
Time Travelers - fern12
http://inference-review.com/article/time-travelers
======
beautifulfreak
This was Gödel's gift to Einstein on his 70th birthday, certainly one of the
coolest birthday presents ever.

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IntronExon
_Closed timelike curves are intrinsic and irreducible features of Gödel space-
times.12 If they are possible, so is time travel. And with time travel,
certain paradoxes arise. Imagine a traveler arriving in the past and killing
his own grandfather.13 Would he survive the encounter if he broke the causal
chain leading to his own existence?

There are two popular views about how these kinds of paradox might be managed.
The first is committed to an ensemble of equally concrete but different
versions of the physical world. Travelers into the past arrive in worlds that
are distinct from those that they left. They are free to kill their
grandfather secure in the knowledge that their grandfather is not really their
grandfather, but something like his counterpart. David Deutsch and Michael
Lockwood think that restrictions posed by classical systems on the actions of
time travelers imply that time travel must must displace travelers into
different worlds.14 It is by no means clear that time travelers under such a
scheme are really following a closed timelike curve. Closed timelike curves
are paths that return to, or very close to, their own spatiotemporal starting
points.15

On quite another view, time travel really does return an agent to his very own
past. A temporal rerun is possible only if everything he does in the past is
already in place in his history. This means everything. Consistency might be
maintained through the most ordinary of physical processes: the gun misfires,
or the bullet dribbles out inconclusively, or at the very last moment your
grandfather ducks to tie his shoelaces. Your efforts can make the past what it
was but they cannot make the past different from what it was._

There is a third, which is that you would arrive in the past only to find that
you had no agency at all, no free will. In this formulation you would never
attempt to kill your grandfather, and no faulty guns or lucky grandparents are
needed. If the present is a hypersurface sweeping through spacetime, leaving
the past in its wake, and the past is a set structure... you’re an automaton
if you travel to the past. Presumably in this kind of natural order, the
future doesn’t exist except as a word and concept. There is the fixed past,
and the hypersurface of the present.

 _Or_ the future and past are both fixed, and the hypersurface of the present
is some strange artifact we perceive. Or... who knows?

~~~
kbenson
> There is a third, which is that you would arrive in the past only to find
> that you had no agency at all, no free will.

Or perhaps it's only the _illusion of agency_ that is gone.

~~~
IntronExon
Good point, and I’ll freely admit that I try not to think about that too much.

~~~
kbenson
That's probably a good strategy. Either it doesn't work that way, and you can
go happily about your life, or it does work that way, and you're happier not
knowing because knowing only allows for the possibility of negatives.
Ignorance is literally bliss.

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TheOtherHobbes
Amazing.

[https://en.wikipedia.org/wiki/G%C3%B6del_metric](https://en.wikipedia.org/wiki/G%C3%B6del_metric)

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pouta
Slightly off-topic but after reading Douglas Hofstadter's books the one thing
that I never managed to grok was Godel's incompleteness theorem. It's
implications are fascinating but my math background never allowed me to
completely understand it's proof.

~~~
rintakumpu
I'd highly recommend "Gödel's Proof" by Ernest Nagel and James Newman
([https://www.amazon.com/G%C3%B6dels-Proof-Ernest-
Nagel/dp/081...](https://www.amazon.com/G%C3%B6dels-Proof-Ernest-
Nagel/dp/0814758371)). It'll probably require a bit of patience to go through,
but should be fairly accessible to reader without an extensive mathematics
background.

~~~
sidcool
What are the practical implications of the incompleteness theorem?

~~~
ben_w
You cannot ever know for sure that your software is bug free, because no
finite system of logic is both true and complete.

At least, that’s my understanding of it.

~~~
dsr_
Not exactly.

For any sufficiently powerful system (Turing completeness is definitely
powerful enough) there are statements which are true but cannot be proven by
that system. Secondarily, no system can demonstrate its own consistency.

However, if you limit your software enough, you can prove that every possible
input is handled correctly _. That involves removing Turing completeness. E.g.
once you accept a language as a configurator, you can no longer prove that.
CSS3 is Turing complete. JSON is not.

_ One requirement is limiting the size of inputs.

