Josh "cortex" Millard

@joshmillard
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Makes art and stuff, used to run http://www.metafilter.com. he/him, Portland, OR, USA. email at josh@joshmillard.com
Show threadJosh "cortex" MillardJun 20
The Boater in question, along for this dumb ride.
Show threadJosh "cortex" MillardJun 17
“Hello, Joshua. I’d like to play a game. In your past, you have strained your personal relationship. Now, in order to live, you must…strain your pasta. Will you remove it from this boiling water while it’s still al dente, or will your moral convictions prove to be…toothless?”
Show threadJosh "cortex" MillardJun 9
Also a small tragedy: as I was doing some hand-sanding of last week's now-dry shapes, I got sloppy and applied too much pressure to my rhombicuboctahedron that I had been so happy with up to that point. Bone-dry, unfired clay is already at its most fragile state, and these constructions with their thin walls and probably only so-so connecting edges on my part, don't bear stress well at all. Lesson (re-)learned.
Show threadJosh "cortex" MillardJun 9
Got four more solids built yesterday too, drying now in anticipation of bisque firing. Clockwise from bottom left: truncated tetrahedron, truncated cube, truncated octahedron, and cuboctahedron. (Off to the right, bone dry and white, are an octahedron and a square antiprism that are now glazed and headed into the kiln for final firing.)
Josh "cortex" MillardJun 9
These three polyhedra are out of the kiln and look pretty great: an icosahedron, a dodecahedron, and a tetrahedron, all done in a mysterious "sapphire" glaze someone had abandoned at the studio and is now already gone again. It's a nice glaze and I like how it breaks really well at the edges, though the greenish aura at the transition periods isn't my favorite glaze effect I've seen.
Josh "cortex" MillardJun 7
Reading a favorite book, drinking a beer, watching the chickens, and forgetting for some chunk of an afternoon how many things are terrible.
Show threadJosh "cortex" MillardJun 6

You can see in the graph that most nodes have at least three paths to other nodes; 7 is the only one with fewer, with only two connections, to 4 and to 6.

It's not hard to find a way to do a full walk of the graph, visiting every single node, e.g.:
1, 2, 3, 4, 9, 8, 5, 6, 7

What that translates to for Sudoku is that you could put those digits in that sequence in a single row or column and no two adjacent digits would sum to a composite number. Ah, well, drat.

Josh "cortex" MillardJun 6

Today's random thing: got myself thinking about this graph of pairs of digits 1-9 that produce prime sums. Much sparser than the complementary graph of pairs that sum to composite numbers, which I sort of knew would be true but hadn't ever examined up close.

I enjoy the resulting asymmetrical sigil, and how each distinct prime that can be summed to ends up having its own consistent slope among the diagonal connections: all 11s, all 13s, all 7s, all 5s.

Show threadJosh "cortex" MillardJun 5

@ckape So where does that leave us? We can still take that 5x5 7-cell solution and extend it with another cell on the main row and column, but we're back to a ceiling that grows by two for each step, just with a slightly smaller starting value: n = (2m - 3) instead of (2m - 2).

Question is, is there another tack we can take here, or are we stuck?

Show threadJosh "cortex" MillardJun 5
Oh no, pump the brakes! As @ckape just noted, at the 7x7 extension of my 5x5 7-cell solution admits ambiguity after all (and so therefore do all the extensions after that likewise). Both of these solutions fit the clues: I've snuck in a 2x2 checkboard entity without noticing.