
Waiting for Gödel - enkiv2
http://www.newyorker.com/tech/elements/waiting-for-godel
======
sandebert
I can recommend reading _Logicomix_ , a graphic novel about Bertrand Russell
and his work in mathematics. There are lots of other people making
appearances, for instance Gödel who makes quite the splash (as one can
imagine). I read it a couple of weeks ago and thoroughly enjoyed it.

    
    
      https://www.logicomix.com/
    
      https://en.wikipedia.org/wiki/Logicomix

~~~
acqq
Worth considering (especially since the preview button on the main site
doesn't work, gives "the content is restricted"):

[https://www.amazon.com/review/R3FH3WXNKEOZR9/ref=cm_cr_dp_ti...](https://www.amazon.com/review/R3FH3WXNKEOZR9/ref=cm_cr_dp_title?ie=UTF8&ASIN=1596914521&channel=detail-
glance&nodeID=283155&store=books)

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mathgenius
So great to see an article about Godel incompleteness in the new yorker. I
think in general Godel incompleteness and Turing incompleteness should get
more press. Chaitin has written some good books about this, but there needs to
be more. There are these fundamental limits to knowledge and this is an
important fact that people should know about.

> “There is more to truth than can be caught by proof.”

That's a nice way of putting it.

~~~
curiousgal
I can sadly see that quote taken out of context to justify the paranormal or
other crap.

~~~
juk3
Yup. These articles much more than their focus on Godel and his fan club would
do us all a favor to focus on -

How do people day to day deal with ambiguity, where the truth is uncertain or
unknowable?

The default action always is - they choose the truth they want to be true. And
this has long term consequences. They should develop self awareness that it is
a chosen truth and feel a sense of responsibility for its consequences.

The example I given students when I teach where things worked out well, is
Thomas Jefferson's - "We hold these truths to be self-evident, that all men
are created equal".

We still know 240 years later there is nothing self-evident or truthful about
equality. We don't know if it will ever be.

Jefferson knew that. Yet he made a choice about what he wanted the truth to
be. We face similar choices everyday in life. Choose well.

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ericssmith
Although it's nice to see Gödel show up in the popular press, I didn't get
what the point of this was. His Incompleteness paper is not that impenetrable.
Sometimes it does pay to at least look at primary sources in addition to
listening to others' efforts to summarize or dissect. I don't think the author
of this article made much of an effort to understand what or who she was
writing about. Sad, really, given Gödel's importance in understanding the
beginnings of a science of computation (easily one of the most significant
achievements in human history), where there is already too much myth-making
and mischaracterizations.

~~~
brahadeesh
"His Incompleteness paper is not that impenetrable." May I ask what do you
mean by that?

~~~
ericssmith
Sure. The original 1931 paper is 20-something pages long:

[http://www.w-k-essler.de/pdfs/goedel.pdf](http://www.w-k-
essler.de/pdfs/goedel.pdf)

Here's an English translation (with a lengthy introduction)

[http://jacqkrol.x10.mx/assets/articles/godel-1931.pdf](http://jacqkrol.x10.mx/assets/articles/godel-1931.pdf)

Even without trying to follow the proof proper, the sub-sections of the second
part are interesting on their own, particularly Gödel numbering and primitive
recursive functions. Here is another translation that covers just this part:

[http://www.research.ibm.com/people/h/hirzel/papers/canon00-g...](http://www.research.ibm.com/people/h/hirzel/papers/canon00-goedel.pdf)

It's true that if you know nothing about formal logic, history of
metamathematics, and decidability, then it's going to be particularly hard
going, but there are a lot of accessible resources for each of those topics
and the paper is well structured (meaning you can concentrate on the pieces).

The encoding that Gödel used for formulas should be fascinating for anyone
familiar with Turing work on decidability as well as how computers work
generally. Primitive recursive functions don't handle computation generally,
but seem to be a first step in understanding what it means. Anyone familiar
with Alonzo Church, lambda calculus, functional programming, McCarthy's first
paper on Lisp would probably be interested in this bit.

Of course, Gödel's result on formal systems shattered the idea of an axiomatic
basis for mathematics, but I personally think its greater long-term impact is
helping to usher in computation. It's worth recognizing both.

------
Intermernet
>I asked my classmates whether they had heard of the sci-fi writer Rudy
Rucker’s book

Rudy Rucker was/is also one of the most prominent cellular automata
researchers of recent history. I can highly recommend "Cellab" [1], which I
first encountered as CA Lab. You may need to install a virtual machine to get
it running properly [2].

[1]:
[http://www.rudyrucker.com/oldhomepage/cellab.htm](http://www.rudyrucker.com/oldhomepage/cellab.htm)

[2]: _[In the spring of 2010, the Cellab software became semi-obsolete---in
that it won 't run under Windows 7. The "good" news is that Windows 7 can in
fact run a virtual machine in Windows XP mode, if you download and install
some free Microsoft virtual XP software. I tried this just now, and it works
pretty well. You get a little window or a full screen which is an XP desktop.
And CELLAB runs fine in the XP window—to make it easy to find your files, you
drag the CELLAB folder from your normal C: drive (if that’s where it lives)
onto the desktop of the XP Virtual machine window.]_

------
curiousgal
What a fun read!

Probably worth mentioning that Russell's opposition to recursion which lead to
him formulating "his" paradox offered type theory as a solution. Type theory
also has quite the impact on computer science.

~~~
chriswarbo
I think a more precise wording than "recursive" would be objecting to
_impredicative_ definitions; those which quantify over (something containing
or pertaining to) themselves.

For example, it's fine to define an arithmetic function recursively; it's not
so fine to define a set based on whether it contains itself.

------
kazinator
Likely allusion to:
[https://en.wikipedia.org/wiki/Waiting_for_Godot](https://en.wikipedia.org/wiki/Waiting_for_Godot)

~~~
auggierose
Really?

~~~
insulanian
Why not?

~~~
auggierose
Just tried to joke :)

~~~
mirimir
Poe's Law ;)

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Grue3
There's also Godel's completeness theorem for first order logic. Much easier
to prove, and also extremely important.

~~~
lmm
Not Goedel's, is it? I thought that was known long before him.

~~~
jesuslop
he's right, it was Gödel's.

------
kriro
"""Gödel’s masterpiece was his incompleteness theorem, which ranks in
scientific folklore with Einstein’s relativity and Heisenberg’s
uncertainty."""

nitmode: theorems (there's two). It's mentioned later in the article but a
little odd that they don't just add the s and be done with it.

Great article though. Sidenote: I always thought a tragedy about Cantor would
be fun to write.

