## How do you measure a secret?

*First published on website September 15th, 2007* © Copyright 2007 by Robert Krten.

I've often wondered how secret something that I've just been told is. Often, people will say something like "not too many people know about this."

I've been thinking that a number would be a much better way of expressing the secrecy of something.
A practical way of encoding the information would be as an exponent for the number 2, as a binary order of magnitude.
Then, when you disclose a secret, you could give out this number.
For example, a "7" secret means that 2^{7} people know about it — 128, give or take.

Does this mean that a "7" secret is just about like public information? Well, it depends. If it's information about a person (like, "John has just been caught cheating on his wife"), then yes, most likely "7" means that just about everyone who would be interested in it knows about it. If it's information about a corporate project in development, it could still be considered relatively "secret", especially in a large corporation (or the government).

The practical range of "secrecy" might be 0 through 4 or 5 for personal secrets (with "0" meaning that 2^{0} people know about it — 2^{0} is one, so that
means that only the originator of the secret knows about it).
4 or 5 means 2^{4} or 2^{5}, so 16 to 32, which might be about the practical limit for something about a person that's known by people who aren't trained to
keep secrets.
For large institutionalized secrets, the numbers might go as high as 10 to 12. This is a complete guess on my part.

Obviously, not exactly 64 people will know about a 6-secret.
The range should be +/- 0.5, so 2^{5.5} through 2^{6.5}, or about 45 through 91.
In most cases, it's a guess/estimate anyway, whose job it is to give the person to whom the secret is being disclosed some idea of how volatile the secrecy of the information is.

As far as language goes, I think using the term "n-secret", where "n" is replaced with a number, is a fairly straightforward way of stating the secrecy. "I know a 3-secret about Tina", for example.

## What else lends itself to being a power of 2?

Secrets would only have practical values in the whole number range (0..n).
However, other measurements could have practical values in the integer range.
Extending this to real numbers is of less practical use, because people are less likely to be able to compute 2^{5.334} in their heads — the value of
2^{5} is easy enough to figure out (if you don't have it hardwired as a table in your head anyway), and probably has sufficient granularity for most practical purposes.