Most recent bloggy thing: Root Cause Analysis and the Photocopier Question:

solipsys.co.uk/new/RootCauseAn

@ColinTheMathmo I'm reminded of seeing the moon reflectors* at the Moscow museum of technology. They reflect light exactly in the incoming path, so you when you look at them, you see only your own eye(s) looking back at you from each cell. And the person beside you sees theirs. I was intrigued by this, so I decided to get a photo.

An array of round black camera lenses.

* Bounce a laser off one to measure the distance to the moon's surface

@derwinmcgeary Certainly a photo of a reflector array will be ... (significant pause) ... interesting. As you discovered.

But photocopying a mirror is an interesting exercise, and you *can* deduce /a priori/ what the result will be. So many people fail to appreciate the point. Maybe I'm wrong, maybe it's neither important nor interesting, but I do think there is a point, and in general, people aren't seeing it.

@ColinTheMathmo I don't see how it can't depend on the details of the inside of the photocopier, to be honest. If the photocopier is a camera mounted under a pane of glass, you'd expect it to be a picture of the camera and mounting. If we're pinging each point with white light and printing a greyscale point based on how much light is reflected, it'd be a white page as all light is reflected (which is I guess what you'd expect from a chemical Xerox process).

@derwinmcgeary I can give you a pointer to my answer if you like, explaining why the result is an unavoidable consequence of what a good copier must do, and therefore doesn't rely on the details of the interior.

Would you like to see my write-up ??

@ColinTheMathmo I strongly suspect you might be smuggling assumptions in under the phrase "good copier"

I guess the two cases I can imagine are "black and white photocopier which takes reflected light levels, and hence produces a white page" and "idealised light measuring lens which itself looks black and therefore produces a black page because the reflection at the centre of every image it takes is black", but I don't see why one of those is impossible to build.

@derwinmcgeary I don't think so. I'm envisaging things that the copier should be able to copy, thinking about the differences between them, assuming that the copier does good things, and deducing something from that. As I say, I can point you at my analysis if you like, then you can try to pick that apart.

@ColinTheMathmo I'm happy to eat my words of course... I think I've set my stall out for "it depends", and considering the last "photocopy" I made was a photo on my mobile subsequently printed out that may mean I take a broad view on what a photocopier can be. I've also mounted a camera behind a pane of glass in my time...

@derwinmcgeary I'd be happy to hear your thoughts on this, especially if you think I've smuggled in assumptions, or made an unwarranted leap.

@ColinTheMathmo The logic is obviously right. It's not clear to me that "We would want a photocopier to produce the same result in each case. We would not want the glossy version to have extra, spurious ghost images of any kind.". So if we photocopy a card with green glitter, the copy should just have little flat green squares? It's not a bad property, but it's not central to my idea of what a photocopier necessarily is.

@ColinTheMathmo There's also the physicsy question of how our sensor is distinguishing between photons from specular and non-specular reflection...

@derwinmcgeary Indeed, part of the reasoning requires that you can't. If you /could/ then the situation would/could be very different.

So since you can't, the glossy/matte thought experiment tells us that specular reflections must not go to the sensor.

@derwinmcgeary You have a point, but I think a consequence of not wanting ghost images from a glossy brochure implies that "glitter" won't come out "sparkly". But in the case of glitter, motion plays an essential role, and you can't put that onto a photocopy.

A Mastodon instance for maths people. The kind of people who make $\pi z^2 \times a$ jokes.

Use $ and $ for inline LaTeX, and $ and $ for display mode.