Q&A: Complexity
Complexity
Question
Hello Rabbi,
I wanted to ask whether you have a suitable definition for complexity without using the word “complex,” of course.
That is, what is more complex in a human being than in a stone made up of oxygen, carbon, hydrogen, and nitrogen?
Or in what way is a snowflake more complex than a drop of water? And so on and so on.
I know this is a very basic intuition, but I’d still be happy to hear a formal definition.
Answer
The formal definition is given through entropy. I tried to illustrate this in the third notebook; see there.
Discussion on Answer
I referred you there. That was only an example. It’s not the number of particles, but the number of equivalent states.
But if it’s the number of equivalent states, then it’s subjective.
One person sees a dice roll of 6666666 as something that has no equivalent states, while another sees 7384938 as equivalent to it too.
The same goes for gas particles: one person sees each state by itself as unique, even when the gas is spread uniformly, because there is only one state in which particle a is at the top right and b is at the bottom left, etc. There isn’t even one additional state equivalent to it.
It is completely objective, as long as you define equivalence before the outcomes and not afterward. Thermodynamics deals with entropy measurements and their consequences, so this is not a question of our way of thinking. The fact is that a system progresses in the direction of increasing entropy, not decreasing it. That system has nothing to do with human beings, and therefore entropy is also defined objectively.
That’s circular. The system progresses toward state x, and since we defined disorder subjectively according to how impressed we are by the “special” states, it turns out that x is a state that has fewer states equivalent to it, but that equivalence is subjective.
To Dani,
It’s a relative process between the starting point and the current one….
To the Rabbi,
What is meant by equivalent states?
Do you mean imagining that the human body could have been stardust?
If so, then there’s still no difference between a star and a human being, because a star too could have been stardust spread out across space.
Or is the point that a human being could also be posited as the simpler state of being part of a star, but not the other way around? But that too assumes from the outset that a human being is more complex than a star, so it isn’t objective.
In short, maybe there’s a slightly longer explanation :)………..
It’s hard for me to teach physics or mathematics here. What I could explain, I explained in the notebook. The rest is available on the internet or in books.
So you just mean the number of particles per unit area relative to the total area?
So a human being has more particles than a stone. Is that all? If so, then an elephant surely has even more…