Monday, February 23, 2009

A Good Life

Life is what you make of it. So says my sagely friend Dan Urman.

So what, then, would make a good life for you? By this question, I don't mean simply your current living situation -- I'm asking about your entire life, a hypothetical best case scenario that is still realistic.

It's very difficult for me to answer this question (although the difficulty does seem to vary depending on how "realistic" is interpreted). I can think of two reasons for this. The first is pretty straightforward: I implicitly operate under the assumption of free will and non-determinism. Any attempt to define my entire life trajectory would undermine my inherent sense of how life should be lived. In other words, I prefer to view my life as an ongoing journey, where the road ahead is to some degree cloaked in mystery and thus still uncertain.

This first issue can be partially addressed by being less detailed or precise when describing a hypothetical good life. But even if it is desirable to employ such a tactic to answer this question, the second concern remains.

To the extent that it is possible, I am fundamentally an optimist. So if you propose to me a hypothetical scenario, then I will consider ways to improve upon said scenario. As such, any instance of a (realistic) hypothetical life will ultimately be unsatisfying to me, given sufficient time for contemplation.

For example, while I don't expect to live forever, any pre-specified lifespan is completely unsatisfying due to notions such as longevity escape velocity. One can easily relate this idea to some simple mathematics. Consider, for example, a positive random variable X that follows a folded Cauchy Distribution (a folded version F' of F basically means P(0 < F' < K) = P(|F| < K)). The probability of X taking on larger and larger values shrinks to 0, but its expected value is infinite. This is basically following the idea that the function f(x)=1/(1+x) vanishes as x increases, but its integral over the positive reals is unbounded.

Another way to look at this issue is by considering the two envelopes problem. Conditioned upon knowing a realistic scenario for what might be, I can always imagine something better. Not surprisingly, the solution proposed by Chalmers uses a distribution that has an infinite expected value.

But maybe I'm just weird and severely over-thinking the situation (happens pretty often). Maybe this question is relatively easy for other people to answer.

7 comments:

John Carrino said...

Or maybe it is like 1/x^2

The Wrong Box said...

You should believe whatever Dan says. Because he's Jesus.

Yisong said...

John, 1/x^2 is too pessimistic for me.

Yogesh, that's exactly what I'm trying to do... and failing =)

Ryan Stout said...

So what you're saying is that no matter how good your life is, you're not going to be satisfied because you'll be able to imagine some way it could be better? Doesn't sound too 'optimistic' to me.

If you find yourself with a girl you really like, don't dump her just because you can imagine someone better. Appreciate her for what good she can offer you in the time you are together, then move on when you meet a better girl. (This is hard to do if we're talking about real girls, but life isn't something you can insult by changing your mind.)

Yisong said...

On the other hand, saying that you can't imagine wanting something better than what you already have sounds incredibly limiting, doesn't it?

Also, I don't see how anything I said implies that I would break up with any girl because I can imagine a "better" one (defining better is seems tricky). In an ideal setting, your significant other should grow as a person along with you.

In fact, I actually agree with you whole-heartedly. If we extrapolate to a future where humans live healthily for hundreds or thousands of years, then I find it plausible that we would be married to someone for 10 to 50 years, and then move on to someone else. After all, diversity enriches our lives =P

Here's another way to think about the issue. Conditioned on my starting point, one can, in principle, define a 95% confidence interval around that starting point. For some confidence level of your choice, you might declare that picking the best scenario from the associated confidence interval is satisfactory. But I think that other 5% is so awesome that it dominates the expected value of the distribution. I guess you could call it unhealthy optimism.

Dan said...

Related:
The Myth of Sisyphus

Life is only absurd if you expect it to add up to something.

As a corollary, reflection demeans activity.

Yisong said...

That is a very interesting lecture. I guess the one point I don't agree with (although it's kind of beside the point) is his take on science. While I don't disagree with his assessment that science can't answer questions regarding the meaning of life, I think it's more useful to take the view that scientific, technological, and societal progress is empowering and gives us greater freedom to do what makes us happy.