My main calculator is gnu calc which is the calculator built into emails. It tends to hit various ceilings where it can’t go much further but it has lots of nice features:
1. The data I want to work with tends to be in my text editor so it makes sense to have the calculator there too. Macros can be used to fix up formatting to input numbers
2. Speed of input makes it so much nicer to use. If I look at the examples in the article, here is a comparison. Julia:
7 / 4
x = ans + 2 im
exp(x)
A = [...]
A * [...]
[a^2 for a \in A]
Emacs:
7 RET 4 /
(0,2) + s t x (but I probably wouldn’t use a variable)
s r x E (if I used the stack this is just “E”)
[(same but RET or , not SPC)] s t A
s r A [...] *
s r A V M I Q (that’s vector map inverse square root)
These examples make emacs look bad because I’ve replicated saving things to variables it actually I’d just use the stack. I guess in Julia you can press the up arrow. There are other examples like 1 |> exp |> sin is just 1 E S in Calc (and those operations broadcast over vectors automatically, although I think emasculated does the right thing and doesn’t broadcast exp over matrices).
Skipping the massive tangent of non-calculator things about Julia, we move on to a discussion of plotting. There isn’t a Unicode-art plotting mode in emacs because we have had graphical terminals for over 30 years. In emacs you plot with g f and can then modify your plot with other commands. In just about every language you need to call a function called plot so you’re already losing on characters before you’ve even started. If plotting is fast and easy then exploration is easy.
3. The calculator has lots of useful features that fit well together. Plotting is built in. As are unit conversions, a bunch of symbolic algebra (simplification, differentiation, basic integration, curve fitting, solving equations, numeric integration/solutions, and a super nice facility for editing expressions). There’s a bunch of other functions for stats, vectors (both linalg and things like map/reduce), number theory, physics, etc. There are language modes for things like latex output too. Most stuff works on a bunch of number types (bigints, rationals, arbitrary precision floats, infinity, intervals thereof, complex numbers, error forms, symbolic expressions, dates)
4. I want to reiterate the point about speed. The thing I care about being fast is telling the computer what to do. It takes basically 0 time to do most mathematical operations so latency is dominated by input. So even though emacs uses interpreted emacs lisp and doesn’t even use hardware floating point numbers, it still feels faster than Julia with its optimising JIT. If I want to do something with a large amount of data then I can either wait a few seconds or realise that I’ve gone beyond calculator work and use something better suited.
I think Julia is a great language and it has great advantages over emacs for numerical computing. A big one is that the language and type system is much more naturally extensible for this sort of thing. But I don’t feel that it makes a particularly good calculator. The main reason to think that it is a good calculator is that the alternatives (bash/bc/python/matlab) are so bad.