Will we all die some time?
An interesting type of escape velocity concerns the risk of death from
all causes, aging-related or otherwise, and is a strengthened form of
actuarial escape velocity. If we achieve actuarial escape velocity as
defined earlier and exceed it by some way for a long time, we will get
to a point where essentially no one is dying of old age and indeed no
one is even frail. But of course there will still be death from all
the familiar age-independent causes. If we suppose that this risk is
a constant -- not only the same in year X for people of any age, but
also the same in all years from X onward for people of any age -- then
clearly we all have a "half-life", like radioactive materials, which
means we all die eventually, just as all the atoms in such materials
decay eventually. If we all had the mortality rate of present-day
Western 11-year-olds, our half-life would be about 1000 years.
But it
is not actually all that realistic to suppose that our risk of death
from age-independent causes will be constant indefinitely, because we
will probably not be very keen on that sort of death either and we'll
be forever working to improve our technological ability to avoid it.
It is dangerous to presume that there are any real limits to what we
may be able to achieve in this regard in the extremely distant future.
Thus, it's worth considering what our life expectancy would be if we
had a continuous -- let's assume constant, for sake of simplicity --
and indefinite improvement in our ability to avoid death from any
cause. Suppose your chance of dying in the next 1000 years is 0.5, but
if you survive that 1000 years then your chance of dying in the next
1000 years is only 0.25, and if you make it through that 1000 years
then the chance of death in the next 1000 is only 0.125, and so on.
It turns out that this sequence does not have a zero asymptote -- you have a
roughly 28% chance of living literally forever, genuinely never dying
at all, even though your chance of dying in any given millennium is
always non-zero. If the chance of death diminished by a smaller
factor than 2 in each initial half-life -- say it went 0.5, 0.3, 0.18
etc. -- then of course the chance of never dying would not be as high
as 28%, and if it diminished by a greater factor than 2 the chance of
never dying would be higher than 28%. But if it's greater than zero,
i.e. you have some chance of never dying, then it turns out that that
means your life expectancy (the time you have a 50% chance of living)
is actually infinite, because the people whose lifespan really is
infinite outweigh the ones whose lifespan is finite. That's a pretty
strong version of escape velocity!
You might be thinking the above scenario seems unrealistic, because
surely some halvings of risk are going to be harder than others and the
scheme only works if we halve the risk every single millennium. Well,
then let's look at a more pessimistic scenario, where the halvings of
risk take progressively longer to achieve on average. As an example,
suppose the halving time doubles each time. In other words, the risk of
dying in the next 1000 years is still 1/2, but the risk of dying
between 1000 and 3000 years from now is 1/4, the risk of dying between
3000 and 7000 years from now is 1/8, etc. What proportion of people
live forever then? The answer is: just the same proportion, 28%, as in
the previous example! This is obvious if you think about it, because
the proportion of people who live forever is just the limit of the
series (1/2) x (3/4) x (7/8) x .... and thus is independent of the
lengths of time involved. The survival curves of these two examples do
have different shapes -- for the first 5000 years or so one's risk of
death in any particular millennium is lower in this second example than
in the previous one, and thereafter it's higher -- but the two curves
have exactly the same asymptote.
Will we ever make ourselves immortal?
No. None of the above forms of postponement of aging and death --
not even the last one -- can correctly be described as "immortality".
Immortality means inability to die, i.e. a certainty of never dying.
Even in the last case above, there is always a non-zero probability of
dying some time -- and indeed a non-zero probability of dying in any
given year. So this last question has an easy answer: no, we will
never make ourselves immortal.