Finite is quite large

The film Titanic is 3 hours and 14 minutes in length, and available as a DVD file. This file is a sequence of bytes. A byte is 8 bits. A bit is a 0 or 1.

So, the film can be represented as a (very) long, but finite sequence of 0 and 1. Let’s call the length of this sequence a bajillion.

Now, consider a list of all possible sequences of 0 and 1 that are a bajillion long. This is is a long list – it contains 2 to the power of a bajillion items. Again, although long, it is finite. Let’s call this list the Library.

Some items in this library are sequences that are playable in a DVD player (for example, Titanic is in there somewhere). Let’s go through the Library and discard any item that is not playable as a DVD. Let’s call the remaining items the Video Library. It has a finite, but large, number of items.

The Video Library contains every film that is less than three hours in length that has ever been made. It also contains last night’s news bulletin. And tomorrow’s news bulletin. It even contains the Oscar Best Movie from 2090.

But yet, this Video Library contains even more. It contains an item that is exactly the same as Titanic, except for that scene with Leonardo and Kate where she spreads her arms at the front of the boat. There, in the background, leaning against the rail and watching, is you.

How can that be?

Well, if you were actually standing there for 30 seconds when the movie was being shot, then there would be an actual sequence of 0 and 1 which represents that.

Because our Video Library contains every possible sequence of 0 and 1 less than a bajillion long, then it must contain an item which is exactly the same as the original Titanic, but replaced by that sequence of you at that point in the scene.

But there’s more in that Video Library. There is another item with you standing next to Nelson Mandela, in the background watching during that scene. And you, Nelson Mandela and Ronald Reagan. And you with Margaret Thatcher strumming on a ukulele.

In fact there are items in that Video Library which are exactly the Titanic for all 3 hours 14 minutes, but with you in the background standing next to every human who has ever, or will ever, exist.

This is an enormous Video Library. It contains DVD representations of anything that has ever happened and could ever happen that are less than 3 hours in length. So it contains a video of your walk to the supermarket next Thursday. Shot from every conceivable angle.

Yet, it is finite.

All possible human experiences as we move through the world and time are finite. There is nothing that you can imagine which lays beyond that finite horizon.

It’s finite, but very roomy.

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