[FoRK] Non-speech, non-keyboard direct communications will create a new class of humans

Stephen Williams sdw at lig.net
Tue Jun 25 17:28:59 PDT 2013

On 6/25/13 4:31 PM, J. Andrew Rogers wrote:
> On Jun 24, 2013, at 11:40 PM, Stephen Williams <sdw at lig.net> wrote:
>> On 6/24/13 10:07 PM, J. Andrew Rogers wrote:
>>> - They are necessarily "n+k" dimensional constructs for theoretical reasons. There is no 1D, 2D, etc concept bootstrap into non-visualizable number of dimensions because the simplest interesting examples are non-visualizable.
>> I presume the interesting property is effecting clustering distance in the 1D distance / magnitude, a la Hilbert.  You should be able to visualize distribution and density in 1, 2, or 3D.  Or perhaps zigzag (space filling!) 1D projection onto 2D or 3D.
> It is more complicated than that.
> When using a curve as a computational structure there are some abstract types that are not tractable on curves that share their dimensionality. They can be mapped via a transform function onto a higher dimensionality curve in which

I can see that.  But what types of intractableness have you run across?
The obvious examples are non-linear, non-monotonic dimensions that are 
really a combination or function of multiple dimensions already.

> they are more tractable. You could visualize this as a graph of subspaces but it is not explanatory. For every visual depicting a good transform function, there are an unbounded number of obvious but defective transform functions that will produce an identical visual. Don't underestimate the subtlety of the theory; it stumped academics for a couple decades.

What do you call this type of theory / topic?  What are the foundational 
papers here?

> A second reason higher dimensionality is necessary is to guarantee that a set of algorithmic cuts exist that will give a uniform data distribution across e.g. a distributed data structure while preserving spatial locality. This is more obvious.
> Brilliant for building distributed data structures, and more scalable than hash tables with about as much code. Much harder to understand though.

How much more scalable?



More information about the FoRK mailing list