Thursday, August 15, 2013

You are likely special and your friends probably not normal

Squaring the melon. Image source.
I think of myself as a very average person. I like the music on the radio and enjoy books on bestseller lists. I’m somewhat short but not unusually so, my reaction time is average for my age, and I look as old as I am.

Yes, I thought I was normal. Then I read that the average person is cognitively biased to think they’re special. Now I have a problem. I can either think I’m normal then I’m not, or I can think I’m special then I’m normal. Either way, I’m facing mental inconsistency. That shit bothers me. Is this normal?

Things you think about when stuck in small town traffic that’s suffered cardiac arrest by way of garbage truck blockage.

But, I thought, what are the odds of being normal?

Let’s take any variable with a normal distribution and define somebody as “normal” if within, say, a 2σ deviation of the mean. You are probably normal, by definition. Now let’s take N uncorrelated variables that are similarly distributed, like income, follicle density, number of friends on facebook, annual coffee consumption, amount of clothes owned, spectral distribution of these clothes, average number of words spoken per minute, time spent sleeping before the age of ten, and so on and so forth.

I’m sure you could list a few hundred such individual characteristics if somebody pointed a pun at your head. The probability that you’re average according to all characteristics is (0.95)N. This means if you look at about 400 different ways that people celebrate their individuality with, the probability that anybody is normal is less than one in a few billion.

This means there’s probably no normal person living on Earth today. In other words, it’s normal to be special.

That’s why the teenager from across the street’s got a million followers on YouTube, our downstairs neighbor wears shoes in two different sizes, and my colleague has meaningful conversations with moths. That’s why my older daughter is obsessed with boogers, that seventy year old just finished a marathon in 3 hours, the blonde woman is an undercover agent in search of pressure cookers, and the garbage truck driver can probably recite Goethe, backwards, in Latin. Which, for all I know, is exactly what he’s been doing instead of driving the damned truck.

Let’s not miss an educational opportunity here and mention that’s also why, if you analyze a dataset according to sufficiently many properties you’ll almost certainly eventually find something special about it. Or, if you study correlations between sufficiently many parameters you’ll eventually find a correlation. Being special really is normal.

And I - I have a particle data booklet in the glove box. What are the odds?


Arun said...

We'll want you stuck in traffic more often if it inspires you like this :)

Phillip Helbig said...

"This means if you look at about 400 different ways that people celebrate their individuality with, the probability that anybody is normal is less than one in a few billion."

Isaac Asimov wrote an essay, "The Abnormality of Being Normal", on a similar theme, but he was looking at protein molecules and pointed out that it is extremely unlikely that all the atoms are of the most common isotope.

Unknown said...

"Uncorrelated" is doing some heavy lifting there.

Uncle Al said...

Bee, you are filled with light. Flash! Some will condemn fulgurites. How dare they try to end this beauty.
The first time matters.

Sivaramakrishnan said...

I find this visual picture intuitive:

In a large 'N' dimensions, The volume of a ball is vanishingly smaller than that of the cube into which it fits. This is roughly because the number of "corners" of a box scales as 2^N so the "interior" region ("normal behaviour") gets swamped out.

Plato Hagel said...

Correlations do exist in nature and pointing to a square mellon can lead to thoughts about a "square head?":)

Dis-positionally it has not past such attention that such a culture could had been considered so, since it's method by way of entrenchment could have been most matter of fact. An attitude perhaps about change too?


Tom Weidig said...

Claiming to be normal is a bit hypocritical with a Phd in theoretical Physics and doing research into quantum field theory?

Unless you don't mean your mental life, but your interests, outlook on life and bodily skills and features.

andrew said...

Individual traits are not independent of each other; indeed they are massively correlated. And, not all individuals differences make you special - specialness is a culturally created concept that in any given concept includes a fairly narrow set of traits.

Colin said...

In the movie Contact an argument put forward about Ellie's lack of religious faith being atypical implied she was not a typical representative of the human race. The question what is a typical representative seems mathematically ill-defined and based on many priors which somehow culture attaches weighted values. In the end I have come to, perhaps wrongly, think what we can know at any point in time is based on these valuations which we cannot globally control. But moreover, have realized that knowledge is not universal if these weights can change (somehow, somewhere, sometime).

Thanks for all the posts, keep it up.

CapitalistImperialistPig said...

I think that unknown and Sivaramakrishnan made abnormally insightful comments.

uair01 said...

"I’m sure you could list a few hundred such individual characteristics if somebody pointed a pun at your head."

Please do *not* correct that spelling error. It is strangely appropriate :-)

Plato Hagel said...

It seems uair01 and Uncle Al hit the nail on the head :P)

Sabine Hossenfelder said...

It's not a spelling error. In fact, MS office spell check doesn't know "quantization" but it evidently does know that one points guns at heads.

Sabine Hossenfelder said...

Andrew: Here's the question. Can genetic and environmental diversity produce more than 400 uncorrelated human traits, many of which are cultural and highly complex? I think it's almost certainly possible. But no, I can't prove it. Best,