They aren't "our limitations", they are properties of the universe, constituents of its physical nature, unless all our current theory is simply and completely wrong. Chaos is no more a "convention" than the inverse square law of gravitational attraction, or the relativistic modifications of Newton's Laws for handling high speeds. Bell's Theorem is not a "convention", it is a rigorously mathematical derivation from hard core physical theory, and its empirical confirmation has been replicated thousands of times.
According to all modern physics, what we call cause and effect is an illusion. What we call probability is not. One's philosophy should be adjusted accordingly - the option of just carrying on with some kind of bottom up reductive determinism in which all mental events (and by laddering down, all events above the bottom level whatever it may be) are epiphenomena without the causal import one attributes to that bottom level, is irresponsible. Yes, you may be shown correct after the next big discovery has led us to discard all current theory, but that's not the way to bet, eh?
No. "We experience" (with the caveat that there is no "we" outside of the whole of this experiencing) not the connections of neurons but entities made up of the firing patterns - the substrate, the neurons and their connections, is static in the moment - you can freeze it in liquid nitrogen and examine the structure unchanged for months; the patterns of firing this substrate supports exist only in motion through time, must be maintained and recreated continually to exist.
The bulb is not the light. The ink is not the letter. The substrate is not the pattern. The pattern is an entity, an event - it exists, itself. Its causes are not neurons.
Harris is brilliant and entertaining, but he is wrong to take as the basis of his argument that freedom of the will requires that it be supernatural. I suspect his alertness to religious hooha and its common employment of supernaturally bestowed free will has led him astray there.
The central observation is that substrate does not cause pattern. It can constrain pattern, influence pattern, etc, but it does not cause pattern. One is simply misusing the term, if arguing that neurons cause ideas. Mental events in the human brain are patterns of patterns of neuron firing, taking place over time and space, and to some significant degree -> causing each other <-. Ideas cause ideas. The direction of causation, if any, is the reverse - Dreams motivate decisions, cause mental events which lead to behaviors. One of the categories of these patterns of influence of patterns we term "will", and it has degrees of freedom - in some people more than others.
