Recent content by puzzled fish

This is going to be my last post in PhysicsForums as I have decided to go. One must be very careful when dealing with infinities. Does infinity minus infinity when both x and t are infinite in spacetime interval, tend to zero? Or does 0 multiple infinite times ( for our little trivial...

Had this been ds^2 =+cdt^2+dx^2+dy^2+dz^2 it would've been the Pythagorean Theorem.

Note that a singularity doesn't imply that there is an end somewhere. In mathematics you can have a curve extending infinitely in the x and y directions and yet its length could be finite. It all depends on how you define the metric.

Fine! But that's the way automata think, not humans. It would be very easy for a sophisticated computer to come up with various random functions and diff. equations as solutions to various problems. But Gauss and Riemann began with tangible objects and geometry not "functions". And GR is a...

And what is x = 10t-9.8t^2 pray, if not a block universe? The fact that you can change your mind ( initial conditions ) and choose a different solution is irrelevant. A solution to the EFE is a solution. Once you have picked it, you cannot change it. You can transform it covariantly, but this...

No, I cannot because I do not have a manifold to begin with. No overall Gaussian curvature at a point, sorry. So, in GR you tacitly assume that there is a BU. If it's really there or it exists is irrelevant. The fact is that GR as a theory has a block universe at its heart.

Wait a minute... Is there a notion of Gaussian curvature and differentiation without a manifold and an already existing temporal dimension? Put SR aside, how can you do GR without a BU?

No, I would put my station in a geodesic orbit around the black hole and let my rope unfold towards the center of black hole from there. No power needed for hovering thus.

Yes, for equations >= 2nd degree they are the origin of the Group of Substitutions and the foundation of modern Group Theory, historically developed first by Lagrange, then by Ruffini, Abel and Galois.

No need for all this! The substitution : ## I = \frac { i + k } { \sqrt {2} } ## , ## J = - \frac { j + k } { \sqrt {2} } ##, where i,j,k are the usual quaternion units gives the isomorphic quaternionic algebra with the above rules: ## I^2 = -1 ## , ## J^2 = -1 ## , ## K^3 = -1 ##, ## K = IJ =...

From what I could gather from Wikipedia, I have the feeling that Frobenius theorem hinges on definite quadratic forms of this kind : ## a_1x_1^2 + a_2x_2^2 +..+ a_nx_n^2 ##. Now ## x_1^2 + x_2^2 + x_3^2 + x_4^2 + x_1x_4 - x_2x_3 ##, the squared norm I described above, is certainly positive...

I came so far as to think this is an upside-down chessboard, since there are no coordinates on the board, and now White promotes to a Queen, but no, I don't think Sir Roger would play such a trick on us...

You may take my word for it, that by a laborious checking I have proven that my Quaternionoids are in their most general case, associative.

Ok, I take it that permission has been granted now for me to post :They are constructed somewhat similar to the Quaternions, the only difference being : ## k = ij = 1- ji ##, hence they are neither commutative nor anti-commutative, (associativity still holds good.) By this rule only , if ## i^2...

Some time ago, I stumbled upon an interesting set of hypercomplex numbers. I thought that somebody else might have discovered them ( it was too facile a construction ) and forgot about them for many years. Lately, I searched on the web and did not find any mention of their existence. I must...