Friday, December 16, 2011

Trustworthy Thinking

My Awakening

One day in the midst of my primary school years I had an experience that started a train of thought that has continued ever since. A teacher asked the class what we call those sharp teeth 3 over from the centre. I, and a few other kids, answered ‘canines’. The teacher declared that answer incorrect. Perplexed I tried another answer, ‘eye teeth’. Again the teacher’s reply was no. Now I was deeply disturbed. When after a few minutes no one had supplied what she considered a valid answer, she revealed that the correct name was ‘fangs’.

Up till then I had implicitly trusted and believed adults when they told me something. In general they hadn’t contradicted each other on the facts so I had no reason not to. Suddenly one of the gods of truth proved to be not only ridiculously wrong but also incapable of learning otherwise. I foolishly corrected her. I went so far as showing her the facts in a reference book on the topic, thinking that she would be pleased to correct her error. I was rebuked in front of the class. That was the day I learned that the thinking of all adults is not equally trustworthy. I did consider the notion that this was merely a once off error on her part. Unfortunately an unhealthy fraction of the facts she taught proved to be unreliable when I checked them against encyclopedias. Perhaps she was a lone bad apple. That hope too was dashed. Other teachers proved just as bad – if not worse. A few years later another teacher instructed the class to laugh at my sister because her mother believed in evolution.

I felt disappointment mostly but some other intelligent people say they experienced anxiety when they realized they depended absolutely on very fallible people. Ever since then I have wondered about whose thinking is trustworthy. Ignorance and illogicality are widespread. My own thinking isn’t immune either. The very fact that I’ve changed my mind frequently over the years points to that. This question has morphed into wondering who should be trusted with society’s important thinking? One cannot avoid relying on one’s own thinking, even if you try to give up thinking for yourself and rely totally on someone else. Simply making that choice must have been convincing to you. Still I will be having a look at who society actually does trust to think, and whose thinking it reveres, and what mental ‘horsepower’ one needs to earn this. I hope my discussion will prove convincing for many.

Who We Trust to Think

Actually there is no single ‘trusted to think’ level – it’s a continuum. Pretty much all people are entrusted with solving some problems and not others. For example society expects virtually all of us to understand that laws exist, in part, to prevent or resolve disputes. The point of laws on many things is obvious e.g. it’s illegal to kill or steal. Society trusts that we can figure that out without special help. However there are some disputes where the right and wrong of it, and the point of the laws applying to the issue, are not clear. For that sort of problem we move trust from ordinary people to especially selected and trained people we call lawyers.

Lawyers are carefully trained to understand the complexities of the laws and the legal system, but the people who do get this training are not randomly selected. They are selected for their capacity to master the subject adequately. In the USA prospective law students are subjected to test called the Law School Admissions Test. This test heavily stresses the ability to think logically. One of three subtests is concerned with the ability to comprehend verbal arguments, but both the other subtests test the ability to make correct logical deductions, once the concepts are comprehended. Even before they start training, potential lawyers are well above average. Nevertheless at law school they are further drilled in thinking logically. Getting through that process is not the end. In order to be a reasonably successful lawyer i.e. someone a client trusts with their problem, they have to perform sufficiently well in court against others who were similarly selected and trained. Those are good reasons why lawyers are who we trust when ordinary people can’t sort out a legal dispute between themselves. The average IQ of lawyers is 127. That is at the 95th percentile and their logical ability is probably even higher. At best 1 in 10 people can be trusted with this level of thinking. Thankfully not all of them become lawyers.

I am mentioning IQ because it is a useful scheme for organizing all this information.

Judges are the second level of advisors. Society wants them to evaluate the reasoning of lawyers, and whoever else is involved in putting cases together, and decide which of these 'advisors to the population' are themselves correct or incorrect. They are chosen because they have a reputation for particularly good judgment, competence and integrity. This is reflected in the fact that the minimum LSAT score of judges puts them in the top 10% of lawyers and the top 1% of the general population. This is equivalent to an average IQ of 142.

Appeal court judges are the third and final level of advisors. (The constitutional court is really about specialist issues rather than a higher level.) They are selected on the basis of a reputation for good judgments, competence and integrity that puts them on a level noticeably above that of other judges. They are trusted to decide the 'truth' when even judges can't agree on the correct answer. The fact that their minimum LSAT score puts them in the top 1/5 of judges i.e. top 2% of lawyers, confirms it. This is equivalent to a minimum IQ of 144 and an average 148.

Doctors also have a tier system. Patients try to diagnose themselves. They fail and come to interns in the public system (or their GP). One of 3 things happens - the intern/GP gets it right and the problem clears, the intern doesn’t know or the intern gets it wrong and the problem persists. Often the intern (or the patient) asks for a second opinion but this frequently doesn’t help. Even among physicians, diagnostic disagreements run at about 50%. So when interns don’t know, or the problem persists, they refer the problem to more knowledgeable senior doctors or specialists. The process is repeated until the limit of medical knowledge is reached. If anything getting into medical school is even tougher than getting into law school, however the average IQ of basic doctors or interns is also 127. There is good evidence that medical problem solving ability (like every other problem solving ability) is highly correlated to IQ, and it is not far fetched to say that a doctor with the diagnostic ability of Dr Gregory House would have an IQ much higher than 127.

An original finding is required to earn PhD but isn’t for any lower degree, so one could argue that PhD level is where society really starts trusting people to think. The average IQ of someone earning a PhD in a STEM (science, technology, engineering or math) is 138. Tenure (in a STEM field) at a top 50 university is associated with an average IQ of 145. (See Appendix 1 for the method I used.) Another result was that a minimum of 700 on the SAT verbal is needed for truly original PhDs in English literature. That’s an IQ of 142.

What about thinkers who are not only trusted, but revered? I have in mind the award winners like Nobel Laureates in science, economics and literature, Fields Medalists or Crafoord and Abel Prize winners in mathematics, and Rolf Schock Prize winners in philosophy or mathematics. Acknowledged geniuses of the past belong here too.

Using three different methods (Appendix 2) I estimate the average IQ of those elite laureates as 149 – with a typical range of 132 to 167. The average IQ of historical geniuses is 157 – with a typical range of 150 to about 174.

The Kind of Thinking We Trust

We begin to trust people with thinking tasks when they can discover general principles and can think theoretically.

There isn’t an abrupt dividing line but below an IQ of around 116 thinking is concrete. There is little awareness of rules that may be abstracted from a number of specific situations and hypothetical reasoning tends to be about concrete situations like ‘What would A do if I did B?’, rather than abstraction like “Unemployment should rise if there is deflation.”

At IQs above 116, abstract hypothetic thinking becomes possible. At the IQ level of the average lawyer and doctor it is still quite superficial. They are adept at hypothetic thought and abstractions, and although they appreciate that their hypotheses could form a coherent whole they are generally not up to drawing out this whole themselves. At best they can develop low level individual theories but not a whole theoretical system.

Judges and STEM or good English Lit PhDs, at an average IQ level of 138-142, are at a level where they are able to create a new, coherent, abstract theoretical system. If they are to be trusted to advance our knowledge and understanding of the world they need to, and are expected to, be able to do it. Some however can’t do it very well.

Others however, do it supremely well. We tend to revere the thinking of those – like Appeal Court Judges or Nobel, Math or Philosophy Prize winners – who are very adept at creating coherent abstract theoretical systems. Even at this level there is an intellectual pecking order. There are some Nobel Laureates e.g. Einstein, Feynman, intellectuals e.g. von Neumann, or historical geniuses, that Nobel Laureates themselves revere. These are the people who can build several different coherent theoretical systems on the same information, and possibly bring them all under the ambit of a grand meta-theoretical system.


We turn out to trust the thinking of the intellectual elite – surprise, surprise. Those that can be trusted to think of new stuff, or with final appeals, are typically well within the top 1% - probably within the top 0.3% - of ability. These are the better PhD types (in the more demanding disciplines), tenured professors at top universities, members of the National Academy of Sciences, or final level appeal court judges. They are at home with theorizing and system building.

Of course having a high enough IQ does not necessarily mean someone can think wisely. Furthermore being able to think well is not the same as actually thinking, which is why geniuses are much rarer than IQs in the genius range. The trick is to persuade those who can think to do more of it, to do some reality checking and to apply themselves to useful problems.

There are still some issues beyond this if thinking is truly to be trusted. Many Nobel Laureates talk rubbish when they stray outside their fields. Experts are frequently wrong – particularly when hedgehog type intellectuals. Overconfidence, and failure to expose themselves to alternative viewpoints, is the main problem. Still I did learn why the thinking of teachers (mean IQs around 105) is so unreliable. Teachers aren’t known for liking students who ask searching questions either. I guess we should make it a norm to warn kids that adults – even those in positions of responsibility – seldom think clearly and correctly.

I think if we want to know the truth we should never completely trust anyone’s thinking – not least our own. We should make deliberate efforts to expose ourselves to the strongest cases for opposing viewpoints.

Appendix 1

In the Study of Mathematically Precocious Youth After 35 years: Uncovering Antecedents of the Development of Math-Science Expertise by David Lubinski & Camilla Persson Benbow the careers of the top 1% of math talent were followed. To estimate the IQs of STEM PhDs I used La Griffe du Lion’s ‘Jewish Method’ – see Method 1 in Appendix 2. I didn’t use Jews versus Gentiles but instead used the 99-99.25 percentiles and the 99.75-100 percentiles of tested math ability as my reference groups.

Appendix 2

Method 1

The first estimate of Nobel Laureate IQs I had seen was La Griffe du Lion’s use of the so called ‘Jewish Method’ in Some Thoughts about Jews, IQ and Nobel Laureates here. He takes the known IQ distributions of Jews and non-Hispanic whites in the US and using Gaussian curves finds a cut-off IQ which would give a similar ratio in the proportion of Jews and the proportion of non-Jews that fall beyond it as we find in Jewish and non-Jewish white Nobel Laureates from the US. That cut-off would be the minimum IQ. He calculated the mean Nobel Laureate IQ to be 148 (if one uses an sd of 16 rather than the 15 he did).

Method 2

For a second estimate I used figures (in Harriet Zuckerman’s Scientific Elite) of the institutions from which American Science Laureates received their PhDs compared to science PhDs in general. This information permitted me to estimate the ‘educational ability’ distribution of the science laureates in terms of the science PhD distribution. Simply find the percentile of each group that say got their PhD from an Ivy League university and the percentile of each that received their PhD from a university below a set level of selectivity. Convert the percentiles into unit normal i.e. z-scores. Find the difference between the z-scores at each defining line for each group. Now divide the science PhD difference by the Nobel Laureate difference – because the science PhD group is the reference group and if the difference of the Nobel Laureates is a higher number of z-units than the science group then the standard deviation of the laureate ability distribution must be smaller than the science PhD distribution. The ratio of the differences gives you the ratio of the laureate to the science PhD standard deviations directly. Using that I calculated the laureate mean expressed in terms of the science PhD distribution. I got 1.034±0.899 (where the science PhD ability distribution is set at 0±1.

Now the actual IQ distribution of science PhDs is 139±9.56 so the Laureate IQ distribution should be 149±8.6 and 95% of them should fall between IQs of 132-167.

La Griffe du Lion discusses the essentials of this method here. He calls it the Diversity Space method.

Method 3

For a third estimate I used national IQ figures and per capita Nobel + Math Prizes per country. By estimating the number of eligible people who lived over the full prize giving period, counting only men between 25 and 80 years old and correcting for the fact that only 25% of professionals choose science as a career, I calculated that the current populations should be divided by 6.4154 to provide a proper population baseline. Logistic regression methodology would connect the per capita probability of winning one of these prizes to national IQ. So I calculated log(p/1-p) and did a linear regression between that figure and national IQ. The linear equation was

0.2575*IQ-37.6253= log(p/1-p).

That means that someone would have a 50% chance of having the ability of winning a prize of IQ=37.6253/0.2575=146.1. This is essentially an estimate of the minimum IQ which means the average IQ would be 149.

The three methods produce almost exactly the same figure – 149 or just over 1 in 1000 people in most developed Western Countries.

Historical Geniuses

Catherine Cox (with a number of experts in IQ testing) estimated the ratio IQs of 300 historical geniuses by using biographical information to work out the age at which they mastered various tasks and then comparing it to the typical age these tasks are mastered. The result gives a mental age estimate which is then used to calculate a ratio IQ i.e. mental age/chronological age*100. Now ratio IQs are not normally distributed so I converted the ratio scores into equivalent deviation IQ scores. The IQs of the individual IQs might not be as accurate as they would be if they had been tested as children but the average IQ of the group as a whole should be very accurate. I limited the sample to scientists, mathematicians, philosophers and writers – dropping artists, musicians, statesmen, religious figures and soldiers. The kind of person included were Newton, Galileo, Pascal, Leibnitz, Descartes, Kant, Hegel, Hume, Locke, JS Mill, Goethe, Byron, Wordsworth, Milton, Dickens, Voltaire, etc. Typically the minimum IQ was 150, the median 157, and the upper end at about 174.

By the way, from the link between vocabulary size and IQ and an estimate of how many words Shakespeare knew, I estimated Shakespeare’s IQ at 172. I also used the fact that Einstein read Kant with understanding at the age of 13 (typically it takes an adult IQ of 150 to do so) to estimate his IQ at 165. This figure is in keeping with his math progress as an early teenager.


  1. This is amazing. I am wondering what a person with a 165 IQ is capable of. Is this exceptional genius?
    Is it true that IQ's over 150 are extremely difficult to calculate properly? I read that if a person has a 165 IQ, he she has a 60 per cent chance that this IQ may actually be higher. Do you think this is true?

  2. But, what to make about this:
    it seems to disprove your assessment of shakespeare's vocabulary...
    great blog! thank you for it....

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