Can math.atan2 return INF?

[Steven D'Aprano]

On Thursday 30 June 2016 12:13, Rustom Mody wrote:

> OTOH Computer Science HAPPENED because mathematicians kept hotly disputing
> for more than ½ a century as to what is legitimate math and what is
> theology/mysticism/etc:

I really don't think so. Computer science happened because people invented 
computers and wanted to study them.

What people like Turing did wasn't computer science, because the subject didn't 
exist yet. He was too busy creating it to do it.

And as for Kronecker, well, I suspect he objected more to Cantor's infinities 
than to real numbers. After all, even the Pythogoreans managed to prove that 
sqrt(2) was an irrational number more than 3000 years ago, something Kronecker 
must have known.


> In particular the question: "Are real numbers really real?" is where it
> starts off... http://blog.languager.org/2015/03/cs-history-0.html

The pre-history of what later became computer science is very interesting, but 
I fear that you are too focused on questions of "mysticism" and not enough on 
what those people actually did and said.

For example, you state that Turing "believes in souls" and that he "wishes to 
put the soul into the machine" -- what do his religious beliefs have to do with 
his work? What evidence do you have for the second claim? What does it even 
mean to put "the" soul (is there only one?) into "the" machine? 


Besides, the whole point of science is to develop objective, rational reasons 
to believe things. The chemist Friedrich Kekulé was inspired to think of 
benzene's molecular structure as a ring through a dream in which a snake bit 
its own tail, but that's not why we believe benzene is a ring-shaped molecule. 
No chemist says "Kekulé dreamed this, therefore it must be true."

The irrational and emotional psychological forces that inspire mathematicians 
can make interesting reading, but they have no relevance in deciding who is 
write or wrong. No numbers are real. All numbers are abstractions, not concrete 
things. If there is a universe of Platonic forms -- highly unlikely, as the 
concept is intellectually simplistic and implausible -- we don't live in it. 
Since all numbers are abstractions, the Real sqrt(2) is no more, or less, 
"real" than the integer 2.



-- 
Steve