2008/12/1 Kory Heath <kory.domain.name.hidden>:
> Ok, I'm with you so far. But I'd like to get a better handle your
> concept of a computation in Platonia. Here's one way I've been
> picturing "platonic computation":
>
> Imagine an infinite 2-dimensional grid filled with the binary digits
> of PI. Now imagine an infinite number of 2-dimensional grids on top of
> that one, with each grid containing the bits from the grid beneath it,
> as transformed by the Conway's Life rules. This is a description of a
> platonic computational object. Of course, my language is somewhat
> "visual", but that's incidental. The point is, this is a precisely
> defined mathematical object. We can "point at" any cell in this
> infinite grid, and there is an answer to whether or not this bit is on
> or off, given our definitions. (More formally, we can define an
> abstract computational function that accepts any integer and returns
> the state of that bit, given all of our definitions.)
>
> Do you find this an acceptable way (not necessarily the only way) of
> describing a computational platonic object? How would you talk about
> how consciousness relates to the conscious-seeming patterns in this
> platonic object? Would you say that consciousness "supervenes" on
> those portions of this platonic computation?
I struggle with the question of what a platonic object actually is,
even for something very simple. Let's say the implementation of a
circle supports roundness in the same way that a certain computation
supports consciousness. We can easily think of many ways a circle can
be represented in the real world, but which of these should we think
of when considering the platonic object? Is it possible to point to
platonic square and say it isn't round, or does the square support
roundness implicitly since it could be considered a circle
transformed? And is there any reason not to consider roundness as a
basic platonic object in itself, perhaps with circles somehow
supervening on roundness rather than the other way around?
--
Stathis Papaioannou
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Received on Wed Dec 03 2008 - 08:03:18 PST