Born to do Math 147 – Just Add Some More Dimensions (1)
Author(s): Scott Douglas Jacobsen and Rick Rosner
Publication (Outlet/Website): Born To Do Math
Publication Date (yyyy/mm/dd): 2019/12/01
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Scott Douglas Jacobsen: What if there is more than 1-dimensionality of time?
Rosner: Asking what time would look like if it were more than 1-dimension mistakes the character of time, I think time is 1-dimensional. But more than that, time is a succession of points and cannot be anything but that.
To suggest a time that’s more than 1 dimensional, it can’t be. Time has to work the way time works. However, there are multiple potential futures and similarly multiple potential pasts. We know. Eveything we know is based on the past. All knowledge comes from history. The stuff that’s come before.
All that information constrains the possible futures. But since we do not have complete information about the past, there are a bunch of possible pasts, too. So, the diagram of what we know has this big wad of knowledge representing the past with the most known about the immediate and then getting more and more vague as you get further into the past, and somewhat similarly for the future.
We know most about what is going to happen in the current moment and less so as you move into the future. But the cones of spreading possibilities in the past and in the future, I don’t think they have a dimension. It is possible.
Basically, a dimension is how much spread you get at each successive distance from your point of origin. For instance, along a 1-dimensional line, there’s no spread. At each spread along the line, it is a point. If things are spreading along a cone, along a 2-dimensional surface, then the size of the cone or the radius of each cone at each cone or distance is increasing linearly by x.
For a 3-dimensional spread, it spreads by x^2. Maybe, there is some math to be done with the increasing spread like at T2 and T1. I don’t know the math of this and if it is cleanly dimensional
Jacobsen: If something was probabilistically not quite real, it would be a 1.2-dimension of time?
Rosner: No, it is to some extent exponential. Because the possibilities multiply exponentially. At T1, you have, in a very small system, 100 different open questions that can be resolved or each resolved in several ways. At T2, the open questions have compounded. The number of possibilities haven’t increased arithmetically, but more exponentially. If they are increasing exponentially, then that’s not describable dimensionally.
Because if it is x to the n and n is the number of moments in the future, then that’s exponential rather than arithmetic. So, you don’t have a steady increase by x^3, x squared, or x^7. On the other hand, maybe, it is not perfectly exponential because of the future events, the specific events that answer the 100 open questions; those may constrain the open questions at T2. It is 100 open questions at any subsequent moment.
Anyway, I don’t know how to characterize the rate of increase of possibilities moment-to-moment starting at T0 as the present moment and moving forward exponentially. I doubt the spread or increase in possibilities is describable x^n with n as some specific number that doesn’t vary across future moments.
There is a lot of convenient math for combining the 1-dimensionality of time with the 3-dimensionality of space, and any further tweaking of dimensionality due to the curvature of space due to General Relativity.
Jacobsen: If those are emergent phenomena and create the world, are they separate before they come into being?
Rosner: No, they are all part of the same deal. I don’t think you should be tempted into thinking time can vary 1-dimensionally. That you can have time that functions as anything but 1-dimensionally.
Jacobsen: What about space?
Rosner: According to the rules of information, you probably need space that is 3-dimensional. I doubt you can vary the dimensionality of space. You could probably do it in your imagination to simplify your image of things.
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