Imagining life expectancy distributed geometrically
- What are we talking about?
- So will everyone be immortal?
- The rewards of caution
- In preparation
- Old minds
CW: Discussion of death, dying, and assisted suicide.
I believe that people who are born today will likely1 have access to medical technology that will allow them to extend their lifespans indefinitely. This has some strange implications.
What are we talking about?
If you know what I mean by unlimited healthy lifespan, you can skip this section.
I’m not talking about keeping people on the brink on death alive by all possible means. I expect it’s much more desirable and, I expect, simpler, to extend healthy human lifespan: giving someone the body of a 25 year old, forever.
A quick round of objections because that always comes up:
- What about overpopulation? Lab grown meat, increase density, build floating islands, go to space.
- Won’t life get boring? Not within the regular human lifespan, surely. People don’t usually seem to get tired of their grandchildren. Also, there is no downside here: those of us who want to live longer may do so. Once they no longer want to, they can stop taking the treatment. Thirdly, it would be an extraordinary coincidence if life became dull exactly around the time people usually die, especially as healthy human lifespan has been increasing historically.
- What about immortal dictators? Carbon emissions? Scientific progress no longer happening “one funeral at a time”? The wellfare system? Interesting problems, for sure, but I would rather work on them than die.
- Isn’t this against nature? Yes, so is penicillin.
So will everyone be immortal?
No. Whatever technology we come up with won’t help you against wars, accidents, etc.. Rather, it will eliminate age related disease: cardiovascular problems, dementia, many cancers, bone density reduction, etc2.
Your probability of dying in any given year currently increases the older you get. If you no longer age, it will (hopefully3) remain approximately constant once you reach your twenties, or perhaps even keep decreasing as you do fewer and fewer stupid things.
If your rate of death is approximately constant, the length of your life will track an exponential distribution, with one parameter , which is the yearly rate of death. I asked Claude to estimate this number for 35 year old UK males, and it came up with 1:8,000. The expected lifespan is , or 8,000 years. Nice4.
The exponential distribution is memoryless. If I survive for 8,000 years, in this model my expected age at death is now 16,000 years. Or: if your partner dies, you are expected to live for another 8,000 years. Just imagine spending 1,000 years with someone you love, and then 1,000 years without them.
Another morbid consequence: It becomes a coin flip whether it’s the parent who dies first or their child.
While the number itself is very uncertain, I believe this model is directionally correct.
The rewards of caution
In the exponential model, being more cautious has direct and large effects on your lifespan. In the current world, I expect to live to around 80-90, if I’m lucky. If I chose never to take a car again, that would reduce my risk of death from accident by a lot, and I would expect to live to … around 80-90.
If risk from accident is all there is though, halving your risk of accident, doubles your expected lifespan, potentially increasing your life expectancy by thousands of years.
In light of this, is it at all justifiable to go anywhere by car? To have “high-risk” hobbies like climbing or martial arts? To drink alcohol? Should the first thing I do after waking up be putting on a helmet?
In preparation
If I expect to live for a very long time, is there something I should be doing right now?
There are things which are worth doing sooner rather than later, because they will benefit me for the rest of my life. For example, putting money in savings, getting in good physical shape, establishing good routines, forming deep relationships. But are there big upfront investments of time or resources that are worth doing only if I expect to live another 200 years but not for a measly 50?
It is interesting that in order for something to be worth doing now, it must be both an unreasonable upfront investment and also be something that is easier to do now than later. I am not sure something like that exists: the primary thing that healthy lifespan extension buys us is time, so urgency on everything is reduced.
Regardless of whether they’re urgent or not, what are these large up-front investments? I think they fall into two categories: insurance against very low likelihood tail events and deepening one’s appreciation for life.
Insurance is necessary because with a radically extended lifespan, you are now likely to experience once-in-a-century events and you should probably take seriously once-in-a-millenium events too. A simple example is that, assuming you want to fund your very long life using investment dividends, rules of thumb like the 4% rule must be adjusted to be much more conservative5, so that you can make it through the drawdowns you are likely to see.
The other kind of investment helps you get more out of long, long life. I’m thinking of things like learning to appreciate food more and learning more languages so I could talk to locals when traveling around. Neither of these feel nearly ambitious enough, but I struggle to think of anything grander.
Old minds
Neuroplasticity decreases with age, as does intelligence. Hopefully we fix this, but it’s conceivable that we don’t, or at least not fully. Perhaps mental faculties plateau at the level of the “sharp 60 year old” version of you. Perhaps intelligence is fine, but neuroplasticity is not, and we all become incredibly fit grumpy old men6. Perhaps living for a very long time just drives you insane.
Are there things we should do to prepare for scenarios like these? I would love to see targeted increasing of neuroplasticity on the research agenda. It would be amazing if there was a protocol that I could follow before doing a language class that would make everything I learn in that class stick as if I was three, without risking accidentally changing my political outlook to that of the Chinese textbook. Perhaps it makes sense at some point to transfer part of your assets into a trust, or an off-the-shelf annuity product. Perhaps it is worth making sure that you have trusted friends, and to make them promise to tell you if you’re loosing your mind.
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I’ve not spent time building a solid forecast. Gun to my head, conditioning on no human extinction, my probability is 76%. I won’t share my reasoning so that nobody treats this number too seriously. ↩
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It’s possible not all of these will be solved at the same time and we discover new ways for human bodies to fail – until we learn to cure those too. ↩
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What I think is more likely, unfortunately, is that there are multiple separate processes that make the body decline, but some of them are not currently well understood, because others almost always get to you first. Once we solve the common ones, I expect we’ll see a decrease in strokes and heart attacks etc., and an uptick in hitherto rare diseases in the 100+ population. ↩
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Also, obvious nonsense. 8,000 years is more than the human written record. Any constancy assumption over that time frame breaks down. We would do better to at least estimate a risk of death from armed conflict, based, say, on the last 100 years, and probably add x risk into the calculation too, even if we are conditioning on safe AI. ↩
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Another thing to adjust for is that an economy with lots of immortals around will be very different to the one we have. ↩
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Or perhaps there is actually a lot of mental decline while the body stays young, but in that case I would consider healthy lifespan expansion to have failed. ↩