vanesch
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ZapperZ said:It isn't for me mainly because I am not convinced that a toy model that I manipulated by hand that happened to mimick large-scale phenomena is accurate.
That was not the point of course. The point was that toy models can show emergent phenomena such as phase transitions to occur in toy universes (where they are supposed to be "fundamental").
As such, the argument that emergent phenomena *prove* that the reductionist approach is bound to fail in principle is shown to be false as a general argument, because we have a counter example (in a toy universe).
This leaves you with the hope that the same can in principle be done in the real universe: that it is CONCEIVABLE that phase transitions and other fancy emergent stuff MIGHT BE derivable from the microphysics, if only we had enough brains.
I haven't seen one that is able to, for example, mimick every aspect of an antiferromagnetic phase, for example, all the way up to producing a spin-density wave. All you get is a resemblance to one part of the picture. To get the resemblance to another part, you construct ANOTHER toy model, because the previous one just can't do it.
So what we have here are examples where (i) you claim you can show a toy model system resembling a phase transition seen in a larger system and (ii) me showing you other examples where such toy models don't work - in fact, I claim that there are many more examples in this category than there are in the first. If this is true, then it is just a matter of taste on if this is a convincing evidence one way or the other. My taste runs on it being not convincing.
Well, I find it convincing, from the moment that there is ONE example in the bin (i), because that shows that there is no fundamental reason why all the things in bin (ii) could not eventually be moved to bin (i). Bin (i) is not empty. That leaves us with some hope. The hope that the universe is running on a mathematical model. A single one.
it means that even when one obtains complete knowledge of all of our current fundamental interactions, one can STILL end up with nothing more a set of emergent phenomena. We would have known more, but we certainly do not know everything.
Sure. The issue is if this "turtling down" is infinite, or will stop. If we take it that the universe is running on a certain mathematical model, then it should stop, the day we find that mathematical model, no ?
And if it is NOT running on a mathematical model, then anything goes, right ?
That said, we will of course never KNOW if we have it or not (because we cannot do every conceivable experiment). Maybe that's your point.