Month: August 2025
Fractal
I found it in a high school math book, amongst equations and dry mathematical theory. If you blurred your eyes, the pages of that book would blur together into a fuzzy gray mass, each page indistinquishable from the next. What caught my eye however was a small, but colorful image in the midst of that grayness, strangely out of place in this book. The image had brightly colored swirls and eddies, resembling firs, palm fronds, oil in water. As you looked closer at the image, more interesting shapes appeared, similar, but slightly different, repeating throughout the image. It totally sucked me in.
It was the Mandelbrot Set, a fractal. It was a small mathematical equation, where esentially the result of the equation was fed back into the equation, repeatadly. It utilized intriquing concepts like imaginary numbers and iterations. The result, was this amazingly complex and beautiful image, which didn’t look like any of the normal boring graphs that usually result from equations.
Fractals appealed to the artist, creator, and explorer in me. I was intriqued with the ideas of infinity, complexity, and for the first time in working with math, unpredictability.
I have always loved art, and while the beautiful images of the Mandelbrot set and other fractals aren’t really art (it would be a bit like calling a tree, or the Grand Canyon art), they were undeniably beautiful. I think the real art of working with fractals is a bit like photography, the art is in the composition, color, and patience required to appreciate the natural. A fractal is a landscape, and the artist in me composes and decides colors and how best to represent what nature provides, much like a landscape photographer composes their images of the natural landscape. Like the photographer who waits and waits, and then waits some more for the right lighting, the right composition, or for the animal to come back within view, generating a fractal is an exercise in patience. Get the composition right and let the computer calculate, which can sometimes take days, weeks, and even months.
Because a fractal is infinitely large, there are areas of the Mandelbrot set that human eyes will never see. Even now, in my modest attempts at delving ever-deeper into it, I could be looking at areas that no one else has ever explored. As someone who enjoys exploring the physical world, working through the Mandelbrot Set and other fractals generates a bit of a pioneering spirit. I look at them with the same vigor that I explore maps. With a map, my interest generally lies with wanting to explore a place physically. When scouring a fractal image, I see locations and places that I want to explore in greater detail, and to drill down deeper into the depths.
Fractals seem like what we see in nature and the world around us, and in them a mysterious sense of something deeper that I can’t quite place. It’s something that is leading us to deeper into the nature of reality and the world around us, and that there is more to explore and discover. Perhaps when we fully unravel the universe and all is understood, we’ll look back at these beautiful images of iterated equations and recognize them as among the first strings being pulled.
The Bottom Third
In the US currently, it seems as though there are three segments of the population: a group who is pretty much opposed to the current direction that the US is headed, a group that doesn’t care (or is indifferent, or grudgingly going along with one of the other groups), and a final third of the population that is actively cheering this all on.
Of course, the lines between each group are blurry — there aren’t really hard lines defining where one group ends and the next begins. And yes, it does seem a little tribalistic to view things in this way, but perhaps that is a necessary step to realize the issue at hand.
I have started to refer to that final third of the population as the “Bottom Third,” since on a variety of attributes, they seem to rank at the bottom of the list. A few common traits:
- A willingness (and in many cases, a celebration) of believing things without evidence.
- A nebulous love of their country — an unchallenged view that their clan is the best.
- A fear and dislike of people who are different, or not of their same group.
- Lesser importance on education. In some cases, an outright rejection of education.
- A lack of critical thinking and reasoning ability.
- More fearful, but also a greater acceptance and appreciation of violence.
And it would seem as though this same group of people has existed throughout history. While most people in this group aren’t really evil themselves (although perhaps a higher percentage in this group are), the real danger of this group is that they make it possible for the bad (and evil) people to gain power. Because of this, this group is responsible for most of the bad things that have occurred in human history — from Nazi Germany, to [something else].
I’m of course not the first to recognize this group of people throughout history, but as a species, we seem ill-equipped to deal with it. Our systems of government don’t account for it, and in some cases are tailored in ways that allow leaders to fully utilize this Bottom Third (like the current US system of government, where the disproportionate representative system gives individuals in some states a larger voice than their counterparts in other states).
Perhaps it will take a few more cycles of human atrocity before systems are put in place to mitigate the damage of this group. But that should be a foundational goal of the species — a recognition that this group exists, an understanding of the damage it is capable of, and the development of strategies needed to combat the negative impacts of this group.
A Coalition of Cities
I think of great cities. Rome, Florence, Paris, Cairo, Tokyo. Their individual atoms change over time, but the pattern — what we recognize as the city exists, evolving and growing throughout the centuries. Empires and nations rise and fall around them, but the cities remain.
Cities have always been where humanity moves forward. They are the centers of culture, commerce, and knowledge. While rural areas undoubteadly play an important part in civilization, the city is where the majority of our advancements as a species take place. The residents of rural and urban areas have always been different — in and of itself, that’s not a bad thing. However, as political lines drawn on maps neglect to consider such realities, issues will always tend to arise.
A Polarized Nation
The pattern is prevalent everywhere across the US. Cities tend to be liberal. The greater the population density, generally the more liberal a city will be. Venture out from any city to the rural landscape, and the political view will shift towards the right. As people spread out more and more, the more conservative they will likely be.
This pattern isn’t unique to the US — it repeats itself everywhere from the UK to New Zealand, from Japan to Egypt, and is very likely consistent throughout history. As access to higher education has increased, the differences have only become more stark as college-educated individuals flock to cities not only for careers, but also for the culture and the advantages that come from living in cities.
Getting Past Polarization
America faces many challenges, but we increasingly seem ill-equipped within our political framework to do much of anything about it. But maybe there is an opportunity in our polarization, since our polarized society is quite neatly divided between urban and rural. Perhaps this is how we move forward.
The counties that voted for Biden, many of which hold the nation’s largest cities, account for 71% of America’s total economic activity. Source
Many of my fellow liberal urbanites want to see humanity push aggressively forward. We want to see greater investments in health, the sciences, and technology. We want better, more individualized, and accessible education, not only for children, but through all phases of life. We want to confront the large challenges that we face, including homelessness, lack of equality, and climate change.
While I wish everyone held the same level of ambition that I have for humanity, I get that many on the conservative side don’t hold that same view. And that’s ok. Perhaps we should move forward without them — not out of spite or resentment, but because we want to see positive change and improvement in the world around us.
Cities Working Together
The vast majority of the US economy is driven by cities. We’re the economic powerhouses of the most powerful nation on earth. And yet our influence on national politics is dampened as a result of our political system.
I wonder what we could accomplish if all of the large cities of the US worked together and formed a coalition (or several) that drove larger changes throughout society. Could we work within the confines of our national legal agreements, but effectively become a new nation of cities, who tax our citizens a little more, pool our resources, take advantage of economies of scale, and invest in what we can’t seem to do as a larger nation. We could pursue and fund advances in things like education, green energy, and healthcare. Liberals and progressives can seek the world we want to see, and conservatives in rural areas will no longer have to contribute to society. I would like to think there be less resentment on both ends of the political spectrum as a result.
What Could Cities Work Together On
I think there are many critical areas that the cities of the US (and world) could work together on that would not only benefit the inhabitants of our urban areas, but even those that reside outside of our cities.
Education
Education is probably the most important reason to work together. Better education has massive effect across society. A coalition of cities could:
- Provide research into education best practices and new models that could be more effective than current methods.
- Fund technological advances in teaching tools
- Create new methods of delivering educational content that could be utilized by schools everywhere, such as online or hybrid content on subject areas that fuel student curiosity but aren’t currently being provided.
Environment
The environmental crisis is one of, if not the largest issues of our time. We currently seem ill-equipped to handle the challenge currently, but perhaps with a motivated population we could make progress on this front. Amongst other things, we could:
- Grants for research into technology that will be necessary in the future, like desalination, improvements to renewable energy.
- Providing funds and incentives for greater adoption of renewable resources within cities.
- Working towards reducing costs and improving what’s possible with urban and vertical farming.
Science & Technology
If the citizens of cities wanted, we could help fund larger scientific enterprises, not only on subjects that directly impact cities, but also which help to fuel curiosity and imagination. Perhaps offering additional funds to NASA, providing research grants for general science studies, or funding research into innovative new technologies.
Government
Since the citizens of this newly established government are generally more accepting of government in general, it could be an opportunity to find innovative new ways working together for the common good. We could create better systems for determining representatives, providing transparency, and using technology to create a better system of government.
Other Issues
I suspect there are other issues that could benefit from a unified approach, including healthcare, homelessness, and home affordability.
Towards Something Better
There is an opportunity with our neatly sorted nation — like-minded people who want to see change are neighbors and co-workers, random acquaintances that we pass on the street. We live together in our cities, sharing similar views and ideologies. But our neighborhood of like-minded citizens extends well beyond the city we personally inhabit. Each and every city has citizens who share similar views to those of other cities. Perhaps we need to start seeing ourselves as citizens of the same nation — a nation composed of cities. A nation that has the ambition to tackle big challenges, the economic prowess to accomplish them, and a unified view to move the world in a positive direction.
Long Blocks
As I was running through downtown San Diego yesterday, I found that I was very appreciative of the minor streets that allowed me to keep running and not require me to stop and wait for a light to change. I could have longer sections of running, which helps me get in a better workout, and is just more enjoyable. For both cyclists and every-day pedestrians, those nice long stretches without having to wait for a traffic light are just as beneficial.

This idea could be taken further. In a city-from-scratch scenario, it could be a great arrangement for creating a more walkable, transit-oriented city. We could have longer, more arterial streets running in one direction, with streets on the perpendicular axis treated in a lighter fashion. They could be smaller and spread further apart, perhaps even having significant distances between actual streets on the minor axis. Pedestrian-only walkways could be provided along that minor axis to maintain accessibility throughout the neighborhood.
In existing cities, some streets could be narrowed to single lanes or when population density could support it, converted to pedestrian-only plazas. Updating several streets in succession could create long stretches of great, pedestrian strolling zones, along with benefits to cyclists and runners.

Wide Streets
Many low-traffic neighborhood streets are remarkably wide—far wider than necessary given their usage. On the scale of a single street, it already feels like a misallocation of space. Multiplied across an entire city, the inefficiency becomes striking.
These broad expanses of asphalt are often encountered on a run, where every step pounds against the hard concrete. Dirt paths surrounded by trees and plants offer a much more welcoming and joint-friendly alternative. And it’s easy to imagine a better use for all that space. With modest changes, wide streets could be narrowed, and the reclaimed land transformed into linear parks—spaces for picnics, benches for rest, and soft, shaded trails for walking or running. Community gardens could dot the landscape, and the new green corridors could serve as natural gathering spaces for neighbors.
Beyond recreation and aesthetics, there are environmental and infrastructural benefits to this kind of reimagining. Parks and greenspaces can aid in flood control during heavy rains, help sequester carbon, and provide some mitigation of the urban heat island effect—small but meaningful improvements in a warming world.
There is no single blueprint for redesigning streets, but several options stand out. In many cases, converting the center portion of the street into parkland would be ideal. This approach avoids conflicts with driveways and provides a continuous, uninterrupted greenspace. On longer blocks, a consistent paving pattern at intersections could visually reinforce the idea of one extended park, rather than a series of disconnected segments.
Some neighborhoods already feature medians running down the center of the street. These are often underutilized, little more than strips of grass or concrete. These spaces present a perfect opportunity to pilot new designs—enhancing what already exists, rather than starting from scratch.
Rethinking the purpose and layout of wide streets offers cities a chance to reclaim valuable land for public use. By weaving greenspace into the fabric of residential neighborhoods, communities become more livable, more beautiful, and more resilient. What once was wasted pavement could become the connective tissue of a greener, healthier city.