3 ms·

Well I wouldn't put it quite like that either.. because you have to be careful what you mean by 'simulate' and 'easier'. There could be multiple ways to simula

by niobe 2y ago

Well I wouldn't put it quite like that either.. because you have to be careful what you mean by 'simulate' and 'easier'. There could be multiple ways to simulate the same system, i.e. produce the same evolutionary output steps. Wolfram tends to imply there is only one most-expensive way for systems that are computationally irreducible and that way is grinding through a recursive computation. I think that's partly because the simple experiments, like cellular automata, he used to come up with this principle actually explore the 'space of simple rules', not the 'space of ordered sets of states of systems'. Of course the latter is a much more computationally expensive things to do but it seems to me it would generalise better to the universe. Because in the universe what we're really observing is the evolution of states not the outputs of rules. There may be other hidden assumptions in the principle if you assume that all systems can and do evolve from simple rules as much of Physics does. Nevertheless, you need a high bar if you're going to state universal principles. Perhaps the simplest way to state the principle is: say we set up a simple iterative computation where the input to step n, is the output of step n-1. Then there's no way to compute state n without having previously computes states n-2, n-3 etc. That's what he means by irreducible. In other words it's "necessarily recursive" which may be a better and more focused term. I'm cautious about making it mean more than that, since Wolfram tends to write in great leaps of conclusions without showing us his working. Nevertheless I enjoy following his ideas, and I did find aspects of this article quite thought provoking.

kouru225 2y ago
> I think that's partly because the simple experiments, like cellular automata, he used to come up with this principle actually explore the 'space of simple rules', not the 'space of ordered sets of states of systems'. I think it’s the opposite actually. He chose to study these recursive systems because they seem to describe reality, and then when he found more evidence that they do a good job describing reality, he kept studying… so on and so forth. Basically a sort of hermeneutic circle type deal. You do a much more thorough job of describing it. I should’ve mentioned the recursive part earlier. I just kinda assume we all already know we’re talking about recursion and time steps and that’s not a useful assumption
- kridsdale3 2y ago
  It's pretty dang hard to give the output to Fibonacci(x) for any x up to infinity without having done the work up to that point.
  - Xcelerate 2y ago
    Actually there’s an explicit formula for Finonacci(x) that involves phi. I think you can use generating functions to derive it. (But your overall point still stands.)
  - kouru225 2y ago
    Good point. We’re still not describing it perfectly. Admittedly I’m doing it by my memory of the last time I read Wolframs ideas. I think we unfortunately have to describe it using Kolmogorov complexity: what is the length of the shortest computer program that produces the object as an output? What Wolfram means by computational irreducibility is that he asserts that reality itself is the shortest length computer program that can produce its own output, and it can’t be shortened (reduced) any further without losing information. Edit: sorry I think I still haven’t fully described it. Will have to come back to it tomorrow when I’ve had some sleep
PaulDavisThe1st 2y ago
Your comment makes me think about statistical mechanics and microstates. That is to say ... in a complex system with properties that are a function of microstates, whether the internal structure of the microstates that correspond to a given property matter can depend on your point of view or interest in the system. Heat, for example, is a statistical property of a system, and a given temperature can correspond to a vast number of possible microstates of the system. For some purposes, you care precisely which microstate the system is in; for others, you do not, and the temperature property is entirely adequate to describe the system. Rules may describe the microstate, but may be (depending on your POV) be irrelevant to the property. Using Wolfram's model of the world, there may indeed be a cellular automata following rules that underlies the property, but there may be no reason to care about it in a given instance; instead you're interested in the "evolution of states" (i.e. values of the property). Some complexity scientists are quite taken with this idea of not needing to care about the lower levels of a system when consider higher level behavior. In their view (and rightly so, IMO [0]) you don't always need to consider the rules that drive (say) physics when considering (say) psychology. [0] except that I think that Hofstadter's "heterarchy" idea is likely to be even more accurate - interesting systems are the ones in which there are complex feedback systems between different levels of the system.
- kridsdale3 2y ago
  It seems pretty clear to me that this desire for "perfect" layers of abstraction is something we strive for due to our own intellectual limits, and that in reality all abstractions are lossy to some degree. Heat as a single integer in Degrees F is good enough most of the time but when you're designing CVD for a Silicon Fab you might actually care about the positions and orientations and vectors of the gas molecules.

by niobe 2y ago

kouru225 2y ago

> I think that's partly because the simple experiments, like cellular automata, he used to come up with this principle actually explore the 'space of simple rules', not the 'space of ordered sets of states of systems'. I think it’s the opposite actually. He chose to study these recursive systems because they seem to describe reality, and then when he found more evidence that they do a good job describing reality, he kept studying… so on and so forth. Basically a sort of hermeneutic circle type deal. You do a much more thorough job of describing it. I should’ve mentioned the recursive part earlier. I just kinda assume we all already know we’re talking about recursion and time steps and that’s not a useful assumption

kridsdale3 2y ago
It's pretty dang hard to give the output to Fibonacci(x) for any x up to infinity without having done the work up to that point.
- Xcelerate 2y ago
  Actually there’s an explicit formula for Finonacci(x) that involves phi. I think you can use generating functions to derive it. (But your overall point still stands.)
- kouru225 2y ago
  Good point. We’re still not describing it perfectly. Admittedly I’m doing it by my memory of the last time I read Wolframs ideas. I think we unfortunately have to describe it using Kolmogorov complexity: what is the length of the shortest computer program that produces the object as an output? What Wolfram means by computational irreducibility is that he asserts that reality itself is the shortest length computer program that can produce its own output, and it can’t be shortened (reduced) any further without losing information. Edit: sorry I think I still haven’t fully described it. Will have to come back to it tomorrow when I’ve had some sleep

PaulDavisThe1st 2y ago

Your comment makes me think about statistical mechanics and microstates. That is to say ... in a complex system with properties that are a function of microstates, whether the internal structure of the microstates that correspond to a given property matter can depend on your point of view or interest in the system. Heat, for example, is a statistical property of a system, and a given temperature can correspond to a vast number of possible microstates of the system. For some purposes, you care precisely which microstate the system is in; for others, you do not, and the temperature property is entirely adequate to describe the system. Rules may describe the microstate, but may be (depending on your POV) be irrelevant to the property. Using Wolfram's model of the world, there may indeed be a cellular automata following rules that underlies the property, but there may be no reason to care about it in a given instance; instead you're interested in the "evolution of states" (i.e. values of the property). Some complexity scientists are quite taken with this idea of not needing to care about the lower levels of a system when consider higher level behavior. In their view (and rightly so, IMO [0]) you don't always need to consider the rules that drive (say) physics when considering (say) psychology. [0] except that I think that Hofstadter's "heterarchy" idea is likely to be even more accurate - interesting systems are the ones in which there are complex feedback systems between different levels of the system.

kridsdale3 2y ago
It seems pretty clear to me that this desire for "perfect" layers of abstraction is something we strive for due to our own intellectual limits, and that in reality all abstractions are lossy to some degree. Heat as a single integer in Degrees F is good enough most of the time but when you're designing CVD for a Silicon Fab you might actually care about the positions and orientations and vectors of the gas molecules.