Beaming Neutrinos Through Earth?
TheMatt writes: "An article at PhysicsWeb talks about a proposed project by scientists at FermiLab. The project would involve sending a beam of neutrinos 10,000 km through the earth to a detector at SuperKamiokande. The hope is that passing through so much matter would alter the beam enough to better study CP (charge-parity) violation."
-- ;-)
Kuro5hin.org: where the good times never end.
1^2=1; (-1)^2=1; 1^2=(-1)^2; 1=-1; 1=0
;)
Cute! However, the same logic can be applied to determine that 2=-2, 3=-3, 4=-4, ad infinitum, ad nauseum. In fact, using a third order mapping function you can show that three values (X1,X2,X3) are equivalent. Using a fourth order mapping function you can show that four values are equivalent. And so on . . .
And now you see the problem of trying to apply a tautology to mapping functions that are not homeomorphic -- i.e. "one to one" and "onto".
The function X^2=Y involves the loss of some information when mapping X to Y. There are two X values which will resolve to the same Y value. Therefore, the assertion that X1=X2 is correct since the inverse function is ambiguous as to which value of X was used to produce the given Y value. However, to assert that the value is zero you must impose the restriction on your mapping function that it is monotonically increasing or decresing -- i.e. that it is homeomorphic. X^2=Y is not.
Still, very cute