genius

noun

1. exceptional intellectual or creative power or other natural ability.

2. an exceptionally intelligent person or one with exceptional skill in a particular area of activity.

Do we need some geniuses or is it genii?

The definition of genius as ‘exceptional’ is a place to start.

Of course, we all have a little bit of above average in us, that is a rule of nature when it comes to human beings. There are no below-average drivers, photographers or singers in the world. Anything a person spends time on will automatically make them better than the norm. So says our ego.

When it comes to genius we maybe need a little more objectivity; to know what we mean by an exceptional intellect, creativity or intelligence.

What level or amount of these qualities and attributes do we say is necessary before the holder is exceptional or out of the ordinary?

It could cover the one in twenty occurrences of an intelligent person, or perhaps the one in a hundred, or one in a thousand individuals. These are the standard probability levels for statistical significance, the P-values that did your head in at school.

Let’s just for the sake of discussion say that genius-level starts at one in 1,000 individuals, that is P<0.001

This would make the genius uncommon, not so frequent as to be among the passengers on a crowded bus, although a commuter train has one or two of them, on average, assuming you are not getting off at the convention centre the week of the National High-IQ Convention.

One person in a thousand is a genius.

### The normal distribution

There is research that suggests that intelligence is normally distributed.

That would mean that most of us are around average intelligence and the smarter folks become fewer in frequency as the level of smarts increases. Same for the ‘not so clever’ in the other direction on the variable of smartness.

Here is the normal distribution, the classic ‘bell-shaped’ curve.

This pattern means that of the 50 people on the bus, we can expect 34 of them to be within one standard deviation of the mean (average) intelligence however that might be measured, IQ-score for example.

Only 2 of the passengers would be at the tails of the distribution being either smarter or a little short of a picnic. These are the folk that are better or worse than 2 standard deviations of the mean. The standard deviation being a measure of the spread of the distribution, in this case of intelligence.

Go as far as three standard deviations from the mean and just three people in 1,000 will be really smart or really dumb — 0.28% of the distribution.

That’s close enough to 1 in a 1,000 for our genius estimation.

Alright, so not very many.

This calculation applies to the normal distribution whatever the measurement and whatever the actual mean and variance parameters for the sample. They are a property of the distribution and not the data. Whatever the measurement in a thousand observations just 3 observations would be expected by chance to be greater than and less than the mean plus three standard deviations and the mean minus three standard deviations.

### How many geniuses in Australia?

Let’s assume that the normal distribution of intelligence holds for such an eclectic population as that in Australia and the 0.14% is what we are looking for as those in the above-average tail of the distribution.

Given the adult population is roughly 20 million in 2020, then there are around 29,000 adult geniuses in the country over the age of 20 and another 6,700 young geniuses learning and growing into adulthood.

Roughly 35,000 in total.

This should be enough to have a genius or two in the higher echelons of each major walk of life.

Or is it?

As of June 30 2019, there were 2,375,753 actively trading businesses in the Australian economy. This means one genius for every 67 businesses.

Not all of these businesses employed people, indeed there were 4,271 businesses with more than 3,200 employees, so they could at least get a genius each.

It would be good to have a genius on staff at each high school (9,393) and maybe a couple at each university (43) or perhaps each faculty (250+).

Then we need some in government departments (200+), hospitals (1,350) and even a few in the military where there are 58,650 active personnel and 21,700 reservists, so a couple of hundred there at least.

*Source: Australian Bureau of Statistics*

After a few of these needs are met, the 35,000 begins to get allocated pretty quickly. And if we do use them all up then there are allocations and distribution issues to consider. What sectors should get their full genius allocation?

### Do we need any more geniuses?

Australia has plenty of genius-level capacity.

There should be enough smarts to figure out solutions to our problems among the 35,000 plus people who are more than 3 standard deviations above average intelligence.

There is a problem of where they are, who they work for and who listens to them. It also assumes that being a genius will be enough to solve problems and that may not always be true.

Then there is another statistical problem.

Suppose that the average intelligence, 𝞵 = 100

While the average person scores 100 on the intelligence test what the genius will score depends on the variability in test scores, 𝝈

If the variability is high ( 𝝈 = 15) a genius might need a score of over 140 to get into that upper 0.14% of the population. If the variability is lower ( 𝝈 = 5) then a genius need only score over 115 on the test.

The number of geniuses stays the same, scores differ.

If a specific level of genius score is required of a true genius, say 150, and the variability in intelligence in the population is low, then very few geniuses would be present in the population.

A score of 125 is 5 standard deviations above the mean. On average there would be one person scoring 125 in every 3.58 million in the population.

If this were the new genius level there are only 100 in the country.

This really is a problem.

Definitely not enough genii to go around.

Perhaps we should gather these elite individuals together, a bit like we do for sports, put them in a convivial environment and add some folk with a modicum of common sense and management nouse. The set them some of the real problems society has to face.

Worth a try?

1119