Re: Why one school changed from Pascal to C++

[Spencer Allain <sallain@lasker.dc.teknowledge.com>]

I was hoping this thread wasn't going to start.  I have a healthy
respect for both Richard and Robert, and I personally have mixed
feelings about this notation discussion.  I don't claim to be an
expert in notational theory, but as far as I'm concerned, we don't
have enough symbols on the keyboard to even make a pretense of doing
justice to the true accepted mathematical syntax.

I can already see the arguments about cross-products and dot-products
starting, and which notation to use for which, etc.  I'd be much
more happy to discuss getting support for real symbols and not
even talk about the "*" operator, which is a computer science convention.

I think the real issue is not "*", but consistent representation.  If
the world agrees that "*" on matrices always means standard matrix
multiplication, and there is an assumption that there is some good
way to have it "blow up".  Ie what happens when you take A (3x4) and 
B (4x2) matrices.  AB is valid, but BA should throw some type of
exception.

Where is the "computer scientist's" handbook of mathematical
representations?  Maybe we should all have one of those and this
discussion won't keep cropping up.

-Spencer

dewar@merv.cs.nyu.edu (Robert Dewar) writes:
> 
> Richard says
> 
> << Well, yes and no. There's a limit to how many special cases one
> can hold in memory at once - * usually denotes multiplication. What
> you do to matrices is not by any stretch of the imagination
> multiplication, so why should it have the same name ?>>
> 
> It should have the same name because mathematicians have called this
> operation matrix multiplication for a long time, since long before
> computers had even been thought of. It is NOT helpful for computer
> scientists to try to revise standard mathematical terminology in
> this way. If matrix multiplication is not in "any stretch of
> [your] imagination multiplication", then your notion of multiplication
> is entirely idiosyncratic, and too unfamiliar to be helpful!
>