Information is Additive but Evolutionary Wait Time is Not

[swamidass (S. Joshua Swamidass)]

To be clear,

@gpuccio

So, you see, 100 objects with one bit of FI each do not make 100 bits of FI. One object with 100 bits of FI is the real thing. The rest is simply an error of reasoning.

This is not true. If these objects are independent, than they are exactly 100 bits of FI.

@glipsnort

You are quite correct.

I’d like to know in what context you think it is correct. Can you tell me @glipsnort?

Look at the example offered:

@gpuccio

A thief enters a building, where he finds the following objects:

a) One set of 100 small safes.

b) One big safe.

The 100 small safes contain, each, 1/100 of the sum in the big safe.

Each small safe is protected by one electronic key of one bit: it opens either with 0 or with 1.

The big safe is protected by a 100 bit long electronic key.

The thief does not know the keys, any of them.

He can do two different things:

a) Try to open the 100 small safes.

b) Try to open the big safe.

What would you do, if you were him?

Rumracket, maybe, would say that there is no difference: the total sum is the same, and according to his reasoning (or your reasoning, maybe) we have 100 bits of FI in both cases.

My compliments to your reasoning! If the thief reasoned that way, he could choose to go for the big safe, and maybe spend his whole life without succeeding. He has to find one functional combination out of 2^100 (about 10^30). Not a good perspective.

On the other hand, if he goes for the small safes, he can open one in, what? one minute? Probably less. Even giving one more minute to take the cash, he would probably be out and rich after a few hours of honest work!

What is going on here is that @gpuccio has (wrongly) equated wait time with exp(FI). Wait time and FI are not the same thing though, and are not related this way. Wait time is much lower than this equation indicates if the system is decomposable. This is not precise (and I can derive the exact if you are curious),

1. In fully decomposible system (100 safes) the wait time is about log 100. Note that you can try all the safes at once. So 100 theifs on 100 1-bit safes.

2. In a non-decomposible system (1 safe, with a 100-bit combination), the wait time is 2^100.

The computation above is not precise (the log 100), and it has a distribution. I can work it out exactly if people want. Though, perhaps @Dan_Eastwood or @nwrickert wants to jump in.

What is the FI? In both cases the FI is 100 to achieve full function. It both cases there is one configuration in a space of 2^100, so the FI is 100 bits. The point is that FI is not wait time. You cannot equivocate the two.

As the OP states, for an independent multi-component system, FI is additive but wait time is not.