4 ms·
> Hang on, is that a Natural number, or a signed Integer? Is it place-value, and if so what's the base? Big- or little-endian? I fail to see how that makes any
by faller 4y ago
> Hang on, is that a Natural number, or a signed Integer? Is it place-value, and if so what's the base? Big- or little-endian?
I fail to see how that makes any sense. OP clearly referred to the unidimensional nature of a scalar in contrast to the n-dimensional nature of a vector, or the n*m-dimensional nature of a matrix. It makes no sense to try to go off on a tangent regarding, say, the resolution of a scalar representation. Perhaps the concept of a ray gets halfway there. Perhaps the concept of a line at infinity.
The concept of a scalar is familiar, as is the concept of a vector. Using the terms "scalar with a direction" to describe a vector makes no sense if you come from that starting point. Perhaps magnitude+direction vector rings a bell, because that's also a basic description of a vector.
Perhaps the author made a mistake, or does not have a good math background, or is filing in his knowledge gaps by coming up with definitions . Or perhaps he's actually referring to different concepts that the readership is not familiar. Who knows?
> This is tongue-in-cheek; but from a software perspective, all those representations have the same "API" (arithmetic).
This assertion is quite wrong. Both scalar and vector, in this context, are data types. Describing a data types as a data type of a data type is meaningless and does not compute.
- chriswarbo 4y ago> The concept of a scalar is familiar, as is the concept of a vector. > Using the terms "scalar with a direction" to describe a vector makes no sense if you come from that starting point. Now I'm confused: what is a vector, if not a "scalar with a direction" (or indeed "an oriented scalar value", as the parent quoted)? > Both scalar and vector, in this context, are data types. Describing a data types as a data type of a data type is meaningless and does not compute. I disagree; "scalar value" is an interface, supporting addition, multiplication, negation, etc. (e.g. https://hackage.haskell.org/package/base-4.16.1.0/docs/Prelude.html#t:Num https://hackage.haskell.org/package/base-4.16.1.0/docs/Prelu... https://smlfamily.github.io/Basis/real.html https://smlfamily.github.io/Basis/real.html ). Many data structures can implement this interface (Float, Double, Rational, Fixed, Nat, Int, etc.). Likewise, "vector" is an interface, supporting vector addition, scalar multiplication, and (crucially in this context) inner, wedge and geometric products. Many data structures can implement this interface (e.g. a tuple of scalars, as coefficient of a fixed orthonormal basis; a scalar length paired with angular spreads projected in fixed perpendicular planes; etc.)