Econstudentlog

Random thoughts

So, imagine this scenario. You live in a (parallel universe/future world/space setting/…) where people know how long they have to live; you know the exact date that you’ll die. It’s quite important to note early on that this date cannot be changed by any future events outside the models below. You have X years left of your life when you get the offer.

You’re now presented with the option, A, of living ‘twice as long’, in the sense that you will have 2*X years left of your life if you pick option A. There’s a downside to the arrangement; you have to double the amount of sleep, Z, you get pr. day (/time period).

Let’s plug in some numbers just for fun. Say you’re 20, you know you’ll die at the age of 70 (X=50), and you can at the current point in time expect to get (Z=7) hours of sleep/day on average during your life. If you pick A, you’ll live to the age of 120 – you’ll gain 50 years – but you’ll have to sleep 14 hours/day. If you decide not to take the offer, you will have 310,250 hours [(24-7)*365*50] left in a conscious (non-sleeping) state and you will die in 50 years. If you take the offer, you’ll have 365,000 hours [(24-14)*365*100] left in a conscious (non-sleeping) state and you’ll die in 100 years. In this case, you both live longer and you will have more hours available to you to do stuff. But what about a 60 year old who sleeps 9 hours/day and can expect to live to the age of 85? In that case, A will give you 109,500 hours and 50 years, whereas the alternative will give you 136,875 hours but only 25 years. When looking at A more generally, it seems clear that the older you are the less years you gain and the worse the tradeoff looks because the natural/baseline sleep requirement is increasing in age. At which points in people’s lives would this look like the most interesting proposition? Would it necessarily be the case that ‘the younger, the better’ – what about, say, sociological factors? How big an impact will the decisions of people close to the decisionmaker have – would the longevity of individuals in this model depend on social ties/skills; and if so, how?

Interesting things happen if you change A and make different restrictions on the choices offered; for instance, what happens in a model, A’, where you gain one hour for each extra hour you sleep? Basically this is just saying that you can decide freely when to live your life (looking forward in time), but not how long you’ll actually live. How would people deal with this choice? What if you made the sleep requirement an increasing function of the years gained and further imposed the restriction that people could at most sleep for 23 hours/day? (you have to add some sort of restriction like that or it starts to get really weird) Like, say, model B, in which you’d gain the first 10 years by just sleeping one extra 1 hour/day, whereas the next decade would cost you an additional 2 hours of sleep pr. day – at which point would people think that the arrangement maximized their lifetime utility, and how would this maximum depend upon the choices made by the people closest to them? Note that in model B, the 20 year old guy from before would (still, just like A) be able to live for another 100 years, but he’d have to sleep 22 hours pr. day to do so; and he’d spend much less time awake in this case than if he did not choose this option.

In the above models, the cost of getting to live longer than you’d otherwise do is ‘sleep’ but it could be other things as well. In the real world, you have a lot of people who stay alive long after their minds are gone – before my grandfather’s mind had gone completely he did live something close to 23 hours in an at least ‘semi-conscious state’, paired with a few clear moments during the day. You also have cancer patients who spend the last weeks or months of their lives either writhing in pain or simply knocked out by painkillers. In these cases, what are ‘we/they’ optimizing? In the real world setting, there’s also stuff like physical exercise, which might add half a decade or more to your life – if you’re willing to incur the cost of actually get sweaty/take time out of your calender and/or sleep more (restitution).

Now imagine another model, C, where what is on offer is not years gained but rather hours awake. It’s the flip side to the first models here. In this model, if you’re willing to drop 2 years of your life you can cut down sleep by 1 hour/day in the years you have left. Say you’re that 20 year old guy again. He can at most cut 7 hours of sleep, which would leave him with 36 years left. The cost imposed is made up for by an additional number of total hours awake while alive: For instance, with the baseline scenario the guy gets 310,250 hours awake, but if he opts to die at the age of 68, he’d get 315,360 hours awake. Given this specification of the model, the total number of hours awake is maximized at the point where he dies after 42 years at the age of 62, sleeping 3 hours/day during his remaining life (hours awake is a parabola; giving up even more years will decrease his total number of hours awake) – this will give him 321,930 hours awake. Would some people choose this model? If you set it up like this, probably not many. But the funny thing is that given how people behave around other variables which are also well known to impact both longevity and subjective utility in not too dis-similar ways (smoking, alcohol, drugs), the obvious answer should be yes. People make not all that dis-similar tradeoffs all the time without even thinking about it.

Also in some of the alternative universes in which one might contemplate making these offers, what is here called a ‘sleep requirement’ is there universally known as ‘sleep dependency’; a chronic, debilitating and incurable disease which causes recurring long-term periods of unconsciousness.

March 17, 2012 - Posted by | rambling nonsense, random stuff

3 Comments »

  1. Reminds me of my analysis of modafinil vs lifespan. You could deal with the doubling issue by adopting a logarithmic scheme: you forfeit half your time awake each deal. 8 hours of sleep and 16 hours awake becomes 16 hours of sleep and 8 hours of wake, then 4 hours of wake, then 2, 1, 0.5, 0.25…

    In any case, I was under the impression old people slept much less than young or middle-aged sleep, due to their generally lower sleep quality.

    Comment by gwern | March 17, 2012 | Reply

    • “In any case, I was under the impression old people slept much less than young or middle-aged sleep, due to their generally lower sleep quality.”

      A quick google supports that notion. Interesting, I’d have thought that the sleep requirement was increasing in age (in the relevant interval) – but that was just an idea based on little (nothing?) but anecdotal evidence. Here’s one link:

      “Misconception 4: People need less sleep as they grow older.

      Older people don’t need less sleep, but they often get less sleep. That’s because the ability to sleep for long periods of time and to get into the deep, restful stages of sleep decreases with age. Many older people have more fragile sleep and are more easily disturbed by light, noise, and pain than when younger. They are also more likely to have medical conditions that contribute to sleep problems.”

      sleep

      This was news to me. Thanks for giving me the opportunity to learn something new today.

      Comment by US | March 17, 2012 | Reply

      • Incidentally, the recent discussion in Danish in the other comment thread is about problems people have had with commenting here. So if you’ve had trouble, you’re not the only one. I’ll try to see what I can do tomorrow, but the problems people have told me about don’t make sense right now.

        Comment by US | March 17, 2012


Leave a Reply

Fill in your details below or click an icon to log in:

WordPress.com Logo

You are commenting using your WordPress.com account. Log Out / Change )

Twitter picture

You are commenting using your Twitter account. Log Out / Change )

Facebook photo

You are commenting using your Facebook account. Log Out / Change )

Google+ photo

You are commenting using your Google+ account. Log Out / Change )

Connecting to %s

%d bloggers like this: