I recently read the novella The Story of Your Life by Ted Chiang, and heck, it was some of the most mind-bending shit I've read in a few months. It brought the same intuition-breaking experience I underwent when first hearing Sean Carroll talk about quantum physics or WaitButWhy on AI (my first-time reading about emerging tech) or even 3blue1brown talk about Euler's formula. These concepts are too good for me to not try my hand at writing about them.
Note: the post contains some spoilers. If you would rather consume these ideas via the book, you can read it here for free. (It's worth the 1 hour read trust me)
To describe the refraction of light, this is how my Grade 10 science teacher taught it:
When a ray of sunlight hits the surface of the ocean, it changes direction.
Why? How does light know what direction to change in? This is completely given by the speed of light through each medium, calculated like this:
In 1650, Fermat discovered a way to explain this change of direction using a completely different method: light will take the path which minimizes the time it takes to reach its destination.
Some paths may be of shorter distance, but will take more time because light spends more time travelling through the slower medium (water).
Other paths may lead light to travel less distance through water, but the longer total path length offsets these time savings.
When I first heard about this principle, this was how I looked at it: Surely, the fact that light happens to take the path of least time is not a cause, but an emergent effect out of the laws of refraction. Least time just happens to happen out of Snell's Law, and is not the defining feature of what refraction is.
If the principle of least time were the cause, that would mean that light had to not just 1) know its destination in advance but 2) will "try" different paths and "choose" the one that minimizes the time spent. That could not possibly be.
I'm not the only one whose mind is bent - Planck "wrote volumes" about this topic, according to the book. In the story, Louise was bothered by this phenomenon, as she put it, "The ray of light has to know where it will ultimately end up before it can choose the direction to begin moving in... That’s what was bugging me."
But, what if one based their worldview off the principle of least time? That it wasn't emergent out of refraction, but the cause? This is where things get interesting.
The principle of least time is grouped in a branch of laws known as "variational principles." Almost every law of physics can be expressed as a variational principle, which means that in principle (no pun intended), physics can have variational principles as its starting point, and concepts such as sequential actions or cause and effect will get worked out through layers of mathematics. Just like how in our current physics, we start with sequential action and then variational principles emerge from integrals and derivatives - two completely different ways to arrive at the same understanding of our universe.
Gary Donnelly, a physicist in the book, sums up this mode of understanding - "while the common formulation of physical laws is causal, a variational principle like Fermat’s is purposive, almost teleological."
Amongst the variational principles is the path integral - what Hilary Diane Andales describes as "perhaps the greatest generalization in physics" - one of the most elegant pieces of physics that is often overlooked. The theory does indeed describes something seemingly trivial - why objects travel in straight lines. Essentially, the principle states that all the non-straight ones destructively interfere with each other and the average of all the paths is the straight line. She beautifully sums it up as "nature tries all possibilities; but only the harmonious ones flourish." (Here's a great video by Hilary to learn more.)
But we're not here to fangirl and nerd out over physics, as much as I would enjoy that. We're here to talk about the philosophical ramifications.
In the book, a group of 7-legged aliens visit earth. The heptapods use variational principles as the starting point in their physics, and then arrive at basic cause and effect using their equivalent of calculus. Concepts that are basic for us are difficult from them to grasp, yet principles taught at a graduate level such as Fermat's are elementary to them. Their difference is physics is caused by the fact that they look at the world through a different lens.
Heptapods fundamentally think differently.
For one who knows the future, it makes sense that they would develop their physics through the teleological, purposeful lens. You know the future. So light already knows its destination. Thinking of the world "teleologically" means thinking of everything at once, of all time periods at once, in a "simultaneous mode of awareness", and so you view all events across different times through the same lens. Light-now and light-future can have a relationship, and it makes sense for light-now to consider light-future. However, cause and effect becomes irrelevant - as Louise says, "Freedom isn’t an illusion; it’s perfectly real in the context of sequential consciousness. Within the context of simultaneous consciousness, freedom is not meaningful, but neither is coercion; it’s simply a different context, no more or less valid than the other." This can be taken one step further to say that when you know the future, cause and effect loses meaning.
That's one of the main arguments of the book - that if you can either know the future, or have free will, but not both. Once someone reads the Book of Ages, a Greek mythological book that records every event in the past and future, she will not act in any way that contradicts it, given the premise that the book cannot be false.
After interacting with the heptapods and learning their language, Louise starts to see the world how they see it, getting "visions" of the future written in the same way that characters experience flashbacks. She knows her child will die of a rare disease at 25, but "chooses" to have her anyway.
Or... did she choose... did she have a choice at all?
The reason why humans have trouble conceiving variational principles as starting points or have philosophical barriers from accepting it as reality is that we think of the world through a sequential lens, through cause and effect. that one thing must happen and then the next - that's the foundation of free will. The light hits the water (cause), and then the light changes direction (effect).
For ones who have choice and don't know the future, such as human beings, the sequential way of looking at it makes more sense, and you can see why humans evolved to see the world this way.
Likewise, for the heptapods, who look at the world through a teleological lens, who experience the past and future all at once, you can see why they evolved an understanding of physics that considers Fermat's principle as simplest explanation for refraction. To quote the book,
When the ancestors of humans and heptapods first acquired the spark of consciousness, they both perceived the same physical world, but they parsed their perceptions differently; the world-views that ultimately across were the end result of that divergence. Humans had developed a sequential mode of awareness, while heptapods had developed a simultaneous mode of awareness. We experienced events in an order, and perceived their relationship as cause and effect. They experienced all events at once, and perceived a purpose underlying them all. A minimizing, maximizing purpose.
Next time you're struggling to understand variational principles or wrap your head around some intimidating integral calculus, remember that, to a different species, these concepts are not calculus-heavy unnatural math to which one may ask, "Why am I even learning this," but the foundation of math and science.
If we can know the future, should we? Would you read the story of your life? When this was asked in the TKS UN Challenge afterparty, a group of 10 students all had different answers, ranging from "no way that will get rid of serendipity" to "I'll ask my parents to read it and see whether they want to tell me."
Knowing your future isn't some glorious ideal that will allow you to make better decisions, because knowledge of the future removes the need to make decisions. Knowing your future will rob you of something we fundamentally consider as part of being a human - your free will.
As this video puts it, there is no definite answer to free will or determinism. Both are representative of the ways that humanity and heptapods see the world.
The book is written from Louise's point of view, as a letter to her future child. This book is even interesting from a purely literative standpoint - written in second person future tense - a combination of two tenses each of which are not commonly used, and yet, Ted Chiang combines the two of them! Only this book's unique circumstances regarding teleology / free will allows for this unique literary expression.
Does living to "act[ing] to create the future [they already know], to enact chronology," as the heptapods do, lose the meaning of life? To Louise, it doesn't. She experiences joy as a parent, calling her child " a daily delight" although she knows that she will die at 25. She still finds joy in being with Gary although she knows that they will divorce.
I mean, you reread books, right, and you can still find joy in them while knowing the outcome. As one commenter says, "I was marveling how they pulled off [the movie adaptation of The Story of Your Life] when I watched it for the first time instead of feeling sad that I knew how the story would go."
This means if you liked this blog post, you will enjoy the book too. Even after you read some spoilers already. Beauty doesn't have to be in the unknown.
This book is a masterpiece. I had forgotten how it felt to experience such enlightenment.
Ted Chiang explains all these physical and philosophical concepts better than I. If you want to further explore the connections between free will vs determinism, sequentialism vs teleology, and cause and effect vs variational principles, read the book.
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