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?


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