Category: Science and Math

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Life Hacking Science and Math

Your 3 p.m. Coffee Is Still Awake at Midnight

I learned something fascinating this week that completely changed how I think about drugs. Remember in health class when we learned that alcohol goes out of your system at about 1 drink per hour? I used to think all drugs worked that way. I used to believe that if I take a pill and then after 4 hours or whatever it says on the bottle, the drug is out of my system. Wasn’t that true for caffeine, antihistamines, painkillers—everything.

Turns out, alcohol is the exception, not the rule. Most drugs don’t fade out in a straight line—they follow something called a half-life. And once you understand that curve, your medicine cabinet (and your coffee habit) start to look very different.

What Half-Life Means

The half-life of a drug is the time it takes for the amount in your body to drop by 50%. Think of it like a leaky bucket that loses exactly half its water every few hours, no matter how full it starts. After one half-life, half is left. After two, a quarter. After three, an eighth. After four, a sixteenth. The pattern keeps halving until the levels are so low they’re basically gone.

When it reaches 5 half lives it’s only 1/32 of its original stregthn and said to be fully out of your system. And here’s anoher thing about how drugs work. If you take double the dose, it doesn’t last twice as long—it only lasts one half-life more.

Why Does Alcohol Work Differently from Other Drugs

Most drugs leave your body in fractions. Imagine your liver and kidneys as workers who get faster when there’s more drug around. If there’s a lot, they clear a lot; if there’s only a little, they clear a little. That’s why most medications follow a half-life curve: every few hours, the amount is cut in half—½, ¼, ⅛, and so on.

Alcohol is different. The enzymes that process it get overloaded quickly, even at normal drinking levels. Once they’re maxed out, they can’t go any faster. So instead of clearing a fraction, the body clears a fixed amount per hour—about one drink’s worth.

How This Plays Out in Real Life

To see how this works with drugs you probably have in your medicine cabinet, let’s look at some household names:

  • Ibuprofen (Advil, Motrin): ~2 hours. Quick in, quick out.
  • Naproxen (Aleve): 12–17 hours. Still hanging around the next day.
  • Diphenhydramine (Benadryl, in Tylenol PM, Advil PM): 4–9 hours. This explains why if you take Tylenol PM at bedtime, you’re effectively still taking half a Tylenol PM when you wake up. Hello, morning grogginess.
  • Loratadine (Claritin): ~8–10 hours. “Non-drowsy,” but very much alive in your system all day.
  • Sertraline (Zoloft): ~24 hours. Miss a dose and you’ll feel it for days as levels drop.

Unlike alcohol, which just grinds away at a constant rate, these drugs all taper off in fractions.

What Does This Mean for Caffeine

Now, about that 3 p.m. coffee. Caffeine’s half-life is about 5 hours, but it can range anywhere from 3 to 10 depending on your genetics, smoking, pregnancy, liver health, and even other meds.

So that medium coffee at 3:00 p.m.?

  • At 8:00 p.m., half of it is still in you.
  • At 1:00 a.m., you’ve still got a quarter left.

Which explains the midnight tossing and turning after what felt like an “innocent” afternoon pick-me-up.

Even though your “last cup was hours ago,” you’re carrying the equivalent of a small coffee’s worth of caffeine into the night. Your body doesn’t reset between doses—it accumulates.

Summing Up

That 3 p.m. coffee keeping you up at midnight isn’t bad luck—it’s math. Once you see the curve of half-lives, you realize your body isn’t careless or mysterious, it’s consistent. Drugs don’t simply vanish after the label’s “every 4 hours.” They fade in halves, and those halves shape how we sleep, how we heal, and how we feel the next day. The trick is not to fight it, but to learn the rhythm and work with it.

Categories
Ideas Science and Math

Who Really Said That?

“The definition of insanity is doing the same thing over and over again and expecting different results.”
– Albert Einstein

We’ve all heard that quote. At meetings. In self-help books. On motivational posters in office break rooms. It exemplifies Einstein’s legendary cut-to-the-chase brilliance.

The only problem is, Einstein didn’t say it.

As far as I can tell, the quote first appeared in a Narcotics Anonymous pamphlet in the early 1980s. Einstein died in 1955 without mentioning anything remotely close to it in anything he’d ever written or said.

And yet, the misattribution stuck. Why? Because it feels like something Einstein would have said. Like Churchill, Lincoln, or Mark Twain, Einstein has become a kind of general-purpose intellectual that we can attribute our cleverest, pithiest thoughts to, whether he said them or not.

This misattribution happens all the time. So often, in fact, that there’s a name for it.

Actually, there are several.

Stigler’s Law of Eponymy

In 1980, University of Chicago statistics professor Stephen Stigler gave this phenomenon a name: Stigler’s Law of Eponymy. It states that “No scientific discovery is named after its original discoverer.”1

The best part? Stigler didn’t even claim to have discovered it. He credited the idea to someone else—sociologist Robert K. Merton. In other words, the law named after Stigler was… not discovered by Stigler. The law proves itself. Here’s what he wrote in the paper:

If there is an idea in this paper that is not at least implicit in Merton’s The Sociology of Science, it is either a happy accident or a likely error. Rather I have, in the Mertonian tradition of the self-confirming hypothesis, attempted to frame the self-proving theorem.

Stigler’s Law of Eponomy

But it’s not just a clever academic joke. Stigler’s Law points to something more systemic: we don’t just forget who discovered what—we misremember it. Over time, we start attaching credit to the loudest name, not the first one.

In the original paper, Stigler and others have documented example after example:

  • Halley’s Comet? Observed by ancient Chinese and Babylonian astronomers. Halley just did the math.
  • Newton’s First Law of Motion – Better known as inertia, it was described by Galileo decades before Newton refined and popularized it.
  • Fibonacci sequence – Long before Leonardo of Pisa wrote about it, Indian mathematicians like Pingala and Virahanka had described it in the context of Sanskrit poetry and combinatorics.

Fame creates its own kind of gravity and inertia. Once someone becomes famous enough, many other discoveries are attached to them.

The Matthew Effect

Now let’s look at Robert Merton—the person Stigler credited. Back in 1968, Merton gave this bias its own name: the Matthew Effect, based on a verse in the Gospel of Matthew, “For to everyone who has, more will be given…”

In the world of science, that means prominent researchers get more recognition, more funding, more citations—even when the original insight came from someone else. It’s not always malicious. Sometimes, people just assume the famous name must be behind the breakthrough. Other times, the lesser-known researcher gets buried in the footnotes.

The Matthew Effect isn’t limited to academia. It shows up in:

  • Publishing, where established authors get bigger advances regardless of quality.
  • Tech, where investors back founders who’ve “done it before.”
  • Education, where early reading success snowballs into long-term achievement.

It’s a feedback loop. Once you’re seen as successful, you’re more likely to be treated as successful. And then the cycle repeats.

Churchillian Drift

If Stigler’s Law and the Matthew Effect explain why discoveries get mislabeled, Churchillian Drift explains why quotes get misattributed—especially to famous people like Winston Churchill.

Coined by British broadcaster and quote sleuth Nigel Rees, Churchillian Drift describes how pithy or profound lines migrate toward famous names over time. If a quote sounds wise and ancient, we give it to Confucius. If it’s cynical and funny, it goes to Mark Twain. If it’s about strategy or war, it’s Sun Tzu. And if it’s about perseverance, logic, or nobility? Einstein gets the nod.

It’s branding by attribution. The quote becomes “better” if we imagine a titan of history saying it.

So What Do We Do With This?

At the surface, it’s just cultural laziness—there are only so many “famous” people in the public’s mental Rolodex, so we assign them everything. But it’s also more subtle and damaging: it reinforces the idea that only a handful of people in history are worth listening to.

This doesn’t just happen with quotes. It happens with scientific discoveries, artistic breakthroughs, and even entire branches of mathematics. As I wrote in The Fibonacci Sequence, Brought to You by Fibonacci (and Absolutely No One Else), history often remembers the person who popularized an idea, not the person who actually created it. The result? We get a distorted picture of how progress really happens.

The next time you hear a clever quote—or a “fact” about who discovered what—you don’t have to just nod along. You can check. Quote Investigator, run by Garson O’Toole, traces famous lines back to their earliest appearances. That’s where I found the true story of the Einstein quote.

You might find that the quote in your PowerPoint isn’t from Churchill, but from an obscure 19th-century pamphlet. Or that the mathematical sequence you love owes more to India than to Fibonacci.

Finding the truth behind these attributions means going beyond the headline version of history—the one where “Einstein was smart” and “Newton discovered everything.” What you get instead is the messy, collaborative, and far more human version of how ideas actually spread.

  1. https://en.wikipedia.org/wiki/Stigler%27s_law_of_eponymy ↩︎
Categories
Human Behavior Science and Math

The Cafeteria Conspiricy

Voronoi diagram of people enjoying a park from Kottke.org

The strangest thing happens to me when I visit the cafeteria at work. People will come in from out of town and we’ll go to lunch with about 10 people. But there’s nowhere that we can find for 10 people to sit together. There will be a number of seats in a row and then one or two people there to break it up.

It’s like everyone is intentionally spreading out across the room as far as they can. It feels like there’s a conspiracy to keep us from finding a table.

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Science and Math

The Fibonacci Sequence, Brought to You by Fibonacci (and Absolutely No One Else)

If there’s one thing I learned in high school, it’s that math was created by white men. Or at least, that’s how it seemed at the time. Names like Pythagoras, Pascal, and Fibonacci loomed large in my textbooks as if they had singlehandedly invented the building blocks of mathematics. No mention of where these ideas actually came from or the long, complex history behind them—just the neat, tidy story of how white men had supposedly figured it all out.

Take the Fibonacci sequence. I remember being fascinated by its elegance: 0, 1, 1, 2, 3, 5, 8, 13…

Each number builds on the two before it, showing up in nature from sunflower spirals to the curves of seashells. It felt almost magical.

And it was all thanks to this Italian mathematician, Leonardo Fibonacci—or so I was told.

But here’s the thing: Fibonacci didn’t invent it. By the time he wrote about the sequence in Liber Abaci, it was already centuries old.

Uncovering the True Origins of Mathematical Ideas

By the time Fibonacci wrote about the sequence, it had already been described in ancient India. Around 200 BCE, Indian mathematicians like Pingala were using it to analyze patterns in Sanskrit poetry. Later, Virahanka and Hemachandra expanded on it, applying it to combinatorics and other mathematical problems.

This wasn’t just a random observation—it was part of a rich and evolving tradition of mathematical thought.

So how did Fibonacci’s name get attached to it? The answer, as is often the case, is timing. Fibonacci’s Liber Abaci wasn’t just about the sequence; it was an introduction to the Hindu-Arabic numeral system, which he encountered during his travels in North Africa. By bringing these ideas to Europe, Fibonacci made them accessible to a new audience, and in the process, his name became forever linked to a concept he didn’t create.

I don’t blame Fibonacci for this—he wasn’t trying to take credit for the work of others. But the fact that his name stuck, while the names of Pingala, Virahanka, and Hemachandra faded into obscurity, says a lot about how credit is distributed in history.

It’s not just about who made the discovery—it’s about who told the story.

Reclaiming the Stories of Forgotten Pioneers

If we’re serious about recognizing the true pioneers of mathematics, we should go beyond just retelling their stories—we should honor them in the way we name the concepts they created. Imagine learning about the Pingala Sequence instead of the Fibonacci sequence, or studying Yang Hui’s Triangle in place of Pascal’s.

These small but significant changes would give overdue credit to the mathematicians who first discovered these ideas:

• Rename the Pythagorean Theorem to Baudhayana’s Theorem, after the Indian scholar Baudhayana.

• Replace Newton’s Binomial Theorem with Khayyam’s Binomial Expansion, in honor of Persian mathematician Omar Khayyam.

• Honor Brahmagupta’s Formula instead of Heron’s Formula for the area of a triangle.

These aren’t just symbolic changes—they’re a way to correct the historical record and emphasize the global nature of human innovation.

Renaming isn’t about erasing anyone from history. It’s about restoring balance to a narrative that has long skewed toward a select few. By doing so, we open up new ways for students and scholars alike to see mathematics not as the work of a single culture, but as a shared achievement that connects us all.

The Power of a Fuller History

Books like The Secret Lives of Numbers: A Hidden History of Math’s Unsung Trailblazers by Kate Kitagawa and Timothy Revell shed light on these overlooked contributions. The book dives into the rich, multicultural origins of mathematics, unearthing stories of mathematicians who were pushed to the margins of history.

It highlights figures like Pingala and Al-Khwarizmi, whose work laid the foundation for much of what we take for granted in modern math, and explores how cultural biases have shaped the way these achievements are remembered—or forgotten.

What’s powerful about The Secret Lives of Numbers is how it reframes math not as a series of isolated discoveries, but as a deeply interconnected, global endeavor. The book doesn’t shy away from the uncomfortable truth that many of the mathematical ideas we associate with Western figures had roots elsewhere.

It’s a reminder that restoring these stories isn’t just about fairness—it’s about painting a fuller, richer picture of the world we live in.

A Shared Legacy

The next time someone gushes about the Fibonacci sequence, I hope they think of Pingala. It’s a reminder of just how rich and interconnected the history of math really is. Math doesn’t belong to one culture or one group of people—it belongs to all of us. And its history deserves to reflect that.

The Fibonacci sequence is beautiful. But for me, it’s even more beautiful when I know the whole story.

ChatGPT writing note: I left the final edit to ChatGPT on this one. I think it did a pretty good job!

Categories
Science and Math

What is “Normal” Body Temperature?

“Never express yourself more clearly than you can think.” — Niels Bohr

I’ve been reading Ben Orlin’s new book, Math for English Majors. Ben always has a brilliantly philosophical way of looking at numbers and math, and it got me thinking about how we often misunderstand precision.

I’ve always been fascinated by the way we handle precision—how we assume that if we know one number exactly and another is only “about right,” the overall result is still only “about right.” It’s a reminder that even when we want precision, the world often delivers something a little fuzzier.

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Adventures Science and Math

The Beauty of Standards: The Royal Observatory of Greenwich

London, April 27, 2024, 7 PM

On an average day, when I pause to ask myself where I am and what time it is, I get back the following:

New York: 40°46’30.9″N latitude, 73°59’07.4″W longitude, with a time of GMT-5.

Those coordinates make my existence seem so random, so routine. But today was different. Today, we were heading to a place that felt like the very center of standardized space and time.

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Science and Math

A Biography of Numbers

In the past few years, I’ve seen books written about lots of different things like elements, molecules, and colors. I’m surprised that no one has written a biography of numbers.

Math nerds like me would love this book. I’m thinking it would look like Elements: A Visual Exploration of Every Known Atom in the Universe. Each page would have a fancy drawing of the number with some text.

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