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:

985310887760040894785325790923110733569172313379698201920279221700657547827237932471087377722789194213347050172859028902826144505754240
465202252512859932265719684847826169738590770955277681881351603369916573502999977803432701983844771993748428541001189867229498362250127
201872670675855738544351755083202528277487083408625895927813111546363452891140837110582572452013104751839194200293681882170077708003469
753532062099163405437488825802552778657469472741364369659170062563957766899607454778824042305378749651925327685934303799260447100163731
881720296705492480657476668192306753633024301619863772611891558137619296470872078778887369302251684639439179821679362636654905742282897
410612462568733140982749313103762845457417321502698188762252176286634107424335002548174623665959947647503141761039107452249097275964038
071007019601645089950090403544349778240409742719235941376106657139122427077979104025003944470936751542981001493980965094985705141517883
8061071767515174350125673535138393450945984317006308570
...

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

33929337262974345875303704307539509446776859172215037587736165296279633238892798409773824624619503009193022800305162
04855379484183556732853493170022645264310734781848419878535253686980578641094034906588585349168858930598429316375925
13471438693394396472584536757865773457617753325125066297384417129240442681180628239905897525476788153800107278776364
74113999790170377893021268552992451373394407472059137219183486332485466118950364158109425567910460650731981978885070
54361337970210930167434117109115533811431263474907534167816114154365937765331780305057832703525871996666529503159468
28575686598283710452988596234670718538308089133565152633073541636120296653338379480498893430400553627561704954442336
60369842387990312683868020040003803851729730104264447685712258052912609009755011196713365725734337017548877110754003
88255532748796606938181457549775416587771754763824488174160895061397902908293224552062744455310674480668080511240349
305121261237541757230368117165727977853174984193548044532176953305040241

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.

Annonser

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 etsy.com. 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