Feigenbaum's Singularity

Doomsday catastrophizing to avoid the mundane.

Money and anxiety swirl messily in my mind like a half-used jar of Goober peanut butter and jelly. My dad lost his job several times during my childhood, and when he did, worry suffused the entire household. When I’m the adult, I vowed, I will do things differently. I will own a home that I’m proud to invite people to. I will have a job so lucrative I won’t have to think about money.

The underlying emotional promise was to myself, that when I have achieved those things, I will be O.K. I didn’t yet know that permanent security or contentedness was nothing but a compelling illusion. Because despite exceeding all of my promises to myself, but I was not O.K. One afternoon, my depression prevented me from standing up in my office, a particularly memorable low point. My body and mind were full-on rebelling.

“You can quit,” My husband Brad told me when I was recuperating on medical leave. “You are not stuck there.” I welcomed the permission because I was the primary breadwinner, and yes, if we are to pay our mortgage in perpetuity we will eventually need more than his income. But we have a fair amount of runway before that becomes a real problem, and continuing to throw my sanity against Big Tech’s insatiable maw didn’t feel viable. With his support, I was eventually able to buy into the idea that it would be okay for me to take a break. I put in my resignation for the start of 2025 and felt intense relief.

Then over the holidays, before my break had even started, my husband said, “Hey, we need to go over the budget.”

“Okay, we can do that sometime,” I replied, but inside I wanted to scream. It took me months to get the courage to leave the safety net of my overcompensated-but-soul-crushing job and before I have even a taste of freedom, he wanted me to face the family budget head-on? Even at the best of times, thinking about budgets made me feel like I’m wearing a too-small jacket with a stuck zipper. Something will be taken away from me, and there’s nothing I will be able to do about it.

To avoid my dread of budgets, I immediately distracted myself with a book on complexity. I learned that chaos has an underlying order. It may not be predictable by definition, but it follows metapatterns that are.

A logistic map is one example of a function that despite being a relatively simple nonlinear function, exhibits complex and dynamic behavior. For some parameters, the function will converge to a single value. As the parameter increases, though, the outputs begin to ping-pong between two values. Then four, then eight, etc., until the resulting pattern is too chaotic to predict at all.

Each doubling of the values, or bifurcation, happens 4.6692016x faster than the doubling before. This precise value applies to all unimodal functions in the same class, not just this one. It’s a constant amidst the chaos, repeated time and again, and named Feigenbaum’s constant after the mathematician who discovered it. Once more I am reminded that the universe is wonderful and mysterious—and far more interesting than our little family budget.

I decided to write a short story about a doomsday cult driven by mathematical constants and their relationships with societal change instead of religious revelation. The advance of technology is not exactly a unipolar logistic map function, but this was a piece of short fiction, not a logical proof.

With a spreadsheet, I tracked the years between notable advances in information technology. I considered several different events to begin my trek through time. The first integrated circuit was developed in 1958 but I’m not that into hardware, and so neither is my fake religion. The World Wide Web was invented in 1989, but mass adoption took quite a bit longer. I settled on two moments that impacted my adulthood—Web 2.0 dawning in 2004 and OpenAI releasing ChatGPT in 2022. Given those points, the last complexity conjunction should have occurred in 1938.

And BOOM, Alan Turing created the conceptual framework for computing in 1937. The next jump back put me at 1624—the nearby invention of the slide rule was not nearly as much of a slam dunk, but it worked if I waved my hands enough. I kept going, the next target date matching up to the second century AD—when Cai Sun invented paper in China.

The historical record before then gets very wobbly, so I could basically choose anything I wanted. 5000 years before paper was the invention of protowriting—to a best guess, anyhow. Neolithic art, the invention of weaving.

So what happened when I looked forward? The next bifurcation predicted by applying Feigenbaum’s constant should happen in 2026. The time between steps continued to shrink until it was no longer worth calculating. That felt an awful lot like Kurzweil’s predicted singularity, giving me a sensation of having seen through the fabric of our universe. While I knew this was some silly bullshit I made up with math and handwaving, that knowledge couldn’t fully erase the pulse of certainty. Conviction felt so good despite the lack of evidence. I understood the appeal of the doomsday cult, the psychotic delusion, and the conspiracy theory.

“I figured out when the singularity will happen,” I announced to Brad.

“Oh yeah?” He was pretty nonplussed despite the insanity of the thing I just said. (This may be one reason we’re married.) “When?”

“2027 or 2028. From then on out, it’s runaway chaos.” I briefly described my gum-and-duct-taped theory.

“Nice,” my husband replied, still cool. “So, we don’t have to figure out the budget?”

Temporarily dodging that conversation is almost sweeter than discovering the key at the heart of the universe.

The old buzzkills of logic and reason eventually filtered their way back in, but it was fun while it lasted. If the parameters of my neurochemistry were slightly different, though, I could easily be pushed into ignoring the real but mundane problems I have control over to obsess over abstract and universal patterns and their inevitable realization of global-scale emergencies. At the other extreme is succumbing to despair about there being no overarching plot, no grand design, and no one coming to save us.

I guess I have to face the budget.