April 16, 2009

Monumental egos

Upward!There are some people who are much more confident in their importance than others, a trait we can call ego. Of course, in what way importance is measured differs: academics may consider their research important, a politician their power or historical legacy, an athlete may measure it in speed, strength or wins. That the athlete and academic may not recognize each other's greatness does not matter for the size of their respective ego: everybody measures it based on what traits they think are the most important.

This enables a rough measure of relative ego:

Compared to all living people, what fraction of them are inferior to you in respect to the traits you regard as truly important?

Someone thinking themselves to be better than *everybody* would get 1.0 on this scale. Somebody thinking themselves inferior to *everybody* would be zero. The Lake Wobegon effect means that the average person will be above 0.5. Given the size of the effect plus that we usually care more about the things we are good at, I would expect the average person to score about 0.75 or more.

During the dinner discussion leading up to this definition the foreword to one of the Mathematica books was mentioned, where Stephen Wolfram (in third person) wrote "Stephen Wolfram is the creator of Mathematica and is widely regarded as the most important innovator in scientific and technical computing today." In honour of this self-assessment I suggest we call the unit of ego the Wolfram.

I don't know if he would consider being an important innovator the most important aspect of himself: maybe he would rather be recognized for his scientific work. But since he does seem to compare himself favourably to Newton in A New Kind of Science, and Newton tends to be on any "greatest scientist ever" list we can probably assume that he thinks he has a chance to be among the top 100 scientists at the very least. So we should expect his ego to be between 0.999999985 and 1.0 Wolframs.

A clear Wolfram 1.0 case is Gene Ray, the discoverer of the Time Cube. He seems to regard himself as the wisest human *ever*, which suggests an extended version of the ego measure (the Ray?) where one compares oneself with all humans who have ever lived (about 90-110 billion or so). We also briefly considered comparisons to all humans who will ever live, but that measure seems unworkable except for people like Gene Ray who would doubtless claim 1.0 on that scale too.

Hentakoi Thumbs UpAn interesting case might be athletes, who actually have objective measurements of their abilities relative to everybody else: the world champions *know* they are the best, and hence are entirely justified if they reach 1.0 Wolframs. In practice I would expect them to take time averages into account and tend to be slightly below 1.0.

As for myself, when I consider my achievements, I seem to be about two standard deviations above average (whether this is actually true does not matter; we are looking at subjective ego here). This would put me in the top 5% of all people. So I'm probably about 0.95 Wolframs.

In fact, so many of us humans crowd close to 1.0 that it might be more sensible to use a logarithmic scale, the logWolfram: -log10(1-W). 1.0 Wolframs is infinity logWolframs, 0.999999985 Wolframs is ~7.8 logWolframs, my 0.95 Wolframs is ~1.3 logWolframs, the modest 0.5 Wolframs is ~0.3 logWolframs and the "I'm the worst in the world" 0 Wolfram person is 0 logWolframs. Roughly it counts the number of nines in the decimal expansion when you approach 1.

Note that subjective importance is of course separate from real importance. The world has many 1.0 Wolfram people, but very few of them matter (Gene Ray is definitely in the top quartile in regards to fame, competing with a few self-proclaimed messiahs with personal cults and a bunch of happy world champions). Compared to most others at the same ego rating Stephen Wolfram is clearly enormously successful: he is a successful and well-known innovator, scientist, businessman, author etc. So one could define a dimensionless ratio between the actual level of importance in some field (measured as fraction of mankind being less able) and self-estimated importance. Many depressed and pessimistic people may have ratios far above 1, and thanks to the Dunning-Kruger effect we should expect incompetent people to have rather low ratios.

So while it might not matter much how many Wolframs of ego we have (humility is overrated in my opinion), we really should aim for mediocre (but healthy!) ratio scores close to one. The more important you think you are, the harder you should strive for this.

Posted by Anders3 at April 16, 2009 10:14 PM