## Wednesday, October 12, 2005

### Life , Immortality and Probability

Life , Immortality and Probability

Probability in a mathematical sense is defined as the ratios of the number of occurrences of equally likely possible events . It is a circular argument , as “equally likely” introduces the probability concept in the definition of probability .

Example: flip a coin .

The ideal coin has only two sides , with equal likelihood between heads or tails .

The real-world coin is totally deterministic on one throw , but can become chaotic on multiple throws . Also , it can be heads , tails or side . So , not only the initial states of the throw has to be considered , but also the end-states (ie if the coin lands on a grid of vertical slats where only sides are allowed , or horreur ! ,slanted.).

Life insurance:

The risk concept here was based purely on statistics :

An example is the best explanation :

Choose a group of humans and an age , say ,45:

Count (all humans with Age 45) = L45 and count the survivors of the group a year later at age 46 =L46 .

The frequency of deaths in the 45 year old echelon per start for your chosen group is :

q45 = (L45 – L46 ) / L45

This factor is (q45) is then assumed to be the probability of death in the next year for somebody in the 45 year-old echelon and belonging to the chosen group .

This qx factor (where x is the age ) , is fundamental concept of the whole trillion-dollar life insurance industry . Of course , it can get very complicated , but this is the core .

For example :

The statistical probability of surviving from age 45 to age 46 = ( 1- q45 ) by definition .

The statistical probability of surviving from age 45 to age 77 is

(1-q45) * (1-q46) * (1-q47) * … * (1-q76) , where * denotes multiplication .

So , to get an age from where you would have a 70% chance of surviving to age 77 ,

Begin with (1-q76) and multiply with successive (1-q75) , (1-q74)) etc until the product equals 0.7 .

Obtaining the qx’s :

The mortality experience is different for different groups . Britain , Japan ,SA are obviously different for all ages and socio-economic groups . Because of the multiplication in calculating the end-probability , even small successive differences in the qx’s can make a huge difference .

For insurance companies , this makes the difference between profit in loss when in a competitive situation . They also cheat , and price-fixing is rife . The amounts involved are huge . A major problem is that an insurance company cannot tell whether is solvent or not , as the inherent uncertainty in the underlying figures , as well as the lack of record-keeping of all previous fudging of the qx’s obscures the company’s liabilities . The actuaries will keep on hedging on the high side , until collapse is unavoidable . Hence , Insurance companies usually collapse rapidly and with little warning (eg Sage , etc)

Actuarial tables of qx’s or Lx’s are available from most libraries , but only for the very broadest of groups (ages per country) .

As Insurance companies became more competitive , the groups of qx’s were sliced finer ( per sex , race , Socio-Economic group , etc ) . The mortality (qx) of a female ,white wife of a company director is obviously much lower than that of shanty dweller .

The problem of the finer slices is that the number people in the groups falls sharply . The statistical side of things get a bit dicey . They are also usually propriatal . (Think thumbsuck)

Notice that the cross-subsidization ( the whole point of insurance) is now only inside the group (unless the company cheats and subsidises the rich from the poor to get bigger premiums : a common occurrence)

Enter genetical testing :

This is a “real” probability based on the individual or on a group of genes , not on a statistical probability . At the present moment , this is still an imperfect science . As it becomes better , the moment of non-accidental death becomes more-and-more fixed and the incentive to insure becomes the same as the incentive to save .

Cross-subsidization vanishes except for accidents and cheating .

Immortality (except for accidents):

An immortal needs only take out accident insurance . It is interesting that the same is true of someone whose genetic risks are perfectly known , but who ages .

How long will an immortal live?

A meaningless question . More insightful is how many out of 1000 immortals will survive after 24 000 years . According to present accident mortalities , about 5 . But the accidental mortality rate for immortals would be much , much smaller than for mortals . It makes much more sense to talk of the half-life of immortals . A power-law is more likely . More immortals in the short term , but about the same in the long term. Still about 5 after 24 000 years.

How many immortals can a society support?

Max about 5 % . The same percentage as the leadership in any human group , regardless of size . Think of it as a recessive virtual gene . Longevity is enhanced as recessives match in the lower strata of society , displacing the top ones . Societies are inherently unstable , because the longevity genes are not dominant . (Dominant longevity genes in any life-system suicided in Malthusian extravagances very early-on)

The 5% leadership class acts like a virtual immortal class , but with internal and external pressures forcing change . Quite elegant , actually .

For human societies , it is immaterial whether the ruling group is immortal or not . An end state which must be extremely frustrating to actual immortals , since any action they take will wiggle back to the start point after a few centuries .

You can do the rest yourselves

Andre