Assignment 3 Reflection

(Link to slides)

(This blog post will be formatted in relatively disconnected bullet points.)

• Firstly, I'm very happy with the assignment, and very thankful for JJ's contributions and wonderful partnership. When the project was announced, I had a few ideas circulating around my head: the history of prime numbers, history of zero, and most notably the history of mathematical notation and symbols. When I approached JJ to ask him to partner with me, we had a discussion about what topics he wanted to focus on, and he proposed cellular automata. ... What? What's a cellular automata? (Suffice to say, I was relieved to know that my classmates didn't know what those were either -- overwhelmingly so.) It actually took a while for me to warm up to his idea because I had some excitement towards the idea of mathematical notation and other symbolic arbitraries because of this complete lack of knowledge in the field. However, I still went along with JJ's idea, and I have to say I am glad I did. I learned about something new and it ended up being highly interesting (and based on the reactions of my classmates, that's the going consensus on the topic)!

• If I could think of some possible BC curriculum tie-ins to the topic of cellular automata, it would likely be on the representation-centered competencies. While coding is the first thing that comes to mind, we did mention that cellular automata are actually abstract concepts that are meant to be implemented. It could be on a flipbook of graph paper, a checkerboard, or something improvised like the floor tiles in our mathematics education classroom, but the idea is that there is an encapsulation of mathematical representation that cellular automata presents. More on the curriculum, we can definitely connect and reflect as intended; in the research we did on CA, we found that people have made countless connections and applications. Some fields were (not limited to) biology, computer science, epidemiology, physics, philosophy, and even recreation. Looking one last time at the curricular guide for BC mathematics, there are also points on visualization and story-based learning, which CA complements perfectly. However, I would probably be cautious using CA as a vehicle too early on; although the setup itself is very simple, there is much pre-loading to be done in terms of abstract thinking before students could reasonably be expected to handle going in depth with the field. But, a high-level overview and appreciation are always welcome.

• As for the actual presentation, it is a bit unfortunate that we were unable to cover the entire slide deck... though honestly, it might've been for the best. The choice of things to cut was relatively wise; it was important to cover the basics of cellular automata and the parameters, as well as the quick histories of prominent figures like Stephen Wolfram and von Neumann due to their foundation-rocking influence on the field (with the former revitalizing the field, and the latter conceptualizing the very basis of the field to begin with). I also want to note that I wish I could've found the actual location of where von Neumann's corner (the one where he constantly found himself in car accidents) was, but Google kept showing me articles that said he was so terrible of a driver that he had a corner named after him... without specifying where exactly the corner was! I was very thankful that we had more time though; while I was surprised that we had 8 minutes after the first section on how CAs worked (which I think was still vital), we were gracefully given more time so that we could show off all our art pieces.

• Speaking of the art pieces, this is where JJ deserves a large chunk of the credit considering that he programmed everything on his end (though I did my share of the work on the slide deck and research -- in other words, we had an equitable workload, rest assured). I was involved in providing feedback and suggestions; the window of the generated cellular automata would show how many time steps passed. We weren't able to demonstrate this more elaborately, but on the slide where we showed the lifeforms of Conway's Game of Life (still very proud of the fictional phylogenic tree that I made, haha) we were going to draw the lifeforms in in real-time. Yes, JJ even made it so we could draw in cells on the CA screen! Because of that, I think that while the exact CAs with their exact initial states made could be considered the art pieces we're presenting, I think that the canvases of these little universes are the real artistic pieces. They really do generate art themselves. Perhaps from that, we can say that our own universe is an artistic piece that built on itself.

• Getting into the connective philosophical, biological, and physical aspects of cellular automata (since these played big parts in the conceptualization of cellular automata), since we ran out of time and I had to condense it to a food-for-thought now: my question still stands. Is free will real? The last CA we showed eventually stagnates on the initial states that we tried, and it got me connecting: this is a lot like the heat death of the universe. If I recall correctly, the Wikipedia page for the timeline of the far future has a line that really resonated with me, paraphrasing roughly to "in the end, the lonely photon is the king of the universe". Wow. Let that sink in. Such a small, insignificant particle has become the most prominent thing in the whole wide expanded universe because nothing else is left to contend with it. Looking back at the CA we made, it eventually reached a death state with only flying photons that will never collide. Further connection made me trace back to the present and past; we have the Big Bang which was a bit like the first step out of an initial state, and the organisms could be seen as us. Are we all just manifestations of local rules applied on a universal neighbourhood around the cell? A while back on a previous blog post (in 450 I believe), I got philosophical and proposed that mathematics is the true deity above all, in its unshakable permeation in the truths and states of the universe. Maybe Pythagoras was right. If I were an Ancient Greek, I probably would've joined his cult and the belief that numbers were everything... but I digress. 

• I won't keep rambling much longer, but all-in-all this project ended up being a lot more enlightening to me than I thought. With the whole free will argument and the universe being deterministic based on a set of rules, it made me wonder on the way home on the bus: if our universe is just one big product of a cellular automaton (remember, CAs are an abstract concept to be implemented), who's setting the geometry of the board? Who's setting the initial configurations of matter, antimatter, and everything in between? Who's deciding the local rules, rather, the physical laws of the universe that dictate how things go? Even though we might have people arguing against determinism and fate and destiny, even randomness could be seen as a part of the cogs. Something is driving even the random number generator. And the real tripper is this: whoever set the parameters for our universe's cellular automaton, are they also a product of a grander cellular automaton? Does the chain keep going up? Where did it all begin, and when are we going to reach the point where we play God and create our own universes on a machine, or even a checkerboard? What are the implications on nihilism? Does nothing matter, or does everything matter, and how should we as clumps of cells interpret it all? When we think, "I'm going to defy my fate", are we really just dancing to the script? These are a lot of questions with no answers, but after mulling it over here I have to say that religious people are probably onto something that my presently agnostic mind is not aware of.

I lied, I have more thoughts.

• Do lifeforms in a cellular automaton know they are in a cellular automaton? Can they prove it?
• Could we prove that we or our gods don't exist on a cellular automaton ourselves?
• With universal constants that aren't bound to mathematics like the gravitational constant. who set those when defining our rules? Why did they pick such specific, likely irrational numbers? Does it hold meaning for a higher order sentience, much like how we chose a base of 10 for our number systems?
• There's a beautiful similarity between CAs and our universe: with simple rules, we cannot predict the sheer complexity that arises. Much like how CAs are beautiful, we can confirm even more that our world itself is the most beautiful thing out there. And even if one could theoretically predict the future if they accounted for all the rules on all the cells, it's so implausible that the ability to predict the future is effectively impossible. And that makes thinking about it so fun.