Wednesday 16 June 2021

Two-Dimensional Time?

The space-time continuum we inhabit has three spatial dimensions and one time dimension - as far as we know.  For us, it is easy enough to visualize fewer spatial dimensions.  A one dimensional world is merely a straight line.  A two-dimensional world is a plane; e.g. x and y axes on a graph.  In 1884 Edwin Abbott published a fun book called Flatland: A Romance of Many Dimensions, exploring how life might be for two-dimensional creatures, and how mystified they are by a 3D visitor to their plane.  Some mathematicians claim to be able to visualize a four-dimensional space with tesseracts, hyperspheres, etc., but that is difficult for us, stuck as we are in 3D space.  Some cosmological theories of reality; e.g. String Theory, call for 6 or 10 or even more dimensions in all, but some of those are supposedly curled up so small that we cannot detect or experience them.

In all of these cases, however, there is but one temporal dimension.  Aside from relativistic time dilation effects, we all share the same passage of time, and the time where you are is the same - apart from time zones - as for me.  We all pass through time - which no one fully understands - at the rate of 60 minutes per hour, and your hour is the same length as mine, even if they feel different subjectively.

One temporal dimension is well understood, even if we do not quite know what time itself is (a deep philosophical conundrum).  An existence having no time - a zero time dimensional reality is easy to think about as a fixed space where nothing ever happens: no movement, change, or even thought, as in a still photograph - not a very interesting existence.  Looking for more complexity, we can ask, could there be more than one time dimension, even in principle?  I have spent some time trying to wrap my mind around what that might mean and how it would work, and finally chanced on a simple way to express and visualize an existence with two temporal dimensions - 2D time.

Consider a teen playing a video game.  The teen has his own passage of time, and the game has another, virtual timeline as events in the game occur.  These two times need not be the same, indeed, they often are not, yet they exist together.  In the game, hours may pass in a few minutes of the teen's time, or the game time may slow down, taking several player minutes to get through a few seconds of intense action in slow-motion.  What's more, the player may save his game and then shut it down, effectively freezing time inside the game, while his own clock continues to tick.  With the "save game" feature, he can even go back to an earlier game time if his avatar "dies" in the game.

Such a game is an example of a computer simulation.  An engineer develops a program in some software to simulate some physical process, in order to better understand what is going on, or to test and optimize his design.  The time dimension in the simulation does not begin until the engineer starts the simulation running at t = 0.  Note that in the simulated reality, there is no "before" this time.  Simulated time does not exist before the simulation begins - or alternatively, it is stuck at t = 0 until the engineer presses the "go" button.  Meanwhile, of course, the engineer's own timeline continues undisturbed; he works, goes home, eats, has coffee breaks, sleeps, etc.

This two dimensional time reality can be visualized in the following graph.  It has two independent time dimensions, te for the engineer's time in the real world, and ts for the timeline in the simulated world.  In this example, there are no spatial dimensions shown; size, shape, motion, etc. do not matter for this explanation.  Of course, a spatial dimension could be added, but that is harder to do on a 2D screen, and unnecessary for the description.  We can walk through events in this 2D temporal plane as follows:

1. At te = 0, the engineer has not yet started the simulation, so ts is stuck at zero, while his te proceeds at the usual rate.

2. the engineer presses "go" and the simulation begins.  If the rate of time passage is the same, the line would then rise at 45 degrees, but in this case, the simulation time runs faster than the real time te.

3. the engineer decides the simulation was running too fast, perhaps missing some details. So he slows down ts to run slower than his own time.

4. the engineer doesn't like what he sees, so he shuts it down, resetting ts to zero.

5. after a break, during which he tweaks some initial conditions or parameters of the simulation, he starts over, this time with a different ts speed.

6. stopping the simulation, he spends some time looking at the results.

7. liking what he sees, he sets ts back to an intermediate value, so that he can watch it again, 

8. finally, the engineer lets the simulation carry on for a longer simulated duration.

With this example, it is easy to see how different realities could experience different time dimensions in the "same" world.  In such a situation, the simulation "experiences" one time dimension, as programmed by the engineer.  The engineer however, experiences, or at least understands, two time dimensions; his own and that inside his simulation.  Note that the engineer's time, te always increases at the same rate.  He cannot stop or go back in time, only move forward at the normal rate.  Note too that other engineers may be running other simulations, each with its own timeline, but presumably those simulations do not interact with each other on different timelines, and so, while there may hypothetically be other parallel time dimensions, they are just different versions of the 2D time discussed here and do not truly add more dimensions.

Another way of considering 2D time is while reading a printed fiction story.  Time begins in the story when you begin reading the book, and it passes as you turn the pages, until you put the book down, which freezes the story's timeline.  The story time may pass quickly or slowly as you read, depending on the context of events in the book.  Indeed, many books jump back and forward in story time as one reads, but you understand the book has a single unified timeline.  In principle, after reading the book through, you - like the author - can consider all of the story timeline at once, at least in memory.

Having understood this approach to two-dimensional time, we could postulate a third time dimension; perhaps God's own timeline above us, in which his eternal time dimension encompasses but transcends ours.  Whether time truly "passes" for God, we do not know, because we cannot envisage, much less experience God's time.  However, he may see all of our timeline at once as we do for the engineer described above, by looking at the above graph.  Over all, in addition to his own divine time dimension, td, God may experience or at least observe and control our created time line, te, along with that in the engineer's simulation, ts, if he is interested in that detail.  Hence, in some sense, for God there can be three-dimensional time!

In principle, the engineer could "play God" by programming a simulation that includes a built-in simpler simulation with its own separate timeline, tss, but that gets rather convoluted, so I won't go there.  Suffice it to say that the concept of a simulated reality makes thinking about two or even three dimensional time more understandable.  Now if your timeline and mine were different, yet we could somehow interact when they came together, that would be closer to actually experiencing two independent time dimensions at once.  That is harder to wrap our minds around, although some sci-fi tales and superhero movies try to do that; e.g. stopping or slowing time for the world while the superhero action continues.

For some further exploration of the weird possibilities that God's control of our timeline might allow, see my previous posting at: https://thopid.blogspot.com/2019/01/our-simulated-world.html  For example, as in the engineer's simulation, God could perhaps stop or even reset our timeline for his own purposes, and we would never know!