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Which hypercube unfoldings tile space?

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Re: Which hypercube unfoldings tile space?

#31

Post by pontifier »

flir wrote: post #8
pontifier wrote: post #2

Once, while at a hockey game in Colorado I had this idea that I wish the stadium could be filled with people all thinking about the same problem and trying to solve it. This result is astounding, and shows the power of mobilizing many people to think.

I suspect the trick is harnessing them in the right configuration. Otherwise you've got the old (n^2 – n) / 2 problem.

I knew it had to be this. Number of edges in complete graph of order n, K_n.

https://oeis.org/A000217

There's no way for everyone to talk to everyone. The solution I came up with at the time was to have a rudimentary chat bot connect parts of conversations intelligently. Now, of course just throw an AI at it.

A well designed website with different conversations going on in different places might work almost as well. This site does an adequate job actually.

Re: Which hypercube unfoldings tile space?

#32

Post by flir »

pontifier wrote: post #31
flir wrote: post #8

Earlier quoted context omitted.

I suspect the trick is harnessing them in the right configuration. Otherwise you've got the old (n^2 – n) / 2 problem.

I knew it had to be this. Number of edges in complete graph of order n, K_n. https://oeis.org/A000217 There's no way for everyone to talk to everyone. The solution I came up with at the time was to have a rudimentary chat bot connect parts of conversations intelligently. Now, of course just throw an AI at it. A well designed website with different conversations going on in different places might work almost as well.…

That's an intriguing approach (AI summaries).

I've got an intense dislike for the scrum-of-scrum approach. If you've ever happened to read A Fire Upon The Deep there's a cool alien species in there that has, essentially, a configurable brain topology. Interesting musings there on how those configurations modify their thinking.

Re: Which hypercube unfoldings tile space?

#33

Post by sethhovestol »

tizzdogg wrote: post #29

If all 261 unfoldings tile space, it makes me wonder if all arbitrary collections of 8 connected cubes do as well. Is there an example of 8 cubes that are proven to not tile space?

I think a ring of cubes wouldn't:

    xxx
    x x
    xxx
To fill the hole they'd need to interlock, and I think that might make it too hard to tile

Re: Which hypercube unfoldings tile space?

#34

Post by pontifier »

flir wrote: post #32
pontifier wrote: post #31

Earlier quoted context omitted.

I knew it had to be this. Number of edges in complete graph of order n, K_n. https://oeis.org/A000217 There's no way for everyone to talk to everyone. The solution I came up with at the time was to have a rudimentary chat bot connect parts of conversations intelligently. Now, of course just throw an AI at it. A well designed website with different conversations going on in different places might work almost as well.…

That's an intriguing approach (AI summaries). I've got an intense dislike for the scrum-of-scrum approach. If you've ever happened to read A Fire Upon The Deep there's a cool alien species in there that has, essentially, a configurable brain topology. Interesting musings there on how those configurations modify their thinking.

I enjoy Vernor Vinge's books. Intelligence augmentation plays a role in many of his books and short stories.

I have recently become aware that the brain topology of the Tines may be more similar to our own than I thought.

A brain structure mediates the communication between our hemispheres, but just like individuals in a Tine pack, they process things independently and contribute their specific value to the whole. I think it is possible that they even have their own personalities and moods.

People having a conversation use language to collaboratively create shared meaning between all the lobes available to them.

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