The Math Forum

Search All of the Math Forum:

Views expressed in these public forums are not endorsed by NCTM or The Math Forum.

Math Forum » Discussions » Inactive » comp.soft-sys.math.mathematica

Notice: We are no longer accepting new posts, but the forums will continue to be readable.

Topic: Mathematica and Lisp
Replies: 16   Last Post: Mar 7, 2013 3:58 AM

Advanced Search

Back to Topic List Back to Topic List Jump to Tree View Jump to Tree View   Messages: [ Previous | Next ]

Posts: 51
Registered: 12/8/10
Re: Mathematica and Lisp
Posted: Mar 7, 2013 3:58 AM
  Click to see the message monospaced in plain text Plain Text   Click to reply to this topic Reply

[Moderator Note: This thread is now being closed. Those users who
want to continue the discussion should do it privately.]

On Wednesday, March 6, 2013 4:04:52 AM UTC-7, David Bailey wrote:
> On 06/03/2013 03:13, Richard Fateman wrote:

> > 4. There is really no question of the precedence in my form.
> So perhaps we should extend your principle to maths itself?

My old friend Bob Frankston liked precedence-free notation, so he made the first VisiCalc precedence-free. He now acknowledges this as a mistake:

> This
> principle would be even more useful when they got to calculus, where
> notations like dy/dx and integrals are hopelessly ambiguous in that the
> terminating dx looks superficially as if it could commute with the
> integrand!

Yes, and that very ambiguity has inspired mathematicians to extend mathematics to embrace its implications. Consider "operational calculus". At several levels, that illustrates the profound differences between programming and mathematics. Consider that the word "function" can have have different definitions in different mathematical contexts, while to a programmer a function is simply a computable map. A user of a language, like Lisp, that treats functions as computable maps can't easily make contact with the more abstract properties of mathematical functions. You can't write DiracDelta[] in Lisp. It isn't a map, and cannot be computed. But expressions containing DiracDelta[] can sometimes be rewritten to eliminate it. Those rewriting rules are its implementation. That's the kind of thing that that Mathematica does that Lisp cannot (unless you write a language that's Mathematica-like in Lisp, but then you're no longer working in Lisp).

Point your RSS reader here for a feed of the latest messages in this topic.

[Privacy Policy] [Terms of Use]

© The Math Forum at NCTM 1994-2018. All Rights Reserved.