Holiday: as far as i know (and im just a student here), the rate of firing of a neuron doesn't change, it's either on and firing at a certain rate, or it's off. That said, the neuron can fire ON and then OFF, at a certain rate. In hearing, for instance, the rate of neuronal firing is synchronised to the frequency of the sound being heard - but the 'voltage' of the action potential itself is the same when it is fired. For example, a sound at 100 Hz might activate a single neuron on and off 100 times in a second, although the pulse sent down the axon will be constant and unrelated.
The brain is both binary and analogue. Neurons and conscious function can work in an amazingly simple way at times. In hearing, for instance, the neurons involved are laid out just like a pipe organe across the brain, with one end dealing with the lower frequencies and the other end the higher frequencies. Hearing is a very old (evolutionarily speaking) ability, so the way hearing works is actually very mechanical in nature, very analogue, easily understood.
Other neurons, particularly of the cortex (where most 'thinking' happens) might be simple in basic function, but are actually very adaptive, constantly changing and hard to figure out in the same concrete way. Each neuron in the cortex might have thousands of receptor sites, with each connected to thousands again of other neurons, in a massive tangle. Despite this, each single neuron primarily transmits information in a binary sense, being 'on' or 'off'. We can say with some certainty that some areas
of the brain are involved in certain abstract functions, but tracing this back to neurons is almost impossibly hard. This is complicated by the fact that the brain is plastic, and can adapt to damage, particularly when young. It's unlikely that the cortex functions in the same mechanical way as the older parts of the brain.
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I would guess that conscious thought is a very abstract process, with little if any direct
neurological correlation. I don't know how memory works (other than certain areas of the brain seem to be more heavily involved than others), but i believe that that neurons have a 'use it or lose it' function. When a neuron is used, it creates more receptor sites, so that in the future it is itself more likely
to be used. A bit like evolution, the neurons of the cortex succeed and survive if they are useful, and lose receptors or die if they are not. This is evidenced in addiction, where neuronal activation causes it to create more receptors for the extra neurotransmitters floating around in the synapse.
That way, memory for some things, like your own name for instance, could be represented as a complex combination of neurons, heavily re-enforced by multiple dendrites and receptors, such that your name 'comes to mind' more often in normal thought than a strange name that you might have only thought about once or twice. A strange name by comparison would be less connected, therefore less activated, and again, have less receptors. A massive tangle of these neurons could represent certain ideas, thoughts, processes, associations etc.
That said, i wouldn't think a name, or any other 'thought' or 'memory' has its own neurological path in the brain, more likely the neurons spell out an association
of different things, which together your own cognitive processes decode and reveal themselves to you. Neurons, after all, are just information transmitters, there's nothing special about them as individuals. As a crude example, imagine you're trying to remember someone's name at a party. You can't think of the answer immediately, but you stand there hurriedly trying to remember memories of this person, their face, their voice, their association to you, their job, etc. etc. And it's only when you've hit enough of these associations that suddenly that particular combination of neurons is lit up, and you remember their name. Now in your brain, that person doesn't exist in a physical fashion of neurons, but the combination of other
different associations is what gives you the memory of that name.
In this way conscious and subconscious processes are totally relational, with no meaning individually other than their combined relationship. When you consciously
think of your name, the information would be redirected to the speech understanding centre (Broca's area, with its own connections and associations, in this case specialised for carrying out speech), where the abstract form is realised and presented to you as a conscious thought.
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