Patterns, Fibonacci and Our Awesome Universe

While watching an episode of Rod Serling's Twilight Zone, "Night Call" (Episode 139 -- February 7, 1964) there is a scene where the old woman has been assisted into a wheelchair. The camera angle is from the viewpoint of an adult looking down to the woman. Across her lap is a knit afghan with a zigzag pattern similar to the kind my grandmother used to make, and for just a moment the camera lingers on the pattern.

One of the thoughts I had in that moment: what would an afghan look like if instead of being knit into a pattern, the colors and knitting were totally random? Isn't it the pattern or design that gives the afghan its interest?

In 2008 I wrote about color as a facet of making or appreciating art. Design and pattern could be added to the list of things which can make a drawing or painting interesting.

Nature is full of patterns, from atomic structure to the design of galaxies... from the incredible Fibonacci sequence to the rhythm of waves... from the phenomenon of day and night to the miracle of a heartbeat...

In the Renaissance, artists did not see beauty as accidental. They believed it could be discovered, studied, and deliberately constructed. Pattern—whether in proportion, repetition, or geometry—was one of their primary tools for doing so.

Figures like Leonardo da Vinci and Leon Battista Alberti were not only artists but thinkers who sought underlying order in the world. They were deeply influenced by classical ideas of harmony, especially the belief that mathematics revealed the structure of reality. This conviction shaped both painting and architecture.

One of the most intriguing patterns associated with Renaissance art is the Fibonacci sequence and its related “Golden Ratio.” While not always applied consciously in a strict numerical sense, its proportions—roughly 1:1.618—appear repeatedly in compositions. Painters arranged figures, horizons, and focal points along these invisible lines, creating balance that feels natural rather than forced. The eye is gently guided, not commanded.

In architecture, this pursuit of proportion becomes even more explicit. Alberti and others designed buildings where height, width, and spatial divisions followed harmonious ratios. The result is not merely structural integrity but a sense of calm coherence—spaces that feel “right” even if the observer cannot explain why.

What makes this especially compelling is that these patterns mirror those found in nature: the spiral of a shell, the arrangement of leaves, the unfolding of galaxies. Renaissance artists believed they were not imposing order but participating in it—echoing a design already embedded in creation.

In this sense, pattern is not decoration. It is revelation. It is the quiet framework beneath the visible surface, the hidden scaffolding that gives a work of art its unity and power. And once you begin to see it, it is hard to unsee—the world itself starts to look like a carefully composed canvas.

Elton Trueblood once suggested that if the world is the product of an Infinite Mind, its beauty should not surprise us. That idea becomes more than philosophical speculation when you begin to trace patterns—not just in art or music, but in mathematics itself.

Educator/mathematician James Nickel describes how for him this realization did not come through formal schooling, but almost by accident. While preparing to teach high school mathematics in the early 1980s, he began exploring resources that connected numbers to the real world—books on geometry in art, the growth patterns of nature, and the Fibonacci sequence. What struck him was not merely the elegance of the numbers, but their recurrence—in shells, architecture, spirals, and proportions that seemed to echo across creation.

What had been presented in school as isolated facts suddenly revealed itself as something cohesive, even luminous. Fibonacci—Leonardo of Pisa—was no longer just a historical figure attached to a number sequence, but a doorway into what Nickel called “an opulent beauty,” a harmony linking human creativity with the structure of the natural world, and ultimately pointing the Creator God of All, all nature declaring His glory.

Equally striking was what had been missed. Traditional math education, with its emphasis on deduction and abstraction, often stripped away this sense of wonder. Geometry became a system of proofs rather than a language describing reality. The “pattern” was still there, but the meaning had been muted.

And so the rediscovery of pattern becomes, in a sense, a recovery of vision—learning again to see what was always present.

Check out this interview with author/mathematician James Nickel on The Wonders of the Fibonacci Sequence.

A Warning from Gustave Le Bon's The Crowd: A Study of the Popular Mind

"The masses have never thirsted after truth. Whoever can supply them with illusions is easily their master; whoever attempts to destroy their illusions is always their victim."
--Gustave Le Bon

I have long been interested in the subject of crowds and mass movements, perhaps stirred in part by having come of age during the antiwar Vietnam protest era. In my second semester I took a sociology class related to this theme (mass movements, not Viet Nam).

Gustave Le Bon's The Crowd: A Study of the Popular Mind (1895; often subtitled The Psychology of Revolution in later editions) is a seminal work in social psychology. Le Bon argues that individuals in crowds lose rationality, descending into a collective mind driven by emotion, suggestion, and impulsivity. I witnessed this first-hand on two occasions while in college, the first during the Mayday protests in Washington D.C., 1971. The second was at Ohio University. 

I remember a hilarious Dave Berg cartoon in Mad Magazine in which four self-conscious teen-aged boys of the "Aw shucks" variety are hanging out. Once together they are suddenly hoisting a battering ram to break into a house where there's a party of girls. Berg's amusing cartoon illustrates how we often change when part of a group.

What is a crowd? Gustave Le Bon described it as a group of people brought together by a shared idea or belief. But this shared belief isn’t necessarily formed through careful thinking or by weighing evidence. Instead, crowds tend to accept ideas quickly and emotionally, often using them as motivation for action—sometimes even radical action.

According to Le Bon, when a person becomes part of a crowd, something changes inside them. They no longer think or act the same way they would on their own. In a real sense, they stop functioning as an independent individual and begin to take on the mindset of the group.

Crowds can become barbaric, credulous, and led by simplistic ideas, images, and prestige rather than logic, Le Bon correctly observes. He classifies crowds as heterogeneous or homogeneous, explores leaders' manipulative role via affirmation, repetition, and contagion, and applies this to revolutions (e.g., French Revolution), warning of democracy's risks from mass irrationality. His writings influenced both Freud, and Hitler, as well as modern crowd control.  

Le Bon argues that "when societies decay, it is always the masses that bring about their downfall. This is a controversial but thought-provoking idea, especially in today’s era of viral outrage and mass protests."*

Critique

Le Bon's insights on suggestibility and deindividuation prefigure modern psychology (e.g., Leary's deindividuation theory) and remain relevant in analyzing mobs, social media echo chambers, or populist movements. Deindividuation explains how people in groups or anonymous situations can lose their sense of individual identity and self-awareness, leading to reduced inhibitions, less accountability, and behavior that deviates from personal or social norms—sometimes impulsive, aggressive, or antisocial. LeBon's emphasis on emotional contagion explains rapid idea spread.

Critics, however, say the work is pseudoscientific: anecdotal, elitist, and racist (portraying "inferior races" as crowd-prone). It overgeneralizes, ignoring rational crowds (e.g., protests achieving reform) or positive collective action. Deterministic and anti-democratic, it influenced authoritarian propaganda. Empirically weak by today's standards—no data, experiments—but historically pivotal for understanding group dynamics' dark side. Having witnessed the manner in which crowds can seduce people into abandoning common sense, I would suggest that LeBon was to some degree on taret with his own early observations.

* Tapan Desai

James Nickel on Stanley Jaki and the Worldview Behind Science and Discovery

The Soil That Grew Science

We tend to think of the rise science as inevitable—as something that would have arisen anywhere, given enough time and curiosity. But what if that assumption is incorrect?

That question animates an essay by James Nickel, who revisits the work of physicis Stanley L. Jaki, historian of science, and Templeton Prize winner. Jaki’s claim is striking: modern science had only one true beginning—and it happened within a culture shaped by belief in a rational Creator.

“I was drawn to Jaki because he challenges things we take for granted,” Nickel told me. “He asks not just what science has achieved, but why it arose at all.”

Jaki argued that science depends on a set of underlying convictions: that the universe is orderly, that it operates according to consistent laws, and that the human mind is capable of understanding it. Those assumptions, he believed, were not universally held across civilizations.

Nickel is careful to clarify the point. “Jaki isn’t saying other cultures lacked intelligence or ingenuity,” he said. “But their efforts didn’t develop into a self-sustaining, ever-advancing enterprise in the way science did in the West.”

The difference, in Jaki’s view, comes down to worldview. If the universe is seen as cyclical or ultimately impersonal, the search for universal laws may never fully take hold. But if the world is the creation of a rational mind, then it invites investigation—and rewards it.

That raises an uncomfortable question for modern readers: Do scientists today still rely on those same assumptions, even if they no longer recognize their origins?

“You can’t do science without trusting that the universe is intelligible,” Nickel said. “The question is whether we understand where that trust comes from.”

Jaki also warned that certain philosophical trends—whether reducing knowledge to raw data or dissolving reality into perception—can quietly undermine science by weakening that trust. (I think here of Sowell's Is Reality Optional? and notions suggesting that reality is a projection of our minds and doesn't really exist.)

At the same time, science has limits. It deals in measurement and prediction, not meaning or purpose. Those questions, Jaki insisted, belong to philosophy and theology.

“When science becomes the dominant voice,” Nickel observed, “there’s a tendency to act as if those larger questions don’t matter.” 

Perhaps the deeper point is this: science did not emerge in a vacuum. It grew out of a particular way of seeing the world.

And if that is true, its future may depend on whether that vision still endures.

* * * * 

Check out my interview with James Nickel regarding the work of Stanley Jaki. Nickel's "Jaki Musings" is part of a series exploring  the the vistas and power of mathematics as seen through Biblical Christian eyes. Here is the series thus far:
Math Circle 1: Whither Mathematics Education in the 21st Century
Math Circle 2: Introduction: The One and the Many
Math Circle 2: Calculus, Meaning and Beyond
Math Circle 3: Quotable Quotes

Bonus Tracks by James D. Nickel
Science and Creation: A Rare Jewel of a Book
In Honor of Stanley L. Jaki (1924-2009)

Hans Rookmaaker’s Modern Art and the Death of a Culture:

After philosophy, much of my college study (1970-74) was dedicated to the fine arts. I immersed myself in painting and drawing, as well as continuous rummaging of the art books housed in the school library, which was almost the nearest building to  my dorm. Though captivated by much of what I saw, and at times sought to emulate, there was plenty that I wasn't really attracted to. I did, however, have a great love for the process of laying paint on canvas. I found the process of creation magical.

During that time I had a friend who periodically told me, "The artist is the vanguard of the revolution." His meaning was clear. Art was to be subservient to political ends. My friend Walter Urban created powerful works of this nature, a life-sized soldier on a cross (protesting Viet Nam), a family in the future taking a walk in the park wearing gas masks.

I myself saw many ends that art could serve. After the death of a best friend in high school art served a therapeutic function for me. There were dark things in my heart that words seemed inadequate to express. Beyond the grief there were other emotions and art was a means of working it out.

As one stepped back and surveyed the previous 100 years, one could see that art also served as a mirror of the culture. This is the theme tackled by Dutch author, professor and Christian scholar Hans Rookmaaker.

 

Hans Rookmaaker’s Modern Art and the Death of a Culture (1970) explores how the development of modern art reflects the spiritual and philosophical collapse of Western civilization. Writing as both an art historian and a Christian thinker, Rookmaaker argued that art is never created in a vacuum—it mirrors the worldview of its time. As Western society drifted from its biblical foundations, art, he says, became a visual record of man’s alienation, fragmentation, and loss of  meaning, themes taken up by mid-century existentialists like Camus and Sartre.

Rookmaaker traces the story from the harmony of classical and Renaissance art, where beauty and order reflected divine creation, through the Enlightenment’s turn toward human reason, and finally into the modern era, where faith in transcendence eroded. Artists like Van Gogh, Picasso, and Pollock emerge as prophets of a disintegrating world: their work cries out with spiritual yearning but lacks the hope once rooted in a Christian understanding of reality.

For Rookmaaker, the “death” of culture meant more than a shift in artistic style; it pointed to a deeper moral and spiritual drift. When God is no longer at the center, both art and life begin to lose their unity and meaning. Yet he did not fault the artists themselves. In their confusion and despair, he saw an honest reflection of the human condition. His response was not condemnation, but invitation—a call to recover beauty and, through it, a renewed sense of order and purpose.

[This seems to be a good place to insert a couple of comments by my eight-year-old grandson who visited New York's Museum of Modern Art this week. My daughter said, "He was so funny at the art museum with his sort of pithy, harsh reviews of the art: 'So, um ... How did this get so famous anyway?' and (no doubt responding to Pollock)  'Huh. It kinda looks like they just splattered paint on the paper.'"]

Ultimately, Modern Art and the Death of a Culture is not an argument against modernism but a plea for spiritual reawakening. The book invites readers to see that the renewal of art depends on the renewal of belief—that culture can be reborn only when it again recognizes its source in the Creator.

                                         "Red Star"  

Now that we are more than fifty years removed from Rookmaaker’s diagnosis, the story of art has not reversed itself so much as it has unfolded along the very trajectory he observed.

The boundaries are gone. The gatekeepers have loosened their grip. What once required training, patronage, or institutional approval is now open to anyone with a vision—and sometimes even to those without one. From installations and performance pieces to digital art and street murals, expression has multiplied in every direction. In this sense, there has indeed been a kind of liberation.

And yet, with that freedom has come a curious diffusion. Without a shared center—without a commonly held sense of the true, the good, and the beautiful—art often speaks in a thousand private languages. Some works are deeply personal, even therapeutic. Others are expressions of love. And then there is art that is simply functional, enriching us more than endless halls of empty walls.. And we still have the overtly political, echoing my friend’s conviction that the artist stands at the vanguard of revolution. Still others seem to revel in irony, fragmentation, or shock, as though meaning itself were suspect, though what shocks some seems to miss the mark because many of of oldsters have seen it all before and, yawn...

But beneath the variety, one thread persists: art continues to tell the truth about us. It reveals our longings, our confusions, our search for identity and transcendence. If the last century showed us the fracture, the past fifty years have shown us what it is to live within it.

Which leaves us, perhaps, where Rookmaaker left us—not with a neat conclusion, but an invitation.

If art is a mirror, then what we choose to create—and what we choose to behold—matters. The question is not only what art has become, but what it is for. And whether, in the midst of all this freedom, we might yet rediscover not only expression, but meaning… and perhaps even beauty in its myriad forms once again.

Related Links

The Painted Absurd

https://pioneerproductions.blogspot.com/2009/05/painted-absurd.html

A Century of Rebellion: Exploring 20th-Century Art Movements

https://pioneerproductions.blogspot.com/2025/03/a-century-of-rebellion-exploring-20th.html

The Future of Work in the Age of Automation: Proceedings of a Workshop on Norbert Wiener’s 21st Century Legacy

"If you're not thinking about AI, you're not thinking." ~ Chris Meyer

Norbert Wiener (1894–1964), has been famously cited as the mathematician who founded the field of cybernetics with the publication in 1948 of his seminal book Cybernetics: Or Control and Communication in the Animal and the Machine. His work was the direct intellectual precursor to modern AI and automation. 

Wiener was hardly optimistic about the effects of AI on the future of work. He repeatedly warned that unchecked automation would cause massive unemployment, treat machines as the “precise economic equivalent of slave labor,” and force human workers to accept slave-like economic conditions.

In 2023, an IEEE Workshop on Norbert Wiener’s legacy examined how AI and automation are reshaping the future of work. Drawing on Wiener’s warnings about job displacement and the ethical duties of technologists, participants critiqued overly optimistic “technological determinism” narratives that ignore social costs. 

Discussions highlighted qualitative losses — reduced meaning, creativity, and human connection in work — alongside risks of growing inequality and environmental harm. The workshop called for interdisciplinary collaboration, stronger governance, and a shift toward human-centered values like dignity and flourishing, rather than pure efficiency or profit, to ensure technology serves society rather than disrupts it.

One of the paricipants of this workshop was Pedro H. Albuquerque (Senior Member, IEEE.)  Born in Brazil he obtained an Electrical Engineering degree from the University of Brasilia, and a Ph.D. in economics from the University of Wisconsin-Madison. Our paths crossed while he was teaching economics at UMD here in Duluth approximately two decades ago and became part of the philosophy club we hosted in our home.

             

He is now a Research Fellow with the Aix-Marseille School of Economics in France and a Cofounder of ACCELERATION & ADAPTATION. He has published articles in a large number of scientific journals and has presented at leading international conferences, in fields as varied as occupational science, engineering, economics, finance, and social studies. His areas of interest are technology studies, economics, occupational science, sustainability, and finance. 

Over the years Albuquerque has been a gracious resource, and the increasing adoption of AI I've been leaning in to hear his cautionary thoughts on this topic. What follows are a batch of short answers to long questions pertaining to the workshop on Norbert Wiener of which he was a member/participant.

EN: Norbert Wiener emphasized the moral duty to anticipate risks and societal impacts. How do you balance that responsibility with the risk of overcorrecting—where caution itself might slow or block beneficial innovation?

Pedro Albuquerque: Generally the opposite risk doesn't exist, when it's mentioned it's normally a political narrative in favor of some status quo. The real challenge is not having enough restraint (example, development of nuclear weapons).

EN: Some argue that technology threatens “meaning” in work and life. But isn’t meaning ultimately an individual responsibility? To what extent should technology be held accountable for something so personal?

PA: The effects of technological innovations on our lives are hardly under our control (example: parents are unable to avoid the consequences of Internet misuse on their children, no matter how much they try hard).

EN: There’s concern about “loss of human engagement” in an AI-driven world. How much of that is driven by technology itself, and how much is the result of individual choice and personality differences?

PA: It arguably affects all, some more than others though.

EN: When we talk about “fairness” in the age of AI, what does that actually mean? If technological progress raises overall prosperity, is it inherently problematic if some benefit more than others?

PA: It doesn't necessarily raise overall prosperity, technology is neutral on that. Prosperity in its use is a political choice, not a technological matter.

EN: The discussion often emphasizes “justice” and “equity” in AI outcomes. How do you define those terms in practical ways, especially compared to clear historical injustices like redlining?

PA: Redlining is a good example, technology may be politically chosen to be the instrument of oppression.

EN: We currently see large numbers of unfilled jobs in certain sectors. Could AI and automation actually solve labor shortages rather than displace workers—and how should we think about that distinction?

PA: Again, the outcomes are not driven by technology, but by political choices.

EN: Many discussions focus on what could go wrong with AI. How do you weigh those risks against the possibility that the opposite—positive, transformative outcomes—may be just as likely?

PA: As humans are risk averse, normally risks and damages are the central concern.

EN: There’s a concern that efficiency may come at the expense of artistry or human connection. But in areas like housing or healthcare, speed and scale can meet urgent needs. How should we balance efficiency with human-centered values?

PA: Efficiency can be evaluated both as quality and quantity. Modern societies have been lobotomized by a "quantity over quality" productivist ideology, where what can't be measured or financially evaluated is thrown under the rug.

EN: AI’s energy use is often criticized. How should we evaluate that concern in the broader context of energy innovation—such as nuclear or other emerging solutions?

PA: It's a whole other Pandora box. Let's just say for now that this new technology will put increasing and extreme pressure on a system that's yet unsustainable and under great danger of collapse.

EN: When people talk about “ensuring worker wellbeing” in an AI-driven economy, what does that mean in concrete terms? What should actually be measured or protected?

PA: Another Pandora box, we'd need to ignore economics, which isn't very helpful for these matters, and let the public health and occupational scientists speak. But in the current political and economic systems their voices remain mostly unheard.

EN: AI outcomes are often described as unpredictable. But uncertainty has accompanied every major technological shift. At what point does uncertainty become a reason for caution versus a normal condition of progress?

PA: History tells us we've always done less than optimal in prevention.

EN: Efforts to design “ethical AI” often focus on minimizing inequality. How do you balance that goal with the reality that individuals make different choices and define success in different ways?

PA: Public policies are known to successfully address these matters.

* * * * *

Download The Future of Work in the Age of Automation: Proceedings of a Workshop on Norbert Wiener’s   https://drive.google.com/drive/search?q=Love%20et%20al 

What Are Your Thoughts on These Things?
Please leave a message in the comments.

Related Links
A Visit with Futurist Calum Chace on his new book The Economic Singularity
https://pioneerproductions.blogspot.com/2016/06/a-visit-with-futurist-calum-chace-on.html

Surviving AI by Calum Chace Is a Must Read for Those Who Plan to Be Here in the Future

https://pioneerproductions.blogspot.com/2016/06/surviving-ai-by-calum-chace-is-must.html

Will Computers Put Journalists Out Of Business? Check Out These 7 Stories

https://pioneerproductions.blogspot.com/2016/04/will-computers-put-journalists-out-of.html

A Dozen Quotes to Mull Over on a Dreary Day

The weather outside is dreary and grey. As for me, I draw my strength from the weather within. Right now it's blue skies and, yes, here comes the sun.

When I lived in Mexico I bought a notebook in which I began recording quotes from my readings. It was nice having them all in one place, like a personally curated Bartlett's Familiar Quotations, which every serious writer was encouraged to acquire before the Internet em
erged.

Wikiquote is a website that arranges quotes by both author and by theme. If you are a writer and unfamiliar with it, I believe you'd find it worth your while to explore. 

The quotes on this page are arranged neither by author nor by theme. Their common denominator is that I found them interesting because they give you something to ponder and mull over. It's a bite-sized list to be savored slowly, not gobbled up in a rush to get on with your day.

Recently I discovered an extremely interesting page of quotes about Mathematics that you might want to explore. Harvested and assembled by mathematician James Nickel it's titled Quotable Quotes in Mathematics. James is a longtime friend, and an author of numerous books pertaining to math from a Biblical Christian worldview perspective. This past week I interviewed him about his 30-page collection of math quotes. You can read the interview here.

Without further ado, here my dozen quotes to mull over. Read them all, pick one and roll it around in your mind till it yields fruit.

"Don't you ever wonder sometimes what might have happened if you tried?”

—Kazuo Ishiguro 

“The greatest hazard in life is to risk nothing.” 

—Steve Jobs

“In science, there is only physics; all the rest is stamp collecting.”
--Lord Kelvin

“Don't pay any attention to the critics—don't even ignore them.” 
—Samuel Goldwyn

“More law, less justice.” 
— Marcus Tullius Cicero

"Quality is remembered long after price is forgotten."
—Aldo Gucci

"Of all sad words of tongue or pen, the saddest are these, 'It might have been."
—John Greenleaf Whittier

"We cannot solve our problems with the same thinking we used when we created them."

—Albert Einstein

"A man hears what he wants to hear and disregards the rest."

—Paul Simon

"Behaviorism is a flat earth view of the mind."

—Marvin Minsky

"Love all, trust a few. Do wrong to none."

—William Shakespeare

"I believe in Christianity as I believe that the sun has risen: not only because I see it, but because by it I see everything else."

—C.S. Lewis

Let the sunshine in!