Seeing red

[emjay]

That might be true in a computer system... if one component fails it might bring down the whole thing... but in the brain, redundancy is 'built in' so where I talk about single neurons they're actually populations of neurons, having the effect of averaging out 'noise'. So there's never going to be a place where a single neuron's failure will catastrophically affect the whole network, but rather the signal strength will just weaken with progressive damage to a population of neurons.

This is the argument in QM or in general with the "butterfly effect."  The idea is that in very complex systems, even though things normally average out, there are so many events that SOMETIMES a tiny variation snowballs.  It comes down to arguments about determinism, because we can never actually know whether the chaos could have turned out any other way than it has.

Consider whether a brain is really a binary device or whether it functions as an analogue device (I'd argue it has components of both, actually).  Then consider the concept of constructive interference in waves, and the fact of rogue waves (aka the "perfect storm").  In binary systems, you'll never get a perfect storm.  In GENERAL, the complexity of the ocean leads to relatively uniform waves over the surface, but due to very-small-chance statistical interactions, you sometimes get harmonics that lead to freak incidents.

So even if people disregard the butterfly effect in general, in any system with sufficient complexity, and given that it is not digital, you will sometimes end up with unpredictable results.

Yeah, I understand what you mean. Rational AKD was talking about all this stuff as well... QM effects in the brain... microtubules etc. I accept that there could be quantum effects in the brain, and following that discussion, that they could have much more influence than I ever gave them credit for (I assumed before that they had no real effect at the relatively macro scale of molecules and cells), and even perhaps being leveraged by the system in some way - in microtubules etc, adding yet another level of complexity and even perhaps connectivity. But even if quantum shit   is an integral part of the system - and the jury's out on that for me but I'd think probably not - it doesn't really effect my ideas on determinism and the clockwork universe because whether random or determined 'I' still have no say, so looking backwards in time, any choice, behaviour or whatever that was the result of quantum activity still cannot be attributed to 'me' and was only one way - even if it could not be 'predicted' beforehand by the clockwork universe, 'afterhand' it's a fait accompli with no way of predicting (even theoretically) what else it could have been, if anything.

I'd agree that the brain is both binary and analogue, in that the outputs of a neuron are spikes of variable frequency (the analogue part) but they only fire after a certain threshold value has been reached (the binary part). As a general rule I don't actually think about the brain in terms of brain waves. I should do perhaps but I don't, so I don't really know what it means by saying 'slow wave sleep' etc. But I'll assume that what you mean is that for a given population of neurons they could all be spiking at exactly the same time and at the same frequency resulting in perfectly synchronised pulses of maximum activity (or the reverse... no activity)? And the question being what effect would that have on the system? It's an interesting question... what would it take to 'break' the neural network?

I don't know but the first thing that comes to mind is that neurons work by exchanging ions with the extracellular fluid, and therefore maintaining different concentrations inside and outside the cell. Electronics is not my strong suit so perhaps you guys can help me understand this better I'm referring to the book I recommended to you (CECN) to try and summarise the following... The firing of a neuron relies on three ions, Na+(Sodium), Cl-(Chloride), and K+(Potassium). And learning and other stuff at the synapses relies on Ca++(Calcium). The makeup of the extracellular fluid is similar to seawater with dissolved salt accounting for the Na+ and Cl-. The membrane potential is the difference between charge inside and outside the cell across the cell membrane (wall). The resting potential is the membrane potential when the neuron is at rest and not receiving any inputs. This resting potential is maintained by the sodium-potassium pump in the cell membrane that actively pumps Na+ out of the cell and a smaller amount of K+ into it, resulting in a negative membrane potential of -70mV when the neuron is at rest. The book says the sodium-potassium pump uses energy and can be likened to charging up the battery that runs the neuron. Since the neuron lets ions into or out of the cell either through pumps or channels, channels allow ions to move not just by electrical forces but also by diffusion, so these concentrations that are maintained take diffusion into account. The main ion involved in firing action potentials is Na+ and there are two primary ways it can get into the cell passively through channels (which it 'wants' to do because of the sodium-potassium pump actively pumping it out and creating an imbalance). One way happens at the synapse, when Na+ channels are opened by the binding of the neurotransmitter glutamate, and the other happens at voltage gated channels (which represent the threshold value of neurons) at the axon hillock where an action potential originates. In either case the result is the 'depolarisation' of the neuron as the membrane potential moves closer towards 0. At the axon hillock, the voltage gated channels that open allow Na+ to flood in and this increased excitation activates another bunch of channels that allow that inhibit the neuron and the result of this is a spike of excitation followed by inhibition, and where the inhibition (among other things) causes the membrane potential to overshoot the resting potential - ie go lower than -70mv - resulting in a 'refractory' period following a spike where it is unable to fire again until the membrane potential climbs back up to the threshold level again, and thus resulting in an effective fixed maximum rate that the neuron can fire spikes. Anyway, the axon is insulated in sections along its length with a 'myelin' sheath separated by relay stations called nodes of Ranvier, and they perform the same function as at the axon hillock, serving to re-amplify the degrading signal as it propagates up the axon. When it gets to the end of the axon and enters one of the axon terminals (also known as axon buttons) which is the pre-synaptic site it triggers voltage gated channels to allow Ca++ into the terminal (and from internal stores), which causes little sacks - called vesicles - of neurotransmitters to bind with the cell wall and release their contents into the synaptic cleft. By the way, the neurotransmitters themselves are produced in the soma and transported up to the axon terminals by microtubules, acting kinda like a pipeline, so that's one use for the little guys that doesn't rely on quantum shit   Anyway once the neurotransmitter is in the synaptic cleft it diffuses across and binds with specific receptors poking out of the dendritic membrane on the post-synaptic neuron and depending on the type causes different things to happen in the receiving neurons, either opening channels, or causing chemical cascades of reactions. Finally, about the other two ions I haven't talked about, Cl- channels are used to inhibit the neuron and are triggered by the neurotransmitter GABA which is sent by inhibitory interneurons, and K+ constantly leaks out of neurons in small amounts through an always-open channel, there is a voltage gated channel that lets out K+ when a neuron gets very excited, and another type of channel K+ opens as a function of how much Ca++ is present in the neuron, with more indicating extended periods of activity, so K+ is used to inhibit overactive neurons and is involved in 'neuron fatigue'.

Anyway, the point of all that was to hopefully understand what could go wrong if a butterfly effect, snowball thingy happened So I was thinking, since the neurons rely on maintaining very specific potential differences and concentration gradients relative to the extra-cellular fluid then I think it would be fair to say that the content of the extracellular fluid must be regulated just as much as it is inside neurons. And for that the blood-brain barrier springs to mind, because it requires active transport of nutrients that it allows through the barrier (which is not everything... not toxins in the bloodstream for instance) via special transport molecules/cells, whatever they may be. So the question is if you've got an edge case where say all neurons are either in the resting state or in the fully excited state, what would be the situation in the extracellular fluid? Would there be enough ions to go around for a start to even allow that to happen. If all the neurons were in the resting state therefore with a greater concentration Na+ outside than in, how would that effect the balance for all neurons... could they even function properly given that if they all pumped out Na+ then presumably the concentration of Na+ in the extra-cellular fluid would skyrocket creating a very different resting potential? Conversely if all neurons were fully excited - ie having a membrane potential of 0, then what would be the effects? Any ideas from you two brainboxes?   But one thing I think is for sure, is that a neuron has a maximum firing rate so even if it received massive amounts of excitation at the same time on its dentrites from different neurons all firing at maximum rate, they would open channels all over but it would still result in the same depolarisation, just coming in through more openings. That makes sense.

As for your question to both of us, about pulling neurons 1-by-1, I really don't know I'm sorry. I think a neural network will always find a way to represent whatever it can, depending on its connectivity, but with decreasing neurons and thus indirectly decreasing connectivity, the scope of the representations would reduce. But how to translate that into stable or variable I don't know... I think it would always be pretty stable whatever size it was but I don't really know what you mean.