The Wikipedia articles on telomeres and telomerase have plenty of further resources[2][3].
[0] http://learn.genetics.utah.edu/content/chromosomes/telomeres...
[1] http://www.ncbi.nlm.nih.gov/pmc/articles/PMC3370421/
[2] https://en.wikipedia.org/wiki/Telomere#Cancer
[3] https://en.wikipedia.org/wiki/Telomerase
edit: formatting
That this formula works would seem to indicate that you are right. Death is natural, but it's "planned". The easiest way for such a formula to work would be that your genes somehow contain a death clock.
But there are multiple death clocks. One limits number of cell divisions. There is another one known that limits the amount of energy that can pass through a cell, after which it will kill itself. There are various others, one that kills the cell if it isn't deactivated on a regular basis (presumably meant as a check on DNA integrity), one that is triggered from the outside of the cell, ... the list goes on.
That's my uneducated but logical sounding assumption.
When the telomere is in bad condition, your cells divide slower or even not divide itself.
When this happens your tissues do not repair fast enough, and everything gets a worse condition, your skin, your hair, your brain, your heart.
Restoring telomeres means your cells could start dividing again. At 75 your body will go back to "young adult" 20 years old, without the hair, teeth and whatever you have lost in your life, and the scars, and broken bones soldering, or damaged ligaments that you already have got in your life.
However, lots of animals could grow hair and teeth again so they will probably find a way to make that too.
People will continue dying, but young in their 100s, or in their 20s like today, in things like accidents, wars, terrorist attacks and so on.
People won't die from old age, like most people do today.
Of course this will change the world and will have terrible social consequences.
We will need a better (bigger and cheaper) energy source(fusion) that what we have today to sustain a population that mostly never dies, population and social controls(because old-now young people will have a terrible advantage, experience while being young, and all their accumulated compound wealth) and a way to start exploring other planets and living there.
Not for long. Years from now living without a backup of yourself will be as abhorrent as currently operating a database with no backup.
You'd then have all the time in the world for them to find improvements.
Average telomere length in tissue is a measure of health in general: since telomere length decreases with each cell division it is a proxy for some combination of cell division rates and rate of influx of fresh new cells with long telomeres provided by the stem cell population maintaining a tissue. Since average telomere length is often measured in white blood cells it goes up and down with health and generally downward with age. Stem cell activity declines with age, so this shouldn't be surprising.
Lengthening telomeres via telomerase may extend life in mice for any number of reasons, some of which actually have nothing to do with telomeres. Telomerase, like all biomolecules, has a lot of roles, not all of which are fully understood. Alternative and more controllable methods of lengthening telomeres should help narrow down what is going on in those studies. Is it greater stem cell activity, something to do with telomerase influencing mitochondrial function, something completely different?
In general if you're thinking of aging as accumulated molecular damage, telomere shortening looks like a consequence not a root cause. It may cause further issues itself, but targeting it is probably not as effective as going for the actual root causes that lead to it. The interesting question is why telomerase therapy does do comparatively well in extending life in mice.
I guess if you could compare many strands you could find the spots that are the same in all.
But then to somehow repair them all?
