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- #21
Physics:
In a Hopfield network (which is omniconnected binary), the "state" of the network is determined by the contribution of each element to the Hamiltonian.
(You can easily find the original paper online, Google "Hopfield 1982").
Whenever a neuron changes state, the network has by definition also changed its state. Therefore, if we can divide physical time (which in our computer model becomes Monte Carlo time) into "sufficiently small" intervals so we have one neuron changing state every .05 picosecond or so, then the entire network is changing state that fast.
So in essence what we have is a very special case of "phase velocity", where things seem to move faster than the speed of light. If it takes a fraction of a nanosecond for an electromagnetic wave to get from one end of the brain to the other, then the network has changed state 10,000 times in that interval! !!!
What does this mean? What does it mean when the network changes state? To change state, a bit has to flip, which means information determines state. State changes are information driven.
Why is the "speed of light" important, why am I mentioning it at all? Physics. Atoms, molecules, chemical reactions. It's all about the limit as dt => 0. Because the Hawaiian earring is fractal, and when you zoom in on the origin those hoops get mighty mighty small.
Is this even physically possible? Can I get information from one end of the brain to the other "faster than the speed of light"? Yes, I can. The Planck time is 10^-43 seconds, I have 20 orders of magnitude headroom. It's all about the spike times. Could I, say, cause a bit to flip on the opposite side of the brain before my EM signal gets there? Sure I can - I just have to do two two things:
1. set the state so that the desired bit will flip
2. ensure that the desired neuron is the next one to be updated
For point 2, what do you call it when two neurons need to fire together, or close to each other sequentially? "Coherence". Synchrony. You can see it in the spectra, in the EEG, MEG... heck, you can just stick two electrodes anywhere in the brain and you'll get some coherence.
Offered as food for thought...
In a Hopfield network (which is omniconnected binary), the "state" of the network is determined by the contribution of each element to the Hamiltonian.
(You can easily find the original paper online, Google "Hopfield 1982").
Whenever a neuron changes state, the network has by definition also changed its state. Therefore, if we can divide physical time (which in our computer model becomes Monte Carlo time) into "sufficiently small" intervals so we have one neuron changing state every .05 picosecond or so, then the entire network is changing state that fast.
So in essence what we have is a very special case of "phase velocity", where things seem to move faster than the speed of light. If it takes a fraction of a nanosecond for an electromagnetic wave to get from one end of the brain to the other, then the network has changed state 10,000 times in that interval! !!!
What does this mean? What does it mean when the network changes state? To change state, a bit has to flip, which means information determines state. State changes are information driven.
Why is the "speed of light" important, why am I mentioning it at all? Physics. Atoms, molecules, chemical reactions. It's all about the limit as dt => 0. Because the Hawaiian earring is fractal, and when you zoom in on the origin those hoops get mighty mighty small.
Is this even physically possible? Can I get information from one end of the brain to the other "faster than the speed of light"? Yes, I can. The Planck time is 10^-43 seconds, I have 20 orders of magnitude headroom. It's all about the spike times. Could I, say, cause a bit to flip on the opposite side of the brain before my EM signal gets there? Sure I can - I just have to do two two things:
1. set the state so that the desired bit will flip
2. ensure that the desired neuron is the next one to be updated
For point 2, what do you call it when two neurons need to fire together, or close to each other sequentially? "Coherence". Synchrony. You can see it in the spectra, in the EEG, MEG... heck, you can just stick two electrodes anywhere in the brain and you'll get some coherence.
Offered as food for thought...