In a previous posts I estimated Terance Tao’s IQ from SAT data.  In this post, I will estimate his reading IQ using historiometric data.

According to The New York Times Magazine, Terance Tao taught himself to read at age 2.  What IQ level does this equate to?  In order to answer this question, we need statistics about when kids learn to read.  The problem is, the distribution would not be normal, because most kids learn in school during first grade, so you get a pile up of kids all learning at one age.  But since Tao learned to read before entering school, it makes more sense to compare him to a sample of unschooled kids, both because they learned under similar circumstances, and because the distribution is presumably more normal when kids learn naturally.

In order to find such data, let’s turn to the unschooled movement, where kids are encouraged to learn on their own.  Scholar Peter Gray writes:

The stories sent to me by readers of this blog include 21 separate cases of children learning to read in which the age of first real reading (reading and understanding of novel passages of text) was mentioned. Of these, two learned at age 4, seven learned at age 5 or 6, six learned at age 7 or 8, five learned at age 9 or 10, and one learned at age 11.

Although this is not a random sample of American ability, it’s the only sample we’ve got, and the ages of unschooled reading seem to be:

4,4,5.5,5.5,5.5,5.5,5.5,5.5,5.5,7.5,7.5,7.5,7.5,7.5,7.5,9.5,9.5,9.5,9.5,9.5,11

The mean age is 7.14 (SD = 2.02).

Thus, Tao learning to read at age 2 makes him 2.48 standard deviations more precocious than average than the average American kid learning without the interference of schooling.  Thus, on the modern deviation IQ scale where scores are made to have a mean of 100 and a standard deviation of 15, Tao’s IQ is 138 (U.S. norms).

Although an IQ of 138 is extremely high (obtained by one in 177 Americans), it seems way too low for someone reading at age 2.  After all, a 2 year old who has acquired the mental skill of a 7.14-year-old, has developed at 357% the normal rate, implying a ratio IQ of 357.  I realize ratio IQs tend to be much higher than deviation IQs, especially at the extremes, but there’s no way in hell one in 177 kids have a ratio IQ of 357.  Obviously the deviation IQ of 138 is too low.

Age ratio IQs

A second approach is to assign ratio IQs to each of the 21 kids in the sample, and then see how man standard deviations above average Tao’s ratio IQ is.

In order to convert these ages into ratio IQs, we simply apply this formula:

Ratio IQ = [7.14/(age child learned to read outside school)]

Using this formula, we get the following distribution:

179,179,130,130,130,130,130,130,130,95,95,95,95,95,95,75,75,75,75,75,65

The mean ratio IQ is 108 (SD = 33). Thus Tao’s ratio IQ of 357 is 7.55 standard deviations above the mean.  Converting to the modern IQ scale where the mean and standard deviation are set at 100 and 15 respectively, this puts Tao at 213.

But this is way too high.  The normal curve predicts fewer than one in 190 billion cases should be above 202, so obviously an IQ of 213 is almost meaningless.

It shouldn’t be surprising that Tao’s ratio IQ is an absurd 7.55 standard deviations above the mean, because many people have argued that ratio IQs do not have a normal distribution.  But why not?  Because of non-linear brain development in childhood?  Because of sudden cognitive growth spurts?

And then it hit me.  I had another one of my flashes of genius 🙂

Pumpkin Person’s insight

The beauty of ratio IQs is that they are a true ratio scale, meaning not only are they based on age which are units with equal intervals (not exactly equal, since mental growth is faster at younger ages) but a true zero point.

Except they’re not.

When we are born, we are not 0 years old, but 0.75 years old, because we’ve been developing in the womb for 9 months.  Thus all of us need to add 0.75 years to the age all of the kids in the sample learned to read to get the true age:

4.75,4.75,6.25,6.25,6.25,6.25,6.25,6.25,6.25,8.25,8.25,8.25,8.25,8.25,8.25,10.25,10.25,10.25,10.25,10.25,11.75

Now the mean reading true age becomes 7.89.

When we calculate ratio IQs based on these true ages, we get the following distribution:

166,166,126,126,126,126,126,126,126,96,96,96,96,96,96,77,77,77,77,77,67

Now the mean becomes 107 and the standard deviation becomes 29.

To compare Tao to this new distribution, we must add 0.75 to the age when he learned to read, giving a true age of 2.75, compared to the average reading true age of 7.89, making Tao’s reading development 287% of the normal rate (ratio IQ 287).

This is 6.21 standard deviations above the true ratio IQ distribution, so on a modern scale where the mean and standard deviation are set to 100 and 15 respectively, his reading IQ would be 193.

The distribution is probably still not perfectly normal given the non-linear rate of mental growth in childhood, but I think it’s a lot better than it was before age was converted to true age.