# Can physical object hiding be quantified with entropy?

If it works in the virtual world, why can't the same principle work in the real world?

For example if you want to hide a private key, you need a virtual haystack to hide it inside, which is the entropy of it's random source.

So if we want to generate a 21.9 bit key we need to select one random one out of 4000000 possibilities.

The same way in the physical world if we have a 10 m^3 size room, but only 2m^3 area can be used to hide things, then if we were to hide a small object like a dice which is like 0.5 cm^2, then we have 4000000 possibilities, which would be 21.9 bits.

So could the real world hiding of object be quantified in the same way ( excluding the fact that our eyes have a wide vision range so it would be easier to find, but also we could not go through all possibilities as fast as a computer could)

• Area, or volume, is not the right measure here - the units didn't even line up (2 m^3 / 0.5 cm^2 ~ a length is a result). No matter how much volume is under my couch I can check it all in pretty much the same amount of time I can look in a very small jewelry box or on a much larger table. Perhaps if you could enumerate all the possible distinct hiding places that would be a better measure. There are 3 book shelves with 7 shelves/underneath (+21), 2 couches with 6 cushions each and 2 distinct covered floor areas (+14), a floor that can be fully viewed from 6 glances/standpoints (+6) etc etc. – Thomas M. DuBuisson Feb 4 '17 at 2:55
• When I look for stuff I can miss things while they are right in the field of view. Try to catch that in a formula I dare you. – Maarten Bodewes Feb 4 '17 at 16:02

If you can quantify it with a probability distribution, yes—any probability distribution has an entropy.

Here's an analogy: Suppose a line of 256 people each flip a coin, and put it in their left hand if it comes up heads or their right hand if it comes up tails; then they close both hands in a fist. If you can't watch them flipping and placing the coin in their hands, you can't tell which hand each person has the coin in. The probability distribution on your state of knowledge about where the coins are has 256 bits of entropy.

The fact that it's people playing the which-hand game instead of a CPU storing a 256-bit key in a register in silicon is immaterial; entropy is a property of the probability distribution characterizing your state of knowledge.