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Can math.atan2 return INF?


On Monday, August 1, 2016 at 8:23:49 AM UTC+5:30, Steven D'Aprano wrote:
> 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? Schr?dinger? 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 Poincar? -- 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.

My agreement vis-a-vis this essay is basically this:
Abstruse philosophical how-many-angels-on-a-pin type arguments amongst 
philosophers of math/logic across 19-20 century gave rise to Computers and Computer Science.

Some of the other detailed points you make, I agree with, eg.

1. There were more than 2 parties in the dispute
2. There is some arbitrary line-drawing there

(Un)fortunately arbitrary line-drawing is the name of the game everywhere:
Religion?Philosophy?History?Politics

<OT-Aside>
Right now as we speak there looks like a war ? maybe world-war ? in offing:
https://www.thenation.com/article/the-united-states-and-nato-are-preparing-for-a-major-war-with-russia/

Possibly democrat-engineered to discredit Trump:
https://www.thenation.com/article/neo-mccarthyism-and-olympic-politics-as-more-evidence-of-a-new-cold-war/

All starts with the disorder in the middle-east and a whole lot of arbitrary lines
drawn there
[Going backward in time]
- A line drawn in space called ?Israel?
- Based on a line drawn in time called the ?Exodus of Moses?
- Based on the supremely authoritative history-record called ?The Bible?
  (or Torah depending on the speaker)

Leaving aside the first and the third, why specifically the Exodus as a definer?
Before Canaan they were in Egypt, so Israel=Egypt is equally legitimate
And before?before? they were in Eden.
Why not set Israel up in Eden?

May it just be the (in)convenient fact that knocking the Palestinians out of
their homes is easier than removing Mr. God from Eden?

Collapse of borders:
http://www.independent.co.uk/news/world/middle-east/isis-in-a-borderless-world-the-days-when-we-could-fight-foreign-wars-and-be-safe-at-home-may-be-long-a6741146.html
</OT-Aside>