Intelligence Measurement

Population intelligence can be measured at any given time with any test which produces standard normal distribution results for the population in question. All valid tests which an individual may take in the course of his education, like high school or college entrance tests, course exam tests, graduating tests, company placement tests, international competition tests, etc., are all valid test measurements whose results can be mapped isomorphically to results from a standard IQ test.

The Universe gives hundreds of opportunities to most individuals to have their intelligence measured via such tests and these chances are precisely the set of all tests an individual may take/has taken in the course of his education.

The fact that there are many such tests and opportunities during the regular life course of an average individual indicates that The Universe is fair on this issue and desires to give any individual more than one chance to improve on this measurement, for otherwise there would be no need for multiple opportunities for measurement. This implies that if t₁<t₂ are two different testing times and your measurement at time t₂ is better than at time t₁, you may take the better measurement between the two as a better indicator of your intelligence.

If we call this measurement IQ, it is then clear that it is a function of time t^[1], so let's notate it as IQ(t). This implies that this measurement is not something static, rather it evolves as a function of time.

The question is how does IQ(t) evolve. Can we perhaps find a functional equation for it? Let's list some initial facts to try to determine some of its parameters.

The first fairly obvious fact which comes from the definition of this measurement, is that its range is bounded:

If an individual has taken n such tests up to today, there exists one of those tests which has concluded with a maximum measurement and hence there is a time t=t₀, for which we have:

The next important step is to find how IQ(t) evolves as a function of t. The IQ distribution function varies exponentially with respect to population, as exp(-(x-μ)^2), therefore any evolute of IQ as a function of time, must vary again exponentially, but inversely with respect to time, as exp(-1/(t-t₀)^2).

IQ Evolute Fairness

The above suffers from one small defect: The inclination of the IQ evolute of two people with unequal IQ's cannot be the same. A smarter person evolves faster in time than a dumber person, by the very definition of what IQ means and this should be indicated in the evolute. Therefore we also need to adjust the expression by one last factor and the obvious location for this factor should be in the denominator of the exponential, since this is what determines the derivative (inclination) of the IQ evolute. Ergo, this "advantage" factor must be exactly^[2] the deviation of the initial IQ₀ itself from the mean. In other words this factor should be exactly: C=IQ₀-100.

Here is this advantage shown graphically for two people with a small IQ₀ difference.

> p1:=plot(IQ(30,101,t),t=30..35,color=red):
> p2:=plot(IQ(30,100.1,t),t=30..35,color=green):
> display({p1,p2});

The IQ of a person with a higher IQ₀ evolves faster as a function of time.

In other words, a person with exactly average intelligence, can never evolve into anything above average, because otherwise people with above average intelligence wouldn't have any advantage relative to those who have exactly average intelligence. If A, B and C then are constants, in view of equations (1) and (2), we get the system:

(3)

System (3) has the complete solution:

(4)^[3]

Let's see a specific example with Maple, then, where an individual measures his\her IQ at age 30 and finds it to be 110.

> with(plots):
> IQ:=(t0,IQ0,t)->IQ0+(200-IQ0)*exp(-1/(IQ0-100)/(t-t0)^2);
> plot(IQ(30,110,t),t=30..35);

IQ Evolute for a person with IQ=110@30.

The Concept of Karma

Although The Universe is fair with respect to giving many opportunities for intelligence measurement for most individuals, it may not be fair with respect to assigning intelligence to the offspring of humans^[4]. What this means: A certain person may have a certain IQ@t, but this person's father may have had a much higher IQ@t. We can therefore model mathematically the concept of Karma, according to whether the offspring has smaller or greater intelligence than that of his father. Accordingly, if x is the father and y is the offspring,

1. IQ_x(t)>IQ_y(t) => BAD Karma^[5].
2. IQ_x(t)≤IQ_y(t) => GOOD Karma.

In order for the comparison to be fair mathematically, it must be made relative to the same age for both father and offspring. A particularly bad case is the case of this author, whose father had an IQ@18=136^[6]. An IQ of 136 at this age is unimaginable by common human standards, because such an IQ evolves incredibly fast as a function of time. The author's father's IQ evolution as a function of time is shown below.

> plot(IQ(18,136,t),t=18..56);

IQ Evolute for the author's father.

At the age of 23, the author's father had an IQ of:

> evalf(IQ(18,136,18+5));
199.9289284

A Measure for Karma

A measure for good/bad Karma K can now be defined, as:

For example: The author's father had an IQ=136@18, which implies an IQ=199.99@46 based on (4). This author has a measured IQ=124@46, therefore a measure of his Karma K is,

> K:=evalf(IQ(18,136,18+28)/124);
K:=1.612

Because the author's father had a much higher IQ@46 than the author @46, the author's Karma is bad or negative^[7].

Karma Deprecation

Bad Karma can be deprecated only in one way: Through work. How much work? Exactly equal to K times the work of the father who has higher IQ. Therefore in order for this author to be released from the burden of his bad Karma, he must show work equal to at least the work of his father times K~1.612 in a similar field. In order for the work comparison to be fair, this work has to be in an area that the author has chosen as his profession, via a universally standard test measurement. For this author, this area was Mathematics^[8].

A measure of the workload of an author based on Google Scholar is given in Google Scholar and the Spectra of the Scientists. Therein, this author's measure evaluates to C(y)=1.082661059, while the author's father's measure in the field of Mathematics evaluates to C(x)=1.163654584. Karma K~1.612 implies an additional workload differential of at least d(x,xK)=|C(x)-[1;K*6,9,18,29,17,13,6,2,1,1]|~0.061^[9]. On the other hand, the workload differential between this author and his father evaluates in the aforementioned article to d(x,y)=|C(x)-C(y)|~0.081. Since d(x,y)>d(x,xK), this author has paid-off his bad Karma debt to his father^[10][11].

Resistance to Karma Deprecation

Besides Karma deprecation, there's also the issue of resistance to Karma deprecation, which starts being in effect as soon as the offspring encounters the singularity @t₀ for him/herself.

Resistance to Karma deprecation happens precisely because the offspring's father (or if you prefer The Universe which has assigned intelligence to the offspring) resists any and all efforts for IQ normalization by the offspring, at any time. If the evolute of the father's intelligence is IQ(t_F,IQ_F,t), the evolute of the offspring's intelligence is IQ(t_s,IQ_s,t), with both given as in (4), the birth date of the father is b_F and the birth date of the offspring is b_s, so that Δt=b_s-b_F, then the resistance the offspring encounters @t>t_s is defined as:

R(t) is shown on the following figure:

IQ(t_F,IQ_F,t) (red), IQ(t_s,IQ_s,t) (green), ΔIQ (blue) and R(t) (magenta), for this author and his father.

R(t) is shown in detail on the following figure.

R(t) for this author

Karma deprecation resistance R(t) for the offspring is related to pressure on the offspring (to deprecate his/her bad Karma). Because it is an opposing force on the offspring, its sign is negative. The time of maximum pressure on the offspring, can be found by solving the equation dR/dt=0. For this author, it gives t_max=2/2010. This pressure will dissipate gradually, until about year 2012^[12].

Notes/References

1. Although IQ is a function of time, this function doesn't make sense prior to an individual getting an IQ₀. Therefore the domain of this function is necessarily t>t₀. Note that the time point t=t₀ is a singularity in the evolution of a person's intelligence, because the function is not defined there, which is intuitively correct.
2. Even if the C factor is not exactly equal to IQ₀-100 empirically, it will likely be some function of it, in which case the result might as well be approximated using C=IQ₀-100.
3. Note that this expression is valid for IQ₀≥100. In particular, if IQ₀=100, then IQ(t)=100=const. If IQ₀<100, the function which describes the IQ evolute must necessarily be something different, because something which lies below average, cannot possibly evolve into something which lies above average, even after infinite time. If above average intelligence evolves asymptotically towards 200, then by duality, below average intelligence must evolve asymptotically towards 0, using a similar/dual function. Details left as an exercise.
4. Offspring intelligence depends highly on genetics and education, hence there's no reasonable way to model/predict offspring intelligence in advance, as such intelligence is a function of the genomes of both parents. For simplicity in this presentation, we choose a comparison only between fathers and sons, making the assumption that fathers usually are the ones who determine the financial evolution of the family. This assumption may be replaced by the assumption that mothers determine this evolution, provided we operate in a society which is sufficiently developed/advanced to allow this.
5. When the father has a higher IQ@t than the offspring, Karma is bad precisely because The Universe in general abhors stupidity and in such a case the offspring delays the intellectual development of the father's evolutionary line in time.
6. This author was lucky, in the sense that such a measurement is known for his father. For details, consult a short biography of the author's father.
7. When the offspring has bad Karma relative to the father, many bad things start happening in the offspring's life, which compound the bad Karma even further. When the offspring has good Karma, The Universe does not oppose the overall development of the offspring, whether financial or otherwise.
8. The author's father in 1982 heard that his son (this author) successfully entered the Mathematics department upon successful completion of national examinations, therefore it is reasonable to choose this field as the field of Karma workload.
9. Because the main weight of the work-measure is carried by the term a₁ in the continued fraction expansion of C(x)=[1;a₁,a₂,...]. Details in the article Google Scholar and the Spectra of the Scientists.
10. Although bad Karma can conceivably be cleared as in the case of this author, it is not a good idea to stop working and start lazing around after the fact. The IQ of a father who has a higher IQ than his offspring continues to evolve as a function of time asymptotically tending to its limit (200) therefore bad Karma is continuously added to the offspring while the father is alive.
11. Because it is often difficult to deprecate Karma this way, many religions including Christianity, Buddhism and Hinduism attempt to do the same for people who are not fortunate enough to have the capacity to do it themselves, using measures of "goodness". Details on this article.
12. That's why it is a good idea for anyone to always work, continuously, 24/day, 365/year, because when the pressure strikes, things are going to be fairly difficult. 2 Thessalonians 3:10: "For even when we were with you, we gave you this rule: "The one who is unwilling to work shall not eat."."

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