Wednesday, March 07, 2007

Levels of Abstraction

Hong Lei's talk on 1/24/07 brought up the old issue of whether we're smart enough to understand our own minds, the self-servingly appellated "most complex object in the universe". All of his statistics are motivated to try to capture the a priori differences observed in the spike waveforms. But just because we can see a difference doesn't mean our mathematics can [accurately] capture it. For example, his algorithm for labelling bursts uses an arbitrary cutoff and binning, so that some information is lost going from the original analog to the digital output. Again, when he measures constancy of spike number in bursts, there is an arbitrary distinction between "same number" and "different number" [with no regard for spacing of spikes]. But information is lost in each analog-to-digital conversion: information is lost at each analytical step. Today in Genetics class Dr. Pierson cautioned that we can make theories about biological mechanisms, but inevitably the biochemistry is more complex and nuanced. Eventually you are just taking averages of averages of averages. This is the danger in statistics of, say, finding the standard deviation of standard deviations.

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