Hey mathematicians or just all-around math-savvy people, I have an offer for you: I pay 50 GBP for the best suggestion that is using a mathematical concept that captures indefinitely long Open Lifespan in a way that gives me an a-ha moment so I can incorporate it into my philosophical treatment of the topic.

You have until 17th of December, 2018 to come up with suggestions that can be rewarded. Comments here please, or email to openlifespan at google dot com. By default I can only pay for 1 worked out analogy. Also the best suggestion will be acknowledged in my Open Lifespan book in case it gets published one day.

You need to understand what am talking about first to be able to come up with analogies and for that let me start from the beginning of the story science/tech-wise, then take a philosophical turn: In the last 2 decades there’s been a breakthrough reached in terms of our understanding of the major molecular and cellular processes behind biological aging and now we have comprehensive knowledge on the major hallmarks of aging, and treatments are under development in all the different classes. It seems unlikely that new hallmark classes of aging are ‘discovered’, so theoretically a comprehensive algorithm can be designed to counteract these processes at separate times and continue them indefinitely.

So it seems possible now that the maximum longevity barrier of 122 years will be broken and there is a separate longevity industry now that aims to turn this possibility into a high probability. How far science and technology will take us in terms of longevity we genuinely don’t know, there’s 30fold increase reached in some lab animals in terms of lifespan, but human is a different beast. So uncertainty in terms of the outcome of combined longevity interventions might add to the concept of indefinite lengthening of human lives.

Hence, from a philosophical point of view if we want to take the limit concept of what is possible we need to take indefinite healthy lifespan. And at this point most philosophers (without a scientific background) get the whole thing wrong, not because they are underestimating what’s possible but because they are overestimating it. They talk about immortality and fall into, what I call, the Immortality Trap.

Meet my central concept, ‘Open Lifespan’. Open Lifespan is open-ended, indefinite healthy lifespan, it will be also called simply ‘Open Life’. Open Lifespan is based on Open Healthspan a technological possibility to counteract ongoing biological aging processes in the human body, to keep age-associated functional decline and increasing mortality continuously at bay.

While an open-ended, indefinite life is mortal, it is not essentially finite or infinite. It is what it is: indefinite. Uncertain. Just because we don’t know the bounds, it does not mean it is boundless and we can still die in any minute due to external circumstances. Open Lifespan defined this way is sandwiched between our current, mortal and naturally capped Closed Lifespan and the imagined scenario called Immortality constructed with infinite lifespan.

I’m using the following 2 terms to grab the 2 opposing aspects of indefinite Open Lifespan to pinpoint the source of confusion.

‘Indefinity’ is used to denote the feature of Open Lifespan that is shared with ‘infinity’, it’s open-endedness, it’s being not essentially ‘finite’. Its a radical way of departing from our current experience, but it is not leaving our biomedical humanness and our mortality behind. It is more like conserving it.

‘Indefiniteness’ will be used to denote the feature of Open Lifespan that is shared with ‘finiteness’, it’s being still mortal when understood in the context of fragile biomedical human lives.

‘Indefinity-ness’ when these 2 features of Open Lifespan are highlighted at the same time. Not a paradox, not a dilemma but a simple in-betweenness, a non-binary.

So with this conceptual story I hope I’ve given you enough clues to think of the mathematical analogies of Open Lifespan. In what follows I mention some brief examples I considered, seemingly not helping too much, or I’m just missing the mathematical imagination and knowledge for that.

First of all, when one searches for how the concept of ‘indefinite’ is used mathematics, there’s not much to be found, or I have not found special review papers on the different usages of the ‘indefinite’ concept in mathematics yet. Pointers are welcome, not paying for them though. 🙂

- There’s indefinite integral, which does not seem to apply.
- There’s indefinite product, does not seem to offer much of an analogy here.
- Then there’s topology with its infinite and bounded surfaces.
- There’s even indefinite quaternion algebras too, but I have no idea what they mean.
- Things get quite interesting thinking about series and limits of series, divergent series particularly, but here I need good, annotated examples showing some inner structures that can be applied to illuminate the concept of Open Lifespan [1].

So people of math, can you provide me some examples to discuss them and pick one to pay for? Something that captures both indefinity and indefiniteness explained above while not becoming trivially infinite or finite?

Sorry, I can only provide one such award now. Comments here please, or email to openlifespan at google dot com.

## Notes

[1] When one thinks about the actual technologies, which I dubbed Open Healthspan reaching indefinite lifespan (a more well-known term calls this reaching longevity escape velocity) there’s a strong camp in the current longevity industry placing extra emphasis (sorry, no references) to claim that all that will be done here in terms of interventions is to just extend healthspan, the part of our life we live healthily, without diseases but there’s a 100% guarantee that maximum lifespan won’t be lifted, maximum longevity barrier won’t be broken. So how a convergent series analogy: we set the limit for a healthy lifespan extending technology similarly to constructing a convergent series where the sum and partial sums of the terms of the sequence of numbers is approaching a number arbitrarily close. For instance, the reciprocals of powers of two form a series converging to 2:

Consider a convergent series where the limit is X, maximum life expectancy and all the terms of the sequence correspond to one particular bit of technology that will provide healthy lifespan for a limited amount of time. In this case you might be troubled by the fact that the sequence is infinite so even if one term corresponds to only a small amount of time (say a month) then the healthy lifespan gained, and capped by maximum longevity will only need a finite amount terms to rely on. So a partial finite sum of the infinite series will provide stability for the healthspan under X. Is this tenable or practically impossible to regulate?

Can we ever develop healthspan technologies that will be programmatically stopped in order to not go over a pre-defined threshold?