Welcome to the Nebulous Future
An Introduction to Complex Systems
A Speech at Toastmasters, February 21st, 2018
Toastmaster, members and guests, good evening.
Around three hundred years ago, after setting the foundations of Calculus (ahem), Sir Isaac Newton wrote down his three laws of motion.
First – A body will stay at rest or constant speed motion unless acted on by a force.
Second – The acceleration a body experience is proportional to the net force applied.
Third – For any force, there is a force with equal magnitude and opposite direction.
Maybe we can also count in his universal gravity. The laws of motion unified previous theories of mechanics: the human study of motion and change, and demystified the laws that govern celestial bodies.
In the view of the developing subject called natural philosophy — “physics” — they are no different from the most mundane of earthly objects, and vice versa.
It was a hopeful time. Newton himself, perhaps, first had this dream, that were we to measure every component of the universe to its most accurate, we can predict how anything will be in the future. In fact, every edge and angle of the future will be as crystal clear as the past, and there will be no distinction in the flow of time, it will just be another direction we freely traverse.
[Uncertainty and Chaos]
Either fortunately or unfortunately, this dream did not withstand the test of time. Letting alone the complexities that arise due to quantum mechanics, the classical mechanics itself already contained issues so hard to tackle that an exact prediction seemed impossible.
Have you heard of the Butterfly effect? It was coined by mathematician and meteorologist Edward Lorenz, after one atmospheric model he created.
To me, who thinks about physics in bed to aid my sleep, you can use this term not only to attribute the potential impacts of a minute change but also the futility to summarize any event by its exact causes, even in simulation.
In a simulation once, a scientist placed two test particles one-millionth of an inch apart in his earth model over the Atlantic ocean. After five days of simulated time elapsed, one flew to the west coast of US, the other point, initially placed virtually at the same spot as the first one, was sent to India.
No wonder why I sleep so well every night… Seriously though, I sometimes feel” powerless to explain such things, not perhaps due to their scale and momentum — the mathematician trapped in my head can take care of that — but the sheer degree of computational complexity: every single component so easy to deal with, but together, they become so powerful and intriguing; they wreck computers.
To give you a better picture, another example might be from our everyday experience.
If you have a driver’s license, you might remember the trouble of parallel park. Why is reversing harder than driving forward?
Because when you drive forwards, your steering wheel point where you are going. If you are reversing, you adjust the wheels, which in turn PUSH your car to the desired direction.
There’s one more degree of freedom. Try reversing with a trailer.
Actually, every process, in reality, is reversing with billions after billions of trailers behind you.
What if I have been thinking about these problems wrong? What is a scientist’s way of approaching this? Are there alternative angles?
Anyway. Why bother?
I realize in every public physics talk there must be a moment “Why do you work on all this?” It’s actually an excellent time for introspection (apart from attracting funding. Every medicine somewhat takes after some chaos theory).
Just like how Newton’s simple axiomatic rules gave birth to all the dynamics in the classical realms, other complex systems also gradually attracted our interest, out of different settings throughout science.
My math professor once gave me a problem to think about. Try to model a group of birds or a school of fish with as few lines of code as possible. If you remember seeing Finding Nemo, you might know what I am talking about. I would ask myself, did they program the motion of all hundreds of fish one by one?
One would walk away from this problem looking like this. ©Disney / Pixar
However, my teacher’s suggestion shocked me. Her solution only effectively has three line of code, applied to every individual “animal”:
First: Follow neighbors’ motion.
Second: Keep some distance with your neighbors.
Third: Avoid obstacles.
With this code, the computer produced swarms that is natural looking. And yet, the construct remains surprisingly compact and succinct.
Each component does not possess any specific line of instruction saying that they MUST make such-and-such-and-so patterns. Working on each’s own accords, amid possibly chaotic environments, they produce effects as a whole.
(Ref: https://en.wikipedia.org/wiki/Swarm_behaviour, looking for better sources)
I remember admiring ants. Very soon after I dropped some food onto the floor, a worker ant would discover it, and working on each’s own accords, amid a variety of other interests, the entire squad would turn that single discovery into every member’s dinner with astonishing speed.
An ant might be cognitively incapable of much we call intelligence, but in a group they are smart — in this way they become complex.
They are systems like this.
As I talk, and you listen, molecules in our cells work on each’s own accords, amid chaotic environments, produce effects that keep us alive and (hopefully) engaged. So does every cell that they make up.
Molecules only follow the law of chemistry — thermodynamics — but as a whole we are undoubtedly alive, casting changes to this world single atoms never could. Going even bigger, all of us, humanity, our interactions, economy… We are part of the same pattern.
We are systems like this.
[RE: Newton’s Dream]
In this short amount of time, at best, I have only scratched the surface of complex systems. It is, indeed, complex, as reflected both by chaotic behaviors, and the emergence of interesting patterns. These two might be more closely linked than we know.
Some computer scientists are investigating how such phenomena might translate to the fabrics of the universe.
In their ideas, was there someone that started our universe, it might not need to tune every dial of fine structure but perhaps set a few simple rules for everything to naturally emerge.
There’s still much to do in physics, and so I dream of devoting my efforts to it. Newton’s dream may be in shambles, but there’s still something we hold on to. That with science and rational thinking, nothing will be completely in the dark forever. And step by step, we see more pattern in the nebulous future, and understand the universe deeper.