Why Bother with What Three Words?

Re:Why Bother with What Three Words? by ltbarcly3 on Friday March 29, 2019 @12:43PM (#19523254)

I took a 256 square hilbert curve and took random points in it (discarding points where the euclidian distance was > 8).

Here is the plot: https://gist.github.com/justinvanwinkle/22a15bb33536095b05dc...

Notice the Log y axis. I don't you think you could consider this even roughly continuous. This is only even bounded because I only took points within the 256x256 grid, if I let it run over say a 1000x1000 grid the hilbert distances wouldn't plot well even on a log plot.

The second plot I took any random point within euclidian distance 8 from a random first point, and didn't restrict it to stay in the same 256x256 grid. 10k points total. Even at distance 1, you get hilbert distances like:

4469269309980865699858008332735282042493121940197464459241187147907254676691182325600624766055634475896677286062162016951251294270648856648811216335320387

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Re:Why Bother with What Three Words? by kevinventullo on Friday March 29, 2019 @05:20PM (#19525789)

I'm not sure why that first plot wouldn't be considered continuous. There's a pretty clear positive correlation, which should be more pronounced with a non-log scale y-axis, and more pronounced as you increase the order of the curve.

I'm confused about the second plot; what order is the curve? It seems weird that there are no points between 10^12 and 10^156.

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Re:Why Bother with What Three Words? by ltbarcly3 on Saturday March 30, 2019 @11:21AM (#19529848)

The second graph has a huge jump because the left side of the area I'm taking points from is a boundary between two very distant parts of the curve. In any space filling curve you will be able to find arbitrarily large jumps like this.

The difference would be more pronounced on a non-log scale, except the huge numbers at the top of the range would squish the graph down so you couldn't see what was going on.

The first graph isn't just not continuous, it's not even 1-1. (I'm ignoring the fact that is also discrete so that any formal sense of 'continuity' can't exist. Even if you tried to make it continuous by filling in the gaps it would be impossible.)

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Re:Why Bother with What Three Words? by kevinventullo on Saturday March 30, 2019 @02:56PM (#19531088)

Unfortunately I think we're talking past each other and this is not the best format for technical discussion.

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