The upcoming episode of Westworld season 2 is entitled “Phase Space”

If you haven’t yet seen the preview, you can find it here.

I’m going to attempt to explain the concept of phase space is the simplest way possible, because there are a couple of interesting points: cat’s, cradles, and a man named Arnold. Not to mention a bit of tinfoil, to wrap it all up.

Phase Space

Chaos theory is broadly defined as recognition of mathematical and physical patterns that define an underlying order to occurrences that otherwise seem random. A phase space is a way of defining every possible outcome related to a set of variables, mapped in space.

It evolved from the work of a meteorologist named Edward Lorenz who wanted to create and electronic weather simulation. The resulting model looked something like this:

It has been said to resemble a butterfly from certain angles and an infinity symbol from others. On the right, is the butterfly we are shown in Shogun Sweetwater.

One of the findings of the early studies was that the outcomes of the model were extremely sensitive to changes in the variables. This came to be known as “the butterfly effect”; if a butterfly flaps its wings in China, it could cause a blizzard in Chicago.

Another interesting thing about phase space is that one of its pioneers was named “Arnold”, Vladimir Arnold to be exact. Arnold created a set of 4-dimensional modeling to provide solutions to dynamic systems, such as planetary evolution and the behavior of an electron in an electromagnetic field. It’s all very fascinating, but way over my head.

The cool thing is that Arnold came up with a method of explaining the concept in two dimensions, a concept known as “Arnold’s Cat Map”.

There’s more than one way to skin a cat

Arnold observed that just as matter is composed of atoms, a picture is composed of pixels. Individually, each pixel represents no more than a colour value, but together they form a coherent picture.

To illustrate the underlying order in a seemingly random system, Arnold developed a simple transformation algorithm that reorders the pixels in a photo. If enough iterations are performed, the photo will return to its original state.

I’ll bet you were thinking that the “Cat” in Cat Map was an acronym for something. But no, it actually refers to Arnold’s own kitten whose photo he used as his example. Our furry friends have been sliced and diced into feline fibonacci by wannabe physicists ever since.

You’ll notice how the first iteration and the second to last iteration look like mirror images of one another. The picture becomes less recognizable as the iterations continue, but ghostly images of the original image soon start to manifest and the picture is eventually restored to normal.

Arnold’s algorithm provides the capability to predict the number of required iterations based on the number of pixels. The example to the left used a 150*150 picture and required 300 iterations.

For further reading about Arnold and his cat, I largely used Wikipedia and this Sheffield University programming tutorial.

Cat’s Cradle?

There was mention earlier in the season of “The Cradle”. From the clues on the website, this is described as a simulation environment for guest experiences. The diagram provided looks like a technical architecture diagram for file storage and computations. It also seems incredibly valuable to Delos.

So, it’s not hard to believe that the Cradle could be where Arnold’s Model is stored.

Imagine an algorithm that is built over 30 years of guest and host experience, across 6 different cultures. Facebook on acid. This would provide a way of predicting all possible outcomes based on the smallest change in variables; the butterfly effect. Question is, can the Cradle be used to update variables in real-time? How about in time past? That would certainly make it a good weapon.

I’m not convinced that Delos is even fully aware of its capabilities.

We’ve seen from this past episode, “Akane no Mai”, that Shogun world has the same characters and stories as Westworld. The Delos website has also added a map of Shogun World that mirrors the Westworld map. What if all the other worlds are designed as mirrors of one another so that only the culture variable is changed. How does that impact choices? This seems like a good way to test the model. Perhaps that’s why there didn’t appear to be any guests in Shogun World.

There is a flag in Shogun world that stands out from the others. It appears to be the mirror image of the Delos Corporate Research Group logo. That logo doesn’t appear anywhere in the park in Westworld. It seemed to be hush-hush. It seems odd that it would be displayed so prominently in Shogun World.

By the way, “Cat’s Cradle” is a book by Kurt Vonnegut. Coincidentally, this is the same author that wrote “Sirens of Titan”, which we see on the bed in James’ room.

“Books are essentially mosaics made up of a whole bunch of tiny little chips…” (Kurt Vonnegut)

Cat’s Cradle explores themes of free will and dependence on potentially destructive technologies. At the heart of the story is a made-up religion, created to ease the suffering of the people on a small fictional island. The religion is built around the principle of “foma”, which means harmless untruths. As a result, followers of the faith embrace, and even delight in, the inevitability of everything that happens.

“Some people choose to see the ugliness in this world, the disarray. I choose to see the beauty.”

I mention this only because harmless untruths seem to be a tool that Ford is not shy to use. For example, never mentioning a partner, suddenly fessing up to Bernard that he had a partner, then finally telling Bernard he was that partner. Another example of this could be seen last season where Teddy’s recollection of Wyatt seemed to go through a few variations. In fact, all the hosts are given backstories that have no basis in reality. Foma?

The tech itself in Cat’s Cradle is a substance called Ice-9, which was developed for military, until it was discovered that even a trace amount of Ice-9 would cause a global catastrophe.

What does it mean?

In another post, I propose that the park is a bigger version of the room that James is in. A really big fishbowl. A discrete environment like that would provide the required boundaries for the phase space model, by providing control over environmental factors, including flora and fauna.

However, the bigger takeaway from the fishbowl idea is that James’ room is the centre of William’s maze. That William is a host with James’ consciousness. Long story short, I speculate that William and James have completely different natures. William needs to find his way to James, realize who he is, and then journey back outwards to find William again. Only then will he have conquered his demons, gained empathy, blah, blah. “Start where you end and end where you began”.

It’s not a bad theory, if you have time to check it out.

The point of raising it again here is that I had been trying to find a way to represent the concept of getting to the centre and not recognizing himself, then having to make the journey back outwards. Then, Arnold’s cat gave me the answer:

I’ve shown every 10th iteration for illustration purposes. This image of MIB required 222 iterations, but I speculate that William actually needs 941 iterations to return to himself. I also believe he has not yet reached the halfway point, but he’s almost there. I also explain my reasoning for 941 in the fishbowl theory.

Unfortunately, I don’t know the exact number of pixels in a real live William to confirm.

All that said, I have yet to convince one single person that William is James. And for those who think it’s crazy, then you most certainly will not like my idea that Emily is actually Logan. I will just drink my Koolaid alone.

As for Arnold, I am not sure this solves the mystery, but it is food for thought. I’ll post speculations on Bernard separately.

I have bored you enough for now, but I hope you will walk away with some food for thought.

Thank you for visiting. Please come find me on twitter @ jezzie_bell and let me know what you think.