sDNA and geometry nets

[Ripheus23]

So a net in geometry is a set of contiguous n - 1-dimensional facets that, if all folded together in the right (simple) way, give a simple n-dimensional structure. So, like, a cube's net is six squares arranged like a crucifix.

Now I'd been going off a visual of Spiritwebs as like graphs, and granted you could get some kind of a graph out of a net (in abstract-enough theory), but a net gives us a more DNA-y gloss of a Spiritweb, in the sense that calling it "sDNA" gives off a vibe like, "It's a simple structure that unfolds into something more elaborate-looking." So, my quasi-theory of sDNA is that Spiritwebs are higher-dimensional simple shapes that are compacted such that if viewed in Physical/Cognitive frames of reference, they unfold out into "nets" for the Physical/Cognitive objects.

For the 600-cell:

The 600-cell decomposes to some degree into these things: 

DNA is a double-helix so if you can map helices into some of these fancy higher-dimensional shapes...

(The only story value this would have, besides relating to Pattern's head and suchlike, is that if Spiritwebs "look like" these things, then Splintering/Shattering has a decent chance of "looking like" a crystal breaking into pieces, just in a higher dimension.)

[Zelly]

*attempts to read*   O_O   *sets down wineglass and tries again* 

You know, disclaimer, I'm probably not the first person you want to respond to this. Sincere apologies.

35 minutes ago, Ripheus23 said:

So a net in geometry is a set of contiguous n - 1-dimensional facets that, if all folded together in the right (simple) way, give a simple n-dimensional structure.

........uhh......

35 minutes ago, Ripheus23 said:

So, like, a cube's net is six squares arranged like a crucifix.

Oh, ok got ya now.   *nods nods*

39 minutes ago, Ripheus23 said:

Now I'd been going off a visual of Spiritwebs as like graphs, and granted you could get some kind of a graph out of a net (in abstract-enough theory), but a net gives us a more DNA-y gloss of a Spiritweb, in the sense that calling it "sDNA" gives off a vibe like, "It's a simple structure that unfolds into something more elaborate-looking."

Graphs like......what kind of graphs?  I mentally view them as spider webby, which I can compare easily to the mesh of a net....

Are you talking about DNA as a double helix?  In which case, wouldn't it be a simple structure (2 strands) that folds up into something more elaborate looking (d-helix)? Instead of unfolding?

51 minutes ago, Ripheus23 said:

So, my quasi-theory of sDNA is that Spiritwebs are higher-dimensional simple shapes that are compacted such that if viewed in Physical/Cognitive frames of reference, they unfold out into "nets" for the Physical/Cognitive objects.

So we're like, "Ah it's a triangle" but in fact it's like a super complex 3D pyramid thing.  Which would actually fit what how we're not really able to view or understand the Spiritual Realm.  Characters peek at it, but it has to be warped to make sense to human thinking.

52 minutes ago, Ripheus23 said:

For the 600-cell:

I have no idea what this is, so I looked it up on Wikipedia.  I still have no idea what this is.  It's very pretty though.

56 minutes ago, Ripheus23 said:

DNA is a double-helix so if you can map helices into some of these fancy higher-dimensional shapes...

(The only story value this would have, besides relating to Pattern's head and suchlike, is that if Spiritwebs "look like" these things, then Splintering/Shattering has a decent chance of "looking like" a crystal breaking into pieces, just in a higher dimension.)

While this math is all very much over my head, I admit I'm curious if perhaps there is a magical way for a facet of something to represent ALL facets of said thing.  So perhaps what is done to one is reflected in all the other facets.

[+Hoiditthroughthegrapevine]

I will edit this post in detail more, but I was just watching a pretty amazing podcast about n-dimensional polytopes. It's a Numberphile podcast with Mathematician Carlo Sequin talking about Perfect Shapes in Higher Dimensions (spoilered below):

Spoiler

 

At about 14 minutes in he talks about the 600 cell, which is a 5-Dimensional tetrahedra. Pretty rad stuff.

10 hours ago, Ripheus23 said:

So, like, a cube's net is six squares arranged like a crucifix.

This is a tesseract, a 3 dimensional unfolded 4 dimensional solid. Just like you can unfold a 3 dimensional cube into a 2 dimensional shape (basically 6 squares with shared edges, in the shape of a cross), you can unfold a 4 dimensional shape into a three dimensional shape with shared edges. There's a great story by Robert Heinlein, House on a Crooked Hill, about a house built in the shape of a tesseract. After all of the cuboid rooms are built, there's an earthquake and all of the cubes fold in on themselves to make a 4 dimensional hypercube. Pretty awesome story.

10 hours ago, Ripheus23 said:

So, my quasi-theory of sDNA is that Spiritwebs are higher-dimensional simple shapes that are compacted such that if viewed in Physical/Cognitive frames of reference, they unfold out into "nets" for the Physical/Cognitive objects.

Interesting. I think you may be onto something, but I don't think we have enough information to say for sure. There are some variations of string theory that posit up to 26 dimensions, and the string's themselves are one-dimensional constructs that exist in n-dimensional space. Some of the big mysteries of Quantum mechanics could potentially be explained by strings existing in an entangled state in n-dimensional space, some of the things we percieve (like quantum entanglement) as "spooky action" could be simple translations of force through a linkage in a dimension that we can't percieve.

I really don't have a ton more to add to this, but I am interested to see what else you come up with. Your posts @Ripheus23 are always interesting to read.

Edited January 18, 2019 by hoiditthroughthegrapevine