Natural science

Natural science is the broad field of science that seeks to understand the natural world — its phenomena, laws, and structures — through systematic observation, experimentation, and reasoning. It studies everything that occurs in nature, from atoms and organisms to planets and galaxies, aiming to discover universal principles that explain how the physical and biological world works.

How Random Molecules Might Have Sparked the First Life

~ Manuel Castañón-Puga

Imagine you’re sitting at your desk with a messy pile of LEGO bricks. You’re not trying to build anything specific. Still, every so often, pieces snap together in a way that unexpectedly resembles something recognizable—a tiny house, a creature, or a spaceship. Now, picture that instead of LEGO bricks, you have thousands of small molecules floating around on a particle or droplet somewhere on early Earth. According to Dyson, a similar process may have happened billions of years ago: random molecules bumping into each other until, by pure chance, some formed structures that helped create more structures like themselves.

The idea Dyson describes is that life didn’t begin with a perfect genetic system, such as DNA, but with small ‘islands’ of molecules—clusters where a fixed number of monomers gathered and occasionally joined into tiny chains. Most of the time, these chains were useless, but every now and then, one of them would help another chain form. Dyson refers to those as ‘active’ monomers. When enough active ones appeared at once, a kind of order emerged: the molecules on the island became good at helping each other grow. To make this easier to imagine, think of a group of students working on a group project. If only one or two people are doing the work, not much happens. Still, if the group randomly ends up with several motivated people at the same time, suddenly the whole project becomes productive. Dyson’s model suggests that a similar team effect could have happened among primitive molecules.

Dyson’s calculations highlight that, even without natural selection, a small island of a few thousand monomers could have shifted from chaos to order through chance. Early life may have begun as a random event that stabilized once sufficient beneficial molecules accumulated. Dyson describes this early ‘ordered state’ as a messy mix of simple catalysts rather than modern cells. Once such an island became ordered, it could grow, absorb more material, and eventually split into two, making natural selection relevant only later. The main point is that significant changes in nature—and in life—often begin with small, unlikely steps that become possible when many small things come together.

Reflecting on your own life, Dyson’s model offers a simple lesson. Order doesn’t always come from careful planning; sometimes it emerges from many small attempts, even failed ones, that eventually align. Just as those early molecules needed luck and numerous small fluctuations to reach a stable, productive state, young people often require time and space to try, adjust their direction, and gradually form habits that support growth. What matters is staying in the game long enough for your ‘active pieces’—your motivation, interests, and skills-to come together. Once they align, progress feels natural instead of forced, much like how Dyson suggests early life first found its order.

Reference:
Dyson, F. J. (1982). A model for the origin of life. Journal of Molecular Evolution, 18(5), 344–350. https://doi.org/10.1007/BF01733901

Privacy Notice & Disclaimer:
This blog provides simplified educational science content, created with the assistance of both humans and AI. It may omit technical details, is provided “as is,” and does not collect personal data beyond basic anonymous analytics. For full details, please see our Privacy Notice and Disclaimer. Read About This Blog & Attribution Note for AI-Generated Content to know more about this blog project.

When Simple Rules Create Surprising Chaos

~ Manuel Castañón-Puga

Imagine you’re adjusting the volume on your speaker. You turn the knob a little, and the sound increases in volume smoothly. Now imagine a different knob—one where a tiny twist suddenly makes the music jump, echo, or even break into unpredictable noise. That second knob is similar to what occurs in many natural systems. Things seem calm, but then they suddenly start behaving in strange and unexpected ways. This jump from simple to chaotic behavior is precisely what Feigenbaum and colleagues explore in the attached document.

The authors explain that many systems in nature—from the flow of fluids to the growth of populations—don’t suddenly become chaotic for no reason. Instead, as a system’s control parameter changes (something like temperature, pressure, or population growth rate), its behavior shifts through a clear pattern: first it repeats every time step, then every two, then every four, then every eight, and so on. This repeated doubling is called period doubling. You can picture it like a bouncing ball that always hits the ground at the same rhythm, until you slowly change one condition. Suddenly, it needs two bounces to repeat, then four, then eight, and finally no simple rhythm at all. The remarkable aspect is that this route to chaos follows a universal pattern that appears everywhere, even in systems that seem entirely unrelated.

One of the most intriguing ideas in the document is that very different systems (such as liquid helium becoming turbulent or a mathematical function used in a random number generator) can behave almost identically as they approach chaos. The spacing between each stage of period doubling shrinks by the same factor every time. This constant number appears regardless of the system you study. That means that if you can observe how a straightforward model behaves, you can understand the behavior of much more complicated things in the real world. For a young person, this is like realizing that the trick behind a magic show works on every stage, not just the small one in your school auditorium.

What does this mean for everyday life? It suggests that unpredictability doesn’t always come from randomness—sometimes it comes from simple rules repeated over and over. Think of your favorite app recommending videos: one tiny change in what you watch can send you down an entirely different path, not because the system is random, but because minor differences snowball quickly. Or consider friendships, routines, or habits: small, repeated choices can lead to significant and sometimes surprising outcomes. The message from Feigenbaum’s work is that complexity has structure. Chaos has a pathway. And understanding that path helps us see patterns where we once saw only confusion.

Ultimately, this theory presents a hopeful perspective. When things feel messy or unpredictable, it doesn’t always mean they’re out of control. Sometimes, they’re just following a universal route toward a new kind of behavior. And knowing this can help us appreciate that even chaos has its own type of order.

Reference:
Feigenbaum, M. J. (1983). Universal behavior in nonlinear systems. Physica D: Nonlinear Phenomena, 7(1–3), 16–39. https://doi.org/10.1016/0167-2789(83)90112-4

Privacy Notice & Disclaimer:
This blog provides simplified educational science content, created with the assistance of both humans and AI. It may omit technical details, is provided “as is,” and does not collect personal data beyond basic anonymous analytics. For full details, please see our Privacy Notice and Disclaimer. Read About This Blog & Attribution Note for AI-Generated Content to know more about this blog project.

When Small Things Trigger Big Avalanches in Everyday Life

~ Manuel Castañón-Puga

Imagine you are slowly piling up notifications on your phone. A friend texts you, a teacher posts a new assignment, a group chat explodes with memes, your bank app pings you about a payment. For a while, you handle everything with a few quick taps. Then one more message lands at precisely the wrong moment, and suddenly you miss a deadline, forget a meeting, and end up in a mini-crisis. From the outside, a slight extra nudge has caused a surprisingly big mess. This feeling that “nothing much changed, but suddenly everything tipped over” is at the heart of what Bak and colleagues call self-organized criticality.

According to Bak et al., many large systems in nature and society slowly move toward a special state where they are just barely stable. To explain it, they use a simple picture: a pile of sand. Grain by grain, the pile grows steeper. Most grains fall to the ground and do almost nothing. But sometimes a single grain makes a small slide, and sometimes it sets off an enormous avalanche that runs all the way down the side. The rules that describe this sandpile are straightforward, yet the result is remarkable: the pile naturally settles into a state where avalanches of all sizes occur. There is no single “typical” size or time. The same idea can be applied to many systems that change incrementally, such as the flow of rivers, the light from distant quasars, the Sun’s activity, and even the movement of prices on a stock market.

Bak and colleagues demonstrate that in this special state, small causes can have effects on multiple scales. This is why they discuss “1/f noise,” also known as flicker noise. Instead of random, short blips, the system displays slow, long-lasting fluctuations alongside quick ones. If you think of your life, you can picture days where nothing much happens and then a period where many things change at once: a new job, a new city, and new people. In their models, this occurs because the system is constantly balancing on the edge between calm and collapse. Energy, pressure, or “slope” builds up everywhere, and then it is released in bursts that can be tiny or huge. The pattern in space also looks special: instead of neat, regular shapes, you get messy, repeating patterns that look similar at different scales, like mountain ranges or coastlines.

The most striking message of Bak et al. for everyday life is that constant small changes can quietly push systems toward a critical point. A friendship, an online community, or even your own schedule can become a “sand pile” where tension slowly builds up. One more careless comment, one more late night, or one more task added to your to-do list may then trigger an “avalanche” of reactions. This does not mean that everything is always on the verge of falling apart. It means that in many real situations, there is no single obvious warning sign or simple knob you can turn to avoid all problems. Instead, it helps to notice how often you are adding “grains of sand” to your life without giving the system time to relax. Taking breaks, solving minor conflicts early, and not letting every part of your day reach its limit is like gently smoothing the sand pile before it gets too steep. Understanding self-organized criticality is a reminder that significant changes often emerge from many small steps, and that paying attention to these steps is one of the most practical skills you can develop.

Reference:
Bak, P., Tang, C., & Wiesenfeld, K. (1987). Self-organized criticality: An explanation of the 1/f noise. Physical Review Letters, 59(4), 381–384. https://doi.org/10.1103/PhysRevLett.59.381

Privacy Notice & Disclaimer:
This blog provides simplified educational science content, created with the assistance of both humans and AI. It may omit technical details, is provided “as is,” and does not collect personal data beyond basic anonymous analytics. For full details, please see our Privacy Notice and Disclaimer. Read About This Blog & Attribution Note for AI-Generated Content to know more about this blog project.

Climbing the Peaks of Progress: How Small Steps (and Occasional Jumps) Help Us Improve

~ Manuel Castañón-Puga

Picture a group project that starts messy. Everyone tries tiny tweaks—renaming a file, switching slides, or fixing one chart. Each fix helps a bit, but soon you’re “stuck” on a version that’s decent, not amazing. To get something truly great, you might need a bigger change—like rebuilding the deck around a sharper story. That’s the basic idea behind how improvement often works in life: we take small steps up a hill, but sometimes we need a jump to reach a higher one. Kauffman and Levin use this simple picture to explain “adaptive walks,” their way of describing how things—organisms, ideas, even study plans—get better over time on a rugged landscape full of peaks and valleys. 

According to Kauffman and Levin, imagine every possible version of something as a point in a huge space, and give each point a “fitness” score—how well it works. Moving to a version that’s one small change away is like taking a step to a neighbor on this map. Many maps are bumpy, with lots of little peaks where nearby options are worse, so small-step climbing can end early at a “local optimum.” On totally random (uncorrelated) maps, there are tons of these local peaks, so most improvement paths are short—think a handful of steps before you top out. A greedy strategy that always picks the best neighboring step is even shorter. That’s why quick tweaks often help fast, then stall. 

Here’s the twist that matters for everyday life: progress slows as you get better because you have fewer “better neighbors” left. Early on, lots of options beat what you have, so branching out is easy; later, choices shrink and things feel stuck—Kauffman and Levin call this pattern “radiation then stasis.” One fix is to allow bigger leaps—try several changes at once. When the jump is big enough, you can escape the local peak and discover fresh ground. In that “long-jump” mode, they find a simple rule of thumb: the number of improvements grows roughly with the log of the time you keep searching. Translation: early wins come quickly, then the gaps between wins get longer, which feels slow but is normal. 

What can you do with this? When your workout, study routine, or side hustle stops improving with tiny tweaks, treat that as a signal. First, accept that short bursts of progress are followed by plateaus, which are built into the rugged nature of maps. Next, plan occasional, safer “jumps”: test a new schedule for a week, learn a different tool, or reorganize roles on your team. Expect that the better you already are, the rarer the easy wins—and that’s okay. Take small steps for steady gains, and reserve bold experiments for breaking out of ruts. That mix—patient climbing plus brilliant jumping—is how you keep finding higher peaks in school, work, and everything in between.

Reference:
Kauffman, S., & Levin, S. (1987). Towards a general theory of adaptive walks on rugged landscapes. Journal of Theoretical Biology, 128(1), 11–45. https://doi.org/10.1016/S0022-5193(87)80029-2

Privacy Notice & Disclaimer:
This blog provides simplified educational science content, created with the assistance of both humans and AI. It may omit technical details, is provided “as is,” and does not collect personal data beyond basic anonymous analytics. For full details, please see our Privacy Notice and Disclaimer. Read About This Blog & Attribution Note for AI-Generated Content to know more about this blog project.

Why Crowds Move Like Magic (and How You Can Use It)

~ Manuel Castañón-Puga

Picture this: you and your friends are leaving a concert, and thousands of people flood the streets. Nobody is shouting directions, yet the crowd curves around barriers, speeds up in open space, and slows near the subway stairs. It feels almost choreographed, but each person is just watching what’s right around them and adjusting a little at a time. That everyday scene is the same idea Craig Reynolds describes for birds in the sky and fish in the sea: complex group motion can emerge from simple rules followed locally, not from a central authority.

According to Reynolds, flocking occurs when individuals balance three urges: avoiding collisions with neighbors, matching their speed and direction, and staying close to the group. In practice, that means you step sideways to avoid bumping someone (separation), you fall into the same walking pace (alignment), and you drift back toward your friends if you’re sliding to the edge (cohesion). Each member only “pays attention” to nearby neighbors and what’s ahead—no one needs a full map of the whole crowd. Add gentle steering around obstacles and a shared pull toward a goal—such as an exit sign or your meeting spot—and the whole group flows smoothly.

Why does this matter to you? Because the same rules help in daily life. When biking through traffic or skateboarding in a busy park, think like a flock: maintain a safe distance, synchronize your speed with the lane, and aim for clear space rather than forcing your way through. In team games, you can move as a unit by mirroring a teammate’s direction and spacing instead of waiting for shouted commands. Even your study group works better with these habits: avoid “collisions” by not talking over others, align by matching the group’s focus, and keep close enough that no one drifts out of the conversation. Small, quick adjustments beat big, late corrections.

There’s also a creative twist. Animators and game designers utilize these simple rules to create realistic crowds, schools of fish, or traffic without scripting every path. You can apply the same mindset to planning events or routes: assume people follow what they see around them, not a master plan. Place obstacles so they gently nudge the flow instead of blocking it. Start a “turn” from one side and let it ripple like a chorus line. And remember the secret of smooth motion: prioritize. In a tight spot, safety comes first (avoid collisions), then match pace, and then regroup. When you practice these three habits, you’ll find that everyday movement—leaving a concert, changing buses, or walking to class—starts to feel less like chaos and more like quiet, shared choreography.

Reference:
Reynolds, C. W. (1987). Flocks, herds and schools: A distributed behavioral model. ACM SIGGRAPH Computer Graphics, 21(4), 25–34. https://doi.org/10.1145/37402.37406

Privacy Notice & Disclaimer:
This blog provides simplified educational science content, created with the assistance of both humans and AI. It may omit technical details, is provided “as is,” and does not collect personal data beyond basic anonymous analytics. For full details, please see our Privacy Notice and Disclaimer. Read About This Blog & Attribution Note for AI-Generated Content to know more about this blog project.