Re: Introduction (Digital Physics)
Hi Joel, I have not corresponded with the distribution in quite a while. Your posting below seems to have caused some furor. You wrote: > > Anyway, I represent a small group of people who believe that in fact all > universes do exist and are computed by some very simple structures known as > "minimal cellular automata". > I tend to feel that the position that our universe is a digital cellular automaton is vulnerable, mainly because it implies that we can create universes containing self-aware structures (SAS's) that our much simpler than the one we inhabit, by using some multi-dimensional analogue to Rule-30 below. > > Without knowing anything about the "natural" world, Rule-30 (starting with a > single non-blank bit) - all on its own - generates every possible book, > symphony, or email message imaginable (or unimaginable!). > > Furthermore, this process is reversible - thus preserving the work done by > the automaton and providing a mechanism for reconstructing the past (i.e. > microscopic reversibility of nature). > > It is our belief that there exists a 3D version that is not only minimal > (generates everything) but also universally computational. Meaning... it > generates all PROGRAMS as well. A resolution to the White Rabbits problem accepted by most on the distribution requires us to insist that we live in the simplest possible universe containing SAS's. So it would be impossible or highly improbable that we can create universes with SAS's (e.g., by constructing cellular automata). If you could, and you could prove that you have created a universe inhabited by SAS's, that would indeed be some achievement, and it would force a change of thinking in many. > But the advantage here is that we can more easily envision the existence of > such a miraculous object like a minimal cellular automaton than, say, a > Universal Turing Machine. Cellular automata naturally implement physical > universes without any interpretation. The bits merely exist... and we can > see them with our digital eyes - and the patterns they generate. > Whether our universe is digital or continuous is harder to decide. Even with a set of quantized universes, we could have a continuum of 'different sized' quanta building blocks, though it may not affect the physics for each of the universes. Fred
Re: Introduction (Digital Physics)
> Joel : > And non-local effects must be similarly ruled out, as they too are forbidden > to our intellect. > Just as it is impossible for us to create non-discrete (i.e. continuous) > theories, it is also not possible for humans to construct truly non-local > theories. I hope so. But there are difficulties. In QM, Bell's theorem states that statistical results of experiments performed on a certain physical entity satisfy his inequalities iff the physical reality in which that physical entity is embedded is "local" (local hidden variables). Today is commonly accepted that the QM domain is incompatible with that "local" "realism". That is because Bell inequalities actually are violated. Local hidden variables do not exist. But, fortunately, Bell inequalities imply a Kolmogorovian probability model. So we can keep that "local" "realism" and say that probability is truly non-Kolmogorovian. But, wait. Ehe. There is another problem. The Bohm-Aharonov effect is truly "non-local". And that is hard, very hard to avoid. And, again, Bell inequalities are (also and much more) violated in CM. In our macro-world. Weird. Unbelievable. Is our macro-world "non-local" ? Is our universe "non-Kolmogorovian" ? Or is our (my) mind stupid ? Or is our logic poor ? - S.
Re: Introduction (Digital Physics)
Hi Scerir: >> Joel Dobrzelewski wrote: >> When searching for a Theory of Everything, we need an expression, a >> formula, a program that doesn't have any rounding errors. I still >> claim... it must be finite and discrete. > > Hi Joel. > Finite, discrete, perhaps. But do rounding errors (or other > problems) come from possible "non-kolmogorovian" probability models? > Or from unavoidable "non-local" effects? > - Scerir Possibly. But if they do, then once again... we are doomed. We can't engage truly random numbers any more than we can engage the continuum. rand() is just as evil as pi(). And non-local effects must be similarly ruled out, as they too are forbidden to our intellect. Just as it is impossible for us to create non-discrete (i.e. continuous) theories, it is also not possible for humans to construct truly non-local theories. We're not left with many choices.. discrete + finite + local = cellular automaton Joel
Re: Introduction (Digital Physics)
> Joel Dobrzelewski wrote: > When searching for a Theory of Everything, we need an expression, > a formula, a program that doesn't have any rounding errors. > I still claim... it must be finite and discrete. Hi Joel. Finite, discrete, perhaps. But do rounding errors (or other problems) come from possible "non-kolmogorovian" probability models? Or from unavoidable "non-local" effects? - Scerir
Re: Introduction (Digital Physics)
Ok, sorry for being a smart-ass. Instead of baiting the discussion to make my point, I'll try to simply state the position clearly. We humans cannot deal with infinite structures, like pi. Numbers like pi and e and Omega and all the others are the devil! :) And we all know the devil is in the details... We carry them along in our mathematics all the way to the "end" so that they can be "evaluated" in the final step. But I ask you: When does the universe evaluate its expressions? Is there an "end" to the universe when all the values for pi and e are fully computed and all their magic is brought to life? If we simply carry these finite expressions along so that they can be evaluated later, "if we choose to, but they don't really make a big difference anyway", then what use did we make of the continuum? Maybe we were just fooling ourselves and delaying the inevitable. F = G * m1 * m2 / r^2 That's a finite expression. We always assume that we can calculate F and to any degree of precision we like. But then does this capture the whole picture? If we are guaranteed to have rounding errors because our computers only have so much RAM, then have we really explained all there is to explain? No. Something more (or less!) is necessary... When searching for a Theory of Everything, we need an expression, a formula, a program that doesn't have any rounding errors. I still claim... it must be finite and discrete. Does this make any more sense now? Chasing the real devil / details of pi is a hopeless task. It would be better to just acknowledge that we can never *implement* pi and resolve to work with finite expressions and finite mathematics. I feel that this "bottom up" approach is our only chance fr success. Joel
Re: Introduction (Digital Physics)
Joel: >> Really? So what is the exact circumference >> of a circle with a diameter of 2 inches? Karl: > 2pi. Russell: > The exact circumference is pi. Really, where did you > learn your mathematics! And please explain for me how this calculation involved the continuum or infinite binary expansion of the symbol "pi" in any meaningful way. All you have really said was: 2 * broccoli = 2 broccoli I am unimpressed. It seems to me there is a great deal more information in PI than just the 2 bytes it takes to convey it in an email message. Maybe Mathematica was a poor choice for your counterexample, since it too runs on discrete hardware and software that could easily be run on a CA. So far you have not convinced me that a CA could not perform these same calculations. Do you have some other example? Joel
