Hidden Things in Map of Roshar?

[Argent]

Pfft. Heretics. The Stick permits you to try this thing, for It is all-loving, but it is futile and you will eventually come back into its Fold Stack.

 

Also, I should mention that Julia was a dude - this is his last name. The first one is Gaston, Gaston Julia.

[Aether]

I vote for naming the Rosharan super-continent "Gaston".

[Shardbearer]

Now I have the theme song of Beauty and the Beast running through my head. Thanks for that.

 

Bonjour.

[Ryshadium]

No one's crem's as incredibly thick as Gaston...

[Veil]

Hey, I thought of it at the same time, you just beat me to posting

 

I'm down for naming Roshar-Greatshell Julia!  Do you think she's riding on the back of four giant elephants too?

 

Should I update the first post with all of the Easter Eggs?  (And what are they all?)

 

I did a summary of the whole thread a few pages back. (Here.) We don't necessarily need the ongoing or discarded theories anymore, but I also gathered up the observations people might find interesting.

[RShara]

I updated the first post.  Thanks!

Someone should ask Brandon or Peter how many hidden things are in the map(s) total, so we can make sure we got all of them

Edited April 22, 2014 by RShara

[Youngy]

Here's what I consider a pretty simple explanation of the Julia set.

That's actually a really good way of putting it. Simple, and straight to the point. 

Only difference between the above, and the one that was used is that it was done in four dimensions rather than two. And Brandon has just taken a 2D slice out of that 4D image to make Roshar.

I was (and still am) probably going about this the wrong way - trying to find out if there is any relevance to do with this particular Julia Set to Roshar. (Was hoping the origin in the time lapse sequence would end up at Urithru amongst other things. But it seems to be just a really good looking set that they found.

 

Interestingly, the creator of the code for that particular set had an alternative z₀ commented out - which if he had used instead of the existing one, Roshar may have looked like the one below.

Anyway, enjoy!

 

Edited April 23, 2014 by Youngy

[Shaggai]

That's actually a really good way of putting it. Simple, and straight to the point. 

Only difference between the above, and the one that was used is that it was done in four dimensions rather than two. And Brandon has just taken a 2D slice out of that 4D image to make Roshar.

I was (and still am) probably going about this the wrong way - trying to find out if there is any relevance to do with this particular Julia Set to Roshar. (Was hoping the origin in the time lapse sequence would end up at Urithru amongst other things. But it seems to be just a really good looking set that they found.

 

Interestingly, the creator of the code for that particular set had an alternative z₀ commented out - which if he had used instead of the existing one, Roshar may have looked like the one below.

Anyway, enjoy!

Nope. Not a 2d slice of a 4d object. A 2d "shadow" of a 3d slice of a 4d object. Which means that either the designer was really into weird, complex, and heavily abstracted math, or insane. Edited April 23, 2014 by Shaggai

[Youngy]

Nope. Not a 2d slice of a 4d object. A 2d "shadow" of a 3d slice of a 4d object. Which means that either the designer was really into weird, complex, and heavily abstracted math, or insane.

 

Ooops. I must have misread the code then.

I was pretty certain it projected the intersection between the 4d object and the 3d plane onto 3d space.

This is what happens when I sit up to silly hours of the morning playing with maths...

[Shaggai]

Ooops. I must have misread the code then.

I was pretty certain it projected the intersection between the 4d object and the 3d plane onto 3d space.

This is what happens when I sit up to silly hours of the morning playing with maths...

The animation projects the intersection into 3d space. Roshar, however, is in effect 2d. Since it's shaped like a view of the 3d cross-section, it's a 2d "shadow" of the 3d section.

[Ryshadium]

It's like a foreign language up in here.

[Delightful]

Here's what I consider a pretty simple explanation of the Julia set.

 

Take a mathematical function f(x). Choose a random number x₀, from the domain of that function. Find out what f(x₀) is (let's say f(x₀) = x₁), then feed it back into f. Find out what f(x₁) is. Feed that back into f to get x₂. Repeat to infinity for all possible initial numbers x₀. All the original numbers, or seeds, that give you a sequence x₀, x₁, x₂, x₃, ... of fairly similar numbers are something we'll call "prisoner set of f;" all the seeds that give you erratic sequences x₀, x₁, x₂, x₃, ... will be the "escapee set of f." Well, the Julia set of the function f is the set of those seeds that form the border between the prisoner set and the escapee set.

 

Here, let me edit with an example.

 

---

John Carroll University has a really nice vignette on Julia sets, so I am going to use their example - it's clear enough and it saves me some work.

 

Let's take our function to be f(x) = x² - 0.5. We now need to look at all the possible x₀ we could feed into this function - which, in this case, means all (real and imaginary!) numbers. To illustrate the prisoner and escapee sets, however, we'll only look at a couple of numbers.

 

If we take x₀ = 0 (0 is always nice, makes math easy), we get the following sequence x₀, x₁, x₂, x₃, ... :

x₀ = 0

x₁ = f(x₀) = f(0) = - 0.5

x₂ = f(x₁) = f(-0.5) = - 0.75

x₃ = f(x₂) = f(-0.75) = 0.0625

...

If we continue this, we'll see that the numbers we get never move too far away from the original x₀ = 0. This means 0 is part of our prisoner set.

 

Now, we take a different x₀, let's say 2. Do the same thing:

x₀ = 2

x₁ = f(x₀) = f(2) = 3.5

x₂ = f(x₁) = f(3.5) = 11.75

x₃ = f(x₂) = f(11.75) = 137.563

...

Unlike the case where x₀ = 0, here it's easy to see that the numbers will continue growing (exponentially). This kind of behavior means x₀ = 2 is a part of the escapee set of f. It's also easy to see that any number greater than 2 will also be a part of the escapee set, by the way.

 

Now all you need to do is repeat the same thing for all the numbers (keep in mind, the example I gave doesn't even touch the imaginary numbers / components), plot them, see which one(s) form a boundary between prisoner and escapee sets, and voilà - Julia set!

 

If you are curious, here's how the Julia set of our example function looks like:

 

 

Thank you! This is awesome!

 

[Aether]

It seems like everyone here has written this off as "solved", but have we really? We've found the inspiration behind the shape of the continent, but it hasn't really told us anything about "the history of Roshar", as per the WoB:

Q: Can you give me a hint in the easter egg in the map of Roshar? What particular skill do you need for it? Is it a different language or math related?

A: It's not linguistics. It is math related. Let me remind you this is not going to be a mind blowing revelation. It is going to be a nifty thing. Someone actually got close at one of my signings. They noticed something. But it is a fun easter egg that will tell you more about the history of the world.
<source>

Edited April 23, 2014 by Aether

[Delightful]

It seems like everyone here has written this off as "solved", but have we really? We've found the inspiration behind the shape of the continent, but it hasn't really told us anything about "the history of Roshar", as per the WoB:

I thought the 'history' bit was 'how the geography formed in the past.'

[Youngy]

Thanks, yeah, that was a derp.

For what it's worth I couldn't find any natural occurrence of that kind of set... Not that I looked incredibly hard.

What do you mean by that Delightful?

As in what shape it formed into originally before all the Crem built up?

Or as in, it has slowly been created as per the animation? (And once it was just a square kilometre of land, where Honour and Odiums forces duked it out, and one day the entire land mass will collapse back to nothing)

Or Adonalism got lazy and used a maths equation in four dimensions to create his land mass (The gods must be crazy)

[Delightful]

Thanks, yeah, that was a derp.

For what it's worth I couldn't find any natural occurrence of that kind of set... Not that I looked incredibly hard.

What do you mean by that Delightful?

As in what shape it formed into originally before all the Crem built up?

Or as in, it has slowly been created as per the animation? (And once it was just a square kilometre of land, where Honour and Odiums forces duked it out, and one day the entire land mass will collapse back to nothing)

Or Adonalism got lazy and used a maths equation in four dimensions to create his land mass (The gods must be crazy)

Crem build up, I think. But this isn't exactly my area of expertise. I just remember someone saying that a few pages back.

 

[Sabrina Stormshard]

well this particular julia set is of the quaternions - 1 and the 3 imaginary numbers i, j, k so maybe it has something to do with that?

 

When I get a chance I'll work out what the bisecting plane is that produces the roshar image

[Argent]

I don't know all the terms here, but is "shadow" perhaps the wrong word?

 

"Projection" is the mathematical term - if I've followed the conversation. I am thinking vectors, but it should apply to shapes as well. In the example below, we take an object in 2D space (the vector v₂), and then project it onto all the 1D spaces (lines / dimensions) it spans. Now, in the case of project 2D objects onto (two) 1D spaces, anything you start with will end up turning into a boring couple of lines, one in each direction.

 

 

If you start with a 3D object, however, you will need to project it onto three (not two) planes (not lines), and each projection is going to be a 2D shape (not a 1D line). So I think it checks out. You start with a Julia set in 4D, cut it and take a 3D slice from it (because that's how slices work), and then project that 3D slice onto a 2D plane, a flat surface - say, a sheet of paper used by mapmakers. 

 

It's damnation near impossible to find a good image of a 3D object and its 2D projections, but you can easily visualize it if you imagine any 3D object (for some reason I always think of a sphere), place it in a room (imagine just a corner, one with a floor and the two adjacent walls), and then throw the object really hard at each one of the walls so it gets completely flattened - those flat images are the different projects (which, for a sphere, are all circles; if you started with a cylinder, you should see two rectangles and a circle, and so on).

Edited April 23, 2014 by Argent

[Ryshadium]

I used to think I was ok at math, and then I joined the 17th Shard. 

[Shaggai]

I don't know all the terms here, but is "shadow" perhaps the wrong word? A shadow is the image that falls on a plane, but in 3d graphics, the image is from the perspective of a point considered the camera. I don't think we'd be able to perceive depth in the animation if it were a shadow. Wikipedia has this under ray tracing:

http://en.wikipedia.org/wiki/File:Ray_trace_diagram.svg

(which I can't include as an image, because the forum thinks SVG is evil)

I can't think of a better term than "image". Is there one?

You can't perceive depth in an image of Roshar, can you? Although Argent is right, projection is a better term. I'll use that from now on.

[Standfast]

Forgive me if I've missed this elsewhere, but if Roshar is only a continent on a globe, what's on the rest of the globe? I'd be grateful if someone would point me to where this is discussed.

[Shaggai]

Forgive me if I've missed this elsewhere, but if Roshar is only a continent on a globe, what's on the rest of the globe? I'd be grateful if someone would point me to where this is discussed.

Ocean, for the most part. It's been confirmed that the Rosharan supercontinent is the only major landmass.

[kaellok]

Is it possible that the shape of Roshar changes with each Desolation?  The map from WoK says it's from the Silver Kingdoms Epoch, but I couldn't easily find any information on exactly when that is.  The Coppermind wiki says during the Heraldic Epochs, but the references it listed didn't mention that at all.  Also, I couldn't remember any specific information regarding it.  The Silver Kingdoms could just as easily have been the time period when the Radiants ruled after the Heralds left, right?  (Or am I forgetting/missing something yet again?)

 

Somewhat curious about this because the names 'prisoner' and 'escapee' sets make me think of the Heralds being held prisoner and being tortured over and over until the break or escape.  Probably a stretch, and I tried looking into it myself, but discovered that I'm well out of my depth on this hah.

[Argent]

Those are not the mathematical terms, just mine (well, the university's) words that make imagining what's going on easier.

[happyman]

Those are not the mathematical terms, just mine (well, the university's) words that make imagining what's going on easier.

 

My guess is that projection is the right term.  The term shadow is a good intuitive term, but is only equivalent to a projection if the "light source" is much further away from the object than both the distance to the plane on which it is being projected and the original object itself.  You could say that a projection is a shadow only if the light source is infinitely far away.