Is accumulation about noticing variables' values  or their order of occurrence?  The answer is yes.  (Robert Kaplan asks, " . . . and what are numbers . . . adjectives or nouns?" --The Nothing That Is, p. 26.)

Is the content of each possible x^n an intricately unique shell content or is it some patterned set of multiples?  The answer is yes.

There used to be some malarkey that since we notice one or the other of the vase/faces first, people cannot think of both at the same time.  True, it might be advantageous to NOT think of both the vase and faces at the same time.  (Rather than have your friends complain about your slippery thinking, it can be advantageous to stick to a single perspective's consequences.)

But with much patience and slow re- reconnoitering, the vase/faces and, likewise, shell/shell-values as well as asymmetrical symmetries seen in the power of two shells that add to c², may productively inform each other.  Imagine having to describe the above picture with only concave descriptions.  You would have to alternately refer to the vase and the faces to get around the lines.  Incidentally:  Isn't the vase actually space?  Or, aren't the faces actually one big background? 

I think that double-knowing, ever-shifting types of knowledge sometimes carry a misnomer or even get short-shrifted (or long-shrifted) as "heuristics".  Vase/faces realities might frequently be cases of apparent data that seems apparently too simple for consequent logic.  (After all, how is it that everyone has always comfortably sensed that Fermat's Last Theorem is true without being able to say precisely why?  The logic is there.  Slippery, but there.) 

"Both" is what we see in the worlds of our faiths, sciences, information, emotions, and ethics--no matter how loudly we might protest.  Of course!  No amount of organization or delineation or focus will stop the either/or question from being posited then answered resoundingly, "Yes!"

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Last modified: 12/16/05