 Originally Posted by Whatsnext
Perhaps you misunderstood me.
OK. Words are limited and often ambiguous, unavoidably. So I just respond to what I see, and if I guess wrong I hope for the other person to correct me.
 Originally Posted by Whatsnext
Let's say there's a universe with four spatial dimensions: x, y, z, and arithmetic.
I think that "arithmetic" isn't a spatial dimension. Just because you can put a quantity into symbolic correspondence with a location in a spatial dimension, which seems to be what you're talking about, doesn't make it a spatial dimension.
 Originally Posted by Whatsnext
If you run at one speed in one direction along the arithmetic axis, than any actual combination of two items results in three of them. If you run at another speed in the same or maybe the other direction, any combination of two items results in four of them. And so on. Certain arithmetic rules then depend on velocity along that axis.
You have to be able work it out in a way that makes consistent sense, or at least consistent enough to be able to do something with it. If 1+1=3, then what is 1+2? Or 1+0? You need to be able to define what "1" is and "+" is and "3" is in a way that doesn't contradict itself. If you build in a gross contradiction, then 1=0 and you have no arithmetic at all. There are limited ways this can work. So for instance, you can't make a system that has all the positive integers except for the number 2. As soon as you define the other integers, or axioms that are equivalent to doing that, you get the number 2 automatically.
 Originally Posted by Whatsnext
How, precisely, can it be shown that 1+1=3 is false in every possible universe, if that is indeed what you mean?
This may be completely beside your point, since I was using math only as an analogy for physical laws. But an arithmetic system or any other mathematical system doesn't depend on the physics of our universe. Presumably its possible that there are universes within which certain kinds of arithmetic systems can't be conceived of or expressed. I lack the proper vocabulary to say what I mean here, but a particular logic contraption based on a set of axioms doesn't depend on other logic contraptions like a universe of physical laws. As an example, the circumference of a circle may be more or less than pi depending on whether or not the space it is drawn in is flat. But wherever pi can be known, pi is pi, there aren't other alternatives for it. Since ideas of circles are used to represent physical objects and processes, people often blur the two conceptually. But math is abstract, and quite limited in certain ways. Nature is abstract in a similar sense I think, but its a different system, one that is rich enough for other simpler systems like our math to be represented within it.
It would take me a bit of review to see how to rigorously show that 1+1=3 can't make sense, and you might need at least the equivalent of a graduate degree in math to understand it. So I'll have to pass, and you'll have to believe me or not as you see fit. It would be similar to showing that the existence of some portion of the positive integers implies the existence of the rest of them.
 Originally Posted by Whatsnext
It's actually quite trivial. The anime universe doesn't even necessarily have to result from anything more abstract than quantum physics. There could even be an anime planet somewhere in our universe. Quantum field fluctuations could just happen to spawn virtual particles at precisely the correct locations for the whole lifetime of our universe so as to mime the existence of physics allowing for humans who look like drawings, magic, dragons and what have you to exist, all without there actually being any underlying physics that will consistently spawn such planets.
Certain quantities are conserved, for instance, a virtual particle comes with a virtual anti-particle. Its not an unlimited magic that lets you do whatever you want to at very low probability.
 Originally Posted by Whatsnext
All we need is for there to exist an infinite number of universes in which particles appear, disappear, and move arbitrarily, and that gives us an infinite variety of universes.
Consider a hypothetical world that has these two properties: The animals look like anime characters, and there's at least a 50% probability that its not about to vanish in a fantastic wash of energy in the next instant. Your argument does not support the creation of such a world. (And a many worlds interpretation, where some worlds survive, doesn't help, because our world is not unstable in that way, is not built that way with virtual particles.) So we have an example of a world that your argument doesn't work for. Given that there are hypothetical worlds that it doesn't work for, and given other constraints like charge conservation, I don't think its "trivial" to suppose that it does work for any kind of anime world.
 Originally Posted by Whatsnext
It's possible right now for you to get up and run right through your wall via quantum tunneling. And then turn around and run right back through again. Over and over. It's possible that everyone who runs into a wall starting tomorrow until the end of the universe will tunnel through. It would appear to be a law of physics that humans can run through walls, but it wouldn't actually be.
When I was an undergraduate, our text book had story problems such as where we calculated the probability that a billiard ball can spontaneously appear off of a table. At the time I just worked the problem using the supplied equations, oblivious to all the assumptions and qualifications that those equations are predicated upon. The ball is not a single, coherent wave-function, to start with. Does tunneling through allow a macroscopic, compound object to maintain its molecular integrity with any probability at all, or does the probability go completely to zero? You can't just do some simplified calculations and say it works at some infinitesimally small probability, you have to understand all the implications.
I think its possible for a human being to magically go through a wall. I don't think that quantum physics tells us this though, notwithstanding that it works really well for transistors.
This brings up a criticism I have of some scientists, and of most publicly expert scientific figures and scientific journalists. In physics theory, 'random' events are ones that do not have causes within the scope of the current model, and which can be modeled well if assumed to conform to specific distributions, uniform or Gaussian or whatever. People who are adept at manipulating these models, and proud of it, start thinking that the models are reality, and that anything left out isn't real. Or maybe its not driven by pride, it has just becomes a habit because the models work well for what they use them for, or they have just never asked themselves the question. Whatever the cause, we have the common assertion that the randomness of quantum physics is utterly random in principle. But there's nothing in physics theory that supports this, it amounts to a kind of faith that if we don't know something it must not be important.
Furthermore, its in the extremes where our models break down anyway. We know for sure that they're incomplete simplifications of reality, that they do break down. And when dealing with fantastically improbable events is exactly the kind of situation where we should expect them to break down. This applies to things like proton decay, or the roundness of electron, and I see no reason it doesn't apply just as much to something like running through walls. So no, I don't buy the running through walls argument, I think you do not know that such a thing is possible based on physics knowledge. Our theories aren't good enough to be extrapolated that far. Unless by possible you mean possible in the sense that neither of us knows it to be impossible. But in that case, I still say its not supported by existing theory, because existing theory can't reasonably be expected to extrapolate that far.
 Originally Posted by Whatsnext
Well I have no disagreement there.
I guess that must refer to my statement that one more turd won't matter much.
I think we're both in over our heads here. We know what we're talking about within a certain context, but then can't apply it reliably in general. Pretty much the same as if we were talking about how decoherence implies anime words, but at a slightly higher level. We disagree because we understand slightly different things, but not because we understand enough.
Anyway, thanks for your time and thoughts, and I hope you got something out of it.
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