So. First - What in the universe, that we have some evidence for, is indeterminate..?
Answer. Quanta. And Bell's Theorum
Anyway, I'm crap at maths too, so if Bell says "quanta are indeterminate" I'll simply say "Sir, yes sir." And salute.
So, okay, quantum level systems are indeterminate, anything bigger however quickly succumbs to cause and effect.
So, next question, does the brain have a quantum component..?
Answer: yes, it does.
I remembered a bit from "Shadows of the Mind" by Roger Penrose (pg366-368) about possible quantum activity in the microtubules present in the axonal boutons (the mushroom-like synaptic endings) which together with the influence they exert over the contractile actin threads in the oposing dendritic spines the axons 'attach' to allow them to play a part in the strength of signal conduction across the synapse.
Which is all well and good, but who give a shit about it if quantum effects remain indeterminate at only a quantum level, and the gross brain is a macroscopic system, at which point, any quantum effects would be rendered void.
But, actually
...conditions may exist within these microtubules such that a Bose-Einsteincondensate - superfluid/superconductor like state could be supported. In such states a whole system of particles act as would the quantum state of a single particle although scaled up appropriately - ie - boosting the eccentricities of quantum effects up into the macroscopic realm, termed 'quantum coherrence'.
So, to sum so far:
Quantum indeterminacy: present.
Possibility of macroscopic 'scaled up' quantum inteterninancy effects: present.
But again, it all well and good having macroscale quantum indeterminancy, but no good at all if the system it is a part of is not sensitive enough to be overtly effected by its strange and mysterious ways. I mean, the brain is fucking huge comparitively. It's like expecting a see-saw weighing 20,000 tones with gravel for bearings to move wholly on the addition of a flea to one side.
So, just how sensitive is brainstate to variables..?
Sorry - a very short Neurophys 101.
First, you must think of the brain, physically, as a network. A point is formed anywhere where two neurones contact at a synapse.
Let's use the most famous network of all:
Here let's say the nodes are the stations. You can think of the impulses travelling through the brain's networks as the trains. Each length of track between two nodes has two states - train or no train.
Now - I did some electronic doodling, trying to figure out how many configurations a perfectly connected network with n amount of nodes would be. (I gave up after 4). The bold lines indicate state 1:'train' the dotted lines equal State 2: 'no train'.
But after a little mathematic twiddling came up with the formula:
"The Maximum number of possible configurations within a network of N nodes, where each connection has S states - TC - is:
TC = (S) to the power (n x (n - 1) / 2)"
So, according to the above, the total number of possible 'states' the london underground system could have is:
S is the number of states (train/no train) ie 2
And n is the number of nodes (stations). Which wiki says is 274.
ie: configuration total - 2power(274x273 / 2)
Which is a whopping great 2 to the power 37401. ie. a lot.
The average brain however, has - where you say n = number of synapses:
"There are approximately 1 quadrillion synapses in the human brain. That's 1,000,000,000,000,000 synapses. This is equal to about a half-billion synapses per cubic millimeter. (Statistic from Changeux, J-P. and Ricoeur, P., What Makes Us Think?, Princeton: Princeton University Press, 2000, p. 78)"
Thass a lot of nodes. And probably more configurations than even god can think of.
One thing to notice however is that the above equation is only for perfectly connected networks - each node connected to every other. That's not true for the london underground, nor is it true for the brain. So the real figure for total configuration will be a hell of a lot lower.
The trouble is, this base schematic approach to brain maps is wrong. The 'S' - train/no train - is misleading. The network has more states than simply on/off. There are degrees of on-ness and off-ness. Just as with trains - they might be full of passengers, or thay might just be carrying one drunk with puke on his shirt.
Another picture: A city a night.
This time, the amount of light on any particular street, and the street's broadness also reflects its state. Say this time, the impulses in our 'London at night brain' are people moving about. When the streets are wide and well lit, the peopulses move about rapidly, easily, but when the streets are less well lit, or narrower, they slow down. If a street is almost dark, and very narrow indeed, poor peopulse wets his pants and doesn't go down it at all, or if he does, he does so v e r y s l o w l y.
Which means, though the brain is not perfectly connected, its S number is higher than 2, which more than makes up for it.
By now I'm sure you are beginning to think, who give a shit - what's this got to do with anything..?
I thought so.
Basically, intuitively when we try to visulaize thought processes we tend to think of an impulse speeding around a path in the brain from A to B, with A being somehow thought number one, and B being sequentially, thought number two. Which tends to make us assume causal linkage. ie thought A causes thought B.
But this is not true. Thought A is not a single impulse but a state involving pretty much the whole city of the mind - the whole brain all at once. It's not a case of point A to point B but brainstate A becoming brainstate B.
The brainstate is the true language of the mind/brain/thingy.
You know those weird waves you get sometimes at the beach, or on white water..?
These waves only look static - in reality they are constantly collapsing at one end, and being rebuilt at the other.
Well, not to put too finer point on it - that's a thought. It only seems static while we are thinking it, holding it in our conscious minds but in reality it's constantly being reitterated by the mechanics of the gross brain a gazillion times a second.
Now - back to sensitivity.
So, quantum events in the brain are not like a single set of points opening and closing once in a strict sequence as a train passes along a single track. But more like the sum of all the points opening and closing on all the lines all the time all along the entire world's rail networks.
That's a lot of indeterminacy.
Anyway. If you've got this far, well done, I'd probably have fallen asleep by now.
One last thing, then I'll let you go.
Self-sustaining criticalities. Wassat then huh..? This is the principle underlying things like avalanches, or more mundanely - piles of sand or gravel at quarries.
The snow stacks up and up, beyond sometimes, the point where it should have fallen. And it's the weight of the last snowflake, or the disruption of the last skier, that suddenly collapses the whole lot from state A - cohesive mass - to state B - completely fucking deadly mass of wite death.
Then of course, more snow falls, and the whole systems recreates itself over time.
In the brain, thoughts held consciously during deliberation are like snow banks - the brain expends effort in holding them in a certain form, way beyond the point where they'd normally collapse into the next state - the outcome of deliberation. This renders them increasingly sensitive to very small events...
...very very small events...
...very very very small events.
Well you see where the process of adding very's to the adjective 'small' in a sentence goes... All they way down to quantum.
So, in answer to the initial aim:
All I'm going to do is try to decide if it is mechanically possible for the will to be indeterminate.
I'd say there is at least some evidence for a 'Yes it could be'.
