Can math.atan2 return INF?

[Steven D'Aprano]

On Sat, 30 Jul 2016 03:46 pm, Rustom Mody wrote:

> Lots of questions... I would guess rhetorical.

They weren't rhetorical.

You've made a lot of claims about the origins of computer science, and I've
questioned some of your statements. Answers would be appreciated.


> However under the assumption that they are genuine (or could be genuine
> for others than you), I went back and checked.
> I recollected that I started thinking along these lines — viz. that
> philosophical disputes led to the genesis of computers — after reading an
> essay by a certain Adam Siepel... which subsequently seems to have fallen
> off the net
> 
> I tracked him down and re-posted his essay here:
> http://blog.languager.org/2016/07/mechanism-romanticism-computers.html
> 
> Just to be clear — this is Dr. Adam Siepel's writing reposted with his
> permission


The essay is not awful, but I wouldn't shout its praises either. It looks to
me like an undergraduate essay, taking a very narrow and rather naive view
of the field. There's not a lot of references (only nine), which means the
author is (in my opinion) excessively influenced by a small number of
views, and I don't see any sign that he has even made a half-hearted
attempt to seek out alternate views.

The author makes a claim:

"... Principia Mathematica, between 1910 and 1913, which in its attempt to
place mathematics squarely in the domain of logic, represented the first
new system of logic since Aristotle"

but doesn't give any justification for the claim. Why single out the
Principia and ignore the works of the Stoics, Peter Abelard, William of
Ockham, Augustus DeMorgan, Gottlob Frege and most especially George Boole
dismissed?

I would think that if anyone truly deserved credit for creating a new system
of logic, it should be Boole. But perhaps that's just a matter of opinion
on where you draw the lines.

http://www.iep.utm.edu/prop-log/#H2

That's not really central to his argument, but it does suggest that his
views are quite idiosyncratic. To my mind, that feels like someone claiming
that Stephen Hawking is the first genuinely original physicist since
Newton. Einstein? Schrödinger? Dirac? Never heard of 'em.

A rather large section of the essay is an irrelevant (and, I think,
incorrect) digression about "Mechanists" and "Romantics", neither of which
is really relevant to the philosophy of mathematics. He eventually mentions
the Intuitionists, but I don't think he understands them. By linking them
to the Romantics, he seems to think that the Intuitionist school of thought
doesn't require mathematical proofs, or that they are satisfied with
the "intuitively obvious truth" of axioms. But that's not what the
Intuitionists were about:

https://en.wikipedia.org/wiki/Intuitionism

He mischaracterises and over-simplifies the argument over the foundations of
mathematics:

https://en.wikipedia.org/wiki/Brouwer–Hilbert_controversy

with at least three separate groups involved (Logicists such as Russell,
Formalists such as Hilbert, and Constructivists such as Poincaré -- four
groups if you count Intuitionism separate from Constructionism). He
exaggerates the death of the Logicist school of thought. It continues today
with Second Order Logic.

And I wonder why you are taking this essay as supporting your position.
According to this essay, the Intuitionists won in mathematics. And yet
Turing and Von Neumann (two major pioneers of computing) were "Mechanists".
If Intuitionism influenced computer science, where is the evidence of this?
Where are the Intuitionist computer scientists? On the contrary, academic
CS seems to have come from the Logicist school of thought, and practical
computer engineering from "whatever works" school of thought.

None of this even *remotely* supports your assertions such as "[Turing]
wishes to put the soul into the machine". Maybe he did. But this essay
gives no reason to think so, or any reason to think that Turing's personal
beliefs about souls is the slightest bit relevant to computer science.



-- 
Steven
“Cheer up,” they said, “things could be worse.” So I cheered up, and sure
enough, things got worse.