Infinite Data

Whole Numbers

How much data is there in a list of all whole numbers starting at 0.

i.e. 0, 1, 2, 3, 4, ...

I hope you see that despite the list being infinite, the amount of data isn't. Likewise, the amount of data in the list of all even numbers isn't infinite.

For the maths nerds, like me, we could define all whole numbers like this :

Translating the maths into geeky English :

And the list of all even numbers like this :

How about the amount of data in the list of all prime numbers? This one is trickier because there isn't a simple equation which will spit out the next in the sequence.

We can write a computer program to generate them. That program is small (and finite). But with a finite computer, we cannot generate all primes (even with an infinite amount of time), because the computer would need an infinite amount of memory to store them.

But if we use pure maths instead of a computer program, the definition of the set of all primes *is* finite.

I want to convince you that our world may be similar. It may look like there's a lot of data, but in reality, the whole thing is defined by something finite and small.

A Drop of Water

A single water droplet has roughly a sextillion atoms (1 followed by 27 zeros). That's a lot. (but tiny amount compared to the number of atoms in a star, let alone a galaxy, or the whole observable universe)

So, if a god created our universe, why create so much data? Is there a smaller representation that would achieve the same goal?

Can we find a definition of a water droplet, or our entire universe that describes it succinctly, in a similar way that I defined the infinite list of whole numbers?

A Painting

Let's go from a drop of water to a the painting of Mona Lisa. Lots more atoms, so even more data. We could make a video, starting with a fully zoomed out image (capturing the entire painting, but no detail), We could then zoom in on a tiny patch, so that we can see the brush strokes, and then zoom in even more. Eventually down to the level of individual atoms.

That's a long video, and we've only uncovered the details of a tiny patch of the painting.

Now let's do the same thing again, but with a different picture. Here's one on YouTube video. It's over a hour long (no you don't have to watch the whole thing, a few seconds will be enough!).

Now imagine creating an interactive video, where you are free to zoom wherever you like. How much data would that take?

Note, unlike the Mona Lisa (which is made up of atoms), you can zoom into this image forever, and you will uncover more and more detail. It has no limit. An infinite amount of detail.

Strangely, the amount of data in this image is tiny, here it is :

This is the formula for the Mandelbrot Set.

I believe that the Mandelbrot set is a good analogy of how our universe is constructed. It has detailed swirls, analogous to spiral galaxies. It also has huge swathes of empty space between these swirls.

But the entire thing is defined in just 13 characters. (Okay, you also need the meta-data to explain what each character means, but it is still tiny compared to the YouTube video).

But It's Static

There's an obvious difference between the Mandelbrot Set and our universe. The Mandelbrot Set is a static image, whereas our universe changes and evolves.

Take an old (analogue) movie. Cut up the film, and stack each frame on top of each other. We now have a 3D structure - a tall, skinny skyscraper of static images.

Now imagine another mathematical formula, similar to the Mandelbrot Set, but instead of a 2D image, it defines a 3D "image". It still has infinite detail, this time in 3 dimensions, not 2.

We could then "play" the movie by taking a slice at the bottom floor of the skyscraper, then another at the "first floor" etc. What's more, unlike an actual movie, we could take a slice anywhere we like. Half way between floors 1 and 2, or a quarter... We can pick any point in time.

We now have a seemingly infinite world in space and time. But the *actual* amount of data is only the mathematical formula of this "world", not the 3D "image" that the formula creates.

IMHO, the ultimate goal of physics and cosmology is to uncover this formula.

The Forth Dimension

My skyscraper only describes a flat 2D world (just like a movie is 2D).

Our world is 3D, and changes over time, so we need a 4 dimensional structure, which is hard to visualise. But let's give it a try.

For a 3D world, each "frame" would be a CUBE, not a flat piece of film. Now we need to stack the cubes "on top of each other". But we do NOT stack them like a child stack blocks.

Instead, each cube is stacked not upwards, not forwards, not backwards, but in a another direction entirely. A direction in the 4th dimension. English had no name for this other direction, let's call it "Ana". FYI, I didn't make up this word, it's been in use for quite a while.

We have 4 pairs of directions : Up/Down, Left/Right, Forwards/Backwards and Ana/Kata.

Our cubes are stacked on top of each other in the Ana/Kata direction.

But the Future isn't Fixed

In my model, we can play the movie by moving in the Ana direction of the 4D structure. Each "frame" is a cube. But the structure is fixed. It doesn't really move or evolve. Our universe does.

Are you sure our universe moves and evolves? What observation, or measurement could you possibly make that would distinguish between a static 4D world, and a moving 3D world? IMHO, the two are indistinguishable. More on that later...

Limits

When we were zooming in on the painting, we eventually get to the level of individual atoms, and we can't zoom in any further. Our universe has a similar limit where we can no longer zoom in. This limit is the planks length. (google it!)

So my Mandelbrot Set analogy isn't quite right (because the Mandelbrot Set has no limits - you can zoom in forever).

There's also issues with the probabilistic nature of quantum mechanics. AFAIK, it has been proved that there are no "hidden variables" (google it!).

My 4D Mandelbrot-like structure doesn't have Quantum "weirdness" at all, it is Newtonian.

Alas, this is where my understanding of physics ends. Maybe a 4D Mandelbrot-like world is inconsistent with quantum mechanics. I doubt it though.

Non-Parallel Slices

With the skyscraper analogy (the 2D world, with time pointing upwards), we only took slices parallel with the ground. This seems like a strange, and arbitrary constraint. What would happen is we took slices at a slight angle instead?

We would still see a 2D universe evolving over time. However, if Alice plays the video tilted to the left, and Bob plays the video tilted to the right, they would disagree about their idea of "Now". Alice would think that event A happens before event B, but Bob would think that B happened before A.

Far from being a bug, this is a feature. Einstein's theory of relativity predicted this, and has since been tested, and found to be true.

The amount of "tilt" is related to the speed at which Alice and Bob are moving. If they are travelling slowly, then the tilt will be negligible, and they will agree on their notion of "now". But if they travel quickly (e.g. 1% the speed of light), then they will notice the "tilt". "Now" becomes subjective.

If you think you live in a 3D world that evolves over time, Einstein says you a wrong! ;-) He says you live in a 4D space-time. His model is consistent with observation, yours isn't!

Note, his predictions weren't possible to test with the technology at the time. The fact that future (now past) technology proved him "right" is testament to his genius.

A Movie without a Projector

A regular movie is a long line of frames. Without a projector to advance the film, there is no motion. The movie doesn't change or evolve. Our world, is obviously moving and evolving. Does this mean there is a projector in a meta-universe?

I don't think so.

Some sci-fi stories introduce a device which pauses time. What would that actually feel like? Imagine that as you read this sentence, time is paused for "10 years", and then restarted. You would not notice it at all. Your clock would stop, and start again, your body would stop and start again, so would your brain.

If we imagine characters in a movie were actually "magically" sentient, we (the viewers of the movie), could pause the video, and start it again, and the characters would be none the wiser.

Let's put it another way. What observation or measurement could you make that would distinguish between a world that is moving, and one which isn't. In the moving world, we would have our memories of the past, and then later, we would have new memories. But at any instant in time, we only have a single state.

In the forever-stopped world, we also only have a single state.

At any instant in time the two are indistinguishable.

IMHO, the "movie" (of our real world) is an illusion. We only think it exists because at each instance in time ("now"), our mind has a self-consistent notion of a moving/evolving universe.

However, it is also self-consistent with a world that is forever stopped.

It's also self-consistent with a world controlled by an "outside entity" watching the movie of our universe, pausing to get a snack, skipping boring sections, and even stopping the movie half way through and ejecting the DVD, never to be played again.

We prefer to think that our world is actually moving (because the alternative is horrific), but that is only a belief, based on zero evidence.

I've always thought that people expecting an afterlife are ungrateful and entitled. Be thankful that you have one life, don't be greedy and expect two.

The world view I propose here is an extreme version of the same idea. Instead of being grateful for one life, be grateful for a a single instance.

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