Hacker News Reader

Comment by adamtj | Hacker News Reader

Imprecision (one significant digit) + Benford's law (most numbers start with 1) means most numbers needing citation are of the form 10^n. http://en.wikipedia.org/wiki/Benfords_law

Interestingly, this would be true even if we had 8 fingers per hand. If we had 16 total fingers, 16 (base 10) would be written as "10" (base 16). 15 (base 10) would be a one digit number in base 16.

On the other hand, you'd rather have six fingers. Base 12 would be great because it has whole thirds! Also 12 is divisible by four numbers (2, 3, 4, and 6). 10 is divisible only by only 2 and 5, and fifths are much less common than thirds.

That's why 12 inches in a foot and 3 feet in a yard is a nice way to measure things (though the rest of the imperial system, excepting maybe Fahrenheit, has no excuse!)

View on HN

... and this is why we had Pounds, Shillings and Pence (£./.d) in the UK until 1971. http://en.wikipedia.org/wiki/Decimal_Day

Much more mathematically interesting, and tortured schoolchildren for many years, to their great benefit. Twelve pennies in a shilling, and 20 shillings to the pound sterling. Coins were at or soon before decimalisation: Farthing (1/4d), ha'penny (1/2d), penny, threppence (3d), sixpence or tanner (6d), shilling, florin (2/), half crown (2/6), and the crown (5/). The first paper note was the ten-bob note (10/), tequivalent to 50 new pence, followed by the Pound (20/). Until 137 there had been sovereign and half-sovereign coins instead of the 10/ and pound notes.

That's why many things in the metric system are designed on a grid with edge length 60 - it gives you many possibilities for subdivisions. For example the dimensions of most furniture is based on this - 30 cm, 45 cm, 60 cm, 90 cm, 120 cm and 240 cm everywhere.

Not that furniture might not, say, be scaled to fit human proportions or anything funky like that.

My favorite part about the imperial system is that a pint of butter weighs a pound. 16oz of butter is 16 fluid oz. A pint is a pound, the world round!

That's not exclusive to the imperial system...

One liter of water weights one kilogram which is IMO nicer.

Benford's Law applies because the wider natural distributions tend to be flat in the log space. One example is the log-normal distribution, which is what you get when random variables compound multiplicatively. (When they compound additively, you get a tighter Gaussian.)

So let's say that the values in bank accounts (just for an example) are $10^(N(3.5, 2)). In the log-space, this distribution is relatively flat on [2, 5] so let's focus on [3, 4]. The flatness at the top of the bell curve means there'll be just as much mass in [3, 3.3) as in [3.7, 4); converting back into dollar amounts that means there are as many between [1000, 2000) (10^3.3 is close enough to 2000) as in [5000, 10000). So you have as many leading 1's as you do of all digits 5-9.

I prefer to call it the Benford Effect. It's not a law. You don't get it for all distributions. It's not the case for human height, and IQ's have a hyper-Benford effect (50% of leading '1's) purely on account of how the distribution is defined. You only get it when the distribution is flat in the log space over at least one order of magnitude.

Reply on news.ycombinator.com