[tcaudilllg]

I've been studying Einstein's General Relativity theory, specifically the mathematical end of it. Although I have pretty good grasp on the conceptual end of it, I'm still working on the details. Still, I have learned much about how it works, and how it can be modeled in programming.

"GR" as it is called by physics enthusiasts, is built around the concept of "tensors". To imagine what a "tensor" is, first consider the "vector", which we in programming call a one-dimensional array. A tensor is basically a grouping of vectors (think multi-dimensional array) whose values are all the result of some kind of function. The value of every index in a "tensor" must be calculated this way.

Tensors, like arrays, have dimension. The number of dimensions in a tensor is called its "rank". So for example, a tensor who's dimensions are "<1,2,3>" (where "<" and ">" correspond to "[" and "]" in the C language) has a rank of 3, and is referred to as a rank 3 tensor. Once again, the difference between a tensor and a vector/matrix is that the vector/matrix's values can be arbitrary. A tensor's values MUST be the result of some kind of function.

General Relativity works by assigning a rank 4 tensor of four elements per rank (<4,4,4,4>) to every point in space. These elements each correspond to a possible state that that space could exist as, variously charged, warped, magnetized, or even charged AND warped AND magnetized all at once.

To idealize what this effect is, think of a tile map. Each tile on the map has its own properties: obstruction, impedence (if we want to slow the player down when they cross), rules for interaction with the player when the player attempts to cross over it, maybe even an alpha channel overlay effect. (say, a red transparency of 25% opacity) Each of these properties, in the context of the game engine, exerts a function on the game world whose magnitude and nature is dependent upon the value assigned to the property. This is what point tensors do: depending on the value of the tensor's elements, corresponding functions are exerted in space whose effects are proportional to the values of their corresponding elements.

There is more to tensors, but I can't claim to understand it all now. More to come as I learn of it.

[Bjorn]

So how exactly is it useful to think of a tile map in terms of a tensor? Or are you just using a tile map as an example to explain what a tensor is? There's a lot to be read about tensors on for example Wikipedia, and I'm sure it's very interesting to some people, but I just fail to see its relevance in designing and programming of independent RPGs.

[tcaudilllg]

Yes, I neglected to link to Wikipedia at the appropriate points. Thank you for that note Bjorn. :)

The relationship of tensors to RPGs, is the very notion that by attributing functions to points, a world may be built completely of its own justification. This was the greatness of Einstein's contribution. He used tensors, through GR, to emphasize that upon the simple premise of attributing functions to points, an entire cosmos may be constructed that is incontrovertibly true in itself. The entire world modeled in an equation: this is what he is famous for.

The legacy of tensors to RPGs, and to virtual worlds in general, is that through simple mechanics, fantastic effects may be generated not only visually, but physically. Using tensors, it is possible to generate a world where black holes and white holes exist, wormholes and even transdimensional portals. This concept is unheard of even in the highest ranks of professional gaming; much simpler, Newtonian-based modeling is used instead. Final Fantasy VII, for example, has fantastic effects, but all of them are merely scripted arrangements of imagined images and movements.

What I'm saying is, tensors as a method of controlling phenoma are simple to apply, and limited only by the imagination and CPU speed in what they can acheive. They are the next great frontier for RPGs and games in general. This point alone was the tenant of my post; however, as my mind continues to examine the possibilities, new horizons are taking shape that may make it easier to connect events in RPGs to each other. For example, using a tensor, the same data that controls the degree to which a marsh tile causes poison may also determine the degree to which the marsh is overlayed with green.

What do you think?

[LeoDraco]

[bay]

i think it's better to say that tensors, like other methods, can be used to create a dynamic game world. it's not to say that tensors may be "better", as that is just an opinion. however, once written into a game engine, tensors could become a very useful tool.

i encourage the usage of new and/or forgotten techniques and/or the applications of knowledge in one domain into the other. with that said, i hope to see (in code) an application of tensors for RPG map generation from LG.

.02$
_________________
INTJ

[tcaudilllg]

[LeoDraco]

[tcaudilllg]

I think we're having a misunderstanding over what I was meaning by "tensor-based". I didn't mean procedurally generated; what I meant was, making some events dependent on others through physical means, as opposed to script. I didn't mean to imply random generation of data as a function of tensors, although it certainly is.

What came to me last night, was the idea of representing say, a magic field by permeating the map with the property. This would imply that position is as important in the casting of magic as the caster's own skill, adding a dimension to the gameplay.

[LeoDraco]

[tcaudilllg]

[LeoDraco]

[bay]

[tcaudilllg]

[janus]

[LeoDraco]