Hi Jo,
You wrote:

Marr's analysis indicates that at least in cerebellar cells different synapses are used to convey different meanings to the cell. In simple terms the mossy fibre inputs might mean 'you put your right leg in, you put your right leg out...' and the inputs from climbing fibres, I think from olivary nuclei, would mean 'learn that'. 

I did not understand where that is indicated. In the bit I quoted previously from wiki

From wiki ( https://en.wikipedia.org/wiki/David_Marr_(neuroscientist) ) I read: 

The cerebellum theory^[2] was motivated by two unique features of cerebellar anatomy: (1) the cerebellum contains vast numbers of tiny granule cells, each receiving only a few inputs from "mossy fibers"; (2) Purkinje cells in the cerebellar cortex each receive tens of thousands of inputs from "parallel fibers", but only one input from a single "climbing fiber", which however is extremely strong. Marr proposed that the granule cells encode combinations of mossy fibre inputs, and that the climbing fibres carry a "teaching" signal that instructs their Purkinje cell targets to modify the strength of synaptic connections from parallel fibres. Neither of those ideas is universally accepted, but both form essential elements of viable modern theories^{[citation needed]}.

It did not seem to indicate that the location of the synapse was important, it instead seemed to indicate that the input from the climbing fibre was stronger (so strength of input not location) which seems perfectly compatible with a default model which rather than adding up the number of inputs, fires instead when there are enough positive ions at the axon hillock to reach the threshold to cause it to let in more positive ions. And before looking at any other evidence, I would like to examine this as you previously considered this piece of evidence to be the "best clue" that the location of the synapse on the neuron was important (rather than strength of input for example). 

Regarding the problem I was pointing out I had written:

I am not totally sure what you meant by degrees of freedom, so instead I will relate it to information theory, that you had brought up. A 2 input 1 output NAND gate can receive 4 messages and output 2. The neuron can receive way more, but how many messages can it output, and how does this compare to how many messages it would require to be able to convey what its experiential content was? In case I have not expressed this clearly enough, consider the amount of bits of Shannon information to express its experiential state (which you suggests requires (100-1000 degrees of freedom) ).

You wrote:

The input to a pyramidal cell is probably in the region of 50,000 bits simultaneously. There are a whole lot of ways one can argue that is too generous or possibly too restrictive. I tend to take the conservative view that the cell may have around 5,000 descriminable bits of input. It is generally agreed that even our visual experiences do not require more than that richness of coding. I have neuroscience colleagues who claim that a visual experience only needs 50 bits but I think this is implausible. I tend to think it must need 1000. That is around the right number.

Well with a computer a picture could use 24 bits per pixel (8 bits to indicate the colour intensity of the red, 8 bits to indicate the colour intensity of the green, and 8 bits to indicate the colour intensity of the blue) and so you would multiply that by the number of pixels. Though obviously there are techniques to reduce the amount of information. For example using 32 bits to encode the colour and how many pixels in a row (up to 256) have that colour for example. Now with neurons I assume the firing frequency will go to indicate intensity, but I still do not understand how a visual experience could always be done with only 50 bits (as your colleague suggested) even if the experience was of a 10 pixel by 10 pixel grid of black or white squares. I should think quite a few computer artists when working close up are seeing grids of over 100 x 100 with a variety of colours on their screens, and that is not the totality of their visual experience. I am perhaps getting a little off the point, but I want to relate it to where you wrote:

..., I see no reason to doubt that the cells communicate what it is like to be a human subject  through the mechanism I indicated before if nothing else. With an input meaning 'are minty and this taste consonant' and an output 'correct' the cell has communicated that it is sensing mintyness in the way it does.

But there are numerous inputs and in your theory different combinations would give rise to the neuron experiencing different content. So for the sake of simplicity imagine that there were 10000 different variations of experiential content that the neuron was capable of experiencing. How many bits of Shannon information to were you thinking it would take to express which variation of experiential content (such as the "minty taste" variation) it had, and how many does a neuron output?

Yours sincerely,

Glenn