= 27d567bc2d48d9f40e9ccc20ea370b15)
Pablo_Stafforini comments on Rationality Quotes July 2013 - Less Wrong
You are viewing a comment permalink. View the original post to see all comments and the full post content.
= 783df68a0f980790206b9ea87794c5b6)
Loading…= b715d02e85f7b3b4ae65ca3d3e450868)
Subscribe to RSS Feed
Powered by Reddit
= f037147d6e6c911a85753b9abdedda8d)
You are viewing a comment permalink. View the original post to see all comments and the full post content.
Comments (425)
Tyler Cowen, ‘Caring about the Distant Future: Why it Matters and What it Means’, University of Chicago Law Review, vol. 74, no. 1 (Winter, 2007), p. 10
They are different because when we pack the spaceship with fuel, we control with reasonable certainty whether they make a safe landing or not. As for our millions-of-years descendants, it's very hard to make any statement about us effecting them with >51% confidence (except, "we shouldn't exterminate ourselves").
A lot of what looks like time discounting is really uncertainty discounting.
Cowen is explicitly discussing time discounting. As he writes, "Should we—because of positive discounting—not give them enough fuel to make a safe landing?" (emphasis added) There may of course be other reasons for treating these people differently, including uncertainty about the long-term future, but Cowen is not focusing on these reasons here.
It feels like a terrible example for examining the effects of relativity on utility functions regarding time-discounting; the typical human utility function is going to result in something that approximates Utility(fuel)=stepfunction(fuelpurchased-“100% fuel”) at around 99-100% fuel, regardless of time-discounting. It’s a case of [lands succesffully] versus [runs out of fuel 10 seconds too soon and crashes, killing everyone in the rocket.]
If you’re time discounting heavily enough to not notice that spike, and fuel is somehow the most expensive part of the whole operation, then you’re probably discounting heavily that you’re better off launching two rockets on one-way trips with about 25-50% fuel each, depending on specifics of the rocket.
-In other words, the example fails to probe to the real heart of the mater because it doesn't matter if i use an Einsteinian reference frame or a Newtonian one, my answer is the same: either 100% fuel or very little fuel.
This is backwards. Everyone in an inertial frame thinks other peoples clocks are slower. Acceleration is what causes the opposite, e.g. turning the spaceship around to come back
You're right that Cowen got it backwards, but you're wrong about this:
Acceleration is not the cause. The reason the astronauts age less is that the path they follow through space-time corresponds to a smaller proper time than the path followed by people who remain on the Earth, and the proper time along a path is what a clock following that path measures. So it's a geometrical fact about the difference between the two paths that causes the asymmetrical aging, not the acceleration of the astronauts.
To make this obvious, it is possible to set up a scenario where another group of astronauts leaves Earth and then returns, accelerating the exact same amount as the first group, but following a path with larger proper time. This second group of astronauts will age more than the first group, even though the accelerations involved were the same.
A lot of elementary presentations of relativity identify acceleration as the relevant factor in twin paradox type cases, but this is wrong (or, more charitably, not entirely right).
Just to chime in, in Special Relativity in a simply connected Minkowski spacetime acceleration is required for differential aging, so "Acceleration is not the cause" is misleading. Not that it is relevant to the issue of positive discounting.
But you can get differential aging without any difference in acceleration, so it does seem right to say that acceleration is not the cause of the differential aging. An analogy: Suppose you have two substances in the same lab that are burning at different rates, and you want to figure out the cause of the difference in burn rates. It would be wrong to say that the difference is due to the presence of oxygen in the lab, even though it is true that there would be no differential burning (or any burning at all) without oxygen.
ETA: Perhaps this just devolves into a semantic debate about what we mean when we say "the cause". In the Pearlian framework it seems more natural to talk of multiple causally relevant factors without singling one out as "the" cause. And I admit that the presence or absence of acceleration is a causally relevant factor in the twin paradox. I guess my point was that "acceleration" is not the best explanation for the differential aging. There exists a more fundamental explanation that accounts for many more cases (i.e. when neither observer is inertial, or when the space-time is multiply connected), and allows a precise calculation of the extent of the effect. I think its a useful heuristic to single out the most explanatory causal factor as "the cause" if you want to play that game, but like I said, that's a semantic point.
You cannot. The duration and/or magnitude and/or direction of acceleration has to be different for the two worldlines to be different.
Check out this diagram for an example of two different worldlines (A and B) without any difference in duration, magnitude or spatial direction of acceleration. The accelerated segments are in red.
Thanks for this! I had the same misconception as shminux.
Thanks! I stand corrected. The timing of acceleration also matters. I should have known better. Anyway, I agree that
It just seems like a tautology to me (the difference in aging is due to the difference in subjective clocks). To cause this difference one has to make the worldlines diverge, and this means difference in acceleration profiles.
What I initially was unhappy about is the statement
That last statement is perfectly correct.
I wasn't claiming it was the whole story, but thanks for giving more info. I maybe should have said that you can't have that situation without changing trajectories but I thought acceleration was a simpler way to summarize.
I agree in principle, but I have basically no confidence in my ability to figure out what to do to help people in the future. There are two obstacles: random error and bias. Random error, because predicting the future is hard. And bias, because any policy I decide I like could be justified as being good for the future people, and that assertion couldn't be refuted easily. The promise of helping even an enormous number of people in the future amounts to Pascal's Wager, where donating to this or that charity or working on this or that research is like choosing this or that religion; all the possibilities cancel out and I have no reliable guide to what to actually do.
Admittedly this is all "I failed my art" stuff rather than the other way around, but well, it's still true.
Is it some kind of non-sequitur? How is it related to positive discounting?
Probably because some are more real and others are less so.
Can you explain in more detail what you mean by this?
It's pretty reasonable to care about the live people you know more than about some from potential future generations.