[mojuba]

Someone said that if any object in the Universe has a non-zero second derivative of velocity (aka jerk, or "acceleration of acceleration") it's a sign of intelligent life.

Something similar should exist in the information theory. An encrypted signal can't be "too random", there should be some metric that distinguishes an intelligently designed signal from a random one. With spread spectrum and other tricks they can make it harder but not impossible to detect and separate from pure noise.

What is that metric? I have no idea, just trying to theorize. At least the opposite should be true, that for example the cosmic microwave background can not carry any useful/meaningful information other than just "signatures" of the particles that emitted the signal. So there should be some metric that's different for CMB and any signal that has something else in it.

Edit: I don't think the metric in question is entropy, although someone might convince us that it is. The problem with entropy is that, an object that consists of just a few types of atoms may emit a signal that would look very "orderly". That signal would be the spectrum with a few distinct frequencies in it typically emitted by those atoms.

[romaniv]

>An encrypted signal can't be "too random"

It should if encryption is good. After all, security proofs for encryption define "secure" as "indistinguishable from random".

[mojuba]

A signal that contains anything other than noise can not be absolutely indistinguishable from noise. Otherwise you won't be able to decrypt it.

[stouset]

It's computationally distinguishable from noise iff you have the decryption key.

The key word here is "computationally". A signal encrypted with a non-OTP symmetric key can be distinguished from noise without the key — unfortunately, for modern key sizes (128, 196, or 256 bits), the cost of doing so is prohibitively expensive for even arbitrarily advanced civilizations, unless (as Brice Schneier put it) they are building computers out of something other than matter that occupy something other than space.

[DanBC]

> Otherwise you won't be able to decrypt it.

Why not?

[mojuba]

Because the only way to make your signal appear more random is to add more redundancy. In order to make it look like an absolute random signal you'd have to add infinite redundancy.

[DanBC]

Redundant data is compressible data.

Random data is not compressible.

Adding redundant data to random data will make it more compressible - less random.

[toth]

> Someone said that if any object in the Universe has a non-zero second derivative of velocity (aka jerk, or "acceleration of acceleration") it's a sign of intelligent life.

Not sure what someone could possibly mean by that. Pretty much every celestial body has non-zero jerk. For instance, earth's acceleration is (to pretty good approximation) a constant times the $-e_r/r^2$, and the time derivative of that is definitely not zero.

[78666cdc]

The time derivative of that expression is indeed zero.

[toth]

It is not. $e_r$ is a rotating vector, not constant. Also $r$ is not really constant either.

Actually, if you think about it, the only plausible way you could have something in space with zero jerk and non-zero acceleration would be an interstellar ship maintaining constant acceleration, so the suggested rule is almost exactly wrong.

[78666cdc]

I'm afraid you'll have to explain your perspective to me as if I'm five years old. In your original comment, you say,

>a constant times the $-e_r/r^2$, and the time derivative of that is definitely not zero.

I don't see a term there that is time-dependent.