and (b) it was in response to a nitpick, too. > The notion of “fuzzy logic” is especially relevant: https://en.wikipedia.org/wiki/Fuzzy_logic https://en.wikipedia.org/wiki/Fuzzy_logic Agreed! It indicates that coercing Booleans to numbers suggests fruitful analogies, but, again, says to me that they are not actually numbers. (Once again, I point to their operators, which, from a computer-science as well as a mathematics point of view, are part of what a scalar, Boolean, or whatever is: https://en.wikipedia.org/wiki/Fuzzy_logic#Fuzzy_logic_operators https://en.wikipedia.org/wiki/Fuzzy_logic#Fuzzy_logic_operat... .) These indicate that perhaps one should think of Booleans as belonging to a continuum of values coming from a tropical-type structure (https://en.wikipedia.org/wiki/Tropical_geometry https://en.wikipedia.org/wiki/Tropical_geometry) rather than from a field as 'usual' scalars do.

by burke 7y ago

r-w 7y ago

Wasn’t clear to me at all. A scalar is any kind of singleton number, but it doesn’t exist in contrast to boolean values; rather, it includes them. “Exists on a spectrum/scale” or “is a real number” would be universally understood ways of communicating that particular meaning. The notion of “fuzzy logic” is especially relevant: https://en.wikipedia.org/wiki/Fuzzy_logic https://en.wikipedia.org/wiki/Fuzzy_logic

JadeNB 7y ago
> A scalar is any kind of singleton number, but it doesn’t exist in contrast to boolean values; rather, it includes them. But this was exactly my point: scalars, regarded as 'singleton number's, don't include Booleans, because Booleans aren't numbers, singleton or otherwise. (Unless, again, you wish to regard them as belonging to the field with two elements.) Booleans can be coerced to numbers, but the way to do so, even if we agree that the two numbers are 0 and 1, is arbitrary—unless we require that certain algebraic identities hold, identities that indicate that the (usual) algebra of Booleans is not the (usual) algebra of real numbers. It is a nitpick, to be sure; but (a) part of the point of types is to facilitate, and even automate, exactly this sort of nitpicking, and (b) it was in response to a nitpick, too. > The notion of “fuzzy logic” is especially relevant: https://en.wikipedia.org/wiki/Fuzzy_logic https://en.wikipedia.org/wiki/Fuzzy_logic Agreed! It indicates that coercing Booleans to numbers suggests fruitful analogies, but, again, says to me that they are not actually numbers. (Once again, I point to their operators, which, from a computer-science as well as a mathematics point of view, are part of what a scalar, Boolean, or whatever is: https://en.wikipedia.org/wiki/Fuzzy_logic#Fuzzy_logic_operators https://en.wikipedia.org/wiki/Fuzzy_logic#Fuzzy_logic_operat... .) These indicate that perhaps one should think of Booleans as belonging to a continuum of values coming from a tropical-type structure (https://en.wikipedia.org/wiki/Tropical_geometry https://en.wikipedia.org/wiki/Tropical_geometry) rather than from a field as 'usual' scalars do.