Re: [Axiom-developer] insight

[Tim Daly]

Hal Abelson from MIT explains the difference of mindset at minutes 37-41
https://www.youtube.com/watch?v=Iib713oLFt4

On Sat, Oct 27, 2018 at 3:41 PM William Sit <address@hidden> wrote:

​The number of English words is finite, whereas the number of human ideas is infinite. So words are recycled to refer to different ideas in different contexts. Questions are NOT stupid. Clarification is crucial.

This happens in physics and mathematics, terms like integrals, integrable or integrability, constants, symmetry all have loaded meanings. Even in Axiom, overloading (or polymorphisms) are common. So what exactly does "addition" or the symbol + refer to? That is not a stupid question at all.

Relax, and keep asking!

William  

William Sit
Professor Emeritus
Department of Mathematics
The City College of The City University of New York
New York, NY 10031

homepage: wsit.ccny.cuny.edu

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From: Axiom-developer <axiom-developer-bounces+wyscc=address@hidden> on behalf of Tim Daly <address@hidden>
Sent: Wednesday, October 17, 2018 1:01 PM
To: Tim Daly
Subject: [Axiom-developer] insight

 

I think I finally understand why I keep asking stupid questions and

find statements in class so strange.

  "You keep using that word.

    I do not think it means what you think it means"

    -- inigo Montoya 1987 (in The Princess Bride)

It is like an artist (programmer) taking an art theory class.

We're using the same words but we don't mean the same thing.

You are using types "ABOUT programming" and I'm using types

"about PROGRAMMING".

You use types as a meta-language to talk ABOUT programs

and use type-erasure to eliminate them at runtime. When you say

a program is "correct", you mean "type correct". So a 'plus' function

(\x:nat \y:nat 7) which always returns 7 is still "type correct".

I use types as first-class objects that I can create, modify, and

pass around at run time. When I say a program is "correct" I mean

that the computed result is "correct" in that it agrees with what a

user would expect.

The insight is that we are using the same words but different meanings.

This may be why computer algebra and proof theory seem to be disjoint

disciplines in computational mathematics.

The upside is that I'll finally stop asking stupid questions. Well,

maybe not, as I seem to have a genius for generating them :-)

Tim