5 ms·

> Obviously I know what a scalar is, a scalar is one number Hang on, is that a Natural number, or a signed Integer? Is it place-value, and if so what's the bas

> Obviously I know what a scalar is, a scalar is one number 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? Is it fractional, and if so is it a rational (numerator and denominator), or fixed-point (what precision?), or float (how big's the mantissa?); maybe it's a unum? How about a sequence of continued fractions? This is tongue-in-cheek; but from a software perspective, all those representations have the same "API" (arithmetic). Likewise, geometric algebra is an "API"; that's essentially what an algebra is.

melissalobos 5y ago
I think the GP is trying to make the point that, a scalar in most numerical physics contexts is either a real or complex double precision floating point number(like a double), but they don't see how someone would represent a vector in this geometric algebra(a matrix in Eigen? or a vector in Eigen? myself I would just use a vector, but the GP was interested in the oriented part and seeemed confused). I believe they were looking for an example of someone using this in practice to solve a real problem and have some explanation of the choices made.
faller 5y 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 5y 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.)

melissalobos 5y ago

I think the GP is trying to make the point that, a scalar in most numerical physics contexts is either a real or complex double precision floating point number(like a double), but they don't see how someone would represent a vector in this geometric algebra(a matrix in Eigen? or a vector in Eigen? myself I would just use a vector, but the GP was interested in the oriented part and seeemed confused). I believe they were looking for an example of someone using this in practice to solve a real problem and have some explanation of the choices made.

faller 5y 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 5y 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.)