Whew, Paint on my Apple virtual XP is still sane. So I believe the two segments are now identical. Does anyone think they look identical? --rwg www.tweedledum.com/rwg/6pents.png On 8/20/10, Bill Gosper <billgosper@gmail.com> wrote:
Apologies. I had tried superposing the segments with Windows Paint, which has a mode where white <-> transparent. But for some bizarre reason, it enforced opaque white on this image, and I couldn't test it. (One *very* frustrating hour later:) I tried rewriting it at various pixel depths and as a gif. Paint not only refused to treat white as transparent, it even disabled the feature in the toolbar, and left it disabled when I loaded a file on which it formerly worked! So I tried "physically" moving a rectangle containing the longer line onto the shorter, and the black part became transparent!! Paint has gone criminally insane. If this were something important, I would be, too. Anyway, I just manually fudged the picture closer to equality, and I still see the illusion. Feel free to repair it with some sane software, and see if it still works for you. --rwg On Thu, Aug 19, 2010 at 8:44 PM, Bill Thurston <wpt4@cornell.edu> wrote:
What is your experimental method, guys? I copied the image into Adobe Illustrator and used the measuring tool to check. The leftward segment measured 4.05", and the rightward segment measured 4.17". A 3% difference. Theoretical equality != actual equality.
My experimental method was somewhat cruder: I held up a piece of paper next to one line on my screen, made two marks, then slid the paper over. Going back and forth a few times convinced me that it wasn't just pencil mark error.
--Joshua