Re: Mersenne's Miscelleny
Posted: Fri Feb 15, 2013 4:55 pm
Hi James,
Check "tautology". A must equal A (A=A) before any progress can be made. Definition is tautology or it's unsuccessful.
I've given a definition of an infinity that doesn't involve an infinity. I did so because you were dissatisfied with the "one more number" definition, which itself doesn't, and really ought to do. Play off one chum's failure to understand it against another and you get the "all Cretans are liars" effect, which certainly doesn't invalidate logic. The "limit as x goes to of 1/x" definition is perfectly rigorous, but "infinitely divisible" really is not the same as infinity.
But OK, here's another (I did touch on this); by projection of a point on a sphere to the Cartesian plane by the line through point and North Pole, the projection of the North Pole itself lies at infinity.
Computing is non-rigorous, it's a series of heuristics. A statement such as "A=A+1" is permitted even though it's mathematical nonsense. Check out Turin's argument for incompleteness for the proper use of a computing metaphor (which uses infinities).
The microverse theory is very attractive to me- Carl Sagan suggested that every electron is a universe. CERN to the Hague!
The atomists' imagination failed them. Even their universe containd infinitesimal points; so would your chequerboard universe (at the corners!).
My point on quanutum physics is that a universe grainy at the smallest level of time and space needs an infinite dimensional Hilbert Space to exist. That's what the maths says. Fail to supply the infinity and you can't have your quantum chequerboard Universe. You continue to be in denial.
Check "tautology". A must equal A (A=A) before any progress can be made. Definition is tautology or it's unsuccessful.
I've given a definition of an infinity that doesn't involve an infinity. I did so because you were dissatisfied with the "one more number" definition, which itself doesn't, and really ought to do. Play off one chum's failure to understand it against another and you get the "all Cretans are liars" effect, which certainly doesn't invalidate logic. The "limit as x goes to of 1/x" definition is perfectly rigorous, but "infinitely divisible" really is not the same as infinity.
But OK, here's another (I did touch on this); by projection of a point on a sphere to the Cartesian plane by the line through point and North Pole, the projection of the North Pole itself lies at infinity.
Computing is non-rigorous, it's a series of heuristics. A statement such as "A=A+1" is permitted even though it's mathematical nonsense. Check out Turin's argument for incompleteness for the proper use of a computing metaphor (which uses infinities).
The microverse theory is very attractive to me- Carl Sagan suggested that every electron is a universe. CERN to the Hague!
The atomists' imagination failed them. Even their universe containd infinitesimal points; so would your chequerboard universe (at the corners!).
My point on quanutum physics is that a universe grainy at the smallest level of time and space needs an infinite dimensional Hilbert Space to exist. That's what the maths says. Fail to supply the infinity and you can't have your quantum chequerboard Universe. You continue to be in denial.