Example: *P**roof of circle*
(Album cover <https://www.youtube.com/watch?v=dRjJogNRMSY&ab_channel=Mr_Kenzo>
I used for inspiration - and it's nice music too)
*Let's say you want to convince someone that there is a circle in an image.*
Then you would convey to them something like this:
1. Some preprocessing of the image
Process the image like this:
pixel = if pixel is 1% (or other value) away from black
then black else white
end
2. Creation of the circle pattern
Calculate this image:
pixel(point) = {
d = distance(point, center);
if d between radius1 and radius2
return white
else if d between radius2 and radius3
return black
else
return transparent // Yes, some parts of the image are transparent.
end
}
with some constants center, radius1, radius2, radius3.
This image will look like a white ring directly inside a black ring on a
transparent background.
Now comes the actual proof step:
* Compare these two images (the processed input image and the circle pattern)
pixel-by-pixel, ignoring any transparent pixels in the pattern image
* Sum up these differences and divide them by the number of non-transparent
pixels in the pattern image
* The resulting value is x%, with x higher than an agreed-on value (e.g. 95%)
* Thus there is a circle in the image at <center> with radius <radius2>
This kind of proof can easily be verified by a computer program.
"This kind of proof" here means:
-You keep the structure of the proof exactly identical to the example above.
Some of the constants in it may change.
-The constants used in the pattern creation script must pass basic plausibility
tests and possibly some heuristic ones (e.g. regarding the rings' thickness,
i.e. radius2-radius1 and radius3-radius2).
-The image preprocessing step does not really have to be checked unless you
replace it with a more complex computation that can actually add structure to
an image.
Has this been done before? Proofs as part of image recognition?
Cheers
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Artificial General Intelligence List: AGI
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