Hi Bruno,

Disclaimer: I am under the influence of a terrible cold and thus beg the indulgence of the readers of the Everything list if this post is incoherent.

----- Original Message ----- From: "Bruno Marchal" <[EMAIL PROTECTED]>
To: "Stephen Paul King" <[EMAIL PROTECTED]>
Cc: "Everything-List List" <everything-list@eskimo.com>
Sent: Saturday, November 05, 2005 9:01 AM
Subject: Re: Let There Be Something

Hi Stephen,

Can atoms exist in a 2D universe?

I remember having read that 17 sort of atoms can exist in some natural 2-dimensional QM. I don't know if this is related to the anyons and Hall effects where particles are squeezed in two dimensional trap (by powerful magnetic field).

That seems in line with my recollections. I have been looking into this idea of dimensionally contrained physics and there seems to be a huge amount of interesting features and properties that are very unexpected. One of which is the behavior of quasicrystals.


But this is diverging from the topic! It seems that if we are going to take seriously the idea of 1D or 2D, or whatever D universes, then we have to base our reasoning on models that do not start off by assuming that the universe is "embedded"; otherwise we are just pushing the supervenience question under the rug. It is far better, IMHO, to deal with these kinds of universes as completely independent and deal with the consequences of that independence.

I have independent reason that the 2-dim topological space (and 2 + 1) continuous deformation are quite important in fundamental physics. But this has not yet been extracted from comp (to be sure).

AFAIK, physics is very different when constrained to only 2D. My point is that the notion of computation is meaningless if there is no possibility of a stable structure on and in which to implement the computation.

This is false imo. A computation can be given a sense in pure arithmetic (if only by Godel's arithmetization device).

Sure, but if you are going to do this does it not make sense that all notions that involve or requires some notion of "time" and "perception" be striped away from your notion of computation? If this is done faithfully, what happens to the notion of computation itself? It vanishes like Theaetetus' boat infested with termites!

I seem unable to understand how you can obtain a coherent notion of numbers interacting and 'knowing" other numbers without some ansatz of physicality? It seems that you think that you can postulate a logical structure L that is coherent given some scafolding-like structure L* that can vanish after the construction is done and then turn around that L* was never really necessary for L to exist in the first place. Why not just admit that the scafolding of physicality is an a priori necessity?

If you postulate a physical universe at the start, you need to postulate some ad-hoc highly non comp thesis to attach the first person to it.

Right back at you, Bruno! Your notion of computation requires some kind of perception ab initio in order to even be meaningful. You seem to not be able to go further than an inversion of your Ideal Monism. I salute you for appearing to defend the idea that the physical world is epiphenomena of Numb3rs, but I am not postulating anything: I am merely trying to not assume ideas that require more than I have available here and now in the physical world. Maybe I am blinded by a Popperian bias, and thus I enjoy this exchange. I confess that I find your theory to be very elegant, with the tiny "beauty mark" of epiphenomenalism, but there is still a lot of hand-waving going one in it.

Platonic Numbers or bit-strings have no ability to do anything by themselves (by definition!)

But numbers can do things by themselves relatively to other (universal) numbers. That is what computer science is all about, I think.

Again, Bruno, your theory prohibits *any* kind of notion that involves *change*. That is its Achilles Heel.

and thus appeals to their existence are vacuous.


To recap, it seems to me (and I am not even a tyro and thus very well could be merely a confirmed fool here) that in the thesis that Numb3rs are Everything and physicality is some kind of 1st person epiphenomenona of numbers is such that we can not smuggle into our postulates notions that are contrary to the definition of Numb3rs. Numb3rs are timeless unchanging and non-dependent of instantiations according to your Arithmetic Realism and thus it is your burden to show how *change* (even as a epiphenomena) can emerge from Changelessness.


I must confess to be biased toward an inversion of this idea, in a sense, where changelessness is a "fixed point" aspect of fundamental Becoming, but am happy to be wrong.



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