I use this blog as a soap box to preach (ahem... to talk :-) about subjects that interest me.

Saturday, August 14, 2010


I had known of the existence of Mensa for longer than four decades and had considered trying their admission test since my university years but, for one reason or another, I only did it last year. As it happened, it was precisely on my sixtieth birthday. When I was told that it would take up to two months to know the result of the test, I explored the Web and discovered that there were many other High-IQ societies. And many of them had stricter criteria than Mensa. Now, Mensa (at least in Australia) only tells whether the candidates have an I.Q. within the top 2% of the population or not. That’s one of the reasons why I started answering some of the many I.Q. tests available online.

Wikipedia defines intelligence as follows(1): Intelligence is an umbrella term describing a property of the mind including related abilities, such as the capacities for abstract thought, understanding, communication, reasoning, learning, learning from past experiences, planning, and problem solving. Given such a broad definition, it is not surprising that there is not one simple way to measure intelligence. Somebody who is clever at solving word puzzles and playing Scrabble, is not necessarily as good in figuring out three-dimensional geometrical problems. Therefore, different tests measure different cognitive abilities. Moreover, the results of I.Q. tests depend on a series of other factors, like tiredness, emotional state, use of substances like alcohol and coffee, and others. Ultimately, an I.Q. test measures the ability to answer intellectually non-trivial questions of one or more types and under specific circumstances. If we group the people on the basis of how many questions they are able to answer in an I.Q. test and arbitrarily assign the value of I.Q. = 100 to the most populous group, we obtain a normal distribution as shown in Figure 1(2)
Figure 1: I.Q. curve

To define an I.Q. scale, beside choosing 100 to indicate the peak of the distribution, you also have to decide how finely you want to divide the range of possible values. This is done in Statistics by defining the size of the interval that comprises 68% of the whole population. In Figure 1, it corresponds to the green and blue bands adjacent to the peak. Half of that interval is called the standard deviation (or sd) of the distribution. As you can see, the sd was set to 15. As a result of this (entirely arbitrary) decision, 68% of the world population is said to have an I.Q. between 85 and 115. Unfortunately, different researchers have chosen different values of standard deviation. The two most widely used are 15 and 16, but I am told the standard deviation used in Italy is 24. Therefore, when you say what I.Q. you have, you also have to specify the standard deviation you are using. For example, the I.Q. you need to qualify for Mensa can be expressed as 131 sd15, 134 sd16, or 150 sd24.

I personally prefer to talk in terms of percentiles instead of IQs. For example, you qualify for Mensa if you are in the top 2%. This means that only 2% of the world population has an I.Q. as high or higher than yours. Isn’t it much clearer than talking about I.Q. and standard deviations? If you then divide 1 by your percentile, you obtain what is known as the rarity of your intelligence. For example, a 2% means that walking in a crowded place, only one person out of 1/0.02 = 50 will be as intelligent as (or more intelligent than) you are. If you go to a theatre with an audience of 500 people, you can assume that 490 of them are less intelligent than you are.

When I finally got the results from Mensa, I was not surprised to have qualified, because in the meanwhile I had passed several other tests. Here is a summary of my results:
Test Name
I.Q. sd15
No longer available

Since I passed these tests, two of them (Titan and Get-Y) have been disqualified. A test is disqualified when somebody posts some answers on the Web, thereby invalidating all the answers subsequently given. It’s a pity, because they were very good tests, but some people cannot keep their mouth shut.

As you can see, there is quite a bit of variability. Against every logic, I like to think that my I.Q. is close to the maximum value I have achieved. It’s heady to think that in the city where I live there are perhaps only 70 people as intelligent as (or more intelligent than) me!

I am currently member of nine High-IQ societies, with entry requirements ranging between 5% (I.Q. 124 sd15) and 0.06% (I.Q. 149 sd15), but there are people I know who are members of many societies. The world of High-IQ societies is at times baffling. There is even a society so selective that only one person on earth is likely to qualify, with an I.Q. of 195 sd15. As surprising as it might be, the society has a member. Have a look at unigeg.weebly.com/universal.html and then, just for fun, learn a bit more about the unique member by going to unigeg.weebly.com/memberships.html.

Now, how would you like to be member of a very exclusive High-IQ society? I’ll tell you the trick: make one. If you start a new High-IQ society, as the founder, nobody can prevent you from becoming a member of it, regardless of your actual I.Q.

Another thing: If you check out en.wikipedia.org/wiki/High_IQ_societies, you will see that the PARS society requires an I.Q. in the top 0.00003% (I.Q. 175 sd15). Now, it turns out that founders and directors of “recognised High I.Q. societies” can join as honorary members. Without ever having taken an I.Q. test, you can create a High-IQ society with an interesting enough declared purpose and a not too hight I.Q. requirement. Then, when you have managed to attract, say, 20 members, nothing prevents you from applying for membership to the PARS society, and there is no reason why they should reject you. After that, you will be able to exchange messages and participate in discussions with the “elite” of the High-IQ world.

The main activity of most High-IQ societies consists of discussing issues of common interest in the society’s forum. Sometimes the discussions go off the tangent with supposedly brilliant and amusing remarks. It is clear that one deals with people of above-average intelligence, but that doesn’t always/necessarily make for interesting discussions.

(2) Freely downloadable from en.wikipedia.org/wiki/File:IQ_curve.svg

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