  If spikes are the medium, what is the message? Answering that question is
driving the development of large-scale, single neuron resolution recordings
from behaving animals, on the scale of thousands of neurons. But these data are
inherently high-dimensional, with as many dimensions as neurons - so how do we
make sense of them? For many the answer is to reduce the number of dimensions.
Here I argue we can distinguish weak and strong principles of neural dimension
reduction. The weak principle is that dimension reduction is a convenient tool
for making sense of complex neural data. The strong principle is that dimension
reduction shows us how neural circuits actually operate and compute.
Elucidating these principles is crucial, for which we subscribe to provides
radically different interpretations of the same neural activity data. I show
how we could make either the weak or strong principles appear to be true based
on innocuous looking decisions about how we use dimension reduction on our
data. To counteract these confounds, I outline the experimental evidence for
the strong principle that do not come from dimension reduction; but also show
there are a number of neural phenomena that the strong principle fails to
address. To reconcile these conflicting data, I suggest that the brain has both
principles at play.
