Q&A: Entropy and Relativity
Entropy and Relativity
Question
Hello Rabbi,
Following the debate and the column you wrote in its wake, I wanted to clarify one detail that isn’t clear to me regarding your explanation of the definition of complexity, and regarding Aviv’s approach to the topic: why does identifying complexity with low entropy mean that there is an objective measure? Seemingly, even if entropy is an excellent mathematical definition, that still doesn’t make what it measures absolutely complex, if we haven’t defined some spectrum by which one can identify what counts as very complex and what does not. Isn’t that exactly like speaking about a mathematical representation of a large quantity by means of a very large number—which is of course absurd; large relative to what? In other words, perhaps what Aviv was trying to ask is this: even assuming we have some measure of complexity within the reality we know, the fact that it has a rigorous mathematical representation does not make this level of complexity objectively high relative to a different and unfamiliar reality, with different physics for example. We determine the spectrum of complexity by means of the concept of entropy as the degree of disorder of our system, but why is there no theoretical possibility of much lower/higher entropy in an alternative system, which would cast the identification between complexity and entropy in our universe in a relative light?
Thank you very much in advance
Answer
Because entropy is a measure that can be calculated from any given state without needing comparisons. Beyond that, entropy is a variable in physics that affects physical behavior. It is not just our way of looking at reality, but part of physical reality itself—like Newton’s laws.
The question of what is called high entropy is of course a question addressed to us. But that too does not indicate subjectivity. It only means that there is a continuous range of levels of complexity, and corresponding to them a continuous range of probabilities of accidental formation, and it is not binary. Still, for something at a complexity level of X, the probability that it arose by chance (assuming a uniform distribution) goes like 1 divided by X.