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But when he created his pattern, he found that he had three stones left over. Finally, it dawned upon him that the surplus came from counting the corners of the

by scoot 2y ago

But when he created his pattern, he found that he had three stones left over. Finally, it dawned upon him that the surplus came from counting the corners of the triangle twice. [...] Bochner welcomed the rediscovery of this "discrepancy" so many years after he had created the artwork. Yet he also wondered "about the unwillingness to assume that I already knew what they had just discovered (do mathematicians still think all artists are dumb?). Apparently so, because he failed to understand that what was being commented on was not the absence of three stones (or wallnuts), but rather of significantly more.

ElevenLathe 2y ago
"counting the corners of the triangle twice" is just another way of saying he got the math wrong. It's just a fencepost error. Or am I missing something?
- dullcrisp 2y ago
  The squares overlap on the corners so he only needed to use 47 stones to form the diagram. That’s a separate issue from the stones not being evenly spaced and seeming to show that 4 + 9 = 16.
- lupire 2y ago
  You're not missing anything. The artist didn't understand the difference between fenceposts and fence, boundary and interior. When presented with beautiful evidence of his mistake, he failed to see what it was showing him. The art is good in that it's a puzzle to interpret the mistake and resolve the paradox, even if (especially if!) the artist doesn't understand what they created.
  - brookst 2y ago
    The artist claims it was intentional. Do you know otherwise?
    - CRConrad 2y ago
      From TFA: > "What I had stumbled upon was that physical entities (stones) are not equatable with conceptual entities (points)," Bochner said That's because the relevant conceptual and physical entities when contemplating lengths of sides of triangles, which is what Pythagoras' theorem is about, are lines, not points. >The artist claims it was intentional. Do you know otherwise? His reply reveals that he still doesn't get it, which to me seems to prove that it can't have been intentional.

by scoot 2y ago

ElevenLathe 2y ago

"counting the corners of the triangle twice" is just another way of saying he got the math wrong. It's just a fencepost error. Or am I missing something?

dullcrisp 2y ago
The squares overlap on the corners so he only needed to use 47 stones to form the diagram. That’s a separate issue from the stones not being evenly spaced and seeming to show that 4 + 9 = 16.
lupire 2y ago
You're not missing anything. The artist didn't understand the difference between fenceposts and fence, boundary and interior. When presented with beautiful evidence of his mistake, he failed to see what it was showing him. The art is good in that it's a puzzle to interpret the mistake and resolve the paradox, even if (especially if!) the artist doesn't understand what they created.
- brookst 2y ago
  The artist claims it was intentional. Do you know otherwise?
  - CRConrad 2y ago
    From TFA: > "What I had stumbled upon was that physical entities (stones) are not equatable with conceptual entities (points)," Bochner said That's because the relevant conceptual and physical entities when contemplating lengths of sides of triangles, which is what Pythagoras' theorem is about, are lines, not points. >The artist claims it was intentional. Do you know otherwise? His reply reveals that he still doesn't get it, which to me seems to prove that it can't have been intentional.