On 2019-12-14 09:15, Mike Stay wrote:

I can see the difference between squares 14 and 18, though it's subtle. I can imagine a difference between 8 and 10! Retinas are really good at edge detection but not nearly as good at comparing colors when they're separated.

For anyone planning to use these, note that the smallest feature is not necessarily the edge length of the smallest square. E.g. in problem 5, it's a piece of the lower edge of the upper right square and in problem 6 it's a piece of the lower edge of the upper left square.

Ed Pegg sent me dozens (hundreds?) more of these, textually encoded.

In #19, it looks like the smallest rectangle isn't a square. What's going on there?

It's hard to imagine that much imprecision in the drawing software! But it shouldn't matter, even if it isn't rectangular. The drawing need only be topologically correct. —rwg

On Sat, Dec 14, 2019 at 7:57 AM Bill Gosper <billgosper@gmail.com> wrote:

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http://www.tweedledum.com/rwg/squares.htm problem 2, can you see the color boundary between "18" and "14"? Maximal zoom. Slide "10" and "4" off the left edge to show only the middle right portions of "14" and "18". Slide up and down. Suspicion: Girls can see it better. Color vision is on the X chromosome. —rwg ("8" and "10" are identical shades of light blue. Proof: TextEdit>Format>Font>Show Colors> <eyedropper>.) I used to grumble at color-enhanced astronomy photos. Until I realized I am colorblind compared to most space aliens. _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun

There are various kinds of color blindness. There are the three kinds of dichromats: protanopes don't make the opsin L (long, mostly red sensitive), deuteranopes don't make M (medium, green), and tritanopes don't make S (short, blue). Monochromats don't make two of the three. There are also anomalous trichromats that produce all the opsins but some are shifted. Protanomalous have an L with a sensitivity shifted towards green. Deuteranomalous have an M with a sensitivity shifted towards red. Tritanomalous have a lower sensitivity to blue light. Tritanopy is not sex-linked and can be caused by degeneration with age or by a head injury. Tetrachromacy can arise in a bunch of ways, but the most common is for a woman to inherit anomalous trichromacy on one X gene, where the shift is substantial enough for her brain to understand it as a fourth color dimension. Human eye lenses are opaque to UV light, but those who've had the lens removed report near UV light as being white, tinged towards blue or violet, because all three opsins respond to UV, but S moreso. I wrote to Jay Neitz about inducing human tetrachromacy and the possibility of infrared vision. Neitz is one of the researchers who have induced trichromacy in monkeys using gene therapy. He wrote: --- The vitamin A1 photopigments of all living things known range in peak from about 360 nm (UV) to 560 (the peak of the human red). No one knows why an infrared A1 based pigment has not evolved; it may be limited by the chemical properties of the vitamin A1 based 11-cis-retinal or the opsin protein component of the photopigment. However, this does not mean that humans could not invent a IR pigment that would work. However, presumably if it was too long wavelength or too sensitive, our own body head would fog the retinal image. --- The vOICe (seeingwithsound.com) is a sensory substitution tool for the blind. It sweeps a vertical scan line across an image; pitch corresponds to altitude and volume to intensity. Some selected quotes from a late-blind female PF: "It is as if the voice creates a black and white drawing of what I am looking at…The sound of music or a voice is just that sound. yet the soundscapes generate sight…like looking at a black and white TV show…" Lots more here: https://www.seeingwithsound.com/users.htm Clearly her brain is doing something involving her visual cortex. I'm playing with it to see if I can induce new qualia. On Sat, Dec 14, 2019 at 4:44 PM Brent Meeker via math-fun <math-fun@mailman.xmission.com> wrote:

Some people have four differently pigmented cone receptors in their eyes instead of three. The fourth is on the UV side of the normal blue. This is sex linked and is more common in women.

Brent

On 12/14/2019 6:57 AM, Bill Gosper wrote:

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http://www.tweedledum.com/rwg/squares.htm problem 2, can you see the color boundary between "18" and "14"? Maximal zoom. Slide "10" and "4" off the left edge to show only the middle right portions of "14" and "18". Slide up and down. Suspicion: Girls can see it better. Color vision is on the X chromosome. —rwg ("8" and "10" are identical shades of light blue. Proof: TextEdit>Format>Font>Show Colors> <eyedropper>.) I used to grumble at color-enhanced astronomy photos. Until I realized I am colorblind compared to most space aliens. _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun

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-- Mike Stay - metaweta@gmail.com http://math.ucr.edu/~mike https://reperiendi.wordpress.com