On 08 Jul 2011, at 02:35, meekerdb wrote:
On 7/7/2011 4:59 PM, Russell Standish wrote:
On Wed, Jul 06, 2011 at 10:12:45PM -0700, meekerdb wrote:
Here's my take on it. I guess you read the version I wrote 6 years
One that happens to be incompatible with
theory that our minds are computer programs.
Can you explain that? It seems to be Bruno's central claim, but so
far as I can see he only tries to prove that a physical reality is
Once you allow the existence of a universal dovetailer, we are far
more likely to be running on the dovetailer (which is a simple
program) than on a much more complicated program (such as simulating
the universe as we currently see it). Under COMP, the dovetailer is
capable of generating all possible experiences (which is why it is
universal). Therefore, everything we call physics (electrons, quarks,
electromagnetic fields, etc) is phenomena caused by the running of
dovetailer. By Church-Turing thesis, the dovetailer could be running
on anything capable of supporting universal computation. To use
Kantian terminology, what the dovetailer runs on is the noumenon,
unknowable reality, which need have no connection which the
we observe. In fact with the CT-thesis, we cannot even know which
noumenon we're running on, in the case there may be more than one. We
might just as well be running on some demigod's child's playstation,
as running on Platonic arithmetic. It is in principle unknowable,
by any putative omniscient God - there is simply no matter of fact
there to know.
So ultimately, this is why Bruno eliminates the concrete dovetailer,
in the manner of Laplace eliminating God "Sire, je n'ai besoin de cet
Anyway, Bruno will no doubt correct any mistaken conceptions here :).
That's what I thought he said. But I see no reason to suppose a UD
is running, much less running without physics. We don't know of any
computation that occurs immaterially.
I'm afraid this is not true. Some people even argue that computation
does not exist, the physical world only approximate them, according to
I have not yet seen a physical definition of computation, except by
natural phenomenon emulating a mathematical computation. Computer and
computations have been discovered by mathematicians, and there many
equivalent definition of the concept, but only if we accept Church
Now if you accept the idea that the propositions like "if x divides 4
then x divides 8", or "there is an infinity of twin primes" are true
or false independently of you, then arithmetical truth makes *all* the
propositions about all computations true or false independently of
you. The root of why it is so is Gödel arithmetization of the syntax
of arithmetic (or Principia). To be a piece of a computation is
arithmetical, even if intensional (can depend on the *existence* of
coding, but the coding is entirely arithmetical itself.
In short, I can prove to you that there is computations in elementary
arithmetical truth, but you have to speculate on many things to claim
that there are physical computations. Locally, typing on this
computer, makes me OK with the idea that the physical reality emulates
computations, and that makes the white rabbit problems even more
complex, but then we have not the choice, given the assumption.
So I assumed I didn't understand Bruno's argument correctly.
You seem to have a difficulty to see that elementary arithmetic "run"
the UD, not in time and space, but in the arithmetical truth. Even the
tiny Robinson arithmetic proves all the propositions of the form it
exist i, j, s such that phi_i(j)^s is the s first step of the
computation of phi_i(j). And RA gives already all the proves, and so
already define a UD, which works is entirely made true by the
arithmetical reality, which I hope you can imagine as being not
dependent of us, the human, nor the alien, nor the Löbian machines
themselves (RA+ the inductions).
The arithmetization is not entirely obvious. It uses the Chinese
theorem on remainders, you need Bezout theorem, and all in all it is
like implementing a very high level programming languages in a very
low level "machine language", with very few instructions.
Matiyasevitch has deeply extended that result, by making it possible
to construct a creative set (a universal machine) as the set of non
negative integers of a degree four diophantine equation. This has the
consequence that you can verify the presence (but not necessarily the
absence) of *any* state in the UD (like the galactic state described
above) in less that 100 additions and multiplications. That is weird!
A degree 4 diophantine polynomial can emulate any arbitrary growing
functions from N to N, and even from Q to Q. So if you agree that a
natural numbers is solution or not, of a diophantine polynomial,
independently of you, then all digital computations are realized, or
not, independently of you, me, or the physical universe.
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