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It's not a problem with confusing ordinals and cardinals; the artist's problem is, as others have said, a fencepost error. I suspect that what has annoyed peop

It's not a problem with confusing ordinals and cardinals; the artist's problem is, as others have said, a fencepost error. I suspect that what has annoyed people is that if all the hazelnuts are evenly-spaced, then the triangle the artist created is not a 3-4-5 triangle, it's a 2-3-4 triangle, which isn't a right triangle. To make it look like a right triangle, he's had to arrange the nuts with unequal spacing. He must have noticed that, and it should have annoyed him too. I suppose there's some geometry in which a 2-3-4 triangle is a right triangle; but I doubt the artist was exploring non-euclidian geometries. FWIW, I didn't notice the error immediately - but I did notice the uneven spacings.

YeGoblynQueenne 3y ago
>> It's not a problem with confusing ordinals and cardinals; the artist's problem is, as others have said, a fencepost error. Yeah, my argument is that it's a fencepost error only if the numbers of nuts are interpreted as ordinals indexing the vertices of a lattice on the Cartesian plane, rather than cardinals counting the elements of a set, while the artist intended them to stand for cardinals. That is what the anonymous contributor to the 360 blog, mentioned in the article above, seems to have seen: "To my eye," the commenter continued, "the hazelnut grids look exactly like pins on a Geoboard, or lattice points in the plane. And given that perspective on this image, we see a 2-3-4 triangle, an obtuse triangle, and squares of area 4, 9, and 16." But this is clearly only one way to see things and there's nothing to make it more valid than the other, except of course that this one leads to an error which strongly implies it's not the right view. >> I suspect that what has annoyed people is that if all the hazelnuts are evenly-spaced, then the triangle the artist created is not a 3-4-5 triangle, it's a 2-3-4 triangle, which isn't a right triangle. To make it look like a right triangle, he's had to arrange the nuts with unequal spacing. He must have noticed that, and it should have annoyed him too. Some other comments say something similar, but I don't understand it. What is the issue with spacing? As you point out it would be difficult to get a perfectly mathematically correct spacing with irregularly shaped solids, like hazelnuts. Which suggests that spacing was not part of the intended interpretation. Can you explain?
- CRConrad 3y ago
  > while the artist intended them to stand for cardinals. Oh stop it with that BS already. He fucking obviously intended them to stand for line lenghts, or he wouldn't have arranged them in a right (but wrong) triangle.

YeGoblynQueenne 3y ago

>> It's not a problem with confusing ordinals and cardinals; the artist's problem is, as others have said, a fencepost error. Yeah, my argument is that it's a fencepost error only if the numbers of nuts are interpreted as ordinals indexing the vertices of a lattice on the Cartesian plane, rather than cardinals counting the elements of a set, while the artist intended them to stand for cardinals. That is what the anonymous contributor to the 360 blog, mentioned in the article above, seems to have seen: "To my eye," the commenter continued, "the hazelnut grids look exactly like pins on a Geoboard, or lattice points in the plane. And given that perspective on this image, we see a 2-3-4 triangle, an obtuse triangle, and squares of area 4, 9, and 16." But this is clearly only one way to see things and there's nothing to make it more valid than the other, except of course that this one leads to an error which strongly implies it's not the right view. >> I suspect that what has annoyed people is that if all the hazelnuts are evenly-spaced, then the triangle the artist created is not a 3-4-5 triangle, it's a 2-3-4 triangle, which isn't a right triangle. To make it look like a right triangle, he's had to arrange the nuts with unequal spacing. He must have noticed that, and it should have annoyed him too. Some other comments say something similar, but I don't understand it. What is the issue with spacing? As you point out it would be difficult to get a perfectly mathematically correct spacing with irregularly shaped solids, like hazelnuts. Which suggests that spacing was not part of the intended interpretation. Can you explain?

CRConrad 3y ago
> while the artist intended them to stand for cardinals. Oh stop it with that BS already. He fucking obviously intended them to stand for line lenghts, or he wouldn't have arranged them in a right (but wrong) triangle.