The Bonds Integer

Since the first article on this topic was published on my blog a lot of people have expressed curiosity about this special number of mine, the “Bonds Integer”. “What’s so special about it?” people ask.

Well I think it’s kind of special. It’s three hundred fifty five thousand six hundred seventy one digits long (355 671 digits long).

The first thousand digits goes like this:


For practical reasons i omit 353 671 digits but here are the last thousand digits. You can see that it’s an odd number.


So, what’s the use of this number?

The use I suggest is that we divide the (base 27) “decimal” expansion of Pi in chunks exactly this big

By using this chunk size I claim that examining a completely arbitrary chunk of Pi will make the probability 63.2% of finding there a complete encoded reproduction of Douglas Adams The Hitchhikers Guide to the Galaxy.

World’s dumbest person – with an IQ of 5

Occasionally you stumble upon these articles about some person allegedly having the highest IQ in the world. What’s really amazing is to see how exceptional intelligence can be treated with such great stupidity. You can see journalists report about Americas smartest man – Christopher Michael Langan – with an IQ of 195, or the sensational Korean guy – Kim Ung Yonga – with an IQ of 210. One classic media favourite is the American woman Marilyn vos Savant who once was listed in Guiness Book of Records as having the highest IQ ever measured – 228.

What never seem to have crossed these reporters minds is the question how it’s even meaningful to talk about these specific figures. On what grounds is it possible to evaluate a particular persons IQ to a  score of 210 rather than, say 200?

IQ is defined as to be normally distributed around a mean of 100 with a standard deviation of 15.

With a world population of 6.9 billion people (or to be more precise 6,912,609,896 people when I checked earlier tonight) we can present the following list:

These are the ten most intelligent people in the world today:

(1) IQ 195
(2) IQ 193
(3) IQ 192
(4) IQ 191
(5) IQ 191
(6) IQ 190
(7) IQ 190
(8) IQ 190
(9) IQ 189
(10) IQ 189

Of course no one knows who they are and maybe, you object that this list is just a mathematical artifact, a statisticians dream not based upon actual reality, but I’m saying that the calibration of the IQ-scores can’t be based upon anything else than the parameters of ideal normal distribution.

What I’m saying is that if the IQ scores of the ten most intelligent people on earth, after some serious testing would evaluate to something else than the above list of scores, then we should have to recalibrate the measurement scales so as to fit the list.

There is not so much else we can do. When you measure people’s shoe size you relate to some explicit physical property but in the case of intelligence tests we really don’t know what we measure. We are really only ranking people according to a number of successfully solved test problems.

Even though it may be perfectly okay to rank people in accordance to the number of solved test problems of a certain genre I think it’s naïve to think that the IQ scores could say anything more than just that.

Using my idealistic manner of reasoning we can conclude with great certitude that the stupidest living person on earth today is having an IQ of 5. That guy is in fact a full two IQ points ahead in stupidity compared to the second stupidest person.

One funny thing is that according to another not so uncommon IQ scale – the Cattell scale (using a standard deviation of 24) there exist roughly one hundred and seven thousand people on earth with a negative IQ score.  Using the Cattell IQ scale the stupidest person on earth has an IQ of minus 51.

Assessing and quantifying intellectual abilities through testing is an interresting subject but there’s a big need for philosophical investigation.

I’ve been thinking about these things since I myself took one of these standardized tests last week – the big swedish aptitude test ”högskoleprovet”. I read that over seventy thousand people in Sweden took it on this occasion. I was a bit frustrated because of constant time stress but I think my results were okay. I had five errors in the graphs and diagrams part. Three in the swedish reading comprehension part and one error in the logics and maths part (of which I should be ashamed, becuse I teach maths and philosophy =) ). The grading levels based on normal distribution will be finalized in about two weeks time.

Here are some visual basic formulas I’ve modified that calculates the total number of people in the world expected to have a certain IQ or higher:

Public Function NumberOfPeopleSmarter(IQ As Double) As Double
    Dim L As Double, k As Double
    Const StandardDeviation = 15
    Const WorldPopulation = 6910000000#
    NumberOfPeopleSmarter = (1 - CND((IQ - 100) / StandardDeviation)) * WorldPopulation
End Function
Public Function CND(x As Double) As Double
    ' The cumulative normal distribution function
    Dim L As Double, k As Double
    Const a1 = 0.31938153: Const a2 = -0.356563782: Const a3 = 1.781477937:
    Const a4 = -1.821255978: Const a5 = 1.330274429
    L = Abs(x)
    k = 1 / (1 + 0.2316419 * L)
    CND = 1 - 1 / Sqr(2 * Application.Pi()) * Exp(-L ^ 2 / 2) * (a1 * k + a2 * k ^ 2 + a3 * k ^ 3 + a4 * k ^ 4 + a5 * k ^ 5)
    If x < 0 Then
        CND = 1 - CND
    End If
End Function

You can buy the Standard Normal Distribution Plushy from You can also buy four of his friends you can see behind him: the Log Normal Distribution, the Chi-Square Distribution, the t-Distribution and the Continuous Uniform Distribution