If a 3d Beatrix models the set of 4d spaces, then a 4d snoopy would describe a set of 5d spaces. If you treat the elements of the matrix as a complex sub-matrix, there is no reason it couldn't be a higher dimension super-matrix. Then a higher dimension matrix could be described by a lower dimension compound matrix. It must lead to One.
That's transcedentally sweet, Rob > On Jul 19, 2014, at 8:08 PM, "Rob Withers" <robert.w.with...@gmail.com> wrote: > > I think you guys have created a system that demonstrates a new field of > mathematics, unless I am missed something in my research on the topic. If we > define the system as being an N-dimensional space of R-dimensional subspaces, > does this mean we need to use a real 3D matrix to model the algebra implicit > in the implementation? Here's the catch, I don't mean a 2D matrix modeling 3 > dimensions (square matrix), I mean a 3D matrix with matrix elements > E(x)(y)(z). The dimensionality of the (z) elements of the matrix would be R, > while (x) and (y) would be the number of partitions in a square matrix. What > is the definition of a determinant and such in a matrix that is a volume of > elements? Like with a 4D Voronoi diagram, with the ability to project 3D > "surfaces" out of the 4D diagram, a 3D matrix (vatrix?) could project 2D > matrices. > > So what are off plane elements doing and what operations can be performed > with a 3D vatrix? > > That's neat, thank you for Kafka! > > Rob > >> On Friday, July 18, 2014 at 7:22 PM, Robert Withers >> <robert.w.with...@gmail.com> wrote: >> >> I had some time to consider my suggestion that it be viewed >> as a relativistic frame of reference. Consider the model >> where each dimension of the frame of reference for each >> consumer is each partition, actually a sub-space with the >> dimensionality of the replication factor, but with a single >> leader election, so consider it 1 dimension. The total >> dimensionality of the consumers frame of reference is the >> number of partitions, but only assigned partitions are open >> to a given consumers viewpoint. The offset is the partition >> dimension's coordinate and only consumers with an open >> dimension can translate the offset. A rebalance opens or >> closes a dimension for a given consumer and can be viewed as >> a rotation. Could Kafka consumption and rebalance (and ISR >> leader election) be reduced to matrix operations? > >
