Game Universes Four:The Two Point Universe

14Jan/100

Game Universes Four:The Two Point Universe

In the last Thought Experiment we created, by stipulation, a Single Point universe and we saw how there was very little we could say about it, but what we could say was clearly connected by Logic. The Final exercise of that last Experiment was to "think deep" about the Single Point universe, to become a Philosopher of the Single Point.

Sure, in most ways it was very boring as games go, but I hope it has given us at least some tools to get into the meat of the matter.

Imagine a Single Point Universe; we know from the last experiment that it will be identical to all other single point universes we can imagine, just like all other perfect circle universes.[1] Let’s now do something that we do lots and often been done for us, and that is to label something. When you label something you are in some sense pointing to that thing, referring to it with the aim to distinguishing it. Let’s call the actual point in the Single Point universe, "Point A" or "A" for short.

When we label something like that we are just stipulating a short hand. There is no magic in labelling something and, in terms of Game Universes, there is no special connection between words and the Universe

From the last experiment we know that A’s Truth list will look like this:

True(A):
- A exists.
- A is identical with itself.

Imagine a Universe that consists just of Two Points, A and B. We know that these are the same kind of points, they are just single points. There is no internal difference between A and B, we have, as it were, more of the same. It absolutely crucial to see in this case and in all future cases that we are just Stipulating more points, not new kinds of things.

When we had the Glove Universe the parts of the glove were arranged in a glovelike way. When we have a Two Glove universe we instantly know that they must in some sense be touching. If they were not, then we would be smuggling space into the Game Universe, and that, is against the rules of the game.

The structure of the gloves determines the possibilities of how they can be arranged.[2]

Thinking about the Two glove universe there are countless ways the two gloves can be structured together[3]. With the Two point universe this isn’t the case, there is only one way they can be structured, and that is AB which is identical to the structuring BA. In the same was as without a reference point and containment space we can’t say if a glove is left or right handed, we cannot say any difference between AB and BA. We can say that AB=BA, which means that the truth lists for AB and BA will be the same.

Possibility Space

With the Glove Universe we could imagine what it would be like, it would be like an ordinary ladies glove, but this could be many things. Some things would need to be the case, like athumb next to a finger, a button at one end, at one side of a slit... and so on. But others are completely open within the Stipulation of the Game Universe. It could have two holes in the button or four, seams inside or out, and so on.

This huge space of things that must be the case and things that could be or could not be the case is called the “Possibility Space” of the game universe. The Two Glove universes and the One Glove Universe both have immense possibility spaces whereas the Two and Single point universes do not.

Unlike the glove universe, the A and AB Universes, leave nothing to the imagination.

The AB Truth List

Let us now look at the Truth list for AB. This is the first composite Truth List in that it is made up of the truth lists of other things, in this case single points.

True(AB):
- A exists.
- A is identical with A.
- B exists.
- B is identical with B.

What right have we to simply combine the Truth lists? Might it not be that some truths from one list make other truths in another list false when they are combined? No its not possible because then there would either be a contradiction or a stipulating hadn’t been followed[4]

There are more some more Truths we can add, though not many, but first let's discuss the four Truths we have of the Two point Universe.

New Property: Transitivity

That starter list of four True statements seems to comes for free, we don't have to think about it because we know its true of the parts, of The Single Point Universes. If B had the property of being "Awesome!" all on its own in a Single Point Universe then it would have that property of "Aweseomness!" in any other Universes, of however many points it . This logical property we can call “Transitivity”, you might prefer to call it "containment" or "dependence" but I feel they miss out the long and linear paths of transitivity that exist in our reality. Transitivity is true of all lines, whether they are on railways tracks, graphs, upwards through evolution or through the thought processes in your neurons. Transitivity holds, because if it didn't, there would be contradictions.

Transitivity is hard to understand, not because it is complex, but because it is so very simple. It cannot be any other way, it seems necessitated as soon as there is more than one thing by the law of Noncontradiction. You should note that the Two Point Universe doesn't itself contain any Transitivity, the Transitivity is in the relationship between the universe and its more minimal parts.

When we had one point we had no Transitivity. Now we have two, we do. But, the Transitivity isn’t in the Game Universe in the sense the points are, rather its in our simple representation of the logic of the Game Universe.

Transitivity is an Abstract Property of the Game Universe. We saw in Experiment One and Two how there are Structural Properties and logical properties, now we have a property type that is Abstact. Abstract properties are about the universe without being inside the Universe.

New Property: Difference

We know that A=A and B=B. And we know there are two points in the universe, because if there were not, we wouldn't be playing the Two Point Universe Game. So it follows that Point A cannot be the same point as Point B, because if it was, there would only be one point. So now we have a new Truth for the Truth List:

True(AB):

A exists.
A is identical with A.
B exists.
B is identical with B.
A and B are Different.

What is Difference? It is a property that is entailed, at the minimum, by transitivity and non contradiction. We know that A and B together mean that A and B must be different and we can have some blurry understating of why. In the same way as existence and identity are metaphysically hard to grasp, so is difference. Often when something is hard to grasp some clarity can be gained by expressing it in other ways that still preserve the truth. Let's call this list type "Equivalents"

Equivalents (A and B are Different)
- There are Truths about A that are not True about B
- There is a change of existence between A and B.
- A=A but B does not equal A.

All of the above statements mean, at least relative to the Game Universe, the same thing.

We cannot say anything about the single points other than that they exist and are identical with themselves. But when we have two we know that those two points are not the same existence, they are distinct existences.

The One Point universes had no change. The two point universe has change, it has difference. It might be hard to see because we experience change as a very time, space and causation based phenomenon, but if you think in terms of the True statements of the Two Point Universe you can get at least some grasp on the necessitation of change.

Difference is Change

When we have AB instead of just A, we have something new, even though both Points are Truth list identical with the point from a Single Point Universe. Its crucial that you see this to understand the experiment. In the Single Point universe we had no Change of any kind. It was static in every sense. We couldn't talk about its creation or structural differences, it had none, it was, at best, a bit of existence and identity. So very close to meaningless.

With the Two Point Universe the very act of stipulating two point's rather than one point necessitates the stipulation of Change. As soon as you stipulate an "ordinary glove" you stipulate "five fingers and a thumb" and in the same way, I think, as soon as you stipulate two points you stipulate change.

But, what is change, other than difference?

Imagine a single point again, and now imagine this point can be in one of two sates, A or B. So you imagine a single point that changes state. Don't get distracted by the metaphysics here, we will focus on state changes in a later experiment. So now we have two separate game universes, the Two State Single Point Universe and Two Point One State Universe. I think that if the game Universes can be totally described by the Truth lists then there is no meaningful difference between the two, they have identical truth lists:

True (Single Point Two State Universe AB):
- A exists.
- A is identical with A.
- B exists.
- B is identical with B.
- A and B are Different.

True (Two Point Single State Universe AB):
- A exists.
- A is identical with A.
- B exists.
- B is identical with B.
- A and B are Different.

Although one involves change in the "change of thing" sense and one in the "change between things" sense we can see that there seems no other Truths that can differentiate the two.

One objection to the two lists above might be to say "In the Two State Universe, B doesn't exist when it's in state A." I think that this isn't a meaningful objection because it relies on Time. It uses the term "when" which is a temporal term and this is a timeless universe, by Stipulation.

There is another problem with this objection in that it implies it implied an understanding of "Existence" as a simple property. But we have seen above that there appears no way to get any understanding of existence as being a property shared by all things in a universe, stipulated or real. There seems to me to be no statement that can pick up on this though hence I don’t consider it a valid objection.

What I think this part of the Though Experiment suggest is that Change is a logical property of the Game Universe rather than a property of the structure (or systems) of that Game Universe. It is added necessarily by the Stipulations. Therefore, like Transitivity and Consistency, it's existence can't be denied nor fully understood within the Game Universe. We can, if you will, see the necessary evidence of its existence in the Truth Lists.

New Property: Impermanence

If you believe in the necessity of transitivity and identity and therefore change, then it follows that you must believe that State all possible Game Universes will possess these properties at every point. The act of stipulating the Game Universe entails that every point will be in relationships of transitivity and change. Can you think of a possible universe, of any kind, that would lack these necessities? I cannot because I always end up at inconsistency.

Most of us can see how everything changes in the world, and thus all is impermanent, but can we also see that in the two Point Static Universe?

I think we can. We can see from the Truth lists that there is Difference between A and B. There is this change in their existence . It seems that the existence of one must be impermanent because it is prevented by its nonidenity with the existence of the other point. A was all that existed in the Single Point Universe A, but in AB this is not the case.[5]

If we go back to the Circle universe from Experiment two, is it analogous to say "All halves of the universe are impermanent because they are ended buy their opposite halves?" I am not at all sure about that, but it seems to kind of make sense. I think it is analogous to the case of the impermanence of A and B.

This implies that all things are impermanent without the need for things like change in the “tick-Tock” or “Tickle causes giggle" sense. We will see shortly how impermanence is maintained all the way up, but think about how it starts in a very simple sense with just Two Points.

New Property: Connectivity

Imagine how you visualised the Glove Universe in the first experiment. You could imagine and speak of the relationships between the parts. "Two fingers are between two other fingers," for example.

Can we do this in any sense with the Two Point Universe? Can we pick out structural properties? I think we can, and reason is that if AB contains nothing but A and B, ie, no space or time or other parts ,then it follows that there can be nothing between A and B. Thus, AB must be in a structural sense rather than physical sense , touching. The term we can use for this structural touching with nothing in between is “Connectivity” . We now have a new Truth for the AB Truth list, Connectivity.

Connectivity is entailed by creation of more than one, as is difference. It just can’t be any other way, if it was you would have been stipulating a Game Universe of more than two points.

Conclusion to the Third Experiment

We imagined different glove universes but in the case of the Two point, as the One Point, our stipulations will logically be identical. Maybe I have missed True statements about the Two Point universe that you add to your list, that statement I have overlooked will also be true of my universe.

All possible truths Lists about AB (and thus, BA) will necessarily be the same, they will necessarily be at least:

True (AB):
- A exists.
- A is identical with A.
- B exists.
- B is identical with B.
- A and B are Different.
- A and B are Connected.

We have Properties in the two Point Universe that we don't have in the one point, like Difference or Change and Connectivity but these are necessary, they must be true of all such universes. In the next Thought experiment we will see how with three points we have contingency, and that's when things really start to get possible.

Also in the next thought experiment we will see about Emergence. Difference and Connectivity are emergent properties in the TWO point universe, but in this Game Universe they are Necessarily Emergent. In the next experiment we will look more to the almost magical Abstract Property of Emergence. Ta Da!

(By the way if you would like a PDF of the whole Game Universes essays then please contact me above, no problemmo)

[1] Note that whereas all single point universes and perfect circle universes are identical within their own type this isn’t the case with the single points or the perfect circles themselves. We can imagine a that contains two perfect circles, one being twice the size of the other. In this case there is difference, whereas we cant image two single points with any internal difference.

[2] Its really easy to get confused by the possibility of space in these kinds of two glove universes, and that’s because the structure of the glove contains space as it is. As we saw in Experiment one, you cannot really imagine a single red ladies glove universe but that is fine for the Universe Game.

[3] In these photos of the gloves there is the perspective of the photo, this wouldn’t be in any Game Universe that was a universe of just two gloves.

[4] It seems reasonable to think that “A is the biggest point in the universe” and “B is the biggets point in the universe” are inconsistent truths, this is because they. If they were combined from simpler truth lists then one of them would be falsified at the point of stipulation.

[5] It is easier to imagine an eternal, changeless single point than an eternal changeless two point, because of difference.