I quite agree pancomputationalism is a fun topic! On some level, it seems trivially true that the universe is "computing" itself. I think a key question is whether it is discrete or continuous, a digital computer or an analog computer. Theories like loop quantum gravity feature a discrete background, but GR and most QM suggest a continuous background.
A thing about those Life Gliders is that, as with all our algorithms, they are abstractions designed by an intelligence. My sense is that algorithms are the end of a long evolution process that first creates intelligences capable of abstractions like algorithms (and maths in general).
FWIW, I like Penrose's argument in TENM that mind doesn't seem algorithmic because Gödel. He suggests quantum effects in the book (Hameroff approached him because of it with his microtubules idea), but it could just be that brains are analog computers, not discrete ones. We can, in a sense, "take the mental limit" of an idea like Gödel's to a "divide by zero" true conclusion outside of computation.
Food for thought! I'm somewhere in the strongly agnostic camp about pancomputationalism. I'll try to define this viewpoint in the next article but basically the idea is that, if indeed the universe is computational, or if it's hypercomputational, our methods for obtaining justifiable beliefs about the universe are computationally bounded. This means we might never be able to know if the universe is hypercomputational. Strong agnosticism, i.e., it **can't** be known.
I'll look forward to your next post. I think it depends on how one defines a "computation". As I mentioned, for me intent and design are fundamental. I also look for a "computational dualism" — a physical system implementing an abstract system unrelated to the physical one. A key characteristic of computing then being that different physical systems can implement the same abstract one without loss (Church-Turing).
If reality were a computation representable by a TM or lambda calculus, then it seems Gödel would have to apply, and knowledge would indeed be *in* *principle* inaccessible to us.
Zuse came up with the idea earlier—around 1946-47, when he was in a village in Bavaria and his z4 computer was disassembled in a barn. As for the reception to the idea, he paraphrased Pauli’s comment on the reaction to quantum theory: “not that my idea was crazy; it was not crazy enough.”
Amazingly close to what I've been thinking this week!
If at the ultimate level everything is quantised then the universe is no more than very advanced number theory (in the sense that cellular automata are number theory).
There are an infinite no of natural numbers (integers) - the definition of Beth-0.
There are an infinite no of possible universes - also Beth-0.
There are Beth-1 combinations of natural numbers.
Beth-1 combinations is more than enough to generate all Beth-0 universes.
The universe also comes off as a conscious whole with every action being some form of habit within nature, these habits being the language of expression of the thing existing. It seems with conscious intention and knowledge we can "influence" or "program" the thing, for example we can control electricity. Having knowledge of this force allows us to program by influencing our "language" (desire of what we wish to fulfill with electricity coding, electronics, etc) to the electric field. To me it seems as if the Universe is unfolding itself through language & programming conditions of fields ✍🏾
The halting problem: a computer is a finite state machine. It only has a finite number of states. The question is which will it hit first: one of the predefined "stop" states or a previously-visited state (leading to a loop). [Bit like the knight's tour on a chess board.]
If there are K possible states and H designated "stop" states, then the probabilty of stopping on the Nth cycle is... H/(K-N+1) and the probability of looping is N/(K-N+1)
Obviously this only gets difficult when K is very large, but the likelihood of looping increases with N whereas stopping always has the same probability.
I quite agree pancomputationalism is a fun topic! On some level, it seems trivially true that the universe is "computing" itself. I think a key question is whether it is discrete or continuous, a digital computer or an analog computer. Theories like loop quantum gravity feature a discrete background, but GR and most QM suggest a continuous background.
A thing about those Life Gliders is that, as with all our algorithms, they are abstractions designed by an intelligence. My sense is that algorithms are the end of a long evolution process that first creates intelligences capable of abstractions like algorithms (and maths in general).
FWIW, I like Penrose's argument in TENM that mind doesn't seem algorithmic because Gödel. He suggests quantum effects in the book (Hameroff approached him because of it with his microtubules idea), but it could just be that brains are analog computers, not discrete ones. We can, in a sense, "take the mental limit" of an idea like Gödel's to a "divide by zero" true conclusion outside of computation.
Food for thought! I'm somewhere in the strongly agnostic camp about pancomputationalism. I'll try to define this viewpoint in the next article but basically the idea is that, if indeed the universe is computational, or if it's hypercomputational, our methods for obtaining justifiable beliefs about the universe are computationally bounded. This means we might never be able to know if the universe is hypercomputational. Strong agnosticism, i.e., it **can't** be known.
I'll look forward to your next post. I think it depends on how one defines a "computation". As I mentioned, for me intent and design are fundamental. I also look for a "computational dualism" — a physical system implementing an abstract system unrelated to the physical one. A key characteristic of computing then being that different physical systems can implement the same abstract one without loss (Church-Turing).
If reality were a computation representable by a TM or lambda calculus, then it seems Gödel would have to apply, and knowledge would indeed be *in* *principle* inaccessible to us.
Not only Godel, Rice as well! What would that even mean?
Zuse came up with the idea earlier—around 1946-47, when he was in a village in Bavaria and his z4 computer was disassembled in a barn. As for the reception to the idea, he paraphrased Pauli’s comment on the reaction to quantum theory: “not that my idea was crazy; it was not crazy enough.”
Amazingly close to what I've been thinking this week!
If at the ultimate level everything is quantised then the universe is no more than very advanced number theory (in the sense that cellular automata are number theory).
There are an infinite no of natural numbers (integers) - the definition of Beth-0.
There are an infinite no of possible universes - also Beth-0.
There are Beth-1 combinations of natural numbers.
Beth-1 combinations is more than enough to generate all Beth-0 universes.
The universe also comes off as a conscious whole with every action being some form of habit within nature, these habits being the language of expression of the thing existing. It seems with conscious intention and knowledge we can "influence" or "program" the thing, for example we can control electricity. Having knowledge of this force allows us to program by influencing our "language" (desire of what we wish to fulfill with electricity coding, electronics, etc) to the electric field. To me it seems as if the Universe is unfolding itself through language & programming conditions of fields ✍🏾
The halting problem: a computer is a finite state machine. It only has a finite number of states. The question is which will it hit first: one of the predefined "stop" states or a previously-visited state (leading to a loop). [Bit like the knight's tour on a chess board.]
If there are K possible states and H designated "stop" states, then the probabilty of stopping on the Nth cycle is... H/(K-N+1) and the probability of looping is N/(K-N+1)
Obviously this only gets difficult when K is very large, but the likelihood of looping increases with N whereas stopping always has the same probability.
One problem is that K grows beyond exponentially while N is linear. Are you familiar with "busy beaver" algorithms?