Someone out there just like you

In Greg Egan's book 'Axiomatics', there is a story about someone who believes that there have to be other people who are so similar in personality to himself that they are essentially 'him'. With this confirmed to his own satisfaction, he has no compunction in suicide - after all, 'he' continues to live.

How often have we met someone, and decided they are incredibly similar to someone else we know. We fantasise what would happen if these two people met each other - would they realise they were psychological twins?

It is a spooky thought, that there are other people wandering around the world - seeing things, feeling things - in exactly the same way that you would if you were in their situation. But how likely is it?

What we need is a relationship of similarity between two personalities (an equivalence relation, in the jargon) which holds just when the two personalities are effectively one. As a first try we could take David Keirsey's division of personalities into four temperaments (Guardian, Artisan, Rational, Idealist), or the Myers-Briggs sixteen types.

But these are far too broad-brush. I am an INTP/Rational and meet many typologically-identical people, but I do not think they are me. Like me, in many cases, yes - but a psychological clone, no.

More quantitative metrics come from academic personality theories such as the 'Five-Factor Model'. The NEO Personality Inventory is organised around five traits (Neuroticism, Extraversion, Openness, Agreeableness, Conscientiousness), each of which is further divided into six subtraits.

This gives a total of thirty scales, each measured (say) between 1 and 100. This defines a space of size 100³⁰. If personality was randomly allocated into a space this size, the chances of two people getting the same score would be negligible - you would be truly unique.

But of course, that level of precision is ridiculous - even on re-test, people do not score so similarly. Also of course, people do not score randomly - the distributions are normal and outliers are rare.

Back of the envelope time. Suppose we adopt a coarser measure of similarity and score each of the 30 traits in five categories, i.e. not 1-100 but 1-5, equivalent to percentile intervals 0-20, 20-40, 40-60, 60-80, 80-100.

Then the size of the new personality space is 30⁵ = 24.3 million. If we take IQ as an independent variable (it actually correlates at around 0.3 with Openness) and group IQs in the range 100 to 140 in steps of 5 IQ points (let's assume you are brighter than average), then we have a further 8 categories increasing our space to around 195 million separate personality/intelligence 'boxes'. Let's say 200 million to keep it simple.

Take the world population of adults of one gender between 20 and 60, that comes to around: 5 billion divided by two for gender and divided by two again for the age restriction, say 1 billion people.

Take the 40% with IQ above 100 (average global IQ is a little below 100). This gives 400 million people. Allocating 400 million males (or females) to 200 million personality/IQ boxes gives 2 people per box.

So there are you are: there's someone else out there who is essentially you in intelligence, personality, gender and 'adulthood'.

How do I get to meet them?!

A more accurate discussion would factor in that not all psychological types and IQs are equally prevalent, so that the boxes are not at all evenly filled. If you are more 'average', then there will be more 'psychological clones' in your box, and so 'out there' somewhere. If you're statistically exceptional, your box may be empty apart from yourself and your most similar 'clones' may be in an adjacent box, so not quite like you.

Given the projected world population, your box occupancy will rise, so it may be a relief to know that even after you are dead and gone, someone just like you will still be experiencing the world ...