Tag Archives: configuration space

Irreducible Concepts

Hard to define…

It’s very easy for discussions to get hung up on definitions, so a serious approach to debating a subject begins with synchronizing everyone’s vocabulary watches. Accurate and nuanced communication requires mutually understood ideas and terminology for expressing those ideas.

Yet some concepts seem almost impossible to define clearly. The idea of “consciousness” is notorious for being a definition challenge, but “morality” or “justice” or “love” are also very difficult to pin down. At the same time, we seem to share mutual basic intuitions of these things.

So the question today is: why are some concepts so hard to define?

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Cubes and Beyond

I’ll end these posts about the configuration space metaphor where I began: in a big cube. I started the series in the Neapolitan room, a three-dimensional space where we could indicate our feelings about vanilla, chocolate, and strawberry ice cream with a single marker. From there we visited the Baskin-Robbins 31 Flavors space (which is tasty but beyond our ability to visualize).

Then I focused on spaces with only two-dimensions (which are easy to visualize). These are probably the best use of the metaphor; they turn a tug-of-war into a sensible place to stand. They also strongly differentiate “don’t care” from “care about both.”

Now let’s see what we can do with three dimensions…

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Expanding the Middle

My blog has such low engagement that it’s hard to tell, but I get the sense the last three posts about configuration space were only slightly more interesting than my baseball posts (which, apparently, are one of the least interesting things I do here (tough; I love baseball; gotta talk about it sometimes)).

So I’m thinking: fair enough; rather than go on about it at length, wrap it up. It’ll be enough to use as a reference when I mention configuration space in the future. (There have been blog posts where I couldn’t use the metaphor due to not having a decent reference for it. Now the idea is out there for use.)

And, at the least, I should record where the whole idea started.

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31D Ice Cream

Last time we considered a cube-shaped room where we could indicate our opinion about Neapolitan ice cream with a single marker. That worked well because we were dealing with three flavors and the room has three dimensions: east-west, north-south, up-down.

Later I’ll explore other examples of a 3D “room” but while we’re talking ice cream, I want to give you an idea where this goes, I want to jump ahead for a moment and consider good old Baskin-Robbins, who famously featured “31 flavors!”

So now the question is, can we set a marker for all 31 flavors?

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3D Ice Cream

Have you ever had (or at least seen) Neapolitan ice cream? It’s the kind with chocolate, vanilla, and strawberry, usually as separate layers in one package. As a kid, I didn’t care for the strawberry. I loved the chocolate, and was fine with the vanilla (wouldn’t usually choose it, but don’t disdain it).

That’s just my take on it: one flavor liked, one not liked, and one that’s just okay. Someone else might have the same pattern with different flavors. Or love them all equally, or want just the strawberry. Some might not like ice cream at all — any combination is possible.

What if we wanted to describe our feeling about Neapolitan as a whole?

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