Wow! These plastic cylinders look round - but in the mirror they look diamond-shaped. If you turn them around, they look diamond-shaped - but in the mirror they look round!
This video was made by Kokichi Sugihara, an engineer at Meiji University in Tokyo. How did he do it???
To answer this question, we should "science the hell out of it", as Matt Damon said in The Martian. Figure out how objects change appearance when you look at them in a mirror... and design an object that does this!
So scienced the hell out of it:
The basic idea is this. The top rim of this object is not flat. More precisely, it's not horizontal: it curves up and down! This affects how it looks. If you're looking down on this object, you can make part of the top look farther away by having it be lower.
But a mirror reflects front and back. So in the mirror, part of the top looks closer if it's lower.
By cleverly taking advantage of this, we can make this object look round, but diamond-shaped in the mirror.
And if we turn it around, this effect is reversed!
Here's a bit more of the math. gives the details, so I'll try to present just the basic idea.
Suppose you're making a video. Suppose you're looking down at an angle of 45 degrees, just as in this video. Suppose you're videotaping an object that's fairly far away.
Think about one pixel of the object's image on your camera's viewscreen.
Its height on your viewscreen depends on two things. It depends on how far up that piece of the object actually is. But it also depends on how far back that piece of the object is: how far away it is from your camera. Things farther away give higher pixels on your viewscreen.
There's a simple formula for how this works:
pixel height = actual object height + actual distance back
(It's only this simple when you're looking down at an angle of 45 degrees and the thing you're videotaping is fairly far away.)
But what if we're looking in a mirror? You may think a mirror reverses left and right, but that's wrong: it reverses front and back. So we basically get
mirror image pixel height = actual object height - actual distance back
So, you just need to craft an object for which
actual object height + actual distance back
actual object height - actual distance back
give two different curves: one round and one a diamond!
But now for some puzzles:
Puzzle 1. All that sounds fine: by cleverly adjusting the top rim of the object we can make it look different in a mirror. But look at the bottom of the object! What's going on there? How do you explain that?
Puzzle 2. Sometimes I know the answers to the puzzles I'm posing. Sometimes I don't. Do I know the answer to Puzzle 1, or not?
Puzzle 3. Same question for Puzzle 2.
Finally, I should admit that I simplified the formula for the mirror image pixel height. Actually we have
mirror image distance back = constant - actual distance back
mirror image pixel height =
actual object height + mirror image distance back =
actual object height + constant - actual distance back
In other words, I ignored a constant. This constant is why the whole mirror image looks higher on your viewscreen than the original object!
And it's perhaps not surprising that the consortiums that do own them, which often have companies like Comcast and Time-Warner, don't particularly feel like letting Google become a member.
Meanwhile, I just read another story noting that bringing Google Fiber to a neighborhood typically increases property values by 11 percent.
- Infer IncCo-Founder, 2010 - present
- Software Engineer, 2005 - 2010
- University Of California BerkeleyElectrical Engineering and Computer Science, 2001 - 2005
- Walnut High School1997 - 2001
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