To use a silly example... can I finally realize my dream of two-based indexing?

Yes. And 1.5-based indexing, though I would recommend using rational numbers instead of floating point numbers for this one.

And imaginary is right out.

Maybe you could use complex numbers to index matrices

Sure can:

    # Magic
    julia> Base.to_indices(A, inds, I::Tuple{Complex, Vararg{Any}}) = (real(I[1]), imag(I[1]), to_indices(A, Base._maybetail(Base._maybetail(inds)), Base.tail(I))...)

    julia> A
    4×5 reshape(::UnitRange{Int64}, 4, 5) with eltype Int64:
     1  5   9  13  17
     2  6  10  14  18
     3  7  11  15  19
     4  8  12  16  20

    julia> A[3 + 2im]
    7

```

Story time!

When Octave was getting a lot of traffic from the first Coursera machine learning class, when it was just Andrew Ng doing a course and before the Coursera org existed, we were getting a lot of novice users who would do something like

    some_matrix(i,j) = 5

and get cryptic errors about how matrices cannot be indexed by complex numbers. This is because by default, in Matlab and Octave `i` and `j` are functions that evaluate to the imaginary unit. You have to overwrite the function names with `i=2, j=3` or whatever beforehand, which novices often forget. This was happening often enough that I pushed some patches to warn, "did you forget to assign i or j?" if someone tried to index matrices with complex numbers.

Point is, people in Matlab and Octave often unintentionally try to index by complex numbers.

And quaternions for image stacks in ML? Troll, but not too troll...

That’s a right kind of wrong... and could work with FEA tensor too... ;)