You are missing the point. There are hyper-dimensional topological solutions that can be efficiently implement on vanilla silicon that obviate your argument. There is literature to support the conjecture even if there is not literature to support the implementation.
I’m totally missing how a “hyper-dimension topological solution” could get around the physical limitation of being realized on a 2D printed circuit. I guess if you use enough layers?
Do you have a link to an example paper about this?
It is analogous to how you can implement a hyper-cube topology on a physical network in normal 3-space, which is trivial. Doing it virtually on a switch fabric is trickier.
Hyper-dimensionality is largely a human abstraction when talking about algorithms; a set of bits can be interpreted as being in however many dimensions is convenient for an algorithm at a particular point in time, which follows from fairly boring maths e.g. Morton’s theorems. The general concept of topological computation is not remarkable either, it has been around since Tarski, it just is not obvious how one reduces it to useful practice.
There is no literature on what a reduction to practice would even look like but it is a bit of an open secret in the world of large-scale graph analysis that the very recent ability of a couple companies to parallelize graph analysis are based on something like this. Graph analysis scalability is closely tied to join algorithm scalability—a well-known hard-to-parallelize operation.
I’m totally missing how a “hyper-dimension topological solution” could get around the physical limitation of being realized on a 2D printed circuit. I guess if you use enough layers?
Do you have a link to an example paper about this?
It is analogous to how you can implement a hyper-cube topology on a physical network in normal 3-space, which is trivial. Doing it virtually on a switch fabric is trickier.
Hyper-dimensionality is largely a human abstraction when talking about algorithms; a set of bits can be interpreted as being in however many dimensions is convenient for an algorithm at a particular point in time, which follows from fairly boring maths e.g. Morton’s theorems. The general concept of topological computation is not remarkable either, it has been around since Tarski, it just is not obvious how one reduces it to useful practice.
There is no literature on what a reduction to practice would even look like but it is a bit of an open secret in the world of large-scale graph analysis that the very recent ability of a couple companies to parallelize graph analysis are based on something like this. Graph analysis scalability is closely tied to join algorithm scalability—a well-known hard-to-parallelize operation.