Decoding the Symphony of the Universe: The Unseen Computational Processes Shaping Our World

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Every Aspect You Observe Is Governed by Computational Dynamics, Provided You Understand the Perspective

This narrative was initially published in Quanta Magazine.

In the film "Oppenheimer," early on in his journey, Niels Bohr presents a challenge to the physicist.

Bohr: Think of algebra as similar to sheet music. The key question isn't "do you know how to read music?" but rather, "can you understand its melody?" Are you able to perceive the music, Robert?

Oppenheimer: Indeed, I'm capable.

The algebra isn't audible to me, but I can sense the machinery.

My anticipation for my very first computer, a Radio Shack TRS-80, began in the 1970s, long before I actually interacted with one. I envisioned its operations and even drafted basic programs, mentally following their execution on the hardware I yearned for but hadn't yet acquired. When I eventually input the programs and saw the results directly, the absence of witnessing the internal workings firsthand was somewhat anticlimactic.

Today, the machine itself isn't something I can see or hear, yet it communicates with me; I sense its vibrations as it processes information, cycles through operations, makes decisions, and explores options, until it finally reaches a conclusion and delivers a solution. In my view, a program isn't just a series of static instructions; it's akin to a living entity that executes my commands and ideally achieves the desired outcome. I'm aware that computers don't actually operate in this manner, but this doesn't hinder my figurative perception of the machine.

When you begin to ponder over the concept of computation, you'll notice its presence in numerous aspects of daily life. Consider the act of sending a letter via the postal system. You place the letter inside an envelope, ensure it has an address and postage, and drop it into a mailbox. Miraculously, it finds its way to the intended recipient's mailbox. This journey represents a computational process – a sequence of steps that transports the letter from its origin to its intended endpoint. This method of routing mirrors the processes used for electronic mail or any data transmission across the internet. Viewing everyday phenomena through this computational lens might strike some as peculiar, but to paraphrase Friedrich Nietzsche, “Those who were seen dancing were thought to be insane by those who could not hear the music.”

The inherent capability of machines to process information gives us a computational lens through which we can examine nearly any event, including those that appear entirely unpredictable, like the notion of randomness. Take the example of flipping a coin, which at first glance seems entirely left to chance. However, it can actually be broken down into a complex series of computational steps that determine whether it lands on heads or tails. This result is influenced by a host of factors: the initial force, angle, and height of the toss; the coin's weight, diameter, thickness, and how its mass is distributed; the resistance of the air; the pull of gravity; the surface it lands on; and so forth. The same goes for mixing up a pack of cards, rolling dice, or spinning a roulette wheel—even the creation of "random" numbers by a computer, which is achieved through executing a deliberately intricate algorithm. In reality, none of these processes are genuinely random.

The concept has roots that stretch back hundreds of years. Pierre-Simon Laplace introduced the notion in 1814 through his work, "Philosophical Essay on Probabilities," where he outlined the concept of an entity, today referred to as Laplace's demon, capable of forecasting these results.

It is important to view the universe's current condition as a result of its previous state and as a precursor to its future condition. A being with knowledge of every force at work in nature at any given moment, along with the instantaneous locations of everything in the universe, could, assuming its intellectual capacity was vast enough, encapsulate the movements of both the mightiest celestial objects and the smallest particles in the universe in a single equation.

The converse suggests that to an individual lacking sufficient intelligence, activities like flipping a coin would seem to be governed by chance. Computational language enables us to clearly define this relationship.

In the early months of this year, Avi Wigderson was honored with the Turing Award, often likened to the computing world's equivalent of the Nobel Prize. His recognition came, in part, for establishing a theoretical link between randomness and computationally challenging mathematical functions. Wigderson, along with his team, developed a method that transforms a sufficiently intricate function into "pseudorandom" bits, which are indistinguishable from genuinely random bits through efficient means. It appears that randomness is essentially unpredictable computation.

Is there a method to navigate the unpredictability and intricacy we encounter? The strides made in artificial intelligence, particularly through the avenue of machine learning, offer us a hint of the potential to achieve this. Data can be divided into two categories: one that is organized and another that is unpredictable. For instance, the English language has a complex framework at its core, and the sentences created by people over time can be considered as random extractions from this framework. The advancements in machine technology have enabled us to analyze these random extractions and uncover a significant portion of the complex framework lying beneath. While this framework might seem obscure, it enables us to replicate the random extractions, thus allowing us to create new English sentences as needed.

Reflect on the challenge of translating languages. Picture a person, Sophie, who was raised bilingual in English and French and currently earns her living as a translator. She has the ability to effortlessly interpret an English document, grasp its complete meaning, and then recreate that in French. From a computational perspective, the mechanism at work here is Sophie's mind, which engages in a specific methodology to transition from English to French. It's probable that Sophie isn't fully aware of the intricacies of this methodology or doesn’t consciously consider it a methodological process, yet it unfolds regardless.

Imagine we're looking to convert text from one language to another using a computer. Merely relying on a French-English dictionary to change each word individually is ineffective because languages vary in their grammatical frameworks, and the significance of words can shift depending on the situation. Utilizing linguistic instruments is only partially helpful; the task of computationally grasping language extends beyond our capacity to articulate.

Sophie's proficiency in multiple languages stems from her upbringing in a home where two languages were spoken, allowing her to become familiar with their intricate details. Similarly, machine learning employs a technique that involves educating language models using vast datasets. These models are built on sophisticated neural networks, which are essentially groups of synthetic neurons intricately linked together. Each connection within this network has certain weights that modify the signals passing through. With adequate training, this neural network can accurately forecast the likelihood of the subsequent word in a sequence when translating from English to French.

Just as we usually can't grasp the entire mechanism behind how a trained neural network operates, similar to how Sophie might not fully comprehend her translation methodology, we can still replicate the procedure to determine the likelihood of the succeeding word. If the neural network has been trained flawlessly, the predicted likelihood of the next word it generates would be indistinguishable from what Sophie might articulate. In a way that echoes Wigderson's association between complexity functions and pseudorandomness, forecasting the likelihood of subsequent words allows us to understand the intricate computations involved.

English and French can be considered as arbitrary selections from the broader category of human languages, and the latest technologies have uncovered sufficient patterns within this foundational framework to enable effective translations, including among less commonly spoken languages.

The algorithms used for learning are essentially procedures, and I sense the adjustments in the parameters as we input a growing number of instances to educate the models. The progress made in machine learning over the recent years has enabled us to achieve intricate tasks, ranging from human-related activities such as translating, visual perception, artistic creation, and dialogue, to biological processes such as the folding of proteins.

Machine learning algorithms continue to face challenges in accuracy and can struggle with simple logical tasks. However, we have now reached a point where computational methods can assist us in dealing with the unpredictability that comes from intricate systems.

I consider myself fortunate. I've been able to shape a research career centered around the devices that resonate with how I perceive the world. It feels like I've discovered my true purpose, or rather, it has discovered me. Whether you're drawn to the rhythms of music, the intricacies of algebra, the logic of computation, the wonders of biology, the allure of magic, the beauty of art, or any other means of comprehending the world, pay attention to it. You never know what mysteries you might uncover.

This article is republished with consent from Quanta Magazine, a publication autonomously operated by the Simons Foundation. Its purpose is to boost public comprehension of science through reporting on the latest findings and progressions in mathematics, as well as the physical and biological sciences.

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