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Recent theory based on the work of Eric Kandel is that long term memory is
mediated by new protein synthesis in synapses, which modulates the
responsiveness of the synapse to neurotransmitter release; that is, it
isn't just the "wiring diagram" that characterises a memory, but also the
unique properties of each individual "connection".

But these unique properties would be included in the simulation if you could
record the levels of different neurotransmitters and proteins at each
synapse, no? Wouldn't they still be present in the brain of a person that
had recently died, at least if the individual neurons had not yet died at
the moment the brain was frozen?

In theory, it should be possible to scan a brain in vivo using some
near-future MRI analogue and determine the state of each of the 10^11
neurons, and store the information as a binary srtring on a hard disk. Once
we had this data, what would we do with it? The details of ionic gradients,
type, number and conformation of cellular proteins, anatomy and type of
synaptic connections, etc. etc. etc., would be needed for each neuron

I don't think you'd need the details of ionic gradients at the moment of
death, as long as you know how ionic gradients work in a generic neuron
you'd probably just be able to "restart" them.

along with an accurate model of how they all

worked and interacted, in order to calculate the next state, and the state
after that, and so on. This would be difficult enough to do if each neuron
were considered in isolation, but in fact, there may be hundreds of
synaptic connections between neurons, and the activity of each connected
neuron needs to be taken into account, along with the activity of each of
the hundreds of neurons connected to each of *those* neurons, and so on.

Yes, but the hope is that neurons are not overly idiosyncratic in how they
behave, that once you've learned to simulate a single neuron, then you could
apply the same rules to other neurons as long as you knew their shape
(branching of synapses, length of axon and so forth), the levels of various
significant molecules at each synapse (and maybe elsewhere in the neuron),
and maybe some other parameters I haven't thought of. And if you have a
general algorithm that can simulate any neuron once you've measured the
relevant parameters, then simulating an entire brain would mainly be a
matter of being able to record these parameters in every neuron of a frozen
brain, and of having a big enough computer (although you'd also have to know
how to simulate the way that sensory neurons are stimulated by sense organs,
how motor neurons affect simulated muscles, and how neurons interact with
organs to affect things like hormone levels).