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blennonon Machine-Learning Maestro Michael Jordan on the Delusions of Big Data and Others

This is not entirely correct. There is a lot of evidence that action potentials backpropagate into the dendrites [1]. On a local level, this allows synapses on the dendrites to "be aware" of the activity of the post-synaptic neuron. However, I do not think this accomplishes/implements the ANN backpropagation algorithm (although a few statements and a citation in [1] alludes to this being possible).

[1] http://en.wikipedia.org/wiki/Neural_backpropagation

blennonon Woman of 24 found to have no cerebellum in her brain

Something that can partially implement the function of the cerebellum.

blennonon Woman of 24 found to have no cerebellum in her brain

It's unclear whether the circuitry of the cerebral cortex has the ability to implement the function of the cerebellum (whatever that may be, which we don't really understand). I think we're a long ways off from answering that question.

blennonon Woman of 24 found to have no cerebellum in her brain

My PhD adviser and I have had that debate a number of times. For the congenital case, we can't say one way or the other. But in the acute case, where there are localized lesions to the parts of the cerebellum thought to be involved in cognition, the effect seems to be primarily cognitive. From anatomical studies, we also know that there are "loops" formed between non-motor areas of the cerebral cortex and the cerebellum.

blennonon Woman of 24 found to have no cerebellum in her brain

This condition is known as cerebellar agenesis. A review of many of the case studies was done by a prominent cerebellum researcher [1]. Typically the individuals that survive past birth live relatively normal lives but with impaired motor skills which are slower to develop. Their abilities are remarkable given that acute lesions to the cerebellum result in much more significant impairments (e.g. not being able to touch your nose with the tip of your finger in one smooth, coordinated movement).

These individuals probably also exhibit diminished cognitive function as well. Only recently has it been recognized that the cerebellum is also involved in cognition [2]. It's interesting to note that you don't need a cerebellum to move or think, but the loss of it impairs both. Contrast this to damage to your motor cortex which can result in paralysis.

[1] Glickstein, M (1994). Cerebellar Agenesis. Brain, 117, 1209-1212. [2] http://www.ncbi.nlm.nih.gov/pubmed/23996631