Dunno whether infinite superposition relates immediately to renormalization. You’d need to compare the mathematics.

In quantum computation some people think of a qubit as an infinite superposition. By the same token people talk about “quantum information.” (That seems to be one of Timpson’s beefs IIRC, the arguably loose use of the concept “information.”) There probably is such a thing as “quantum information” in the sense that stuff is communicated at that level. But we can’t read “quantum code” so it’s all basically hand-waving as far as we’re concerned. What I’m leading into here is that when you measure a qubit all you’re going to take away is a classical bit. Is that true because Nature won’t let us “go deeper” in terms of measurement or is it because we couldn’t perceive a superposition anyway or is it some complementary combination of those considerations?

Measuring a qubit and ending up with a bit feels a little like tossing out infinities in renormalization. But I have no idea at all whether there’s any theoretical justification for that fantasy.

I recall that Tegmark bangs on a bit about contemporary Platonism and Aristotelianism and says modern Platonists are many-worlders (or many-minders) who see reality as mathematical and have a Bird overview of things, whereas Aristotelians tend to be verbal and prone to the Copenhagen Interpretation, meaning they have the sweeping overview of Frogs. Doesn’t he also say that in the Level IV multiverse you must have universes that obey entirely different physical laws from any we know or have ever conceived, or could ever conceive — that being true simply because the mathematics must exist out there somewhere?

(Maybe that isn’t relevant to what YOU just said.)

I don’t recall that Scott and Anthony got into Platonism as such. But in the past he’s said he can’t even understand what Tegmark might mean by “a mathematical object.”

Anton seems to be sympathetic to comparatively conventional (although not overpoweringly dogmatic) religious types, e.g., the Dalai Lama, with whom he periodically hangs. You could probably say “Your Holiness” too if it got you and yours an expenses-paid holiday in Dharamsala. His affection for the Gospel of John, verse 1 (“In the beginning was the Word”) might be indicative too. Maybe he’s a closet mystic. Just as long as he keeps working.

Now I’m going to show my ignorance to an even greater degree than previously. Two questions:

1. The paper says “[a]s long as we are willing to neglect a part
of the wavefunction with vanishing Hilbert-space norm,
then we end up with a superposition of a huge number of
different states, each describing outcomes of an infinite
number of widely separated identical measurements in
our infinite space.”

Does this relate to the renormalization technique of tossing out infinities on an ad hoc basis?

2. I was aware that Tegmark generally takes the view that “reality is mathematical and the mathematical is real: any coherent mathematical formulation necessarily has a physical analogue.”

But my reading of the paper was that they only went so far as to claim to have shown that “the Level I Multiverse is the same as the Level III Multiverse (and if ination instantiates more than one solution to a more
fundamental theory of physics, then the Level II Multiverse is the same as the Level III Multiverse).” They didn’t reach the metaphysical heights of the pure Plantonic mountaintop. Perhaps this doesn’t relate to your point, but there it is anyway.

I do appreciate your thoughtful replies.

Anyway, you won’t see Anton or Časlav or Marcus or anyone else from that group up there on the stage with Ray and Nick at the Singularity Summit this summer. Fairly sure of that.

Maybe Anton, though. He shows up at some weird things.

This is a question I have been on various sides of over the years and that has been discussed at length both here and on the FQXi blog. But the more I tinker with crap in the lab (and my car and some op amps I have lying around and…) the more I seriously doubt the Platonic ideal and the “reality” of mathematical objects.

That said, it wouldn’t surprise me if the universe is half-Platonic (or a third or whatever), meaning it wouldn’t surprise me if some of mathematics has physical analogues while some does not, i.e. some mathematical “objects” had an ontological status while some do not.

In fact, I wouldn’t be surprised if someone were to demonstrate that the Platonic ideal could only exist in the presence of hidden variables (now try wrapping your head around that concept!).

You have a cosmological model based on certain mathematical assumptions. The guiding philosophy is Platonic — reality is mathematical and the mathematical is real: any coherent mathematical formulation necessarily has a physical analogue. (Tegmark has said that explicitly, as you doubtless know.) Anyway, I keep thinking about renormalization and QED. According to Dirac, at any rate, Feynman et alii defaced his beautiful mathematics to make their grubby little theory work in the physical world. They did it mainly by tossing out infinities on an ad hoc basis. QED, one might say.

I’m a frog. Brekekekex koax koax.

http://arxiv.org/PS_cache/arxiv/pdf/1008/1008.1066v1.pdf