Correspondence with Graham Oppy on mathematical difference between infinite & indefinitely long lifespans; part 1

Email #1, 8th of February, 2020

Dear Professor Oppy,
Attila Csordas here, aging/longevity biologist and philosopher, based in Cambridge, UK. My philosophical work concentrates on the philosophy of indefinite longevity, the upper limit, still possible scenario of biomedical life extension technologies, with a non-zero mortality rate. ‘Indefinite’ here capture the possibility of technology providing indefinitely long lives but also capture (epistemologically) our current scientific understanding (or better the lack of) of being genuinely uncertain about how far we are able to push human lifespan with technology. Just because we know no bounds here, it does not mean this that there are no bounds. This formulation is new and am working on a book on it, called Open Lifespan However still majority of people are stuck with the term immortality and its connotations when thinking about this, both pro and contra, so am looking for ways and examples to phrase indefinity and indefiniteness helping me clearly to distantiate it from infinity.. And am looking for good mathematical ways to demonstrate and define indefinity, in this post I tried to frame this.
I’d like to ask you whether in your research into the Infinity book have you found any interesting formulations, philosophical and/or mathematical, that can capture the concept of Indefinity-ness clearly and heuristically?

Thanks in advance ,
Attila Csordas
Cambridge, UK

Email #2, 24th of February, 2020

Hi Attila!
Thanks for your letter. I am not sure that I have anything very useful to say.
One thing is this: it seems to me to be pretty plausible that we can set some pretty definite upper bounds on our mortality. Suppose that protons decay. Current estimates of the half life of the proton is 10^40 years. I reckon that we can be pretty confident that no humans will survive past 10^40 years from now. Even if protons do not decay, current estimates suggest that blackholes will all evaporate — by Hawking radiation — within10^130 years from now, leaving a universe that contains nothing but a very dilute gas of photons. I think that we can be even more confident that no humans will survive past 10^130 years from now.
I suppose you might say: neither proton decay nor evaporation of  black holes is certain. We could be wrong about those things. That may be so. But it also seems to me that there is a series of future events, each of which might mark the end of humanity, and to each of which we can attach some reasonably high credence. A much closer event — less than 10^10 years from now — is when our sun goes red giant. We cannot survive that event unless we master interstellar travel AND there are habitable planets sufficiently nearby.
Before the sun goes red giant, there will be collisions between the Milky Way and other galaxies: first the Large Magellanic Cloud and then Andromeda. I am not sure whether either of those events is potentially hazardous to life on earth. And then there are all of the risks that are much closer to home that could wipe us out (the kinds of things that Rees discussed in his 2003 book).
Suppose you can temporally order the things that might wipe us out: E1, E2, …, En. I assume that any list we can make is finite. Perhaps we can assign odds to our being wiped out by any of the Ei, given that we have not already been wiped out by Ei-1. If the odds that we assign to our being wiped out by En is less than one, then that seems to be a way of saying that, for all we know, we might go on living forever. This is still tricky. I think it is certain that we cannot exist in a universe that is nothing but a dilute gas of photons. I think it is certain that we will cease to exist if our sun goes red giant and we have not mastered interstellar travel. Etc. All that I see that we can get is some sort of epistemic uncertainties about what science tells us about the future: science might be wrong, and if it is, we can’t be sure that we won’t survive forever.