I'm not a biologist and the parent poster seems to know in far more detail, but from a bunch of neuroscience lectures on how the dentritic spikes travel up to the soma, my takeaway (as a computer guy) was 'hmmm, it looks like a system implemented in FPGA layouts - the geometry features can work as logic gates or delays'; and 'hmmmm, it looks I could design a dendritic tree geometry for almost any boolean function of the inputs, so any computer-chip-like-functionality could be built out of them'.

I mean, if I needed (A xor B) and (C or D), then my impression is a single neuron with rather simple geometry and appropriate dendritic connections could calculate that in the sense that this neuron would spike iff the A,B,C,D neurons spiked as required by that formula; but since neurons tend to have much much more connections, then each neuron is technically capable of much more complex calculations, even if many of them in the end do something like 'spike iff any 100+ of my 1000 inputs are spiking'.

It's not so simple as that because timing is also relevant, and there were examples of known dendritic structures that do "processing" in terms that a neuron spikes if it receives A slightly before B, but doesn't spike if it receives A slightly after B; so it can be used for detecting motion direction and such.

"[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.

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.

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>

"Processing" doesn't have a consensus definition in the neuroscience community, but a neuroscientist could, with good justification, use that definition if they had a particular experimental scenario. In this article, Smith, et al., use a more narrow definition based on well-known response in which a neuron is selectively-sensitive to a bar of light at a particular angle. How a neuron becomes selectively-sensitive (i.e., how it fires to that angle and not to all the others) is the "processing".

It is overly simplified to say that for the processing to be useful that it has to share the result. If a particular part of the dendritic sub-tree was stimulated enough, it could bring the neuron into a particular electrophysiological state that succeeding synaptic input would cause a wholly different computation to occur. Thus, you can see the importance of timing discussed by the sister comment.