On Randomness

In 1930, a young British mathematician named Frank Ramsey published a paper containing a theorem that would come to bear his name. His insight was deceptively simple: complete disorder is impossible. No matter how chaotic things appear, patterns inevitably emerge. This mathematical truth, now known as Ramsey's theorem, suggests something remarkable about the fabric of reality—that beneath apparent randomness lies an inescapable tendency toward order.

One of the best known findings coming from Ramsey’s theorem has to do with friends and strangers. Consider a party with six people. Ramsey's theorem guarantees that among these six guests, you will always find either three people who all know each other or three people who are all strangers to one another. This isn't a mere curiosity about social gatherings; it's a window into a deeper mathematical reality that governs everything from the arrangement of atoms to the structure of the internet.

To understand why this matters, we need to think about what we mean by randomness. In our everyday experience, randomness suggests unpredictability and chaos—coins landing heads or tails, stock prices fluctuating up and down, or the seemingly arbitrary way friendships form at a party. We often imagine that if we could arrange things randomly enough, we could avoid all patterns. Ramsey's theorem tells us this intuition is fundamentally wrong.

The theorem works by revealing the hidden constraints that operate even in apparently random systems. When we color the edges of a complete graph—imagine drawing lines between every pair of points and coloring each line red or blue—we might think we're creating chaos. But Ramsey's theorem proves that no matter how we assign these colors, certain monochromatic patterns must appear. The mathematics forces structure into being, regardless of our intentions.

This principle extends far beyond abstract mathematics. In computer science, Ramsey theory helps explain why large networks inevitably contain highly connected clusters, a property that makes the internet both robust and vulnerable. In biology, similar principles govern how proteins fold and how ecosystems organize themselves into food webs. Even in physics, where quantum mechanics introduced fundamental randomness into our understanding of nature, Ramsey-like phenomena ensure that statistical patterns emerge from the chaos.

The implications challenge our understanding of emergence itself. We typically think of complex patterns arising from simple rules—flocks of birds forming intricate shapes, or individual neurons creating consciousness. But Ramsey's theorem suggests something more radical: that certain types of order are unavoidable consequences of size and connection, independent of the underlying rules. Structure emerges not because of what the system does, but because of what it cannot avoid.

This mathematical inevitability of pattern carries philosophical weight. If complete randomness is impossible, what does this tell us about the nature of the universe? Some theorists argue that Ramsey's theorem hints at why the cosmos appears fine-tuned for complexity. Perhaps the apparent "specialness" of physical constants that allow stars, planets, and life to exist isn't special at all. Rather, it might be an inevitable consequence of mathematical structure asserting itself even in the most fundamental laws of nature.

The theorem also illuminates the relationship between chaos and determinism in ways that complexity science is still exploring. While we can't predict exactly where patterns will appear in a random system, Ramsey's theorem guarantees they will appear somewhere. This represents a middle ground between the clockwork determinism of Newton and the pure randomness of quantum mechanics, a realm where outcomes are uncertain but structure is inevitable.

Perhaps most intriguingly, there are some suggestions that Ramsey's theorem might explain aspects of human consciousness itself. The brain's neural networks, with their billions of interconnected neurons, create exactly the kind of large, highly connected system where Ramsey phenomena should flourish. Some neuroscientists theorize that consciousness might emerge not from specific neural processes, but from the inevitable patterns that mathematical theorems like Ramsey's force into existence in sufficiently complex networks.

The deeper message of Ramsey's theorem transcends mathematics. It suggests that the universe has an inherent bias toward structure, that randomness and order exist in a more complex relationship than we typically imagine. In a cosmos that often seems governed by chance and uncertainty, Ramsey's theorem offers some reassurance: no matter how random things appear, patterns of meaning and structure will always emerge.

This doesn't mean the universe is predetermined or that randomness is an illusion. Rather, it suggests that chaos and order are partners, where the very attempt to create disorder paradoxically generates new forms of structure. In this light, the emergence of complexity, consciousness, and perhaps even meaning itself might not be accidents requiring explanation, but inevitable consequences of mathematical truth asserting itself in the physical world.

Frank Ramsey died tragically young at 26, just months after publishing his theorem. He couldn't have foreseen how his insight about inevitable patterns would reshape fields from computer science to cosmology. But his mathematical legacy continues to reveal new truths about the hidden order that underlies apparent chaos, reminding us that even in a universe governed by uncertainty, some forms of structure are simply unavoidable.

– Geoffrey W. Smith



First Five
First Five is our curated list of articles, studies, and publications for the month.

1/ Electricity-generating bacteria
“A team has discovered how certain bacteria breathe by generating electricity, using a natural process that pushes electrons into their surroundings instead of breathing on oxygen. The findings could enable new developments in clean energy and industrial biotechnology.” Read more here >

2/ Proximity to Golf Courses and Risk of Parkinson’s Disease
“Does living within proximity to a golf course affect the risk of Parkinson disease (PD)? This case-control study found the greatest risk of PD within 1 to 3 miles of a golf course, and that this risk generally decreased with distance. Effect sizes were largest in water service areas with a golf course in vulnerable groundwater regions. These findings suggest that pesticides applied to golf courses may play a role in the incidence PD for nearby residents.” Read more here >

3/ An 80,000-year history of the tomato
“Walk into a supermarket anywhere in the world and chances are you’ll be able to find a tomato in mere minutes. While technically a fruit, the tomato is more often grouped with vegetables because, due to its low sugar content, it is used more like a vegetable in cuisine. In fact, tomatoes have long been by far the most frequently consumed canned vegetable, as well as one of the most commonly eaten overall. … None of this would be possible, however, without thousands of years of plant breeding and genetic engineering.” Read more here >

4/ Quantum biology: How electron spin manages your body's power at the cellular level
“Growing evidence suggests that subatomic phenomena can shape fundamental activities in cells, including how organisms handle energy at the smallest scales. Quantum biology, as it’s being called, is no longer just a fringe idea among researchers.” Read more here >

5/ Why Catalytic Capital Needs a Better Definition
“The decline and fall of ESG offers a cautionary tale for social impact financing and highlights the need for the sector to sharpen its understanding of catalytic capital. We propose a potential definitional framework for catalytic capital to drive clarity, measurement, and greater market participation.” Read more here >



Did You Know?
Here we seek to demystify common terms and practices in our work as investors.

Carried Interest
Carried interest is a performance-based fee awarded to fund managers, particularly the general partners. It represents a share of the profits generated from successful investments in the fund. Carried interest serves as an incentive mechanism, motivating fund managers to maximize returns for the fund’s investors. It is typically earned once a certain benchmark return, known as the hurdle rate, is surpassed. Fund managers receive this share of profits, typically around 20%, on top of the return of their invested capital. The remaining 80% of profits go to the fund’s investors.

Carried interest is designed to align the interests of fund managers with those of the investors, emphasizing the importance of achieving strong returns and fostering a long-term investment focus. This structure encourages fund managers to take a patient approach, as they realize the benefits of carried interest upon the successful exit of portfolio investments, such as through acquisitions or initial public offerings (IPOs).

– Haiming Chen & Dylan Henderson

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