Game Universes Five: The Three Point Universe

[I heartily suggest you read the other four essays in this series before this one:)]

In the one and two point game universes from the last chapters we saw how restricted the number of necessarily  true statements we could make were, and moreover, we saw that there were no contingent true statements we could make. All truth possible truth lists were the same.

I think the most profound change in the development of these single point game universes comes when we move from two to three points.

Imagine a universe made of three single points, ABC. We know from Transitivity that it will contain the Truths of the Two and One point universe combined. So we can state:

• True (ABC):
  • A exists.
  • A is identical with A.
  • B exists.
  • B is identical with B.
  • C exists
  • C is identical with C
  • A and B and C are Different.
  • A and B and C are Connected.
  • And so on...

We will find that we cant add more contingent truths to the Universe unless we start stipulating not just what exists but how that which exists is structured. We did this automatically when we made a Glove Universe but with these maximally idealised points we need to be more specific.

Structure

Structure is the arrangement in which the points are connected.

When we just have a two points there is no difference between AB and BA in term's of stating truths. You cannot say, A is to the left of B. One might argue that AB is the opposite structure of BA but I can’t really make sense of that. I'm not sure I need to because as soon as we add that Third point, C, then structure emerges.

ABC is not the same structure as CAB. The points are connected differently. In one, B is connected with A and C and in the other, it is not, there is a point in between. In that one we can say “B is interconnected with C and connected with A”.

But although ABC is not the same structure as CAB, it is the same structure as CBA. That is, ABC=CBA because there is no way the True(ABC) and True(CBA) can contain different truths.  In exactly the same way as you cant distinguish between Left and Right in the Glove Universe or AB and BA in the two point universe,  you cant distinguish between ABC and CBA.

The Three Point Universe is the first game Universe that has structure. It must necessarily have Structure.  For example there are these possible structures for the three point universe:

ABC (or CBA)
CAB (or BAC)
BCA (or ACB)

When you Stipulate three or more points you stipulate Structure. If you stipulate ACB and me ABC then we are stipulating different universes, in the same way as my glove may have had two holes in the button and yours' four.

Structure is one possible arrangement from a set of possible arrangements where the possible arrangements are determined by the parts and the rules. Out of all the possible Three Point Universes, those possibilities are just possible structures and only one of them can be actual, that which is Stipulated.

Structural Properties are properties about the actual arrangement of the Game Universes. Structure is the first Contingent property.

It is the first property that is emergent.

The Only Magic: Emergence

In the Universe Game the property of Emergence is perhaps the most important Property to understand. Once you see how it arises in the Game you can keep your eye open for it in real life, it there,  and it is everywhere, from social and moral systems to the realm of the subatomic. It has a substantial metaphysical payload you may need to grapple with, but as a demonstrable phenomenon in theory and reality, its the closest thing we have to an extant creator. Emergence gives us, literally, something for nothing.

If a structure contains a property P and P is not a property of any of its parts then P is an emergent property.

In terms of the Game Universes at least, all we have is nothing but existence, these single points, yet we are making something like meaningful statements about new kinds of things. We get new kinds of meanings out but there are no new kinds of things in. This is emergence; It may well be the only free lunch in Reality.

Betweeness, Connectivity and Interconnectivity

In the three point universe we have a property that is not in any of its parts,  this is “Betweenness”

The law of non-contradiction is not contingent, but ABC or CAB are contingent. They are contingent truths about the universe. For example:

• Truth:(CAB)
  • A is between C and B
  • Truth(ABC)
    • A is not between C and B

These are the Same Universes, fundamentally, but differently structured. We know that in a two point universe Connectivity is trivial, in the Three point universe it becomes Contingent and nontrivial. All points in the Three Point universe are either connected directly or interconnected via the other point. For example:

• Truth(CAB)
  • A is between C and B
  • A is connected with C
  • A is connected with B
  • C is interconnected with A

These emergent properties arise at three points and yet, if you think forward to ABCDEFG kind of Game universes you will see that there don’t appear to be any  new emergent properties. The reason for this is because something is missing, and that something, is dimsensionality.

Dimensionality

So far we have been answering this question by relying on the linear convention of writing them in a line. But I can also imagine and stipulate a three Point Universe arranged so that ABC are not in a line but are all touching.

There is no reason why we can’t imagine this if we can imagine ABC. What is handy about using the Truth List is that we can actually see the difference in connections between the points even if those connections cannot be represented in two or three dimensions. For example, "All points are connected and no points are interconnected" describes a Universe with a different dimensionality to the universe described by "two points are connected and point is interconnected."

The different way the points can be connected, the different possibilities entailed logically make a space of possibilities and this possibility space is what we can term the “Dimensionality”.

I don't know what scientists mean when they talk about ten dimensional space. Or what people who believe in "extra dimensional beings" could possibly know about. But when I look at this most minimal of ABC structures I can see how it is limited not just by the pure logic but by the possibilities that have to exist for it to exists. It is limited by the possible structure.  This is Dimensionality.

The Single Point Universe has no Dimensions. Nothing is possible within it. The two point universes might e said to have dimensionality, but this is necessary not contingent upon the structure.

The Three Point universe has Dimensionality. It has structure. It has different possible structures.

Question: How many Dimensions are in the Three Point Universe?

The answer two this question comes from Stipulation. Suppose we stipulate that its a 3PU but that the points must be arranged in a line. In this stipulation we have limited the Dimensionality to 1 Dimension. But if we stipulate the three point universe  can be arranged in any logically possible way then we can have two dimensions. As the ABC all connected structure shows. These are not spatial dimensions but structural dimensions

Conclusion to Thought Experiment Four

The logical properties of our Game Universe are set in stone very early on. Even when we move from two to three points we see the logically necessary become replaced by the possible. The stipulated entail the emerged. If we were to make a four point universe or a forty trillion point universe we would find that we wouldn't be able to make that many more non trivial truths about that universe. This may sound surprising but to see what I mean, lets take a quick look at a Four Point universe:

This does have some more contingent truths and emergent properties. For example

• True(ABCD)
  • B and C are between A and D.
  • A is not contained by C and D

We have these new emergent properties but they are not that remarkable. It becomes more apparent with the five point universe. For example:

• True (ABCDE)
  • C is between exactly four points.

We have a new property of "being between exactly four points" and we can imagine that when we have a two billion and one point universe we can have a new property of "being between exactly a billion points." but these are , pun intended, Pointless truths.

Its just more of the same variants on betweens, interconnectivity and dimensionality. Now, as the points increase in number so will the dimensionality, but it two seems like it will be diminishing rapidly.  Still something is missing from these Game universes, we will start to see what this is in the next Chapter.

Questions to Ponder

• What new properties could you get from a universe of six points that cannot emerge in a universe of five points?
• Do you see that all of the connections in a There point universe are able to be modelled in this world using Marbles whereas this is not possible with a five point universe?
• Are the  Properties of Impermanence and Interconnectivity necessary properties of  all parts of all possible Game Universes?

Have Fun!