Wednesday, June 01, 2005

Time

The question of the nature of time has always fascinated me. How can we know so little about a physical property that so underpins our lives?

Recent notoriety of one Peter Lynds and a paper he wrote in 2003 has caused me to revisit my assumptions about time.

First, my prior understanding of a working model for time. Then, an examination of Mr. Lynds position. Finally, a revised working model.

The Universe As Computer


I've long been of the belief that the universe is actually a large simulation (ala The Matrix, although this concept was around long before that movie - where do you think the writers got the idea?)

Computer simulations work the following way. The physical space is broken up into arbitrarily small "cells", each of which have some properties and values. Similarly, an arbitrarily small time slice is selected for the simulation. At each time slice, the values of each of the cell properties are calculated and set. Depending on the simulation, what is happening in one cell affects surrounding cells.

Depending on the number of cells and the complexity of the calculations, the "real" time it takes to perform one iteration (one "time slice") of the simulation can be much longer that the time interval modeled in the simulation. (In other words, it might take a minute to calculate the values of a billion cells for a 1 second interval, then another minute for the next second, etc.) This is known as the "time-ratio" of the simulation, and is usually represented as simulation-time/computational-time.

When the time-ratio is equal to one, then the simulation takes place at the same speed as "real-time". Games and virtual reality environments require a time-ratio of 1 or higher. Most physics simulations run at time-ratios significantly less that 1 due to the number of calculations involved vs. the computing power available.

Now, consider The Matrix scenario again, where one lives in a "virtual" environment, a simulation of the real world where the sensory inputs are calculated and fed to your brain, either via your senses or directly. Theoretically, if the simulation is detailed enough (ie, has a sufficiently large number of cells, a sufficiently small time interval, and a time-ratio of 1 or greater), then you shouldn't be able to tell the difference between the simulation and the real world. (This concept has been a problem debated by philosophers for years.)

The next step in understanding The Universe As Simulation is making the assumption that there is no "physical" brain at all, but only a simulation of a brain. In this picture, we have taken a real, physical brain and developed a model of all the neurons, synapses, neurotransmitters, etc at a sufficiently detailed level that the model behaves like a real, physical brain. Given the same inputs, the model produces the same (or within the bounds of non-linear systems, essentially the same) behaviors and outputs.

This is clearly beyond our technology today, but given the orders of magnitude leaps in processor size/performance/cost we've seen in the past 30 years, the extrapolation to the level of computing power necessary to produce a model of the brain in sufficient detail is absolutely within the grasp of technology within the next 30 years.

So, now we have a simulation that simulates the physical external world, and a simulation that simulates a brain. We can put these two together, and see what happens. (In fact, the separation of these simulations is an artificiality - if we can simulate the physical world to a sufficient fidelity, and the brain is just another physical construct in that world, then the simulation of the physical world can contain the simulation of the brain - or many brains, for that matter.)

An interesting observation is that the time-ratio of the simulation has no effect within the simulation itself. By this, I mean that even if it takes 1 minute in the "real" world to simulate 1 nanosecond of the simulated world, within the simulation the calculations (and therefore the subjective experience of the simulated brain) is the same as if it took 1 nanosecond in the real world to calculate 1 nanosecond in the simulation.

Think of simulating a bullet moving through the air. Each time slice, the calculations of the cells that represent the absolute position of physical objects would each increment. The cell that held the front-most atom of the metal of the bullet would, in the next time slice, hold the atom that would be in that position after the calculation interval, say the distance a bullet travels in a nanosecond. The cell next to this bullet containing cell that held part of an air molecule 1 nanosecond ago will now be calculated to hold the front-most atom of the bullet. Interval by interval, time-slice by time-slice, we simulate the motion of the bullet through space.

If we have a time-ratio of 1, then the bullet moves in 1 nanosecond the same distance it would in the "real" world in 1 nanosecond. If we have a much smaller time-ratio, then the bullet would move in the simulation that same nanosecond distance, but in the real world maybe a full second has gone by (because we had to calculate a whole heck of a lot of other cell values as well for that time-slice). In other words, we can adjust the time-ratio all we want, and the simulated bullet would never know the difference. The same would hold true of the "simulated" brain. Because to the simulated brain, time flows interval-by-interval, time-slice by time-slice, regardless of the true clock-speed of the processor performing the calculations.

All these concepts have been used in science fiction for a while. Imagine if we had the computing capacity to run at time-ratios greater than 1, ie faster than "real-time." We could collect inputs from the real world, pass them to the "simulated" brain, and it could react faster than the "real" brain in the "real" world. The simulated brain could think faster than the real brain. The simulated brain could spend the subjective equivalent of a day to think over something that perhaps the real brain only had minutes to ponder. I imagine the simulated brain would kick real brain's ass. (Man, talk about a mixed metaphor).

Okay, three more steps to get to the conclusion of this section.

You can see that to the simulation, time "feels" like it is flowing and is continuous, not broken up into chunks. (Compare this to the Beta Movement visual phenomenon - often mistakenly called "persistence of vision" - effect of your eyes and brain while watching a movie. The movie is really discrete chunks of static images, where each image is displayed for about 1/30th of a second and then the next image is displayed. To your brain, it looks like a continuous image - but it's most certainly not).

This demonstrates that it is very possible that even in the real world, time is broken into discrete chunks of duration that come one after another so fast that it seems continuous to us. The duration I subscribe to is known as a Planck Second, which is the time it takes the speed of light to traverse a Planck length, or about 10 -44 seconds. A Planck length is the theoretically smallest measureable distance. The speed of light in vacuum is the theoretically fastest velocity in the universe. The fastest velocity over the shortest measureable distance produces the Planck Second.

A simulation that ran using time-slices of Planck seconds and cell sizes of Planck length would be a simulation of the universe. And it wouldn't matter the "real" time it took to actually calculate the next value of each cell for each iteration, because within the simulation it isn't detectible. So if we are each simulated brains running in a simulated universe on a big universal computer, then we wouldn't be able to tell the difference.

Now, really smart guys like David Deutsch hate this argument because in one sense all it does it push off the really hard questions like the "true" nature of the universe one more level removed. In other words, if we really are a simulation, then what is the nature of the simulator? What are it's physical properties? How could we even begin to determine these? Deutsch likens this to the "God" argument, in that once you make this argument it really cuts off the possibility of further meaningful inquiry. (ie, if I say the bullet moves the way it does because God makes it move that way, then there isn't much more meaningful I can ask about how that works - it's probably even fruitless to try to make predictions based upon prior observation because God could just change his mind at any time.)

But just because the argument makes the "true" nature of reality harder to discern doesn't necessarily make it an incorrect argument. That too would just be wishful thinking. Science would say we need a way to test the difference between the two theories so we could determine which one is false. Unfortunately, no one has yet come up with a good experiment to falsify the Universal Computer theory. (The closest is to posit finding some phenomena that we can prove mathematically that we can *not* simulate it - the fact that it existed would also prove that we can't be living in a simulation. They're still looking...).

(As a side note, the Universal Computer theory solves some puzzles like Zeno's paradox. The dichotomy of Zeno's paradox basically goes that to get from point A to point B, I must first cross half the distance from A to B. Then from there, I must cross half the distance again. And so on. If space and time are continuous, then they are "infinitely" divisible, so in theory I must cross an infinite number of half-distances to get to point B. Yet we all know it doesn't take infinite time to move my finger from the space bar to the delete key, so something is wrong in the assumptions of this argument. In the Universal Computer, of course, everything is quantized into discrete space and time slices, and objects "jump" from cell to cell with each time slice - there is no infinite distance to cross.)

The next post will address the concepts introduced in Peter Lynd's paper, and perhaps a modified version of Universal Computer theory of time. (I'll also go back through this and set links to referenced information, but right now I'm out of time...)

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