Surprise has the extremely special distinction of being both an emotion and a completely quantifiable thing that scientists and mathematicians talk about very frequently. Whenever probability is a thing, surprise is also a thing. It’s true and it’s not even that complicated! Watch:

For some intuition:

• You’re certain the sun will rise tomorrow; you believe the probability the sun will rise is 100% or “1”; we have that -log(1) = 0. So if the sun rises tomorrow, your level of surprise will be 0. That sounds correct!

• If someone flips a coin, you believe the probability it’ll land heads is 50% aka 0.5. We have that -log(0.5) = 0.3; your level of surprise at it landing on heads is 0.3

• If they flip the coin again, and get heads again, your level of surprise is 0.3 + 0.3 = 0.6 surprise. Yes, this actually works, you can just add them, no need to fuss around with subtracting from 1 then multiplying

• To turn that first one around, you believe the probability the sun won’t rise tomorrow is 0% or “0”. We have that -log(0) = ∞. If the sun doesn’t rise tomorrow, your level of surprise will be ∞. Personally, this is pretty intuitive to me!

Hell is other people’s understanding of statistics

People talk about uncertainty in an intuitive way constantly. They use words like “might”, “maybe”, “could do”, “there’s a distinct possibility”. So weaselly! I often wish people would be more quantitative and use numbers. But when I put a percentage on my own uncertainty, people get frustrated. One must have a little sympathy for them: humans don’t intuitively “feel” percentage points. So to reiterate that argument: surprise is something you do feel!

Besides, when they do try to be quantitative…

Don’t hate the thinker, hate the tool for thought

Maybe seeing those makes you despair for humanity so much that you want to avert your gaze from the whole thing. No! Bad attitude! You do not get to give up like that. Even when I tell you that one of them is a Professor of Neuroscience at Stanford 😀

Seriously though - doctors and nurses have to read survival percentage values out all the time. At many points, decisions affecting your life and those of your loved ones have been made based on them. How many lives have been lost to making mistakes like this? You want to make people’s lives better, get them thinking more quantitatively. So: growth mindset for humanity, please. I did not post those quotes so you can complain about them with your enlightened friends. I want you to think of those quotes as telling you what you’re working with if you want to improve things (you want to improve things).

So how do we help those people? We can change their tools for thought. No more probability! Talk about surprise instead!

Maybe: when people see numbers, they want to add them (they expect “linearity”). Then being able to add surprises is a superpower. Let’s give people that superpower by changing education and everyday conversation to use it instead of probability.

Introducing: the Surprice-Dice!

Here’s a funny and helpful thing: it turns out that there is a god-given unit of surprise.

You already know what it means to have a surprise of 0 (“I knew that would happen”) and infinity (“I thought that was impossible”). Well, it turns out there is a thing it means for your level of surprise to be exactly 1.

It’s approximately the level of surprise you have when rolling a 30-sided dice and getting 11 or less. To be more exact it’s 1/e, where e is that number people learned about during COVID. 1/e = 0.367… ≈ 11/30.

So, public information campaign: mass-produce 30 sided dice, with numbers 1-11 colored green and 12-30 coloured yellow. Mail one to every household, we’ll double everyone’s IQ overnight! “1 surprise” is one roll of this being 1-11. “2 surprise” is that happening twice. 3 surprise is 3 rolls being 1-11.

How surprised would you be if the democrats lost the next election? More than 2 rolls, or fewer? And that’s how a civilized person talks in 2026!

(yes, I know, “die” not “dice”. But I am a linguistic descriptivist, get used to it!)

To be honest, a revolution in thought of this kind seems improbable would surprise me more than 6 11/30 rolls. Alas, status quo has us locked into probability. Same as electrons having negative charge, pi vs tau, and 3D geometry should be done with the cross product. Still, you might as well give it a go, in your own head or with your kids 🙂

Appendix: sciencey arguments

1. Entropy becomes much more intuitive: it’s “average surprise”, or “expected surprise” (that phrase sounds sounds so ridiculous and I love it). Think about it: with more ordered and predictable (less entropic) things, the average result is less surprising - duh!
2. Bayes theorem gets oh-so-much-nicer too, it’s just adding and subtracting!
2. This has been said for super duper serious science, not just wishy-washy human intuition!

Gaussians are nicer too:

By the way surprise also goes by the name “surprisal” and “log-odds”, but it maps very directly to the intuitive sense of the word so I don’t know why you’d say that!

Hi!

As long-time readers of the newsletter know, I’m a fan of variant sudoku puzzles — sudoku with strange rules like thermometers, ratio dots, cages, and other things that you’re probably already confused by. Many times, I’ve mentioned and endorsed James Sinclair’s Artisanal Sudoku newsletter, and I’m going to do the same today — and then some. Because James has a book out, and I have photographic evidence that you’ll like it.

This week, I was in Manhattan and early to an event I was attending, so I stopped by Strand, a famous used book store. I went to see if they had any of my books on the shelves and they did, as seen below. And on the same shelf, next to my book (I rotated the image below), is the book I’m here to share with you today — James’ book of 150 handcrafted variant sudoku puzzles.

I didn’t buy his book because I already owned it — I preordered it when he announced it last fall. Easiest impulse buy in recent memory, too, because his puzzles are fantastic. (I didn’t buy my own book either, but it’s sitting there for $10 if you want a used copy. I considered stealthily signing it but I didn’t have a pen on me, and didn’t want to get arrested.)

But don’t take my word for it — try one of his puzzles yourself. Here’s one from this week’s newsletter, which you can play online here:

The rules:

• Regular sudoku rules apply — place the numbers 1 through 9 in the grid nine times each, so that no number repeats in any row, column, or bold-outlined 3×3 box.
• The sum of the digits inside each cage is equal to the small number in the top left corner, and digits cannot repeat within a cage.
• Those grey lines are thermometers. Digits on thermometers increase from the bulb end, and not necessarily incrementally.

Enjoy, and if you like it, consider buying James’ book. And if you’re like me, copy the pages so you don’t have to write in the book itself.

The Now I Know Week In Review

Monday: A Life-Saving Football Blooper: He got a kick (heh) out of this one, and it sent him to the hospital — thankfully.

Tuesday: A Planely Obvious Punishment: Stupid human tricks, with somewhat predictable results.

Wednesday: Why You Shouldn’t Tick off a Tiger: It may not get you right away, but that may not matter.

Thursday: The Boy and the Blue Cup: A heartwarming story.

Long Reads and Other Things

Here are a few things you may want to check out over the weekend:

1) “Inside the Quest to Mine the Bottom of the Sea” (New York Times/gift link, 11 minutes, June 2026). This is very cool, albeit controversial.

2) “How Long Does It Take to Plan a Bridge?” (Construction Physics, 6 minutes, June 2026). The “New Tappan Zee Bridge” listed here isn’t too far from me, and I felt like it took forever. But it only took five years to build plus another 13 to plan, which … OK, kind of does feel like forever. It’s not out of the norm, though.

3) “The Secret Garden of Rock-Paper-Scissors” (The Shamblog, 6 minutes, May 2026). What happens when you add more options to the classic three-option game? He did the math.

Have a great weekend, and let’s go Knicks!

Dan

You didn’t “have a conversation” with ChatGPT.

It doesn’t “think you should…” It doesn’t think.

It didn’t “tell you that…” It doesn’t speak.

It doesn’t “feel that the best option is…” It doesn’t feel.

AI is a cheap parlor trick. You provide words, and it provides words back that are most likely to occur alongside the words you provided.

…

A useful reminder for the next time you’re tempted to personify or humanise an LLM.

LLMs are statistical tools. There are some things that the statistics of language can be good at, especially on average: stuff like summarisation, sentiment analysis, pattern identification, and checking for internal consistency.

But they’re just maths. They’re not a person.

It’s not even that they don’t care about you or don’t want to help you. They don’t even go that far: they’re incapable of “caring” or “wanting” in the first place. What they do is take all of the information they’ve ingested, plus their training and prompt, plus the conversation you’d had with them so far, plus a random number, and produce output which is, after a fashion, a prediction of what comes next.

As always: that’s not to say it’s useless. (It’s also not to say it’s always useful.) But as a tool, it’s pretty opaque to most normal people.

Unless you’ve really taken a deep-dive into understanding low LLMs work, they must seem like magic (hell; speaking as somebody who has taken such a deep-dive, they sometimes seem like magic!). I’m sure that some of the time, they must seem like they’re a living thing, or at least an approximation of one.

But they’re not. And it’s important to remember that.

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The evidence on AI’s effect on those who use it has been coming in, and it’s not good. While it doesn’t effect everyone, it seems to effect most people, and the worst affected, it seems, are the young. Olds have the advantage of growing up in world where they had to learn how to do things themselves. To be sure, phones and social media seem to have had a negative effect on attention span and learning ability, but AI is yet another assault, and it hits the young hardest.

This excerpt comes from a larger piece from a university professor on the inability of his students to read. The whole thing is worth reading, and the decline is truly precipitous: fundamentally most of them can’t read an entire book, and struggle even with long articles, and they can’t pull out the arguments made. The bit on AI follows:

Another reason for the decline in student reading capability is increasing reliance on generative AI. In June 2025, Nataliya Kosmyna and colleagues at the MIT Media Lab released a preprint titled “Your Brain on ChatGPT.” They divided 54 participants into three groups writing SAT-style essays — one using ChatGPT, the second group using a search engine, the last group using nothing — and monitored brain activity with a 32-channel EEG. The ChatGPT group showed the lowest neural connectivity of the three, with up to 55 percent reduced connectivity compared with the brain-only group, and “consistently underperformed at neural, linguistic, and behavioral levels.” Eighty-three percent of LLM users could not quote a single line from essays they had written minutes earlier. When the LLM group was forced to write without AI in a follow-up session, their brain activity did not bounce back to baseline; the researchers coined the term “cognitive debt” for the lingering deficit.

The fundamental strategy of a lot of tech startups has been to degrade pre-existing infrastructure by under-pricing, for years if necessary, until the old methods are so diminished that they can start charging monopoly pricing. Uber is the classic example: Ubers were far cheaper than taxis for about a decade. Now they’re often more expensive, if the taxis exist at all. Certainly where I live in Toronto, the Taxis did somewhat survive, and cost less.

But overall the strategy was a success, taxi companies were devastated and Uber’s doing great now. All it took was years of losses and predatory pricing: their model wasn’t superior, their product wasn’t superior except having a good app, but they had far more access to patient money, willing to take losses for years to get to the oligopoly pricing end-state.

Neither Anthropic nor Open AI are remotely profitable. Every single query costs more to run than is charged, even to paying clients. A recent increase in prices, still far below running costs, has hit users with massive bills. There’s no evidence AI is better than humans at most tasks, and the real cost (and sometimes, even subsidized, the current subsidized price) is higher than just having employees. AI is often faster, but it makes mistakes humans don’t, and needs to be checked.

But if you make your employees use it they’re going to be degraded and lose the ability to do their jobs well. The more you do something, the more your body and brain optimize for it. The less you do it, the worse you get.

AI’s strategy for replacing workers is threefold: first, sell executives on getting rid of pesky workers for AI, because it’s supposedly easier to manage.

Second: Subsidize while companies lay off the workers and replace them with AI. Once the workers are gone, jack up prices; and,

Third: by encouraging companies to force workers to use AI and to replace workers with AI in some cases, make the workers less capable: stupider. Over time as more and more people become dependent on AI to think and work for them, they will lose the ability to do the work themselves. AI may be shitty, but it will be better than the dullards AI makes its users into.

It’s an ingenious strategy, really. Make people stupid, and replace them with a product which costs more and is inferior to them for most tasks before they were made stupid.

The longer term issue will be that AI isn’t creative: it uses the embodied creativity of past humans, in terms of their writing and their discoveries to simulate intelligence. But as humans produce less and less new creative work, AI will be reduced to eating its own results, and indications are that leads to model collapse: AI’s are dependent on human, and by making humans redundant and stupid they will themselves become stupider and less effective over time.

We live in a time where we can’t look ahead, ever, at technology and make even the smallest effort to control the end results, it seem. At least in the West. Or, rather, we refuse to deal with obvious negative issues if doing so means a few people won’t be able to get as filthy rich.

Dumb.

And soon we’ll be even dumber.

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