Tediously Long Addresses

These days I rarely use the post, and when I do it is often to enclose a payment in a pre-addressed envelope, but on the rare occasions I need to write an address on an envelope I’m often irritated by its length.

How long need addresses be?

The total population of the world is less than 7 billion = 7*10⁹

2³³ > 8*10⁹ , so by using 33 digit binary numbers it would be possible to give everyone a unique identifier, and have lots of numbers left over. 5 bytes = 40 bits so five character identifiers should be enough with lots to spare.

Using a little more space we could include some information, like date of birth, gender and country of origin.

Suppose we allocate a unique code to every day in a thousand year period starting with 1st January 1800 (it might make record keeping easier to have a way of referring to people‘s ancestors). There would be about 365 250 days in such an interval. As 2¹⁹ > 500 000, 19 bits would suffice.

I believe there are about 170 countries in the world, 2⁸ = 256, so 8 bits would suffice for country, 3 bits would suffice for gender even allowing for ambiguous cases and changes of gender.

Annual births for the whole world total around 1.4*10⁸, so daily births must be around 400 000. Since 2²⁰ > 1000 000, 20 bits should be ample to distinguish people born in the same country on the same day.

Unique identifiers would therefore need at most 20 + 19 + 8 + 3 = 50 bits.

7 bytes contain 56 bits and should be more than ample to include identifiers for every person, every building, and every institution on the planet.

Alternatively consider every postal package to be addressed to a particular place on the earth’s surface.

The surface area of the earth, including the surface of the oceans, is about 5*10¹⁴ square metres, and 2⁵⁰ > 10¹⁵ so providing a unique identifier for each metre square would require no more than 50 bits; 7 bytes would be plenty, even allowing for different addresses for different floors of the same building. I assume that the density of occupation of a building does not exceed one person per square metre.

So two quite different approaches both suggest 7 bytes as ample for addresses.