The Shattering and the Dawnshards (a geometric model)

[Kenzal Hunter he/him]

I just realized what has been bugging me about all the Dawnshard's use in the shattering (such as the multi-cut theories).

The issues is one of dimension. Most theories are shown with a circle representing Adonalsium, then divided into 16 pieces like trying to split pizza for a large group. And yes, if there are only 4 "knives" each would have to make 2 cuts.

But, Adonalsium (or Adonalsium's power) isn't a circle, so let's see how a sphere would work:

A sphere (3 physical dimensions) would take a minimum of 3 cuts through the center at right-angles to all previous cuts in oder to get 8 equally sized parts. But going beyond 8 parts to 16 requires 5 cuts (just as annoying as 3 when there are 4 Dawnshards)

However! A hypersphere (4 physical dimensions) would require exactly 4 "cuts" (divisions might be a better word, and its extra weird because those "cuts" are technically a 3-d cell instead of a line) to give 16 equal 4-D objects.

Now, as explained by someone somewhere, I can't remember which book or character, each shard is both bounded and infinite - they have their domain, but infinite power within it.

This is because Adonalsium is/was at least partially infinite. (Going back to the circle division example, if you start from the center you will never reach the crust, the pizza just goes on forever). An infinite thing may still be divided (8 slices of infinite pizza, congratulations, you can now share).

So, if Adonalsium can be represented as a four dimensional hyperplane (the location where all four dimensional objects can be represented - like a square (2-D object) can be represented within a plane), then, with exactly 4 "cuts" you get 16 4-D Orthants/Regions/Shards - each one infinite and bounded.

Continue with the geometry: this would mean that each shard can divide the other shards by how "close" they are:

• 4 direct neighbors (sharing a 3-D boundary/cell)
• 6 near neighbors (sharing a plane/side)
• 4 distant neighbors (sharing only an edge/line)
• 1 opposite (sharing only the center vertex/point)

It also means that each shard was "cut" evenly by each dawnshard. (Each shard has exactly one boundary by each of the four distinct cuts).

This is all pure geometry and geometric representation, and figures in neither Dawnshard Commands nor Shardic Intent.

Not sure what exactly that means for theorycraft, but it’s something to noodle on.

[PanLin they/he]

Ooh, this is interesting! I think I'd have to see a proposed model of the Shards before getting fully on board and abandoning my Intent-led thinking, but I am a big fan of the 4D geometry.

Would you expect the Dawnshards to have had less individual influence over the creation of the Shards than most theories assume, then? As each Shard has four 'edges' (technically 4D hyperplanes, but 'edges' makes my brain hurt less), one for each Dawnshard?

 

[Kenzal Hunter he/him]

Addendum: Multi-Shard Vessel Implications:

This geometry also plays into what shards may be combined and how strong that combination is.

Look at the neighbors each shard has. Direct neighbors can likely be easily combined and working with two shards gets progressively more difficult the less the shards share, with those who only share an edge being extremely difficult as the connection is flimsy. 

Holding truly opposite shards (by this model, not by Intent) would either the most difficult or the easiest, with no middle ground. And before any says something about Ruin and Preservation. They are treated as opposites, but I think they are at most "distant neighbors" sharing an edge. They have too much in common to be true opposites, the least of which being that they are both physically aligned shards. 

 

24 minutes ago, PanLin said:

Ooh, this is interesting! I think I'd have to see a proposed model of the Shards before getting fully on board and abandoning my Intent-led thinking, but I am a big fan of the 4D geometry.

Would you expect the Dawnshards to have had less individual influence over the creation of the Shards than most theories assume, then? As each Shard has four 'edges' (technically 4D hyperplanes, but 'edges' makes my brain hurt less), one for each Dawnshard?

 

 

Yes, each Shard would have a boundary (this is much cleaner than "edge") from each Dawnshard that defines (or bounds) it.

Much like the infinite set of all positive numbers is a bound infinite subset of all real numbers.

Each "cut"/boundary _could_ create a dichotomy (push vs pull), but doesn't necessarily have to (and having 3 Realms instead of 2 or 4 does make some true dichotomies difficult in Cosmere theorycraft)

Edited April 14 by Kenzal Hunter

[Kenzal Hunter he/him]

Addendum 2: The Divisions

I have been struggling to figure out what each division is doing. Each division bisects [the power of] Adonalsium along some axis. Seeing a bitmap someone made wasn't sitting quite right. Such division/bounds are not generally 1/0, true/false, yes/no. That implies that one half has some property and the other half lacks it.

My cousin Michael gave me some of his musings on this and I realized what each cut/division is doing: each division by a Dawnshard divides the power into push (positive) and pull (negative) along some axis (with each of the four axes being perpendicular to the others).

This also plays into how dimensional coordinates are written (positive and negative on each axis).

So, the four dawnshard divided the power into push and pull along four different axes—each shard has a distinct bounding "signature" of four push/pull dichotomies.

The Commands of the dawnshards likely determined each Axis, but I don't know what the axis would be for each.

[Through the Living Potato He/Him]

I don’t know why, but I feel the need to say: 

I believe we have a WOB (sorry, I can’t do citations) that says one Dawnshard was different from the others. In this context I would think it could mean making multiple cuts or no cuts at all. I don’t know.