I'm Feeling Strangely Attracted
I'm Feeling Strangely Attracted
Key Takeaways from Edward Lorenz's Deterministic Nonperiodic Flow
In 1963 when Edward Lorenz first published Deterministic Nonperiodic Flow, he probably had no notion that it would become a catalyst for the development of a whole new class of science. In fact, all he was trying to do is predict the weather.
From it, we have since derived ideas and terminology that have made their way well into the public lexicon. Lorenz’s paper inspired ideas like the Butterfly Effect and characters like Ian Malcom in Jurassic Park.
A mathematician and meteorologist, Lorenz wanted to know if it was possible to create a deterministic model that would allow for an infinite runway of accurate weather prediction.
The spoiler for this line of inquiry, is no.
At the time, the weather was thought of only as a very complex fluid dynamical system. This just means that scientists like Lorenz were using what they knew about simple fluid dynamics to model this more complex system. In a lab setting, scientists could start with a very controlled system, and slowly introduced more complexity, while being able to maintain an accurate level of prediction- so why haven’t we found this possible with weather and other complex systems in nature?
The answer, is chaos.
Origin of the Butterfly Effect
Lorenz found in his data that long term outcomes of models were highly sensitive to initial conditions. Lorenz discovered this when he wanted to resume his computer’s run of projecting future data after a pause, but found that when he entered what he thought were the exact data-points for his calculations, only 25 iteration earlier, they had reached a drastically different state by the time they caught up to the point at which he’d left off at. How could this be? The answer was that in Lorenz’s paper printouts—this was before the age of the spreadsheet—, data was shown carried to 3 decimal places, when in fact his computer was calculating out to the 6th.
Each time Lorenz would try to reset the model with slight variations, carrying out to smaller and smaller changes in the data’s starting point, the outcome of the projections would always reach a point shockingly different than any varied iteration. This breakthrough is the origin for what we now refer to as the butterfly effect.
What did this mean in regards to Lorenz’s initial goal of accurately predicting long term weather patterns?
It meant that unless we know the exact state of the initial conditions that we use to carry our predictions forward, this goal was impossible to achieve.
Finding a Strange Attractor
While we may not ever be able to predict individual states of complex systems, we’re getting better and better at predicting the broader character of the evolution of these systems into the future. The study of these characteristics is called chaos theory.
Chaos theory is an interdisciplinary theory and branch of mathematics focusing on the study of chaos: dynamical systems whose apparently random states of disorder and irregularities are actually governed by underlying patterns and deterministic laws that are highly sensitive to initial conditions.
CC: Wiki
The term chaos theory wasn’t coined until 1975, by another mathematician named James Yorke, but follow any trail to origin and all roads lead back to Lorenz’s paper on weather prediction as the source for this line of investigation into the world around us. But if chaos theory can’t help us predict concrete things about nature, what makes it a valuable area of study?
Going back to Lorenz’s initial paper, despite the fact that predicting the individual states of the weather seemed to be a futile effort, each run of predictions seemed to follow an underlying pattern. To understand that pattern and it’s value, we need to define something called phase space. For simplicity, just picture phase space as a 3D area—when in fact it could also be 2D, 4D or ∞D. That area is made up of {X} number of points, where each point within that space is a possible state for a system being represented.
Again looking at Lorenz’s data as an example, his ‘phase space’ for representing the system of weather was conveniently—for our sake—plotted in 3 dimensions. Even though as discussed above, each iteration of data followed a wildly diverging path based on initial conditions, each iteration also seemed to converge into something like the below shape when plotted in this phase space —
This image is of the first discovered strange attractor, now referred to as the Lorenz attractor. Many other examples characterizing the evolution of different systems would be discovered in time. All strange attractors are a beautiful representation of the superposition between determinism and unpredictability.
Deterministic in that if we could somehow know the exact initial conditions of the system, we could follow its path with precision. Unpredictable in that true initial conditions are nearly impossible to measure in practice.
The Esoteric Conclusion
Ideas like this don’t come conveniently tethered to a—now that I know this, I can {X}—value proposition. It’s for this reason that I sometimes struggle to find the tangible point I want readers to walk away from as I do these riffs. But let me try this…
I am someone who takes preference in believing that I have agency in this world. Maybe you are too. In regards to the idea laid out above, to me, chaos theory suggests that we have a little bit of this agency, but are also the products of our past. There’s an infinitely small pocket of time in the present in which we have the opportunity to collapse upon a direction forward. I like to view that pocket as our own pocket of chaos, where depending on how the initial conditions are set, anything can happen. It is up to us however, to set those conditions with each passing moment.
Next week, I’m going to talk about something I call feature crawl.
Stay on course.
-Benjamin Andeson