Saturday, October 04, 2014

Prodigies Update II

Can Stupid people do Smart things ?

Andre Willers
4 Oct 2014
Synopsis :
They can , and do all the time . There are proven algorithms that enhances this Bootstrap Effect .
Discussion :
Interestingly enough , when I googled “can stupid people do smart things” , there were no hits . Millions of hits for the inverse of smart people doing stupid things .
This shows a thoroughly human bias of stupendous proportions .

1.The Secretary Problem Algorithm
  ~ 37%
The Bootstrap Effect is built into the nature of the Universe : the statistical rules and logic principles .
God’s thumb on the scale .

The secretary problem is one of many names for a famous problem of the optimal stopping theory. The problem has been studied extensively in the fields of applied probabilitystatistics, and decision theory. It is also known as the marriage problem, the sultan's dowry problem, the fussy suitor problemthe googol game, and the best choice problem.
The basic form of the problem is the following: imagine an administrator willing to hire the best secretary out of n rankable applicants for a position. The applicants are interviewed one by one in random order. A decision about each particular applicant is to be made immediately after the interview. Once rejected, an applicant cannot be recalled. During the interview, the administrator can rank the applicant among all applicants interviewed so far, but is unaware of the quality of yet unseen applicants. The question is about the optimal strategy (stopping rule) to maximize the probability of selecting the best applicant. If the decision can be deferred to the end, this can be solved by the simple maximum selection algorithm of tracking the running maximum (and who achieved it), and selecting the overall maximum at the end. The difficulty is that the decision must be made immediately.
Algorithm :
The problem has an elegant solution. The optimal stopping rule prescribes always rejecting the first n/e applicants after the interview (where e is the base of the natural logarithm) and then stopping at the first applicant who is better than every applicant interviewed so far (or continuing to the last applicant if this never occurs). Sometimes this strategy is called the 1/e stopping rule, because the probability of stopping at the best applicant with this strategy is about 1/e already for moderate values of n. One reason why the secretary problem has received so much attention is that the optimal policy for the problem (the stopping rule) is simple and selects the single best candidate about 37% of the time, irrespective of whether there are 100 or 100 million applicants. In fact, for any value of n the probability of selecting the best candidate when using the optimal policy is at least 1/e.

This can be seen from as well from a completely different derivation .

1.2.The second best :
P tends to 0.25 .

The best go off somewhere , and the second-best remain to run things here .
One variant replaces the desire to pick the best with the desire to pick the second-best. Robert J. Vanderbei calls this the "postdoc" problem arguing that the "best" will go to
Harvard. For this problem, the probability of success for an even number of applicants is exactly  \frac{0.25n^2}{n(n-1)} . This probability tends to 1/4 as n tends to infinity illustrating the fact that it is easier to pick the best than the second-best.
2.An interesting application is in DNA editing .
The cell’s own editors and DNA repair machinery use this principle , as can be seen from D(0),which  is the dose producing, on average, one lethal hit per cell, where 37% of the cells survive.
This can be seen as the DNA repair using the 1/e algorithm as above .
3.Just using this algorithm consistently , the user betters his chances over random by (1-1/e) = 0.63212055882 ie 63 % . This is an enormous advantage .
To put it into context : If a person with an IQ 100 does not use the algorithm and chooses as chance happens (regrettably frequent as far as marriage is concerned “Marry in haste and repent at leisure”) , then a competitor will have to have an IQ of 163 to beat ( IQ100+ Algorithm ) .
The irony : ( IQ163 + Algorithm ) has no extra advantage .
Conclusion : This Universe is designed to have liminal IQ’s of 100*(2-1/e)^L   =  100*(1.63)^L   , where L is Intelligence Level = 1,2,3,…
L(1) =  163
L(2) =  265
L(3) =  433
L(4) =  705
L(5) = 1157
This is true for any intelligence , AI’s as well .
L(2) is equivalent to 1 in 4.4 x 10^3939 , which means L(2) personalities will be mostly virtual .(Est number of atoms in universe ~ 10^82 .
Humans can then create AI’s smarter than themselves .  But the first hurdle is high . IQ 265 :
See Appendix IQ below for highest human estimated IQ’s . (The fQuannigton one is dubious : somebody’s little joke)

5.Your kids can be smarter than you .

6.Other Bootstrap Algorithms :
6.1  Make sense of small/dubious data
6.2  NEAT for complexification/decomplexification
6.3    Optimal descriptors exist and can be found . Ie you can be smarter by reorganization .
 A properly chaired committee can reach levels 63% better than the stupidest individual in the group .
 A bad chairman results in the inverse : 63 % stupider than the stupidest individual in the group . In real life these are always remembered .
      6.4.1 Smart individuals making stupid mistakes : think of a person as a collection of traits , habits , etc , with the consciousness as chair of this committee . If the chair is having a bad day , truly stupid things can emerge .
     6.4.2 A happy marriage .
6.5     Machine Learning Meets Human Learning
6.6 Pop-a-pill and Plug in . Common in human enhancement project , from Ritalin to transcranial stimulation . See
6.7 Religion
6.8 Many others I don’t know about .
7.The Giga Society .
Membership of the Giga Society is ideally open to anyone outscoring .999999999 of the adult population on at least one of the accepted tests. This means that in theory one in a billion individuals can qualify.
This is so because the world average I.Q., projected onto this scale, is not 100 but somewhat below 90, probably between 85 and 90. The crux is that the I.Q. scale we use in actuality refers only to the adult populations of Western countries such as those in Europe and North America, and is not correct for the rest of humanity.
One wonders if the elusive Dr William Alfred Quannigton in Appendix A is a member . That L() level would be associated with a virtual intelligence . Ie a machine or hybrid machine intelligence . An AI poking fun at the natives .

8. Further references you will need :


Stupidly yours
Appendix IQ
Here are the top ten highest IQs ever recorded:
1.Phd. William Alfred Quannigton
Child IQ=350+ (Should have been 430+)
Adult IQ=300+
2. William James Sidis
3. Leonardo Da Vinci
4.Johann Wolfgang Von Goeth  
5. Hypatia
6. Nathan Leopold
7. Emanuel Sweedonburg
8. Gottfried Wihlem Lebinitz
9.Hugo Grotius
10.Tomas Wolsey

There is no set way to measure intelligence as there are too many aspects to take into account , so don't put too much faith in your IQ rating. Hope this helps ;-)

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