Which are? I suspect the reasons are a combination of the price of paper and ink, the history of teaching using chalkboards. None of those mean we can’t make the canonical version of an equation the expanded representation.
Why do we all know e=mc2 and not energy = mass * lightspeed^2.
The broader the base of people that have to interact with a formula, the less mathy the terminology tends to be. Think of trigonometry. Instead of greek letters the sides of a triangle and the functions get real world names. Sine(angle) = opposite / hypotenuse. Sure when you write that out you use sin ϴ = O/H but that’s just a compressed representation of human-readable variable names.
How about Gauss’s distribution’s density function? Or a numerically stable version of a simpler formula? Also, you forgot the usual case of implementing a whitepaper with mathematical notation. It is much easier to proof read that, when you copy largely the same in your program as well. And if you pass in the readable energy, mass, etc variables, inside the function you can use the domain-specific mathematical notation. That way it will be readable both outside and inside.
I think we might be arguing different points. I'm not saying use different variable names from the canonical math version - I'm saying the canonical math version should use variable names instead of symbols.
So per your point - I'm not qualified to re-define mathematical notation so I won't go very far with it, but taking the formula you mentioned, Gaussian distribution density function (not focusing on the fact that I had to re-write it in pseudocode to represent it in a text format):
f(x) = 1/(σ * sqrt(2*pi))*e^(-1/2*((x-μ)/σ)^2)
I would suggest a couple changes:
- change σ to `standard_deviation`, or if you don't like snake_case I could handle `stddev`
- change μ to `mean`.
- change x to `input` - there may be a better name than that, and x is pretty widely used in math so I'm not married to this one.
- e should probably stay the same - e means e no matter the mathematical context, while μ means different things in different fields of math.
I accept your position, and perhaps my examples for a difficult formula was not difficult enough — my point is more along the line that the underlying structure of a formula becomes more easily visible with shorter symbols — and for syntactic manipulation one can more easily see patterns emerge.
Which are? I suspect the reasons are a combination of the price of paper and ink, the history of teaching using chalkboards. None of those mean we can’t make the canonical version of an equation the expanded representation.
Why do we all know e=mc2 and not energy = mass * lightspeed^2.
The broader the base of people that have to interact with a formula, the less mathy the terminology tends to be. Think of trigonometry. Instead of greek letters the sides of a triangle and the functions get real world names. Sine(angle) = opposite / hypotenuse. Sure when you write that out you use sin ϴ = O/H but that’s just a compressed representation of human-readable variable names.