## Wednesday, April 30, 2008

### Infinite Probes2

Infinite Probes 2
Andre Willers
30 April 2008

http://andreswhy.blogspot.com/ “Infinite Probes’

From discussing this with various recipients , there seems to be a need for a simpler explanation . I thought I had explained it in the simplest fashion possible . The subject matter is inherently complex .

But , here goes .

How much must you save ?
If you save too little , a random fluctuation can wipe you out .
If you save too much , you lose opportunity costs . If you are in competition , this loss can be enough to lose the competition (ie you die)

Intuitively , you can realize there is an optimum level of saving .

Methods exist of calculating this optimum in very specific instances (ie portfolios of shares ,eg Kelly criteria , or tactics in war eg MiniMax ) .

The General Case
We need to hold a Reserve in case Something goes wrong . But we do not know what thing goes wrong .

Infinite Probes tries to answer the general case . What is really , really surprising is that a answer is possible .

The Infinite bit comes from using the mathematical expansion of the Definition of Eulers Constant e = ( 1 + 1/2! + 1/ 3! + … 1/n! + …)
Where n!= n*(n-1)*(n-2)*(n-3)*…*(1)

This approaches a constant , widely used in mathematics and physics .
(e = 2.718…) .

All we need is a system that can be subdivided indefinitely (to infinity) .

First , we divide by 1
Then 2
Then 3
Then 4

And so forth till infinity .

What is important is not that we do know what these divisions are , only that they are possible . We also do not know which one element goes wrong .

The other critical insight is that it is the relation between elements that is important . (Permutations) (The failure of an element in total isolation cannot affect the whole system by definition .)

We can count the number of relationships where there is failure of one element .
It is n! , where n is number of divisions where only one failure .

Multiple failures are handled by summing :

Our Reserve(R ) is divided by n to infinity and summed .

TotReserve= R*( 1 + 1/2! + 1/ 3! + … 1/n! + …)
TotReserve= R * e

To find the boundaries of our Reserve , we set TotReserve = Cost

Then

R = 1/e * Cost
R ~ 0.37 * Cost

What does this mean?
This method measures the upper boundary of the reserve needed to survive failures in any element of the Cost-Universe . Ie , internal fluctuations .

This is the surprising bit . Any society that keeps at least 37% reserves , can only be destroyed by something outside it’s envelope . It is internally stable , no matter what .

Empires like the Ancient Egyptians , Romans , Chinese are possible , as long as there is no climactic fluctuation , new inventions , diseases ,etc . Rare events . Hence the technological stasis of old civilizations . The two are synonymous .

This is true at any scale (except quantal , by definition.) .

Individuals too . Humans can be seen as empires of noospheres .

The upper boundary does not take any double-counting into account . It is true for any system whatsoever .

A truly remarkable precise result from such general axioms .

The Lower Boundaries .
This is where it gets interesting .
Remember , we are just counting the number of ways in which permutations of one element can fail . We then sum them to get the effect of the failures of other elements

The easiest is the business that just starts and is not selling anything . It fails on n elements on every term . It’s floor capital must then be
R=Cost/(1+e)
R=0.27*Cost

This is the initial reserve to get off the ground .
This is true in any ecosystem . This is why it is so difficult to start a new business , or why a new species cannot succeed . Or why waves of pandemics are scarcer .

For the epidemically minded , this 10% difference is responsible for the demise of the Black Death ( smallpox outcompeted bubonic plaque variants for the CR5 access site.Ironically , the reason why we have only a limited HIV plague is the high competition for this site , probably some flu vectors . As one would expect , the incidence of HIV then becomes inversely proportional to connectivity (ie flights) .

A cessation of airplane flights will then lead to a flare-up of diseases like these .
Not exactly what anybody has in mind . )

When we find that we really need the spread of infectious vectors to stay healthy , then we know we have really screwed ourselves .

These are the two main boundaries .
The literature is full of other limits the series can approach . Keep a clear head on what the physical significance is .

Fat
I cannot leave the subject without the thing closest to human hearts : appearance .
Fat and fitness .
Sadly , the present fad for leanness is just that . The period of superfluous food is coming to an end .
Rich individuals can afford to be lean because the reserves are in the monetary wealth Women have to bear children individually , so they cannot store the needed reserves externally . Hence their fat storage is close to the theoretical optimum even in Western societies (33%) . In other societies the percentage is about 37-40% .

Human males have been bred (Mk III humans) for muscle and little fat (8% in a superbly fit male) . He does not have reserves to withstand even garrison duty (even little diseases will lay him low .) Note the frequent references to diseases laying whole armies low .

Note what is left out : the camp-followers . They survived The women and babyfat children . Every army seeded the invaded area with women and children .

The bred soldier has to eat a high-carb food frequently : not meat or fat , his body cannot store it . This is the definition of a wheat-eating legionary .

Ho ! Ho! Ho!
The Atkinson diet .
No wonder it does not make sense in evolutionary terms .
Mesomorphic humans have been bred not to transform expensive proteins and fats into bodymass .

The soldier-class were kept on a carbohydrate leash , which could only be supplied by farming .

The Smell of Horses .

Horses exude pheromones that promote body-leanness in humans . This has an obvious advantage to horses . Horses are breeding jockeys .

The time-span is enough : at least 8 000 years . (400 generations)

Because pregnant women cannot ride horses , there was a selection pressure to breed horses who have a pheromone that block female dominance pheromones , especially since females have to weigh more because of fat-reserve considerations .

Outside a farming environment , horses will sculpt their riders as much as the riders are sculpting them .

Small Mongolian ponies , small Mongolians .

This is why alpha-males like horses and horse-dominated societies were able to conquer and keep matriarchies .

Note the effect of the pheromones on women riders . Androgeny .
On males it becomes extreme blockage of oestrogen . It seems like a surge of male hormones , but it is just an imbalance . (If too much male hormones , the men just kill their horses )

This is why the auto-mobile had such a big sociological effect . No horses , so the men became more effeminate .

Want to be Lean and Mean ?
Sniff Horse sweat pheromone .
Perfumiers take note .

Dogs

The other leg of the human-horse-dog triumvirate .
Dogs accept female pack-leaders and have evolutionary reasons for blocking horse inhibitions of human female pheromones .

While the males are away , the females look after and rely on the dogs .
(The reason why Mongols ride from yurt to yurt: they are too scared of the dogs.)

With dogs around , the male testosterone activity is ameliorated . This is a well known effect , especially if horses are around .

Hence the female love of lap-dogs . They are actually quite ferocious , and exude large amounts of pheromones that soothes the savage male breast .

Your attention is drawn to the Pekinese lapdog , which has had a disproportionately large effect on human history .

If this sounds convoluted , it is because this is exactly how this type of bio-system operates : by inhibitions of inhibitions of inhibitions ,etc .

Andre