Footnote 2. For a volume of approximately 0.5 micron radius (compare to the 20 micron radius of large neurons) and a basal free intracellular calcium level of 100 nM, it is easily shown that 50-100 calcium ions, a number comfortably in the quantum regime, may occupy this region that will become the "hot spot". Once a calcium ion comes into contact with a ryanodine receptor associated with a bound pool of calcium, the exponential process of calcium-activated calcium release can produce a calcium concentration in approximately the same volume corresponding to 100,000 or more calcium ions, all in a time frame of 50 milliseconds. These numbers are in remarkable agreement with the constraints on quantum coherence recently suggested by Penrose (1994).

Footnote 3. It is also possible that observer-induced collapse is illusory, reflecting the fact that the minimum percept duration must necessarily equal the duration of a U-R interval, creating the impression that observation induces collapse, as opposed to objective collapse determining the minimum duration of unitary perceptual events. However, this scenario would not explain the failure to see the 40 Hz frequency in slow wave sleep (Llinas and Ribary, 1993), if indeed that frequency is the frequency of U-R transition. As long as some sensory stimuli continue to impinge on the nervous system, objective reduction should continue, even in the absence of conscious perception. The failure to see the 40 Hz frequency suggests instead that conscious perception may be intimately associated with the U-R transition.