Cellular Automata — Part One
"Who's this Wolfram guy?" Zac asked. "Have you mentioned him before?"
"No," I replied. "Wolfram is pretty interesting. He wrote three books on particle physics by the age of fourteen. He was also publishing scientific papers on quantum field theory and particle physics by the age of fifteen, so he was a bit of a child prodigy. He ended up joining the faculty at Caltech while also becoming the youngest recipient of the Macarthur Fellowship in the early eighties when he was just twenty-one. The Macarthur Fellowship is more commonly known as the genius grant."
"So, you're basically saying he's a massive nerd?" Zac asked.
"Essentially, yes. My point is, he's not some random crackpot. He is really fucking smart. He's been operating outside the academic system for a long time now, so I have a lot more faith in his ability to avoid groupthink. He also runs a successful company and is self-funded, so he doesn't have to adhere to old, dogmatic ideas to secure grant funding. When you're completely independent, you can do whatever the fuck you want — which makes you very dangerous to big institutions.
Many people believe Wolfram has a lot of unfounded arrogance and an ego the size of Jupiter, and perhaps he does. He definitely has the courage of his convictions, which is really only a bad thing if your convictions are wrong. If your convictions turn out to be right, society puts you on a pedestal. Arrogant crackpot or misunderstood genius: it's a fine line.
Anyway, the thing I'm interested in is his book. In 2002 he self-published a thousand-plus page tome entitled 'A New Kind Of Science,' where he made a bold claim: that we need to start thinking about the universe as a computation, where complexity emerges from simple programs."
"What's a simple program?" Zac asked.
"It's just a simple set of abstract rules that are applied recursively. Wolfram uses cellular automata as an example of a simple program that can yield incredible complexity. I'll explain this using some diagrams from his book. This is an example of a cellular automaton's ruleset."
Rule 1"You start with a grid and a single black square. You then move onto the next line of the grid, coloring each square according to the ruleset. The top row in each box shows one of the possible combinations of colors for a cell and its immediate neighbors. The bottom row then specifies what color the cell should be on the next step. So, according to this rule, if the three cells above a cell are white, you color the cell white. In all other cases, you color the cell black. This particular ruleset produces this pattern..."
Rule 1"Err... cool?" Zac said, sarcastically. "This looks revolutionary."
"It is," I replied. "This is just one rule that gives you a straightforward pattern. Everything ends up being black. But what about this rule..."
Rule 90 is applied"Wait!" Zac gasped. "That's a Sierpiński triangle!"
"It is, indeed. Look — here's the zoomed out version."
Rule 90 produces"This is what emerges when we let that simple program run for five hundred steps," I said. "Notice that this is a very ordered pattern. From your perspective observing this pattern, could you predict what the next 500 steps would look like?"
"Well, yeah," Zac said. "You just repeat the pattern."
"What pattern?"
"You just draw an upside-down triangle inside every right-side-up triangle."
"Is that the pattern, though?" I asked.
"Well, that's what I see," Zac said. "It's all just triangles."
"Yes," I confirmed. "When you observe this pattern, that's what you see: a Sierpiński triangle. You could communicate to another human what the pattern is by talking about triangles. You could write a mathematical equation to describe the pattern, and the equation would draw triangles. But now I want you to think of this pattern as a metaphor for gravity."
"Gravity?"
"Yes, gravity. Gravity is also a very predictable pattern. If I drop an apple, I can predict what will happen to it — just like I can predict what the next million steps will be on that Sierpiński triangle pattern. There is a mathematical equation that describes how fast the apple will fall to the ground — just like there is an equation describing how to draw a Sierpiński triangle."
"So...?" Zac prodded.
"So, the equation is not the truth. The equation is just a human looking at the emergent pattern and describing it using math. At the deeper level of truth, we know that the pattern emerged from a simple cellular automaton." I showed him the ruleset.
Rule 90. This simple, recursive program produces the Sierpiński triangle pattern."Now," I said, "you can see how the triangles are actually an emergent property of this simple program. You'll only notice the triangles if you zoom out and view the big picture, in the same way that you'll only notice space and time if you zoom out and view the big picture. Space and time are definitely emergent if reality and consciousness are the same thing."
"Hmmm," Zac pondered. "I still don't see what's so revolutionary about this. Telling someone how to draw a Sierpiński triangle is pretty simple: draw an upside-down triangle inside every right-side-up triangle. How is this cellular automaton thingy any simpler than that explanation?"
"Good point," I said. "But I started you on an easy one. How about this one..." I showed him another pattern.
"Now, give me an equation, or set of instructions, that describe how to draw this pattern."
"Err..." Zac hesitated. "I mean, the left-hand side seems pretty ordered. I could isolate the shapes on the left-hand side and tell you how to draw those." He took my phone and looked more closely. "What on Earth is happening on the right-hand side? It's chaos!"
"Oh, really?" I smirked. "Maybe observing more of the pattern will help." I showed him a zoomed-out rendering of the cellular automaton.
Zac stared at the pattern, then at me. "I have no clue," he said. "I can describe the pattern on the left-hand side. The left-hand side looks predictable. The right-hand side looks totally random, though."
"How about we extend the pattern even further," I suggested.
"Nikki, this makes no sense!" Zac cried. "It's way too complex. It's chaos. It's random. I can't tell you how to draw that. I have no idea how to predict what is happening on the right-hand side. It just looks like noise."
I smiled. "Remember when I was talking about David Bohm? Bohm believed there was no such thing as disorder. He believed 'random' disorder was just deeply hidden order.
I also want you to think about this passage we read in Conversations With God..."
As for the so-called "accident" — the truck coming around the bend, the brick falling from the sky — learn to greet each such incident as a small part of a larger mosaic.
Neale Donald Walsch
"And this one." I continued reading.
For nothing happens by accident in God's world, and there is no such thing as coincidence. Nor is the world buffeted by random choice, or something you call fate.
If a snowflake is utterly perfect in its design, do you not think the same could be said about something as magnificent as your life?
Neale Donald Walsch
"And then this one," I said.
Accidents happen because they do. Certain elements of the life process have come together in a particular way at a particular time, with particular results — results which you choose to call unfortunate, for your own particular reasons. Yet they may not be unfortunate at all, given the agenda of your soul.
I tell you this: There is no coincidence, and nothing happens "by accident." Each event and adventure is called to your Self by your Self in order that you might create and experience Who You Really Are.
Neale Donald Walsch
"God says, 'Accidents happen because they do. Certain elements of the life process have come together in a particular way at a particular time, with particular results.' Listen to the way he says that. It's not like he says, 'I choose for particular things to happen in a particular way because I want it to happen that way.' Throughout the book, he talks about this as a passive process — as if he's just constructed a cellular automata-type simple program and is sitting back and letting it run. Actually, this passage articulates it better…"
If you believe that God is some omnipotent being who hears all prayers, says "yes" to some, "no" to others, and "maybe, but not now" to the rest, you are mistaken. By what rule of thumb would God decide?
If you believe that God is the creator and decider of all things in your life, you are mistaken.
God is the observer, not the creator. And God stands ready to assist you in living your life, but not in the way you might expect.
It is not God's function to create, or uncreate, the circumstances or conditions of your life. God created you, in the image and likeness of God. You have created the rest, through the power God has given you. God created the process of life and life itself as you know it. Yet God gave you free choice, to do with life as you will.
Neale Donald Walsch
"If God created the process of life, then he created the underlying program that is generating our reality. Now he is letting that program run because he is the observer, not the creator. We are currently operating inside these laws, which means we exist inside the emergent pattern that these laws produce. He talks about this here..."
I have established Laws in the universe that make it possible for you to have — to create — exactly what you choose. These Laws cannot be violated, nor can they be ignored. You are following these Laws right now, even as you read this. You cannot not follow the Law, for these are the ways things work. You cannot step aside from this; you cannot operate outside of it.
[...]
The direct answer to your question is, yes, you may do as you wish without fear of retribution. It may serve you, however, to be aware of consequences.
Consequences are results. Natural outcomes. These are not at all the same as retributions, or punishments. Outcomes are simply that. They are what results from the natural application of natural laws. They are that which occurs, quite predictably, as a consequence of what has occurred.
All physical life functions in accordance with natural laws. Once you remember these laws, and apply them, you have mastered life at the physical level.
What seems like punishment to you — or what you would call evil, or bad luck — is nothing more than a natural law asserting itself.
Neale Donald Walsch
"Let's look back at this cellular automaton that appears so complex and chaotic. Imagine this pattern is a metaphor for our universe. We're sitting here, scratching our heads, trying to figure out how it all works. We might observe the ordered things — like gravity and the various particles and forces — and write a set of equations to describe those patterns. We call this science. That's equivalent to telling someone how to predictably draw the ordered left-hand side of this cellular automaton's pattern.
But then we get to the right-hand side, and our equations break down. We can't write static equations to describe why your child died of cancer, or why your neighbor won the lottery. Those things just seem random; chaotic; pure chance."
I continued. "So on the left-hand side, we have a whole bunch of separate equations describing different predictable phenomena in our universe. On the right-hand side, we have a big question mark because everything looks unpredictable and random. Now, remember back to the Hermetic Principle of Cause and Effect that we read about in The Kybalion..."
"Every Cause has its Effect; every Effect has its Cause; everything happens according to Law; Chance is but a name for a Law not recognized; there are many planes of causation, but nothing escapes the Law."
Three Initiates
"Chance is but a name for a Law not recognized," I repeated. "How come we can write mathematical equations that we call 'laws of physics' to describe ordered phenomena like gravity, but then we call other stuff 'random?' How do we know it's random? Where is the evidence?"