I disagree that this is the kind of simplicity meant when pointing out the unreasonable effectiveness of math. If it is then I believe this line of thought has a glaring hole. Simple systems do not imply simple dynamics in general. Emergence exists. An elementary cellular automata can generate fractals from 8 binary rules, and a simple set of axioms is not held back by this simplicity when it comes to what that those axioms generate.
So the simplicity of the reality describing math generating axioms is interesting, but not surprising.
But lets keep going, and look at the anthropic principle. Assume we’re 18th century Deist gods who get to decide how to build a new universe and we do this by deciding a set of axioms and watching the universe unfold. We have two choices, a simple set of axioms or a complex set of axioms. Which is more likely to generate the human race?
I’d argue the simple set of axioms is more likely to generate intelligence. The more moving parts you have the more likely something is going to break. A pendulum is orderly, a double pendulum exhibits chaos, and the order generalization of this system becomes a piece of string. There’s a sweet spot: life as we know it needs the double pendulum, the chaotic system in which there exists temporally stable basins of attraction.
But then again this is a bit circular isn’t it? Using dynamical systems (math) to argue the dynamics of mathematical formalism and all.
Sorry, I was making an argument from analogy for what I now realize was for no apparent reason. I saw you mention the anthropic principle and got overexcited.
I agree that before the development of cheap widespread compute such a conclusion on the likely simplicity of the generating rules of the universe would be in the reverse (again with the Deism).
I agree, but I think there’s another way to look at it.
I think the answer to the question, “Does complexity require complexity to come into existence?” is directly related to the nature of god, and the logical relationship between the two questions does more for explaining Deism’s existence in history.
If complexity requires complexity, then some form of complexity must have spawned the complexity of the world, and we can call this complex form ‘god’.
If complexity does not require complexity and rather can form from simple systems, then god is no longer implied. (This assumes we do not wish to worship a ‘simple’ system, denoting it some low-dimensional phase-space ‘god’)
What I’m getting at is that the existence of Deism was a product of the technology of the time, but in multiple ways simultaneously. The drawing of the equivalence between the mind and computation is one such way technology of the time produced Deism. Another way is how the understanding of complexity forming from simplicity requires simulation, and at the time only analog simulation was available. There was no reproducible or scalable way to test abstract systems for emergence.
What you said is the push, the cause of why (some) people of the 18th century were Deists.
What I’m pointing out is the pull, a reason why Deism as it was, no longer exists.
I disagree that this is the kind of simplicity meant when pointing out the unreasonable effectiveness of math. If it is then I believe this line of thought has a glaring hole. Simple systems do not imply simple dynamics in general. Emergence exists. An elementary cellular automata can generate fractals from 8 binary rules, and a simple set of axioms is not held back by this simplicity when it comes to what that those axioms generate.
So the simplicity of the reality describing math generating axioms is interesting, but not surprising.
But lets keep going, and look at the anthropic principle. Assume we’re 18th century Deist gods who get to decide how to build a new universe and we do this by deciding a set of axioms and watching the universe unfold. We have two choices, a simple set of axioms or a complex set of axioms. Which is more likely to generate the human race?
I’d argue the simple set of axioms is more likely to generate intelligence. The more moving parts you have the more likely something is going to break. A pendulum is orderly, a double pendulum exhibits chaos, and the
But then again this is a bit circular isn’t it? Using dynamical systems (math) to argue the dynamics of mathematical formalism and all.
Comment withdrawn.
Sorry, I was making an argument from analogy for what I now realize was for no apparent reason. I saw you mention the anthropic principle and got overexcited.
I agree that before the development of cheap widespread compute such a conclusion on the likely simplicity of the generating rules of the universe would be in the reverse (again with the Deism).
Comment withdrawn.
I agree, but I think there’s another way to look at it.
I think the answer to the question, “Does complexity require complexity to come into existence?” is directly related to the nature of god, and the logical relationship between the two questions does more for explaining Deism’s existence in history.
If complexity requires complexity, then some form of complexity must have spawned the complexity of the world, and we can call this complex form ‘god’.
If complexity does not require complexity and rather can form from simple systems, then god is no longer implied. (This assumes we do not wish to worship a ‘simple’ system, denoting it some low-dimensional phase-space ‘god’)
What I’m getting at is that the existence of Deism was a product of the technology of the time, but in multiple ways simultaneously. The drawing of the equivalence between the mind and computation is one such way technology of the time produced Deism. Another way is how the understanding of complexity forming from simplicity requires simulation, and at the time only analog simulation was available. There was no reproducible or scalable way to test abstract systems for emergence.
What you said is the push, the cause of why (some) people of the 18th century were Deists.
What I’m pointing out is the pull, a reason why Deism as it was, no longer exists.
Fun topic :)