8 ms·

Time Travelers

154 points by fern12 9y ago

beautifulfreak 9y ago
This was Gödel's gift to Einstein on his 70th birthday, certainly one of the coolest birthday presents ever.
TheOtherHobbes 9y ago
Amazing. https://en.wikipedia.org/wiki/G%C3%B6del_metric https://en.wikipedia.org/wiki/G%C3%B6del_metric
IntronExon 9y ago
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?
- deleted 9y ago
  [deleted]
- xaedes 9y ago
  "and the hypersurface of the present is some strange artifact we perceive" This! And that makes it a different present for each and everyone/everything.
  - IntronExon 9y ago
    And that makes it a different present for each and everyone/everything. I’ve never thought about it in quite that way before, but yes I suppose so. Each hypothetical observer is going to experience different slices of “present” in something like Block Universe conjecture.
- kbenson 9y ago
  > 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 9y ago
    Good point, and I’ll freely admit that I try not to think about that too much.
    - kbenson 9y ago
      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.
pouta 9y ago
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.
- EtDybNuvCu 9y ago
  Pick some formal system X which can handle basic arithmetic. The basic idea is to take the classic paradox, "This sentence is false," and embed it into maths. The sentence actually constructed is something like, "This theorem is not provable within formal system X," and it's phrased as a theorem of formal system X. The main ingredient we need here is to realize that numbers can represent sentences in formal systems. This should be obvious to computer scientists of today, but it was ground-breaking at the time. Another thing we'll need is diagonalization. Some folks get hung up on this one; ultimately, you'll have to convince yourself that it's a valid technique. Hofstadter's explanations, both the long gentle one in GEB and the quick fuzzy one in "I Am A Strange Loop", are much more detailed and correct on this, so I'd advise going back and making sure you understand each step. Also, something that doesn't get enough airtime is Tarski's Undefinability, which says that a formal system afflicted by incompleteness is not capable of talking about truth in certain basic and important ways which would enable a formal system to fully represent itself.
- rintakumpu 9y ago
  I'd highly recommend "Gödel's Proof" by Ernest Nagel and James Newman (https://www.amazon.com/G%C3%B6dels-Proof-Ernest-Nagel/dp/0814758371 https://www.amazon.com/G%C3%B6dels-Proof-Ernest-Nagel/dp/081...). It'll probably require a bit of patience to go through, but should be fairly accessible to reader without an extensive mathematics background.
  - sidcool 9y ago
    What are the practical implications of the incompleteness theorem?
    - 9y ago
deleted 9y ago
[deleted]

Time Travelers

154 points by fern12 9y ago

beautifulfreak 9y ago

This was Gödel's gift to Einstein on his 70th birthday, certainly one of the coolest birthday presents ever.

TheOtherHobbes 9y ago

Amazing. https://en.wikipedia.org/wiki/G%C3%B6del_metric https://en.wikipedia.org/wiki/G%C3%B6del_metric

IntronExon 9y ago

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?

deleted 9y ago
[deleted]
xaedes 9y ago
"and the hypersurface of the present is some strange artifact we perceive" This! And that makes it a different present for each and everyone/everything.
- IntronExon 9y ago
  And that makes it a different present for each and everyone/everything. I’ve never thought about it in quite that way before, but yes I suppose so. Each hypothetical observer is going to experience different slices of “present” in something like Block Universe conjecture.
kbenson 9y ago
> 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 9y ago
  Good point, and I’ll freely admit that I try not to think about that too much.
  - kbenson 9y ago
    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.

pouta 9y ago

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.

EtDybNuvCu 9y ago
Pick some formal system X which can handle basic arithmetic. The basic idea is to take the classic paradox, "This sentence is false," and embed it into maths. The sentence actually constructed is something like, "This theorem is not provable within formal system X," and it's phrased as a theorem of formal system X. The main ingredient we need here is to realize that numbers can represent sentences in formal systems. This should be obvious to computer scientists of today, but it was ground-breaking at the time. Another thing we'll need is diagonalization. Some folks get hung up on this one; ultimately, you'll have to convince yourself that it's a valid technique. Hofstadter's explanations, both the long gentle one in GEB and the quick fuzzy one in "I Am A Strange Loop", are much more detailed and correct on this, so I'd advise going back and making sure you understand each step. Also, something that doesn't get enough airtime is Tarski's Undefinability, which says that a formal system afflicted by incompleteness is not capable of talking about truth in certain basic and important ways which would enable a formal system to fully represent itself.
rintakumpu 9y ago
I'd highly recommend "Gödel's Proof" by Ernest Nagel and James Newman (https://www.amazon.com/G%C3%B6dels-Proof-Ernest-Nagel/dp/0814758371 https://www.amazon.com/G%C3%B6dels-Proof-Ernest-Nagel/dp/081...). It'll probably require a bit of patience to go through, but should be fairly accessible to reader without an extensive mathematics background.
- sidcool 9y ago
  What are the practical implications of the incompleteness theorem?
  - 9y ago

deleted 9y ago

[deleted]