[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?

>
>
...

sdw



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