Thank you, Brian.  About g1, the linear representation is

    5!:5 <'g1'
(2 * *) +/@, ,&*:

and in that form, with the extra space, it is easier for me to see that the 
central operation (+/@,) sums the append of its arguments, and that the 
arguments being sent are twice the product on the left, and the append of the 
squares on the right.  The arguments will be appended and summed, producing the 
result.  Now clear; without the extra space I was scratching my head!

Brian Schott wrote:
> Kip,
> 
> I love your simple description. I think it is a major contribution to
> explaining the distinction.
> 
> PS
> 
> I could not help myself from rewriting your g as g1, but your g is
> much better for your description.
> 
>       g1 =:  (2 * *)+/@, ,&*:
> 
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