Monday, December 04, 2006

Homage to 'Permutation City'

You are in a dark, silent room. Lying back in comfort, you see, hear, smell, taste and feel absolutely nothing. Suddenly there is a sharp pain in your thumb. Ouch! You feel the pain and wonder what caused it. Meanwhile, five seconds pass.

Assume a space-time view. Your brain is circumscribed by a cube with sides, say, 15 cm. Using the speed of light as time-into-space translation, 5 seconds = 15 x 1010 cm.

So that five seconds of conscious experience is encompassed by a block of space-time measuring 15 x 15 x 15 x 15 x 1010 = 5 x 1014 cm4.

Now, neuron simulation models typically sample at a time resolution of 100 microseconds. That five seconds of painful experience comes down to 50,000 brain-state samples. Through advanced engineering, whilst you were in that room experiencing that brief pain, your brain was being sampled non-invasively: that five second experience is now all on disk.

Note that the four dimensional hypercuboid which circumscribed your brain during those five seconds has now been spread out in space as 50,000 ‘instantaneous-brain-state’ cuboids (mapped into storage), each invariantly ‘travelling through time’ at its own behest.

Here are the questions.

1. If we load brain-state samples [1 ... 50,000] into a computer, in sequence, in real time, is there - within the simulation - your feeling of puzzlement and pain. In other words, have we recreated your conscious experience as described at the start of this note above? (Think of it like a movie).

If you think the answer is no, why not exactly? After all, we are reproducing every single neuron of your brain in its exact behaviour: what else could there be to your experience?

2. If we load the sequence [1 ... 50,000] slower (or faster) than realtime into the computer, does the conscious experience of the simulation change? If so, why? The brain has no internal clock which is different than the firing of neurons.

3. If we run the sequence out of order, does that change anything? Each sample is independent of all the others. When it runs, it ‘doesn’t know’ which sample was previous and which will be next. No sample, after all, is changed in the process.

4. Suppose we don’t ‘run’ the sequence at all, but merely leave it on disk. Does the conscious experience still happen? And then in what order or all at once? The point here is that deceptive word ‘run’. When we ‘run’ a particular sample ‘on the computer’ we are doing nothing special - we’re simply copying the sample-content from one piece of storage (on ‘disk’) into another piece of storage (in the computer RAM). How does this meaningless, low-level act, change anything?

5. In the original space-time hypercuboid of your brain in five seconds of real time, all those instants continue to exist as space-like slices through that specific volume of space-time. Does this mean that the discussion around Question 4 also applies?

I would like to think that all these points are original - what they imply about consciousness is scary - but they were all anticipated (and more) in Greg Egan’s book Permutation City.