On the primary components of the intent space

[Maximus]

Forgive me if this rambles a bit. I wrote it between classes and figured I'd throw it out and let people comment on it before threshing it out.

 

So I've been gone from this place for a few months, and upon my return I discovered that the Map of Roshar Question has been solved. That it is a rendering of a 3-dimentional projection of a 4-dimentional object. I also noted that Brandon had specifically requested this shape, and I had to ask myself, " what was the reason for that? Did he just like the shape or was there a deeper meaning?"

 

This being the 17th shard, there is always a deeper meaning. So I betook myself to linking fancy unto fancy thinking what Brandon could have intended by this? It is most likely a clue, but a clue about what? Fractals? or 4-dimensional shapes? And this connected to an idea I had had some time ago.

 

Let's say you had a 4-dimensional entity. Let's call this entity, oh, Figgledygrak, or something. Lets say it is a hypersphere, nicely balanced in all directions. Now you split it in half, you have two hemihyperspheres(!). These two pieces represent opposite halves of the space-- left-right, top-bottom etc. In 4-dimensions, if you split it accross all orthogonal axes you get 16 such pieces. If this space represents intent, you now have 16 pieces with varying degrees of opposing intent. You may see where this is going.

 

[short version]

Adonalsium was a being of 4-dimensional intent before it was shattered. The 16 shards each represent some combination of polarities of these dimensions.

[/short version]

 

If you accept this hypothesis, and I recognize its tenuity, then one question that springs to mind is, what might the axes be? We have some description and names for I think 8 of the 16 shards. We have some information. Odium seems opposed to all the shards we've seen so far. Honour and Cultivation seem less opposed. I'm not sure where Dominion and Devotion would fit. Preservation and ruin were obviously opposed. At the same time, they were enough alike to create a world together. One could hardly imagine Odium creating a world. To me, Odium represents the "negative" side of all the dimentions, Ruin is more negative than Preservation, Dominion is more negative than Devotion. If there's a pure opposite to Odium I'm not sure we've seen it. Devotion maybe?

 

[Curiosity]

I really like this theory. The origin seems a little bit... far-fetched, but then again, we are the 17th Shard. 

 

However there is this WoB:

 

 

CHAOS

Are Shards all paired? Does Endowment have a counterpart?

BRANDON SANDERSON

RAFO. Also, yes and no. Not all Shards have perfect counterparts like Ruin and Preservation.

QUESTION

Why were Ruin and Preservation linked together?

BRANDON SANDERSON

Because they're such perfect opposites. Basically it's just an opposites attract thing.

 

All of the Shards may have approximate counterparts, but they are most likely split up by Spiritual Ideals (complete guess on my part) but the four-dimension thing doesn't seem to have an exact correlation. 

[Kurkistan]

Huh. I had not known that we'd solved the map problem.

[killersquirrel59]

I like this idea but I don't know if I'm entirely convinced. 4 dimensional physics doesn't really cover Realmatic theory too well. 

[Maximus]

I'm not talking about 4-dimensional physics. It's a 4-dimensional concept space. In this case, an intent space.

[Maximus]

The WB above does put a kink in it though. Hmmm...

[Fallen Rope]

Preservation and Ruin could be the only two shards at opposite polls, with the other shards in a regular pattern that has no other opposites. I think the Ruin Preservation axis is a change/adding axis. Honour and Endowment are on the adding side. Odium and cultivation are on the change side. I think Dominion and Devotion are neutral on this axis.

[Maximus]

Preservation and Ruin could be the only two shards at opposite polls, with the other shards in a regular pattern that has no other opposites. I think the Ruin Preservation axis is a change/adding axis. Honour and Endowment are on the adding side. Odium and cultivation are on the change side. I think Dominion and Devotion are neutral on this axis.

This is very much the kind of thing I was thinking. However, if most of them do not have exact opposites, if some are neutral and some are stronger on an axis than another then it means there could well be more than four dimensions,

 

Or fewer.

 

Maybe there are pi dimensions

[Fallen Rope]

Another axis could be how shards effect things, Endowment is improving things. Cultivation is helping things grow so they improve themselves.

Devotion is on Endowments side. Honor is on Cultivations side. Dominion, Preservation, Ruin and Odium are fairly neutral.

[Seonid]

It is very possible that there are more axes than 4 in the Intent space. Brandon has said that Adonalsium could have shattered in such a way as to result in different Shards. It is highly unlikely that such an arrangement would correspond neatly to a re-arrangement of the current Shattering results.

 

So any given Shattering likely exists in a 4-dimensional Intent space as a subset of a higher dimensionality that corresponded to the whole of Adonalsium. Whatever operator resulted in the Shattering had the effect of contracting the dimensionality. (Alternatively, Intent-space is inherently 4-dimensional, and different Shattering results end up with Shards that have different component vectors, but exist in the same space, but I like a higher-dimensionality space better.)

 

Let us, however, try the following thought experiment.

 

Let x, y, x, and w be the basis vectors of the Intent space. Let them be mutually orthonormal, linear, and let them span the space. (We could also assume an inner product, if you like, and that the space is complete. That makes the space much easier to deal with. And it is possible that the operators related to inner and outer products might reflect different Shardic interactions. Bless you Brandon, if this can actually be expressed mathematically.)

 

Then the Intents corresponding to the Shards can all be expressed by a 4-vector in Intent space, which can be expressed in terms of the basis vectors.

 

(Thus far, I think that I haven't said anything new. Now for my additions.)

 

The objection has been raised that the Shards do not exist in terms of paired opposites. This is only a problem if we assume that the axes correspond to the Shards themselves. If, instead, they correspond to attributes that Shards may possess, then the problem disappears, as there is nor requirement that the Shards exist on opposite ends of axes. For example, if one axis is change vs. stasis and another is giving vs. taking (or retaining), then Preservation might have a large component in the direction of the stasis axis as well as a (smaller) component in the direction of the giving axis. Ruin would be opposite on the change/stasis axis but similar in component on the giving/taking axis. Odium might have a small component in the direction of change and a large component in the direction of taking/retaining). Endowment could be near 0 on the change/stasis axis but have a large giving component. And so on.

 

And that says nothing of the other axes. There are a lot of potential configurations of the Shards and axes here. This needs more investigation.

 

Sorry. This was all just stream of consciousness stuff. I'll come back after my class and see if I can clean it up and make it more formal/rigorous.

[Moogle]

Another axis could be how shards effect things, Endowment is improving things. Cultivation is helping things grow so they improve themselves.

Devotion is on Endowments side. Honor is on Cultivations side. Dominion, Preservation, Ruin and Odium are fairly neutral.

 

Cultivation is most compatible with Ruin, actually. I don't think Cultivation is about improvement so much as change and growth. Kind of a subtle distinction, but I definitely wouldn't say Cultivation is about improvement.

 

WoB:

Nepene

I have a question, if you are willing. Would Ruin be more compatible with Rayse, would he pick up that shard had he visited Scadrial and shattered him? All the shards we have seen that he has shattered seem rather different in intent than him—Honor, Cultivation, Love, Dominion. But Ruin seems more in line with Odium. Rayse has ruined the days of quite a few people.

Brandon Sanderson

Technically, Ruin would be most compatible with Cultivation. Ruin's 'theme' so to speak is that all things must age and pass. An embodiment of entropy. That power, separated from the whole and being held by a person who did not have the willpower to resist its transformation of him, led to something very dangerous. But it was not evil. None of the sixteen technically are, though you may have read that Hoid has specific beef with Rayse. Whether you think of Odium as evil depends upon how much you agree with Hoid's particular view.

That said, Ruin would have been one of the 'safer' of the sixteen for Rayse to take, if he'd been about that. Odium is by its nature selfish, however, and the combination of it and Rayse makes for an entity that fears an additional power would destroy it and make it into something else.

(source)

Edited September 29, 2014 by Moogle

[Maximus]

It is very possible that there are more axes than 4 in the Intent space. Brandon has said that Adonalsium could have shattered in such a way as to result in different Shards. It is highly unlikely that such an arrangement would correspond neatly to a re-arrangement of the current Shattering results.

 

So any given Shattering likely exists in a 4-dimensional Intent space as a subset of a higher dimensionality that corresponded to the whole of Adonalsium. Whatever operator resulted in the Shattering had the effect of contracting the dimensionality. (Alternatively, Intent-space is inherently 4-dimensional, and different Shattering results end up with Shards that have different component vectors, but exist in the same space, but I like a higher-dimensionality space better.)

 

Let us, however, try the following thought experiment.

 

Let x, y, x, and w be the basis vectors of the Intent space. Let them be mutually orthonormal, linear, and let them span the space. (We could also assume an inner product, if you like, and that the space is complete. That makes the space much easier to deal with. And it is possible that the operators related to inner and outer products might reflect different Shardic interactions. Bless you Brandon, if this can actually be expressed mathematically.)

 

Then the Intents corresponding to the Shards can all be expressed by a 4-vector in Intent space, which can be expressed in terms of the basis vectors.

 

(Thus far, I think that I haven't said anything new. Now for my additions.)

 

The objection has been raised that the Shards do not exist in terms of paired opposites. This is only a problem if we assume that the axes correspond to the Shards themselves. If, instead, they correspond to attributes that Shards may possess, then the problem disappears, as there is nor requirement that the Shards exist on opposite ends of axes. For example, if one axis is change vs. stasis and another is giving vs. taking (or retaining), then Preservation might have a large component in the direction of the stasis axis as well as a (smaller) component in the direction of the giving axis. Ruin would be opposite on the change/stasis axis but similar in component on the giving/taking axis. Odium might have a small component in the direction of change and a large component in the direction of taking/retaining). Endowment could be near 0 on the change/stasis axis but have a large giving component. And so on.

 

And that says nothing of the other axes. There are a lot of potential configurations of the Shards and axes here. This needs more investigation.

 

Sorry. This was all just stream of consciousness stuff. I'll come back after my class and see if I can clean it up and make it more formal/rigorous.

Yes. I was assuming a binary space, a hypercube if you will; I didn't explain that very well. If we assume an infinite-valued space then your ideas work. However then we have no particular reason to believe that the space is 4-dimentional as opposed to, say, 7-dimensional, and it's a lot harder to determine what the axes might be.

[Fallen Rope]

I agree about Ruin and Cultivation. They are both same/similar on the change stasis axis. The opposite of change can't be decay because Cultivation and Ruin would become too different. Ruin might even have a bit of growth as he said that Ruin is needed for life.

I think the opposite of grow could be Endowment type improvement. Growth is giving it what it needs to improve by itself, the other is just improving it.

[kaellok]

 

The objection has been raised that the Shards do not exist in terms of paired opposites. This is only a problem if we assume that the axes correspond to the Shards themselves. If, instead, they correspond to attributes that Shards may possess, then the problem disappears, as there is nor requirement that the Shards exist on opposite ends of axes. For example, if one axis is change vs. stasis and another is giving vs. taking (or retaining), then Preservation might have a large component in the direction of the stasis axis as well as a (smaller) component in the direction of the giving axis. Ruin would be opposite on the change/stasis axis but similar in component on the giving/taking axis. Odium might have a small component in the direction of change and a large component in the direction of taking/retaining). Endowment could be near 0 on the change/stasis axis but have a large giving component. And so on.

 

I heartily agree with this in particular.  It would make a lot more sense if the axes are not paired with Shards, but rather the Intents of the Shards.  (I've done some thought experiments as to other ways Shards could have formed from Adonalsium, because it's interesting--but stopped, because it's largely a fruitless task with the limited knowledge we have.) 

 

I'm not sure that I agree with the overall theory, but if so I think it would have to be based off of the Intents/Attributes what-have-you as you've described.

[Chromium Compounder]

It is very possible that there are more axes than 4 in the Intent space. Brandon has said that Adonalsium could have shattered in such a way as to result in different Shards. It is highly unlikely that such an arrangement would correspond neatly to a re-arrangement of the current Shattering results.

 

So any given Shattering likely exists in a 4-dimensional Intent space as a subset of a higher dimensionality that corresponded to the whole of Adonalsium. Whatever operator resulted in the Shattering had the effect of contracting the dimensionality. (Alternatively, Intent-space is inherently 4-dimensional, and different Shattering results end up with Shards that have different component vectors, but exist in the same space, but I like a higher-dimensionality space better.)

 

Let us, however, try the following thought experiment.

 

Let x, y, x, and w be the basis vectors of the Intent space. Let them be mutually orthonormal, linear, and let them span the space. (We could also assume an inner product, if you like, and that the space is complete. That makes the space much easier to deal with. And it is possible that the operators related to inner and outer products might reflect different Shardic interactions. Bless you Brandon, if this can actually be expressed mathematically.)

 

Then the Intents corresponding to the Shards can all be expressed by a 4-vector in Intent space, which can be expressed in terms of the basis vectors.

 

(Thus far, I think that I haven't said anything new. Now for my additions.)

 

The objection has been raised that the Shards do not exist in terms of paired opposites. This is only a problem if we assume that the axes correspond to the Shards themselves. If, instead, they correspond to attributes that Shards may possess, then the problem disappears, as there is nor requirement that the Shards exist on opposite ends of axes. For example, if one axis is change vs. stasis and another is giving vs. taking (or retaining), then Preservation might have a large component in the direction of the stasis axis as well as a (smaller) component in the direction of the giving axis. Ruin would be opposite on the change/stasis axis but similar in component on the giving/taking axis. Odium might have a small component in the direction of change and a large component in the direction of taking/retaining). Endowment could be near 0 on the change/stasis axis but have a large giving component. And so on.

 

And that says nothing of the other axes. There are a lot of potential configurations of the Shards and axes here. This needs more investigation.

 

Sorry. This was all just stream of consciousness stuff. I'll come back after my class and see if I can clean it up and make it more formal/rigorous.

Very well put.  I've been out of college for six years, but that really reminded me of some of my upper level math classes.  And it made a lot more sense than how most of those professors talked.  Up vote for that alone, but it also makes sense to me logically and realmatically.  

 

I hereby support this theory.