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A comment on Strange new phase of matter acts like it has two time dimensions. Parent comment

Re:Strange new phase of matter acts like it has two time dim... by mcswell on Friday July 22, 2022 @04:30PM (#32196769)
Rational/ irrational here depends on the unit of measurement. A full circle (360 degrees) is rational if you measure it in degrees, but irrational if you measure it in radians (it's 2 pi radians).
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Re:Strange new phase of matter acts like it has two time dim... by anamexis on Friday July 22, 2022 @09:55PM (#32199450)
By that logic, couldn't any number be deemed rational by just declaring it as a unit?
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Re:Strange new phase of matter acts like it has two time dim... by function_seven on Friday July 22, 2022 @10:22PM (#32199614)
It just occurred to me that when they’re talking about a “rational angle” they might be talking about a slope that can be specified rationally.

If you have a repeating three-dimensional crystal lattice, and a ray of light that is following an irrational slope, then it is guaranteed to intersect one of the cell units or vertices in that lattice.

If it did not intersect any nodes, then you would be able to express that slope rationally just by counting the number of vertical nodes over the number of horizontal nodes!

I’m assuming an infinite lattice here. For finite ones an irrational slope could still “sneak through”

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