Infinite Probes in Optimization

Infinite Probes in Optimization .
Andre Willers
5 Jan 2008

Definitions:
n! = n*(n-1)*(n-2)*(n-3)*…*1

The Euclidean Constant e .
e = (1/1! + 1/2! + 1/3!+ 1/4!… )
=2.178…

I will make it as simple as possible using costs and temporal sequences as examples .

Assume that the elements of a system are identifiable and repetitive .
The rules of Arithmetic can then be applied .

Take any such system . By definition it can then be subdivided indefinitely . Each subdivision of r elements can have r! possible permutations (or states) .

Let there be a CostReserve to cover unknown costs in the failure of any element in a group .

Key Assumption
Let at least one element of each r be Aristotelian False (ie a failure cost item)

The Total cost of failure will be the sum of the cost of failures of the elements.
(ReserveCost) *( (1/1! + 1/2! + 1/3!+ 1/4!… ))= (TotalCost)

Your Reserve times the sum of individual failures = total
This defines the boundary .

This is the optimization equation .

This is equal to
ReserveCost / TotalCost = 1/e ~ 0.37

This means that you should not consider an endeavour where the rate of return is less than 37% . This is the long-term break-even point from a probabilistic viewpoint .

This equation is independent of space or time .

Any society (any at all ) that does not deliver 37%+ returns gets zapped by the chaotic downturns .

Since vested interests always decrease rates of returns , empires rise and fall .

The probe can be used in any infinite series , but care has to be taken to define the terms .



An Interesting corollary :

The alert reader would have noticed that the above is true for when there is always at least one false item per group .
What if there is at least one true item per group ? This is approached as follows:

In trading systems , individual items can be identified . The cost of failure in an individual item is then = 1/ (r!/r) = 1/ (r-1)!
The summation is then
(ReserveCost/Item)*(1*1/1! + 2*1/2! + 3*1/3!+ 4*1/4!… ))= (TotalCost)
(ReserveCost/Item)*(1 + 1 + 1/2!+ 1/3!… ))= (TotalCost)
(ReserveCost/Item) / (TotalCost) = 1/(1+e) ~ 0.27

As can be seen , trading systems will survive the collapse of empires . There is a whole 10% difference favouring traders . Recovery systems will then also favor traders .

This is the underlying reason why Stalinistic Communism failed and Chinese went trader . The VOC and East India Co . are good examples .

Ten percent is just too much .

Ho-ho-ho !
The average between 0.37 and 0.27 is roughly 0.33 . A third .Can you see where this is relevant in any infinite situation where uncertainty rules?

Non-Failure Ratio
A non-failure ratio of (1- 1/3) ~2/3 summated over infinity = (2/3) / (1-2/3) =2 .

This means that any system that can be described or broken up into smaller groups is strongly ordered . Successful subgroups survive by a factor of 2 . This is built into the mathematics of the Universe . Life is one such sub-group , so are particles ,etc . Negative entropy is the rule . Life is everywhere . Positive entropy only holds in the most primitive and earliest systems .

Beautiful!

Quantum and non-quantum systems are the same .

Singularity Points.
27% and 37% are singularity points , as are (100-27)=63% and 53% . SocioEconomic systems destabilize at these points . Regardless whether they are human , alien , japanese , chinese or any other sort of ese .
Any society where more than a third of productive enterprise is spent without engendering new wealth creation is doomed .

Tax rates of more than 27% reduce trade . Tax rates between 27% and 37% will let it limp along . Tax rates over 37% is a disaster waiting to happen . It is that simple , and no amount of pontificating will change the realities of economics .

The tax rate anchored between 0% and 27% will follow a catenary . The optimal will be halfway (12.5%) . This would be the optimal VAT rate . Note that deviations from this (up or down) leads to social unrest . The unrest is not linear , but catenary . In other words , it gets rapidly worse as it approaches the anchor points of 0 or 27 % . This is true of any civilization , human or alien . It is inherent in the mathematics .

These are absolute rates , not relative .

The RepoRate .
The tax on new money . If the reporate plus profits stay away from the singularity points (27% , 37%) there is no problem.

What about undefined realities ? Refer to
http://andreswhy.blogspot.com “Topos:
Note in the definitions above , that as groups are divided by n , and n->infinity , the system approaches undefined “thingies” . Hence , it can be used as a probe into undefined realms .

Marriage:
An interesting corollary is optimizing pairings of two . The theory above says that random pairing will lead to a failure rate of 37% . Observation seems to bear this out .

To optimize : Note and keep track the best features of the first 37/100 daters , then seriously consider the first anybody after that who equals or better the standards of the first 37
This optimizes your chances .

This result has been independently reached in games theory

Note that your body is independently doing this sort of infinite analysis . Hence speed dating , cocktail parties , mingling , etc .

A good algorithm is to speed date at least 50 persons . Do not do this if you cannot handle rejection , since this concentrates years of normal rejection into a few weeks .

A therapeutic mechanism? Sects use this whipsaw mechanism of rejection (by the outside world) and warm acceptance by the sect to create mini-societies .
Hence cold-canvassing . Rejection binds them closer . Any converts are a bonus . Most real converts are made by on-on-one contact .

But that is also the definition of most successful families .

If you are stupid and ugly , and can handle speed dating , you are a better man than I am , Human .

Virtual speed dating .
Analogous to cures for fear of heights , fear of confined spaces , etc . Considerable success has been achieved in reprogramming the amygdala for these and related phobias using virtual reality .

A Virtual Rejection website will make money .
That’s OK if somebody learns from it .
Another way for actresses or avatars to make money .
“I was rejected 1000 times by Lara”
“Balls rejected by Lara TombRaider as not dusty enough.”
The mind boggles .


Andre