FoME Thinks Too Much: Time Cylinder · 1:44pm Aug 10th, 2013
Well, after five more requests than I expected (which is to say, five requests,) here is my concept for three-dimensional time. If you have no idea where this came from, you haven't read the latest chapter of Sideboard of Harmony, and thus have only yourself to blame. 
Contrary to popular belief, time is not a cube, but a cylinder. Continuity is the first temporal dimension, the past-future axis, corresponding to the z coordinate, or height. Improbability is the second temporal dimension, the likely-unlikely axis, corresponding to the ρ (rho) coordinate, or radial distance. Subjunctivity is the third temporal dimension, the were-were not axis, corresponding to the φ (phi) coordinate, or azimuth.
The origin is the present moment. The greater the absolute value of the continuity coordinate of a point, the further in the past or future that point lies. The greater the improbability coordinate of a point, the less likely that point will lead to, follow from, or coincide with the present moment. The subjunctivity coordinate of a point has no such clean relationship, instead placing the point somewhere on the continuity of circumstance, all the myriad possible combinations of variables that could exist at any given moment in time.
The double-cone model of time, with past and future coming together in an hourglass shape with the present at the pinch, can be modeled by the equation ρ = V|z|, where V is the variability constant, a value that determines how far the timeline can skew along the improbability axis in a given period of time.
Greek letters copy-pasted from Wikipedia.
Time Tube? Or am I educated stupid?
My brain hurts.
I think this a nice way of thinking of it, I really do. Thanks for the thought-food, Foam.
Huh, that's a good way of plotting time probability curves when dealing with multiplicative time lines. And the double cone probability variance shows a reasonable event change variation chain along cause and effect vectors.
1274946
$1000 to anyone who can disprove the Time Tube!
So can we watch TimeTube?
And WOO! It's here!
Can't really argue with that.
So does this mean that all events that could happen and are equally likely to happen based on the collected variables in the universe are on a single ring with infinite thinness at Improbability of "rho prime", with Improbability ranging from 0 to +infty, Continuity ranging based on the exact moment in time from the beginning of time to the end of time, whatever values those may be, and Subjunctivity ranging from 0 to 360?
If that is the case, does it follow that Subjunctivity would, therefore, have little impact on Continuity and Improbability? Since "subjunctivity" is defined as "the relationship between something portrayed and something real", it follows that the subjunctive nature of an event is its very existence as a concept or idea (a "plot bunny", if you will). Improbability determines whether or not it actually happens, and Continuity will determine when, yes?
Additionally, is it accurate to call the plane, constructed of the range of Probabilities and Range of Subjunctivities, a Probability Space at a particular Continuity?
Also, if a timeline follows the sequence of events from one VALUE of Continuity to another VALUE of Continuity, does the line vary in both Probability and Subjunctivity, or does it only vary along Subjunctivity with a fixed probability value associated with that timeline?
1275481
I get the distinct feeling you've thought about this more than I have, and that frightens me.
1275493
Ah, well, I'm taking Aerospace Engineering, so visualizing objects moving in a two dimensional plane is something I've been doing a lot lately. In the case of planes, phi is your heading, rho is your thrust, and z is your altitude.
Anyway.
I've never really thought about time in a physics sense.
I've always just thought about it in a narrative sense. What makes the most sense for the story I'm writing, and all. And the second you start to bring out the greek letters I hold my hands up and just walk away backwards. Very slowly. My brain can't math good.
MY current model of time... the one that I apply to most of my stories, could be best described as a sphere with an infinite volume. I could explain it if you like, but there's no math or physics education involved (I could barely do basic high-school physics), and it probably would seem laughable to anyone at all educated in that area.
1276316
So, you would say your model of time is more a big ball of wibbly-wobbly timey-wimey stuff?
1276359
...I suppose you could say that.
Astonishingly... I never though of it that way until just right now.
I have, for some reason, been thinking about this quite a lot recently, particularly in conjunction with this video (though I think it treats dimensions 5+ kind of superficially, especially once it gets to 8), and had some interesting thoughts.
Suppose that, as suggested in the video, a point in 7th-dimensional space is all of 6th-dimensional space with a particular set of rules (henceforth a "universe"), and the underlying rules of a given universe are defined by its position in dimensions 7 through n (I'm not quite sure how many dimensions you'd need to adequately define all possible sets of rules).
Supposing that, what's the deal with multiverses? Are they just clumps of universes with nearly-identical rules? In that case, how "nearly" does it have to be? On the other hand, it could be a higher-dimensional analog of timeline 28B, in which case our definition of "universe" needs revision. A third possibility is that one universe had several big bangs (or similar events) separated by distances of space and/or time so huge that calling them astronomical is an almost comical understatement, in which case Planeswalking is essentially a very big tesseract (the plot device, not the geometric object). A final possibility I just thought of while writing this is that dimensions 7 through n define a universe's position in its parent multiverse, while dimensions n+1 through x define the underlying rules of that multiverse; this model produces several more lines of inquiry that I'm trying not to think about since it's almost 2 AM and I want to go to bed (I think too much, too, sometimes)
2317033
See, this is the exact reason why I restricted probability space to six dimensions. The Magic Multiverse is a nine-dimensional object. At least. A few seem to come and go. In any case, that's why Ditzy has trouble making sense of the interstice in "Fast, Fine, Fierce." She's used to a place with even more directions.