Don't think "vibe-coding". Think just-in-time models that can help us all learn.
The ability to build models to think through issues has remained the province of the few. Is that about to change? And what does that mean for the classroom?
This post is a first pass at approaching one of the most underdiscussed elements on LLMs in education: they can provide students with a way to model things.
Until now, that ability has been the province of a few. It’s been the social science researcher that knows a bit of python, the programmer who can build 3D representations of the physical world, the spreadsheet jockey who can model financial outcomes based on assumptions. But you had to know code or complex processes.
Not anymore.
Now, as I show below, anyone can spin up a custom model of the world (or in the article, the solar system) to better understand a problem or a phenomenon.
What does a world of “model-first” thinking look like? How do we prepare students for it? How will it shift what happens in the classroom?
That’s going to take more than this post to figure out.
But let me start with a little story.
The earliest sunset is when?
I was doing one of my little fact-checking walkthroughs the other day on an interesting fact that came into my feed: the earliest sunset in Seattle is tomorrow, December 10th.
That seemed weird, or at least it did to me, because the solstice is on the 21st, and you would think the earliest sunset would be on the shortest day.
Here’s a portion of the AI Mode explanation:
The earliest sunset in Seattle occurs before the winter solstice (December 21st) due to a discrepancy between our 24-hour clocks and the actual length of a solar day, a phenomenon described by the equation of time.
Here is a breakdown of why this happens:
Varying Solar Day Length: While our clocks define a day as exactly 24 hours, an actual solar day (the time it takes for the Sun to return to the same point in the sky) varies slightly throughout the year. Around the winter solstice, the Earth’s elliptical orbit causes it to move faster as it gets closer to the Sun (a point called perihelion in January). This faster orbital speed, combined with the Earth’s axial tilt, makes the solar day in December slightly longer than 24 hours (by up to 30 seconds).
Did you get that? I read it and what I felt was what I feel a lot in life:
the sensation of “Oh, I see how that works…”
followed by a feeling best described as “Wait a second, what?!?”
I mean, look at this explanation…
Around the winter solstice, the Earth’s elliptical orbit causes it to move faster as it gets closer to the Sun (a point called perihelion in January). This faster orbital speed, combined with the Earth’s axial tilt, makes the solar day in December slightly longer than 24 hours (by up to 30 seconds).
OK, so why would going around the Sun faster make your day longer? What does that have to do with speed of rotation? What does tilt have to do with it? My sage head-nodding as I initially read it melted away into befuddlement.
Initially I asked Claude to draw me a diagram to help me understand it, but nothing Claude produced really helped me.
So I thought why not learn how this works by building a model? Why not have AI make a webpage that calculates and charts sunrise and sunset and shifting solar noon? Then I can look at those calculations and better understand what’s going on. And in the process of building the model I’ll better understand the phenomenon.
Learning through building a model
I used Claude Code to build it, and I think a lot of people will think that means I wrote a bunch of code. In reality I wrote no code, and really the only coding knowledge I applied was
Choice of platform: I told it to use Python Flask
Because https is still not push button to implement I had to do a little bit of admin to get it to be available on the web (DNS record set up, choosing a webserver model)
The rest of my interaction was just learning about things like the “equation of time” and telling it how I wanted my webpage to make an interactive model of it.
I started by just asking it to build a visualization of how for a given city how the solar noon shifts, and how that impacts earliest sunset and latest sunrise. Here’s one for San Francisco with its earliest sunset on December 6:
And here’s Seattle, with its earliest sunset on the 10th:
(You can play with the webpage here.)
One of the things I note is that the time in between the earliest sunset and the latest sunrise is compressed in the Seattle example relative to San Diego. Is that a latitude thing? I poke around, trying out Houston and Bangor, Maine and the pattern holds.
So if I look at Anchorage, for example, you can see that the earliest sunset and latest sunrise cluster very close to the solstice, presumably because the day shortening is so severe that whatever other variable (supposedly the orbit of the Earth?) is counteracting it has less relative influence.
So what seems to be happening on these graphs is that solar noon (the dotted red line) is shifting about a half hour later over the course of Nov 10 to Feb 9. In places where the days don’t get short as fast, that shift has a lot of impact on the earliest sunset, because every day it’s pushing that sunset a bit later. In places where the days are getting shorter fast right up until near the solstice that impact is less and not really felt until that shortening slows down.
But what’s causing the solar noon shift?
Equation of time
So the explanation we saw online said something about the days being 30 seconds longer. Leave aside how weird that is to think about, does that map to that solar noon shift? Would 90 days of solar noon shift of 30 seconds give you 30 minutes?
Nope. So we have the term “equation of time” and we know it’s a combination of some orbital effect (going around the sun) and some axial effect (tilt of the Earth). Without knowing too much about these terms, let’s ask it to plot out the equation of time with these elements to see if it looks like these things explain it.
I flip around to different U.S. cities and find that the equation of time looks the same no matter the latitude:
The thing that shifts is the green line. After some confusion and boneheaded false starts I realize that the difference of the green line is just about where in the time zone you are. Time zones are apparently calibrated along the midpoint of the zone (I think that might be called the time zone’s meridian, but not sure). So solar noon is at a later time because — wait, how does that work? I think it is like this:
Dallas Texas is “19 minutes” east of the middle of its time zone.
Therefore solar noon happens earlier
But that would mean that the green line should be lower, than zero, right? And it’s not.
Ok, let’s check this out — I ask Claude to add some Illinois cities. After all, Chicago is very east in CST, is its line below or above the EoT line?
It’s below. So I’m reading the graph right, I just was misinterpreting the “+”. Dallas is “19 minutes” west of the time zone meridian, so even without the “space stuff” its solar noon is on average is going to be 19 minutes after clock noon in that zone.
What does this solar noon drift look like across a year? I peek at Santa Rosa Island which happens to be on the Pacific Time meridian. And I kind of wish I hadn’t, because I don’t really understand this, but I can see that there is one trend that is annual (orbital as the orange dotted line, makes sense) and another that is bi-annual (axial tilt, blue dotted line, I have no idea why it has two peaks. Spring and fall maybe? Except it doesn’t peak in either.)
When those two forces intersect you get this weird pattern:
That’s the the general pattern, let’s look at how the orbit shifts it now.
Modeling the orbit
So I read an explanation online about the orbit thing, and this is how it works.
Imagine two dancers waltzing and rotating around each other and there is a pole in the center of the room. If they stay in the same place then every time the lead dancer rotates 360 degrees he will be facing the pole.
But say they are waltzing around the pole as well, in the direction of their rotation (let’s imagine both are counterclockwise). Then each time to face the pole the lead dancer has to turn 360 degrees plus a little more because the angle to face the pole has shifted a bit.
All well and good. There are 360 degrees in a circle and 365 days, each day the Earth on average had to rotate slightly less than one degree extra. In fact, if you want to know something cool: the time it takes the Earth to finish one rotation is 23 hours, 56 minutes, and four seconds, a so-called “sideral day”. The last 4 minutes are spent rotating that extra degree.
So far none of this explains why solar noon shifts. But we’re almost there. But I had to make another diagram to show it.
So when the Earth is closest to the sun it moves faster. The closest is around Jan 3rd. At that point the Earth is moving fast enough around the sun that it would have to rotate an extra 1.02 degrees instead of the average extra 0.9856.
I ask Claude to make me a diagram of the Earth’s orbit with the date that we go the fastest marked and the date we go the slowest. Then allow me to set any date and see the extra rotation we would need
So each day the debt begins to accumulate. Let’s find the beginning and end of the shift of solar noon forward on our chart. I ask Claude code to add some min/max labels and let me hide lines. This one’s a bit of a mess because Claude tells me it’s actually hard to make the labels disappear when I disappear the lines because the graph is server generated, which I don’t quite get, but whatever. You can see the start and end dates of the growth, with Jan 3 in the middle of the upward trend:
So if we are understanding this right, on Oct 5 the extra rotation needed should be 0.9856 degrees (the average needed, ~360/365), then the day after that a little more…
This looks right! And so if we go halfway between here and there, then the debt should be maybe 0.02 degrees?
Close, but not quite, which means I’m probably thinking too linearly about that progression. That equation of time did have some calculus in it, probably important. But the general pattern is confirmed. From about Oct 3 to Jan 6, the Earth starts accelerating and that is part of what causes noon to shift later each day because the Earth is not rotating fast enough to keep up.
And from sometime in April the Earth’s speed slows down enough where the Earth is rotating more than it has to and that pushes noon backwards again.
So if I understand this part right, this should be a global effect, whether it’s summer or winter where you are, the whole earth is speeding up or slowing down so it should be the same effect all over. I decide to test my understanding by telling Claude to put South American cities into the model and then checking Santiago, Chile:
And yep, it’s the exact same pattern. Except — have I done something wrong to my model? It says the longitudinal offset is 40 minutes. Should the max offset in a time zone be 30 minutes? I ask Claude Code — why is this like this? Claude Code answers that Chile would technically be in a time zone one over, but stays in the time zone east of it for political and practical reasons.
I should say that in narrating this process I’ve left out dozens of times where I’ve looked at numbers and asked if the numbers were right, or the model was right and once or twice I caught Claude in a mistake (for example, at first not shifting the rotation figure based on date) and most of the time learning how an assumption I had was not correct or didn’t take into account an unknown factor.
Don’t think vibe-coding. Think just-in-time modeling.
I still don’t know how the axial effect part of this thing works.
It may be a relief to you that I decided to take a bit of a break before I tackled understanding the axial tilt piece of this, so you don’t have to sit through another 2,000 words about why solar noon shifts.
And that’s OK. Because my real point here is this is part of what critical thinking with an LLM looks like. We get an understanding, then we test that understanding by building a model, tweaking it, seeing how it works.
This is a way of understanding the world that has previously belonged to programmers and spreadsheet jockeys. But I am not exaggerating when I say that apart from some tricky stuff around web server setup and SSL certificates, every single thing I did here could have been done by an eighth grader with a bit of instruction about what the names of things on a webpage are, what the names of parts of a chart are (legends, callouts, hovers). The part that writes the code is as simple as telling it what data you want and how you’d like to be able to interact with it.
Now, I know that I have 30 years’ experience making webpages (my god, it really is 30 years since I made my first webpage). There’s a lot I brought to the table here. But I also used a tool that was built for coders. Other tools will follow that hide the mechanics while still having this level of power. AI Studio is an example of that. Claude artifacts are getting better (though I don’t know that it could pull in that Skyfield library this project did).
But I can imagine students working together on an activity like this, building a model to better understand the world and better test their understanding of it. And I don’t know if we’ve comprehended what the world looks like when an eighth grader can say, “that’s a good question, let’s build a model of it.”
Personally, what I found multiple times in this process was that reading the explanations of the effect I thought I got it, but I didn’t really get it at the detail I thought I had until I built a model.
What can education do with this?
I know, teachers already do too much. Maybe this is one more thing.
But I do think that the ability to think and discuss things through the creation of quickly spun-up models that people can tweak, critique, play with assumptions, and test understandings is an underappreciated part of the value this can bring to the classroom. And I do think if we teach it well it is a skill that can transform the world of work as well. It seems to me it’s worth a shot.
Check out the solar time site.
This is fantastic, Mike.