Karthik Srinivasan on Nostr: npub1ary93…5md4c npub1skvad…laky3 npub1zllda…flhfq Hi Luiz, sorry just saw your ...
npub1ary93kr00e2m3zwpf4c5mgyctsr0sr80p07aw6xgcc4pw2v2md8qe5md4c (npub1ary…md4c) npub1skvad2l2wrxgdmt6yxk9kt2rjhw5tucjzhf54pktfq2gg0qhgwyqdlaky3 (npub1skv…aky3) npub1zlldauz82v9n66z0kvjgs7ygm8fqsyhl7qm72mhzkvlhndcq05lshflhfq (npub1zll…lhfq)
Hi Luiz, sorry just saw your message.
I am quite ambivalent about how to proceed for the following reasons:
Chaos, non-determinism, or non-computable reals are features/outcomes of the models (physical and mathematical) we are currently able to prop up. That is, chaos is a consequence of our limited modeling approach to understand the world. Whether the world itself is chaotic or non-deterministic remains an open question. Alternately put, the model/ODE we employ to study phenomena X is incomplete (i.e., it is missing parameters or measurements or variables (hidden?) which we currently don't have access to/are not exploiting). If we do have a better model, it might well be the case that we could have control/predictability. In which case, the the idea of non-computable reals (requiring arbitrary precision) as the intractable problem becomes moot. Finite precision of values might suffice, and computing/simulating such systems will inform us better about the system. One can describe this worldview as "we only have partial knowledge of X and our models of X are constrained/limited by our incompleteness".
On the other hand, if the world itself is chaotic/non-determinstic/has "truly random" aspects, then yes, we might not have that many options (i.e., there are fundamental "limits to knowing") and would have to proceed in the manner you describe. Iterate the process over measurable/controllable periods, look at the system, check it's phase/state space, and if the system has changed/evolved, see if you can find a way to formalize the new system and proceed from that. Rinse and repeat. Whether this is possible for us to do is an equally hard question.
So, my ambivalence is this: are we limited only by our current models, OR (inclusive "or" here) are we also limited by the fact that we have limits of knowing.
Hi Luiz, sorry just saw your message.
I am quite ambivalent about how to proceed for the following reasons:
Chaos, non-determinism, or non-computable reals are features/outcomes of the models (physical and mathematical) we are currently able to prop up. That is, chaos is a consequence of our limited modeling approach to understand the world. Whether the world itself is chaotic or non-deterministic remains an open question. Alternately put, the model/ODE we employ to study phenomena X is incomplete (i.e., it is missing parameters or measurements or variables (hidden?) which we currently don't have access to/are not exploiting). If we do have a better model, it might well be the case that we could have control/predictability. In which case, the the idea of non-computable reals (requiring arbitrary precision) as the intractable problem becomes moot. Finite precision of values might suffice, and computing/simulating such systems will inform us better about the system. One can describe this worldview as "we only have partial knowledge of X and our models of X are constrained/limited by our incompleteness".
On the other hand, if the world itself is chaotic/non-determinstic/has "truly random" aspects, then yes, we might not have that many options (i.e., there are fundamental "limits to knowing") and would have to proceed in the manner you describe. Iterate the process over measurable/controllable periods, look at the system, check it's phase/state space, and if the system has changed/evolved, see if you can find a way to formalize the new system and proceed from that. Rinse and repeat. Whether this is possible for us to do is an equally hard question.
So, my ambivalence is this: are we limited only by our current models, OR (inclusive "or" here) are we also limited by the fact that we have limits of knowing.