
Memories of Kurt Gödel - danielam
http://www.rudyrucker.com/blog/2012/08/01/memories-of-kurt-godel/
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beautifulfreak
It reminds me of this article in the New Yorker about Gödel's and Einstein's
talks. [http://www.newyorker.com/magazine/2005/02/28/time-
bandits-2](http://www.newyorker.com/magazine/2005/02/28/time-bandits-2)

"Although other members of the institute found the gloomy logician baffling
and unapproachable, Einstein told people that he went to his office 'just to
have the privilege of walking home with Kurt Gödel.'"

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yequalsx
I know this post is aimed at laymen but this sentence is not correct.

"A bit more precisely, the Incompleteness Theorem shows that human beings can
never formulate a correct and complete description of the set of natural
numbers, {0, 1, 2, 3, . . .}."

The second order Peano Axioms are categorical and thus, up to isomorphism, the
only model for this axiom system are the Natural numbers {0, 1, 2, 3, ...}.
This is a complete system. We can't happen is a recursively enumerable
axiomatic description of the Natural numbers that is complete.

Another way to get a complete description of the Natural numbers is to take
the collection of all true statements of the Natural numbers and make that our
axiomatic system. It's just not a useful axiomatic system but it is a complete
description of the Natural numbers.

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monet
Thanks for pointing this out. Two questions: (1) Are there any resources you'd
recommend reading to learn more about this? (2) If you are familiar, could you
restate the Incompleteness theorem in your own words? Just looking to learn
more here :)

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nicky0
You're on a dangerous road. I asked these questions once, got a couple of
books. Decided I needed to enrol on a couple of courses... 7 years later I had
completed a math degree. :)

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smallhands
really i will love love to hear your story.i have feeling that there is more
to it ! wow , i am impressed.please what is your email?

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westoncb
I'm surprised no one has mentioned anything about Rudy Rucker, whose blog this
is from. Some credit him with authoring the first cyber punk novel, which was
titled 'Software.' It's the first in his 'Ware Tetralogy' (Software, Wetware,
Realware, Freeware) which I'd certainly recommend checking out.

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Synaesthesia
“Spaceland” was also a hoot. It’s his take on the classic “Flatland”.

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vbuwivbiu
“The illusion of the passage of time arises from the confusing of the given
with the real. Passage of time arises because we think of occupying different
realities. In fact, we occupy only different givens. There is only one
reality.”

Is he saying that our brains exist over all time simultaneously but they
"give" us a sequence of instants from which we perceive the illusion of
passage of time ?

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gfody
he's not making a statement about brains, more the nature of reality. it's a
perspective that's gaining traction lately with the dataist/reality-is-
information line of reasoning.

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vbuwivbiu
ah he's distinguishing between ontology and epistemology ? He's saying there's
only one reality but our instantaneous measurements of it (the given - what we
perceive with our brains) form the illusion of time

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harryjo
Yes,

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vbuwivbiu
but the increase of entropy isn't an illusion

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gfody
the single vast space-time would already be locked in a state of maximal
entropy, nothing moves, the illusion of time is just the universe recalling a
memory.

~~~
20after4
^ This, exactly.

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cicero
That's a beautiful story. I've been fascinated by Gödel since I read _Gödel,
Escher, Bach_ by Douglas Hofstadter back in the 1980s. I'm not a
mathematician, so I can't plumb the depths of his work, but I gain a little
more insight by reading articles like this one.

~~~
ianai
I remember reading the proof of his incompleteness theorem (or the portion of
it that I had time to between classes). It's surprisingly approachable. AFAIR,
he came up with a way to encode proofs as symbol sequences. Proofs that
actually exist have finite representations. He then proved the theorem with
that somehow. (Granted, I read it over a decade ago...)

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Agentlien
You're thinking of Gödel numbering which is an elegant technique used
extensively throughout that proof. He uses it to map logical symbols,
statements and entire proofs to natural numbers and then proceeds to prove
things about those statements and proofs by referring to them via their Gödel
numbers.

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mirimir
So does Gödel's incompleteness theorem apply to scientific knowledge? I mean,
as I understand it, he proved that any useful logical system contains
statements that can neither be proved true nor false. But does that apply to
quantum mechanics, for example? Are there self-referential statements in QM?

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RobertoG
I think it applies specially to scientific knowledge.

There is a connexion there between Gödel and Popper.

Except inside a formal system, you can never prove that something is true,
only that one explanation is better than other in an endless pursue of better
explanations.

I'm not sure there is such thing as not-scientific knowledge, by the way.

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dwaltrip
> I'm not sure there is such thing as not-scientific knowledge, by the way.

I'm fully on-board with the overwhelming, world-changing effectiveness that
the scientific method provides for distilling factual, empirical knowledge and
truth.

Lately, however, I've been contemplating forms of knowledge and understanding
that are more difficult to assess and validate -- things that might be
typically described as wisdom or keen insight. Our scientific instruments
can't provide observations that let us robustly verify such knowledge, but to
me it seems very evident that it exists.

Some examples: What is important to building and maintaining strong
relationships? How can one prepare for and handle personal hardship? If one
finds themselves in a fortunate position with excess resources, what are good
ways to use those resources to help others?

Science can help us with these questions, but humans have useful knowledge to
bring to bear in answering those questions that can't be yet described within
the framework of science.

Differentiating by quality or truthiness is ridiculously hard in such domains,
but I don't think that is a valid reason for dismissing such things
altogether.

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mirimir
Yes, that's what I was getting at. Insight, wisdom, etc.

Even so, one can also apply the scientific method to those sorts of knowledge.
One can look at performance. Quality of relationships. Success at dealing with
hardship. That's part of psychology. But it hasn't received enough attention,
I think.

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pge
For further reading on Gödel, Rebecca Goldstein's _Incompleteness_ is a great
book. It is a biography of Gödel but also places his work in the context of
the philosophical debates of the time.

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chx
Godel's incompleteness theorems are explored by many of Raymond Smullyan's
books in a way that an inquiring high school student can understand it.

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galaxyLogic
I wonder what he would have come up with had he had access to computers

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marktangotango
I wonder what is meant by this question. In a very naive sense of the
question, the type of mathematics Gödel worked on (foundational?) wasn't
really computation oriented or even formulaic, so the ability to perform lots
of calculations very quickly probably wasn't of much use to him. Indeed,
computers where available to him in later years.

A more interesting interpretation of the question (to me) is what if he had
access to computers used as mind amplification devices. For example; such as
by using Mathmatica or Maple to explore and visualize theorems and things. I'd
imagine the benefit of this activity for someone like Gödel would be "not
much". Computations and simulation have inherit limitations; precision and
rounding errors for scientific computation, and the fact they can only model
what we can imagine for another. These people such as Gödel, Neumann, and
their ilk, new this, they begat the era of computation we have today, and all
the limitations that involved. Neumann in particular was famous for, when
presented with your problem, would tell how to solve it.

What's new today that they may not have foreseen is the vast level of
internetworking and human communication that arose from ubiquitous presence of
computers and networks.

Something that strikes me about the present article is the fact that Gödel,
keen to see Rucker before he knew him, was not so keen to converse with him
after their first encounter. One might think Gödel was not too impressed with
Rucker, maybe found him boring and dull for example.

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OscarCunningham
Perhaps the idea of computers would have been more useful than the computers
themselves. Several of the ideas in his proof are simpler if you can say
"computable" rather than "recursive" or whatever. So perhaps if he had been
thinking in these terms he could have done more work sooner.

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dom0
The way things turned out the work from this era defined what computers can
and can't do, not the other way around, which would likely not satisfy many
mathematicians.

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nis10
Aghhh who the ... picked the acid background of this page? cool

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arketyp
Looks like the Rock Paper Scissor cellular automaton:
[https://www.youtube.com/watch?v=lt9ihcg-
bZc](https://www.youtube.com/watch?v=lt9ihcg-bZc)

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fundabulousrIII
He was quite insane. Dopamine is a hell of a drug.

