[bl]

"[I]t looks I could design a dendritic tree geometry for almost any boolean function of the inputs".

That's my outlook on the structure-function link between dendritic morphology and dendritic information processing, with the modification that I'd not restrict it to boolean functions. There are very many more types of functions, linear and non-linear, that can conceivably be built out of neuronal dendrites.

And I like the nuance of your second paragraph. There are all sorts of wacky, complex calculations one can image being possible, but any one neuron may implement a subset. Now, across a few hundred billion neurons in a mammalian nervous system...

You're spot on with regard to timing, too. All this "information processing" with branched dendrites + non-linear ion channels are greatly expanded with a timing component.

[PeterisP]

Well, AFAIK you don't need anything more than boolean functions, since if we're talking about single spikes (not spike frequency), then there either is or isn't a spike, you don't get some spikes larger than other.

The linear/nondigital functions IMHO seem to be used as implementation details - for example, a neuron "fire iff 1+ VIP-input fires or 3+ normal inputs fire" can be implemented in wetware by having 'vip-inputs' have thrice as strong synaptic connection, summing all input values in the dendrite, and adjusting so that the firing threshold is appropriate (i.e. a linear function); but in silicon the same thing can (should?) be implemented as a boolean function / logic gates.

[bl]

I hope no one interpreted my statements to suggest that anything you said was wrong. Just trying to fill in details.

I merely want to avoid prematurely narrowing the range of functions that are possible. If we, for the moment, think of the neural computation of a single neuron as a neural network, then the spike/no-spike decision would be in the last layer and a whole host of linear/non-linear (some not necessarily boolean) functions could be implemented by the dendrites. And some single neuron processing we already know behaves in a non-boolean manner.

Be aware, just because arbitrarily powerful logic could be constructed solely out of boolean components (I don't even know if this is true. Isn't this kinda what is going on in an FPGA?) doesn't mean that neural hardware is purposed the same way. They may very well may be analog, at least for some computations.

And to speak to your second paragraph, I should declare my personal biases. As a dendritic physiologist, I wasn't much interested in whole-cell firing characteristics, but in the dendrite's sub-threshold behavior.

How do a smattering of synaptic inputs, each with varying strengths, interact within the complex electrophysiological scaffolding provided by a branched dendrite layered with non-uniform, non-linear ion channel distributions?

So my perspective is somewhat inverted: To me, neuron firing is the implementation detail! <smilie face>