Can math.atan2 return INF?
On Thursday, June 30, 2016 at 1:55:18 PM UTC+5:30, Steven D'Aprano wrote:
> 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?
Bizarre question -- becomes more patently ridiculous when put into general form
"What does what I do have to do with what I believe?"
More specifically the implied suggested equation "soul = religious"
is your own belief. See particularly "Christian faith" in the quote below.
> 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?
Excerpted from https://blog.sciencemuseum.org.uk/the-spirit-of-alan-turing/
Morcom was Turing?s first love, a fellow, older pupil at
Sherborne School, Dorset, who shared Turing?s passion for
mathematics (who died in 1930)
He was profoundly affected by the death of his friend... Turing
admitted that he ?worshipped the ground he trod on?.
Morcom?s death cast a long shadow. Turing turned away from his
Christian faith towards materialism, and began a lifelong quest
to understand the tragedy. As he struggled to make sense of his
loss, Turing pondered the nature of the human mind and whether
Christopher?s was part of his dead body or somehow lived on.
The October after the loss of his friend, Turing went up to
Cambridge, where he studied mathematics. Our exhibition includes
an essay, entitled ?Nature of Spirit? that Turing wrote the next
year, in 1932, in which he talked of his belief in the survival
of the spirit after death, which appealed to the relatively
recent field of quantum mechanics and reflected his yearning for
his dear friend.
Around that time he encountered the Mathematical Foundations of
Quantum Mechanics by the American computer pioneer, John von
Neumann, and the work of Bertrand Russell on mathematical
logic. THESE STREAMS OF THOUGHT WOULD FUSE when Turing imagined a
machine that would be capable of any form of computation. Today
the result ? known as a universal Turing machine ? still
dominates our conception of computing.
> 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.
They -- reals and their cardinality -- are the identical problem
And no, the problem is not with ?2 which is algebraic
It is with the transcendentals like e and ?
? ? ? ? ? ? A ? ?
is obvious almost by definition
That upto A (algebraic numbers) they are equipotent is somewhat paradoxical but still acceptable (to all parties)
See the Cantor pairing function https://en.wikipedia.org/wiki/Countable_set#Formal_overview_without_details
However between A and ? something strange happens (where?) and the equipotence
is lost. At least thats the traditional math/platonic view (Cantor/Hilbert etc)
"Yes real numbers are not enumerable
That means any talk of THE SET ? is nonsense
(talk with language, symbols whatever can only be enumerable)
Therefore Equipotence is like angels on a pin"