Tag: Probability

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AI AI: Transformers Books

The Updating Machine

Tom Chivers puts Bayes’ theorem in plain English and it sounds almost obvious: “the probability of event A, given event B, equals the probability of B given A, times the probability of A on its own, divided by the probability of B on its own.” A formula for revising what you believe when new evidence arrives. You started somewhere. Something changed. Now you believe something slightly different. Repeat.

The obvious part is the mechanics. The hard part is the loop.

Most reasoning errors I catch in myself aren’t failures of logic — they’re failures to update. I hold a view, evidence accumulates against it, and I find reasons the evidence is flawed rather than reasons the view might be.

Psychologists have a name for this: confirmation bias. But I’ve always found that label a bit too clean, like it describes a bug rather than a feature.

The prior isn’t wrong to be sticky. It represents everything you’ve learned up to this point. The problem is when it becomes load-bearing — when the prior stops being a starting position and starts being a conclusion.

“Strong opinions, loosely held” is supposed to solve this. It’s a useful phrase — it captures something true about the right posture toward your own beliefs. But in practice the second half is harder to honor than it sounds. The strong opinion gets stated, new evidence arrives, and changing your mind in public feels like losing. The “loosely held” part quietly becomes decorative.

What Bayes actually demands is something closer to epistemic humility with arithmetic attached. You don’t get to say I don’t know. You have to say I estimate 0.4, and here is what would move me to 0.6. That’s harder. It requires you to specify not just what you believe but how you’d know if you were wrong.

This is why Bayesian thinking keeps surfacing in AI conversations. Modern language models do something structurally adjacent to this — not consciously, but mechanically. Every token generated is a probability distribution revised forward by context. The model doesn’t know the next word; it updates a prior over all possible words, given everything that came before. It’s not reasoning the way humans reason, but it’s updating the way Bayes updates: continuously, contextually, without the luxury of certainty.

Whether that’s comforting or unsettling probably depends on your own prior.

The deeper thing Chivers is pointing at, I think, is that Bayesian reasoning is essentially a description of intellectual honesty as a process rather than a trait. You can’t just decide to be open-minded. You have to build the loop: form a belief, assign it a probability, watch for evidence that should move it, and then actually move it. Most of us do the first three. The fourth step is where it gets expensive.

I’ve been wrong about enough things by now that I’ve started to treat my own confident views with mild suspicion. Not paralysis — you have to act on something — but a background awareness that the prior I’m acting on was formed by a person who had less information than I do now, and less than I’ll have next year.

Strong opinions, loosely held, sounds right. The trick is meaning it.

Categories
Living Serendipity

The Architecture of the Unexpected

We spend an incredible amount of energy trying to build a ceiling over our lives, a structure made of spreadsheets, five-year plans, and trend forecasts. We convince ourselves that if we just gather enough data, the future will become a navigable map. But Morgan Housel, in Same as Ever, cuts through this illusion with a quiet, devastating observation:

“We are very good at predicting the future, except for the surprises—which tend to be all that matter.”

It is a humbling thought. We can predict the mundane with startling accuracy—the seasons, the commute, the steady inflation of a currency. But the events that actually shift the trajectory of a life, a business, or a civilization are precisely the ones that no model accounted for. We are experts at forecasting the rain, yet we are consistently blindsided by the flood.

This reveals a profound tension in the human experience. We crave certainty because certainty feels like safety. We want to believe that the “tail events”—those low-probability, high-impact occurrences—are outliers we can ignore. In reality, history isn’t a steady climb; it’s a series of long plateaus punctuated by sudden, violent leaps.

The problem isn’t that our models are broken; it’s that we are looking at the wrong thing. Instead of seeking total foresight, we must prioritize serendipity and resilience. If the future is defined by surprises, then the most valuable asset isn’t a better crystal ball—it’s a wider margin of safety.

We must learn to live with the paradox: we must plan for a future that we know, deep down, will not go according to plan. The surprises aren’t just interruptions to the story; they are the story.

Looking back at the last decade of your life, what was the single ‘surprise’ event that defined your path more than any plan you ever made?

Categories
Probabilities

The Fiction of Certainty

There is a profound discomfort in the space between zero and one.

In her book Spies, Lies, and Algorithms, Amy B. Zegart notes a fundamental flaw in our cognitive architecture:

“Humans are atrocious at understanding probabilities.”

It is a sharp, unsparing observation, but it is not an insult. It is an evolutionary receipt. We are atrocious at probabilities because we were designed for causality, not calculus. On the savanna, if you heard a rustle in the tall grass, you didn’t perform a Bayesian analysis to determine the statistical likelihood of a lion versus the wind. You ran. The cost of a false positive was a wasted sprint; the cost of a false negative was death.

We are the descendants of the paranoid pattern-seekers. We survived because we treated possibilities as certainties.

The Binary Trap

Today, this ancient wiring misfires. We live in a world governed by complex systems, subtle variables, and sliding scales of risk. Yet, our brains still crave the binary. We want “Safe” or “Dangerous.” We want “Guilty” or “Innocent.” We want “It will rain” or “It will be sunny.”

When a meteorologist says there is a 30% chance of rain, and it rains, we scream that they were wrong. We feel betrayed. We forget that 30% is a very real number; it means that in three out of ten parallel universes, you got wet. We just happened to occupy one of the three.

Zegart operates in the world of intelligence—a misty domain of “moderate confidence” and “low likelihood assessments.” In that world, failing to grasp probability leads to catastrophic policy failures. But in our personal lives, it leads to a different kind of failure: the inability to find peace in uncertainty.

Stories > Statistics

We tell ourselves stories to bridge the gap. We prefer a terrifying narrative with a clear cause to a benign reality based on random chance. Stories have arcs; statistics have variance. Stories have heroes and villains; probabilities only have outcomes.

To accept that we are bad at probability is an act of intellectual humility. It forces us to pause when we feel that rush of certainty. It asks us to look at the rustling grass and admit, “I don’t know what that is,” and be okay with sitting in that discomfort.

We may never be good at understanding probabilities—our biology fights against it—but we can get better at forgiving the universe for being random.