Your lifelong aversion to any applied science (if I undestood you correctly) shows.
Gopnik obviously doesn't remember 6th grade geometry: point can't have an edge since edge is a line. Sharp edge of a point is nonsense.

His literary allusions might be brilliant (as well as you for noticing them) but based on simple ignorance - if I'd want to praise him, I'd use a different quote.

Brad DeLong really panned Gopnik too.

However, a point can be sharp on a knife, even if it can't in geometry.

Anyone who took analytic geometry knows that a lesson doesn't have many edges. Gopnik shows his ignorance once again.

(I'm pretty sure he's not talking about a point in the geometric sense.)

zizka: I presume you're referring to this; I wouldn't call it "panning Gopnik" (he seemed to like the article as a whole) so much as pointing out something he didn't like. (I didn't like it either -- I'm no Civil War expert, but even I knew Cold Harbor was a mess that Grant later regretted. On the other hand, it's hardly central to the essay.)

And I agree that applying geometrical analysis to this particular piece of rhetoric isn't entirely to the, uh, point.

Zizka, my English could be limited but not to the point (quite dull as it is, I'm afraid) of mistaking edge of a point with a point itself.
My enjoyment of metaphors usually increases when author is using right terms, geometrically (6th grade level, not analytical) or linguistically speaking.

The M-W sez:

point

1b : the most important essential in a discussion or matter

4a (1) : a geometric element of which it is postulated that at least two exist and that two suffice to determine a line (2) : a geometric element determined by an ordered set of coordinates

5a : the terminal usually sharp or narrowly rounded part of something : TIP; b : a weapon or tool having such a part and used for stabbing or piercing: as (1) : ARROWHEAD (2) : SPEARHEAD

Just sayin'.

And what exactly you're saying, PF?

That at least two points constitute a line? Apparently only those versed in ANALYTICAL geometry know that line (edge) consists of many points and although a point could very well be a sharp one it doesn't mean it has an edge.
Here's more information on the subject from your preferred source

I think I'd accept only this merging of "edge" and "point" (it is clearly where I am) :
>>a point near the beginning or the end; especially : BRINK, VERGE

As Orwell pointed out, one of the keys to clear writing is having a clear mental image. I agree with Tatyana that Gopnick's image is anything but sharp (and I was a very indifferent math student).

However, I appreciate the reference to Archilochus's proverb, which did jog loose some fuzzy associations for me. One of them was this short poem, either by Ted Kooser (the new U.S. Poet Laureate) or by his good friend, Jim Harrison, from their co-authored Braided Creek:

Turtle has just one plan
at a time, and every cell
buys into it.

Though it's hard to tell if that's an allusion to A.'s hedgehog, or just happens to bear some family resemblance. [Note to biologists: Yes, I am aware that hedgehogs and turtles are not closely related!]

Tatyana, I think you're trying to plug a square peg into a round hole with a radius of less than the length of the side of the peg times the square root of two. So to speak.