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Polar Fox: Hey Red, these points seem to have identity issues. Are they black or white? Red Fox: An obvious illusion! They are white for sure.
Polar Fox: So what I perceive is not the exact reality? Red Fox: This is just a simple game of colors playing on your retina. It is perfectly explainable and part of the reality. Polar Fox: Yes, most definitely. But, can this be an artful clue of an even bigger reality that there is truth beyond what you see? Red Fox: Here we go again! Polar Fox: A brush mark from a picture? A letter from a book? A note from a symphony? Red Fox: And who is the artist, juggling with colors to deceive our perception? Polar Fox: Deceive? I am not so sure. But looks like someone who knows us inside and out. And I think he wants to talk. Red Fox: Why me? Why me? Polar Fox: Yep, and you have bigger ears than mine.
Dervish Fox: I see some beauty between this one and Fox 316.
Red Fox: Would you please help me see that beauty? Dervish Fox: Not bad for a start my friend, not bad at all ! Bleaug has a solution for this general case.
![]() Labels: General Case, Graph Theory, Number Theory, proof, Rectangle, Tiling a Rectangle
Based on our earlier analysis, the sample picture above will never happen.
Polar Fox: I have a problem with this one!
Red Fox: What's wrong with it?
Polar Fox: Nothing moves continuously?
Red Fox: Come again?!
Polar Fox: The universe is discrete! THERE IS NO CONTINUUM.
Red Fox: Then how do the things move, flow, or slide?
Polar Fox: Nothing moves! Absolutely nothing moves!!
Red Fox: But the time ticks away, no? Clock arms DO advance.
Polar Fox: No, they don't! But they die in one instance and resurrect in the next one. In between no measurable time passes. Matter oscillates between existence and non-existence continuously.
Red Fox: Continuously? Isn't that ironic?
Polar Fox: Between any two existence, there is nothing but emptiness.
Red Fox: I am having the feeling that your intelligence fall into non-existing state just now.
Polar Fox: Hold on. I think I am about to jump back into the reality. Wait a sec.
Red Fox: Take your time dude. Just take your time!
Labels: Graph Theory, Number Theory, proof, Rectangle, Tiling a Rectangle
Bleaug submitted the above fox, saying: "a problem which can be expressed in geometric terms and
that is elegantly solved using pure algebraic arguments, still giving deep insight."
General case of this problem can be found in literature. Here is an old one, re-formatted: Need help? See Fox 3.
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