Space.
Dimensions, distance and similar photos, in five experiments you can touch.
Predict first
Shift a photo three pixels to the left. In pixel space, does it stay close to itself?
Dimensions
One number. For every direction.
A dimension is a direction no other direction can reach. Each one costs exactly one number.
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A picture is a point
Every picture is a point. Every point, a picture.
A pixel is a number. So a picture is a list of numbers, and a list of numbers is a point.
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Every image
Every image already exists. Finding one is another matter.
Any 784 numbers make a 28 × 28 picture. So every digit ever written is already somewhere in this space.
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Proteins
Close is a choice. Fold a protein and see why.
Seven real proteins, one point each. How near you are to the real fold depends on how you measure.
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The album
Like finds like. Build the album your phone builds.
Draw a digit. A small network places it among 2,000 real ones, and its neighbours decide where it belongs.
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Prove it
Three questions. The reasons matter more than the score.
Question 1 of 3
Two directions point along the same line, one forwards and one backwards. How many dimensions can they reach?
Question 2 of 3
You turn a folded protein a quarter turn without changing its shape. What happens to its two distances from the real fold?
Question 3 of 3
Matching by raw pixels names the right digit 93% of the time. Shift every digit three pixels and it drops to 32%. Why?