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Imagine the following experiment: you wait say at a subway exit, and ask everyone passing "please tell me a number" (positive integer, of course). You do this day after day, until you reach say 1M people.

• What is the distribution $\mu$ on the positive integers that you get?

This is a serious question, obviously some numbers are "nicer" than some other, say arithmetically speaking, so $\mu$ is probably a very interesting measure!

Of course, if you would do the poll with very small kids, $\mu$ would be more or less uniform on $2,3,4,5$ or so, perhaps with some mass at 1, and probably at $0$ too (coming from scientists's kids, proud of knowing what 0 is :)

My question of course concerns adults, and results obtained via a real poll like the one suggested above: does anyone know, is anything written on this subject?

(question inspired from The human body's random number generator, I mean from the title of that question.)

[Edit Jan 2: thanks very much everyone, as a partial conclusion: (1) the measure $\mu$ certainly depends on the precise location of the poll, interesting would be for instance the results of an experiment - I mean, the picture/precise formula of $\mu$ - in a "random" place, say Times Square, (2) there are lots on interesting links signaled below (by MP, Joel, JSE..), papers by cognitive scientists, plus some interesting math interpretations/speculations (by quid, Alexander, Andreas, Yuichiro..) but I'm still afraid there's no picture of some particular $\mu$ emerging from all this, (3) will keep looking etc., and of course, if I ever get a huge grant, with some freeness in spending it :) think I'll conduct such a poll experiment myself - it's probably worth it.]

Imagine the following experiment: you wait say at a subway exit, and ask everyone passing "please tell me a number" (positive integer, of course). You do this day after day, until you reach say 1M people.

• What is the distribution $\mu$ on the positive integers that you get?

This is a serious question, obviously some numbers are "nicer" than some other, say arithmetically speaking, so $\mu$ is probably a very interesting measure!

Of course, if you would do the poll with very small kids, $\mu$ would be more or less uniform on $2,3,4,5$ or so, perhaps with some mass at 1, and probably at $0$ too (coming from scientists's kids, proud of knowing what 0 is :)

My question of course concerns adults, and results obtained via a real poll like the one suggested above: does anyone know, is anything written on this subject?

(question inspired from The human body's random number generator, I mean from the title of that question.)

[Edit Jan 2: thanks very much everyone, as a partial conclusion: (1) the measure $\mu$ certainly depends on the precise location of the poll, interesting would be for instance the results of an experiment - I mean, the picture/precise formula of $\mu$ - in a "random" place, say Times Square, (2) there are lots on interesting links signaled below (by MP, Joel, JSE..), papers by cognitive scientists, plus some interesting math interpretations/speculations (by quid, Alexander, Andreas, Yuichiro..) but I'm still afraid there's no picture of some particular $\mu$ emerging from all this, (3) will keep looking etc., and of course, if I ever get a huge grant, with some freeness in spending it :) think I'll conduct such a poll experiment myself - it's probably worth it.]

Imagine the following experiment: you wait say at a subway exit, and ask everyone passing "please tell me a number" (positive integer, of course). You do this day after day, until you reach say 1M people.

• What is the distribution $\mu$ on the positive integers that you get?

This is a serious question, obviously some numbers are "nicer" than some other, say arithmetically speaking, so $\mu$ is probably a very interesting measure!

Of course, if you would do the poll with very small kids, $\mu$ would be more or less uniform on $2,3,4,5$ or so, perhaps with some mass at 1, and probably at $0$ too (coming from scientists's kids, proud of knowing what 0 is :)

My question of course concerns adults, and results obtained via a real poll like the one suggested above: does anyone know, is anything written on this subject?

(question inspired from The human body's random number generator, I mean from the title of that question.)

Imagine the following experiment: you wait say at a subway exit, and ask everyone passing "please tell me a number" (positive integer, of course). You do this day after day, until you reach say 1M people.

• What is the distribution $\mu$ on the positive integers that you get?

This is a serious question, obviously some numbers are "nicer" than some other, say arithmetically speaking, so $\mu$ is probably a very interesting measure!

Of course, if you would do the poll with very small kids, $\mu$ would be more or less uniform on $2,3,4,5$ or so, perhaps with some mass at 1, and probably at $0$ too (coming from scientists's kids, proud of knowing what 0 is :)

My question of course concerns adults, and results obtained via a real poll like the one suggested above: does anyone know, is anything written on this subject?

(question inspired from The human body's random number generator, I mean from the title of that question.)

[Edit Jan 2: thanks very much everyone, as a partial conclusion: (1) the measure $\mu$ certainly depends on the precise location of the poll, interesting would be for instance the results of an experiment - I mean, the picture/precise formula of $\mu$ - in a "random" place, say Times Square, (2) there are lots on interesting links signaled below (by MP, Joel, JSE..), papers by cognitive scientists, plus some interesting math interpretations/speculations (by quid, Alexander, Andreas, Yuichiro..) but I'm still afraid there's no picture of some particular $\mu$ emerging from all this, (3) will keep looking etc., and of course, if I ever get a huge grant, with some freeness in spending it :) think I'll conduct such a poll experiment myself - it's probably worth it.]