On 06 Jan 2009, at 14:07, Stathis Papaioannou wrote:

> 2009/1/6 Abram Demski <abramdem...@gmail.com>:
>> Thomas,
>> If time is merely an additional space dimension, why do we experience
>> "moving" in it always and only in one direction? Why do we remember
>> the past and not the future? Could a being move in some spatial
>> dimension in the same way we move through time, and in doing so treat
>> time more like we treat space? Et cetera.
> You could model a block universe as a big stack of Life boards, where
> the time dimension is represented by the spatial displacement between
> the boards. There's no way the observers in such an arrangement can
> step out of one board onto another, backwards or out of sequence. Some
> would say that the stack of boards does not count as a computation,

To *count* as a computation, you have to make precise the "base" in  
which you count, that is the choice of a universal machine, language  
or system. The initial choice does not really matter, for the  
theoretical purpose.

> and others that even if it counts as a computation it doesn't count as
> a conscious computation; that to reach such states you need causality
> and for causality you need fundamentally real time, not block
> pseudo-time. I don't see any justification for such claims beyond a
> desire to preserve the magic in the world.

I'm afraid you are either pushing the thing to much, or that you could  
give that impression. But thanks for giving me an opportunity to  
clarify. We do need a "universal notion" of  causality, if only to be  
able to define the "displacement" between the boards, and discuss  
"science about them" between us. I agree with you, to invoke  
"physical" causality is *magic*, or *dogmatic* (and useless, by UDA).

But, well, at least assuming comp, we still need a notion of  
"computationalist causality", if only to get the comp supervenience  
"theorem", and then it is just a bit of work to get that such notion,  
with the Church Turing Thesis,  needs "only" 0, succession, addition  
and multiplication.

We could instead use any first order description of any universal  
programming language, or systems (Combinators, Lambda, Cellular  
automata, Gaussian Integers, ...).
  I use mainly 0, succession, addition and multiplication, because it  
is taught in school, but combinators can be very useful too for  
addressing the fundamental questions (like c++ or Java are useful for  
implementing concrete software and uploading them on the net).

Don't forget the universal machine. it is really a bomb. A creative  
bomb, for a change. It obeys the approximable but non unifiable laws  
emerging from the mess brought by addition and multiplication in the  
(positive) integers.

Why is the observable reality so smooth and symmetrical?  Now we can  
ask the universal machine(s).

Surprise! The machine not only can explain the trajectories of the  
snow balls (making comp testable eventually), but the machine can  
explain why it feels cold. The machine can justify also the non- 
eliminability of the person, somehow.

To be sure, I don't interview a machine who believes *only* in 0,  
succession, addition and multiplication. The machine believes also in  
the induction axioms (I will say more on this later). This makes the  
Löbian nuance.

That's enough for making the machine "knowing" its universality and  
capable of discussing about what could be provable or "true" or  
"probable" for itself and its consistent extensions.

If you weaken too much the notion of causality, you take the risk of  
being lead to a trivial theory which would explains nothing and see  
computations everywhere. I am not saying that you do that, but I know  
that some people, near this "stage",  can be tempted to conclude too  
quickly . Some even affronts (for a lapse of time) the ultimate white  
rabbit 0 = 1.

Arithmetics kicks back. Since Gödel we know (assuming comp and betting  
on self-consistency) that Arithmetic necessarily kicks back.



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