Wednesday, August 21, 2013
Summary
(Warning: Yeah, it's one of those days. No quantum mechanics this time, but I can't promise it will be much better...
)
Ah, really a fantastic day. I attribute the large spike in mental throughput to the fact that I finally bought a nice, big whiteboard for my room!!
I've gone through so many different beliefs about location / abstraction / events / power allocation in one day that I'm almost afraid to say anything for fear of being able to prove myself wrong (again) within the hour. But, all in all, I'm definitely closing in on something. I don't know what it is, but it's something
The beginning of the day saw me continuing to think about location as a distribution. First I explored continuous distributions, thinking about simple ways to model general probability functions to "approximate" location. Then I stepped back and noticed that continuous space really isn't important, which led me to the belief that location is actually a distribution over the object graph. Who cares if you're floating in space? What we
really care about is what object you're near to. But that wasn't satisfactory either, so I moved to the belief that location is a distribution over the
edges of an object graph. You're either at A, B, or somewhere in between. Showing a bit of respect for continuous space now
That was a pretty good model, in retrospect. It might have even worked. But still the notion of spreading onself over many nodes in a spatial graph is tedius. How do you know which "pieces" of yourself have which propeties? Kind of defeats the purpose of abstraction to be asking questions like that.
So I came to the conclusion that "splitting" is a necessity. If you're an abstract object and you need to be in two places at once, you've no choice but to slice yourself in half. This led me to an exploration of "divergent forces" and how events can actually "tear" an abstract object into pieces if they pull at it in different "directions." Kind of reminds me of Voldemort...you know, if you want to put your soul in a bunch of different objects in different places, you need to tear it a few times first
But how do you decide where to tear it and how big each piece should be? I don't think they ever discussed the solution to that one in the books...shame
Splitting sounded like a complex nightmare, but, luckily, I was saved towards the end of the night when I realized that splitting is really just power distribution. This led me to a new formulation that
doesn't require splitting (thank goodness), as well as
yet another way to understand location! I've been trying to see location in a similar way to other states. But I realize now that it's not. Location and time are both dimensions, and power allocations are made
with respect to a dimension!!! So we can actually understand location as governing the
start-up cost of allocating power towards an event. Whoa!!
I really think I'm onto something here. I'm exploring the possibility that location is more or less neglected in abstract sim, and superseded by a notion of "allocation time" - i.e., trading with a far-away station requires more time to re-allocate the "cargo power" to that (far-away) event. This is a really neat idea, because it eliminates so many complexities. It also boils everything down to an emphasis on
interactions. Continuous space doesn't matter, even an object graph doesn't matter. What matters is
where you are relevant to the interactions in which you're taking place. I have a really good feeling that this is the droid I've been looking for
With today's great progress, I may need another conceptual day...honestly I'm more excited to finish this sequence of thoughts than to do something "flashy"
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You can visit devtime.ltheory.com for more detailed information on today's work. ]