Notes
[Notebook: DB 58 Bringing god home]
[Sunday 9 April 2006 - Saturday 15 April 2006]
[page 91]
Sunday 9 April 2006
The lesson of all this is that first of all we must speak 'locally' and second that we must submit to the limits of our knowledge if we are to steer the body politic successfully.
Lesser gods can increase their resolution by combining into greater gods. This structure communicates with itself in spacetime.
The geometric mapping of probabilities in a bounded (recursive, periodic) space.
DYNAMICALLY BOUNDED = PERIODIC (a 'bearing')
TURING MACHINE partitions ℵ0 space into periodic and 'aperiodic' subsets. The periodic one is described by wave mechanics, the aperiodic by theology,
Aperiodic: the details only happen once in spacetime, ie no-cloning, every state (and so every event?) is unique. This is the reality, to which we approximate by using periodic functions in a 'Fourier model'.
The Universe evolves by using less and less energy to carry a given amount of entropy. Energy is what we process the entropy with . . . , searching through it for stationary states. Particles are received and emitted as systems make transitions between stationary states.
A Turing machine may take an infinite number of steps between a finite number of machine states and so is necessarily periodic.
To communicate without error, we must confine ourselves to codings that can be processed by a Turing machine. If we are to communicate in a finite time, these processes must halt, and in general the more quickly they better. The speed with which a processor can deal with a given quantity of entropy is a measure of its fitness and (therefore?) probability of observation.
One thing is certain: that will have to work together to achieve peace on earth. The peacefulness or otherwise of a human environment is largely a matter of how one 'gets on;' with the others in the environment.
Cantor symmetry means that at the lowest resolution we are all in the same boat.
[page 93]
Diderot: La Religieuse Diderot
Each problem begins with an alphabet (of questions and answers?) which is to be permuted until an 'answer' is found. The energy applied to a problem divided by the entropy searched tells us how long the problem will take.
Monday 10 April 2006
Turing machines exist in a discrete spacetime; Hilbert machines in Hilbert space. The question is is one more powerful than the other? What do the quantum computers think? What, more to the point, is the answer? The hypercomputation people might say that the Hilbert machines are more powerful because they are continuous. Here we tend to the view that what we are looking for is a property of networks. Let us apply the 'Heisenberg test' to networks, ie we only talk about things that we can observe; further, every observation involved the transmission and reception of a message. The message itself might be quite 'compact' a particle. The message gains its meaning from the context in which it exists.
The network is represented in Hilbert space.
When we connect to a network, we 'see into' the network and what we see is what we describe with quantum mechanics. I am a leaf looking into the whole tree.
All this comes down to proof. Some formal things can be proven, Pythagoras' theorem, for instance. However, formal theory itself ells us that there are limits to proof and so limits to prediction. By prediction we mean using some formal theory (like arithmetic) to imagine a path from some starting position to some finishing position. We do this all the time. Take the lid off the milk; lid on; unscrew; lid off. Some formal predictions are deterministic and so can be made with certainty. All these predictions (and only these predictions can be made with
[page 93]
a Turing machine. All the rest is incomputable, which does not mean that we are completely blind to its structure because incomputable space grows out of computable space.
What we have been talking about is a feature of any formal model of a certain size or greater. Now we ask: do we see this feature of the formal world in the world around us? The answer may be yes. Otherwise, why is quantum mechanics incomplete (in Einstein's sense) in that it cannot tell us which horse is going to win a race, only the odds normalized to one (no percentage to the bookmaker!)
Quantum mechanics is notorious for its counterintuitivity but we propose a model which seems to fit everything together. The model is the transfinite network.
Tuesday 11 April 2006
Wednesday 12 April 2006
Thursday 13 April 2006
Friday 14 April 2006
Saturday 15 April 2006
Ultimately the meaning of every event is only to be found in the Universe as a whole. So a factory is not just machines and workers but simply the physically observable tip of a deep sociocultural iceberg.
