Weak Type Ability for Python

[avi.e.gross at gmail.com]

[THIS CLAIMER: a bit off a bit off a bit off topic, imagine that]

Chris,

You have a gift of taking things I think about but censor myself from
including in my post and then blurting it out! LOL!

The original question in this thread now seems a dim memory but we are now
discussing not how to add a number to a string but how to multiply a string
to make n combined copies and then what it means to have a fractional copy
and finally a way to specify a rotation to the result. Argh!!!!

But since you brought it up as a way of looking at what multiplying by an
imaginary number might mean, as in rotating text, I am now going to throw in
a May Tricks even if it is only April.

So should I now extend a language so a rotation matrix is allowed to
multiply text or even a nested list like:

[ [ cos(theta), -sin(theta) ],
  [ sin(theta), cos(theta) ]

While we are at it, why stop with imaginary numbers when you can imagine
extensions thereof? Unfortunately, it has been proven there are and can only
be two additional such constructs. Quaternions have three distinct imaginary
axes called i,j,k and some see them as interesting to show multidimensional
objects in all kinds of places such as computer vision or orbital mechanics.
Octonions have seven such other imaginary axes and have uses in esoteric
places like String Theory or Quantum Logic.

And, yes, you can use these critters in python. You can add a quaternion
type to numpy for example. Yep, octonions too. See modules like pyoctonion
and pyquaternion and much more.

The immoral moral of this story is that once you start opening some doors,
you may find people clamoring to let in ever more things and features. You
can easily bog down your code to the point where finding the commonly used
parts becomes a chore as you trudge through lots of code that is rarely used
but there for completeness.

Oh, I want to make something clear before I get another message spelling out
what I was thinking but chose to omit.

I slightly misled you above. Yes, it has been proven no number higher than 8
(meaning one real dimension and seven distinct imaginary ones) can exist so
octonions are the final part of that story. Well, not exactly. You lose
commutativity when going from quaternions to octonions and you lose full
associativity if you go higher. But you can make all kinds of mathematical
constructs like sedenions with 16 dimensions.

I cannot imagine ever trying to multiply a string by these critters but who
knows? As I noted above, if you set some parts of each of the above to zero,
they all can look like something with a real part like 3, and no (meaning
zero point zero) imaginary parts. So you could argue you should support all
kinds of things that MAY on examination turn out to be convertible to an
integer or double.

-----Original Message-----
From: Python-list <python-list-bounces+avi.e.gross=gmail.com at python.org> On
Behalf Of Chris Angelico
Sent: Thursday, April 13, 2023 12:12 PM
To: python-list at python.org
Subject: Re: Weak Type Ability for Python

On Fri, 14 Apr 2023 at 02:05, <avi.e.gross at gmail.com> wrote:
> So why not extend it to allow complex numbers?
>
> >>> "Hello" * complex(5,0)
> TypeError: can't multiply sequence by non-int of type 'complex'
> >>> "Hello" * complex(0,5)
> TypeError: can't multiply sequence by non-int of type 'complex'
>

Clearly a missed opportunity to rotate the text through a specified angle.

ChrisA
-- 
https://mail.python.org/mailman/listinfo/python-list