Daniel sent us this one — he's continuing the G. fundamentals series, and he wants to talk about how we write down where things are. Degrees-minutes-seconds versus decimal notation, why four decimal places became the geolocation gold standard, and then the really fun part: what happens when you push precision to eight decimal places, where tectonic drift means the ground literally moves under your coordinates. He's also asking about U. and municipal grid systems, specifically Israel's, and how tools like GeoPandas handle mapping between them. There's a lot to unpack here, but the tectonic drift question is the one I keep coming back to.
It's the part that makes you realize coordinates are a timestamp, not a fixed address. And by the way, today's script is being generated by DeepSeek V four Pro, which feels appropriate for an episode about precision.
Does it do coordinates?
I have no idea, but I'm choosing to believe it would handle eight decimal places with appropriate humility. So let's start with the notation question, because it's the foundation Daniel's building from. Degrees-minutes-seconds, D. , is the system you see on old nautical charts and hiking maps. It divides each degree into sixty arcminutes, each arcminute into sixty arcseconds. Base sixty, same as how we handle time. New York City in D. is forty degrees, forty-two minutes, fifty-one seconds north, seventy-four degrees, zero minutes, twenty-one seconds west. It's intuitive for humans reading a compass, but it's a nightmare for computation. You can't just add and subtract sexagesimal values in a spreadsheet without converting everything.
That's why decimal degrees took over. Forty point seven one four degrees north, negative seventy-four point zero zero six degrees west. One number per axis, precision scales by just adding decimal places, and your computer doesn't have to do base-sixty math. I get why G. software standardized on it. But what I didn't realize until I started digging into this is how elegantly the precision ladder works. One decimal place is about eleven kilometers at the equator. Four decimal places gets you to about eleven meters — that's the corner of a specific building. Five decimal places is roughly one point one meters, so you can distinguish individual people in a room. Six decimal places is about eleven centimeters. Eight decimal places is about one point one millimeters.
There's an xkcd comic from twenty nineteen that laid this out beautifully. It's become the canonical reference for this. Zero decimal places pinpoints a region, four decimal places a house corner, five decimal places a specific person assuming you've specified which datum you're using, seven decimal places finds Waldo on a page, and fifteen decimal places approaches atomic scales. The title text notes that at around forty decimal places you reach the Planck length, where the structure of spacetime itself may be quantized and the whole notion of distance breaks down.
The precision ladder is conceptually satisfying, but here's the thing that drives me crazy. You see G. receivers and phone apps spitting out coordinates to eight, ten, fifteen decimal places, and people treat that as real precision. But a standard consumer G. device has an accuracy of about seven meters ninety-five percent of the time. That extra digit is pure noise. It's false precision, and it's everywhere.
It's one of those things where the display resolution massively exceeds the measurement resolution, and nobody explains this to users. Your phone G. is dealing with atmospheric delays, multipath errors where signals bounce off buildings, satellite geometry issues. The ionosphere alone introduces range errors of sixteen to eighty centimeters on the L one frequency just from fluctuations in total electron content. Dual-frequency receivers and differential corrections can mitigate that, but your phone isn't doing that. So when it shows you coordinates to eight decimal places, it's basically making up numbers after the fifth or sixth decimal.
Which makes the tectonic drift question even more interesting, because we're talking about a level of precision where the errors in consumer G. are orders of magnitude larger than the phenomenon itself. But if you're doing survey-grade work, if you're using R. with centimeter-level accuracy, then plate motion becomes a real thing you have to account for.
Plates move fast enough that this isn't theoretical. Tectonic plates typically move between one and seven centimeters per year. The Australian Plate is one of the fastest, moving about eight centimeters per year northeast. Australia had to adjust all of its national coordinates by roughly one point eight meters a few years back to account for cumulative drift. That's not a rounding error. That's a visible shift on any map.
Wait, they adjusted the whole country's coordinates? Like, every mapped feature shifted by nearly two meters?
Every coordinate in the national spatial reference system. Because Australia sits on its own tectonic plate, and that plate has been drifting relative to the global reference frame since the last time they set their datum. The standard approach for handling this is time-dependent transformations. You take a coordinate at a reference epoch, say X at time T zero, and you apply a velocity vector. So X at time T equals X at T zero plus velocity times the time difference. The velocity vector comes from plate motion models like N. dash one dash A dash N. or the Global Strain Rate Model version two point one, and more recently the I. twenty twenty frame.
being the International Terrestrial Reference Frame.
And this is the key thing that I think most people don't appreciate. eighty-four, the coordinate system G. uses, is not static. It's continuously updated. Each new realization, I. twenty fourteen, I. twenty twenty, incorporates years of G. station velocity data to track how the entire global grid of reference points is shifting. Static regional datums like N. eighty-three for North America or G. ninety-four for Australia, those ignore post-realization motion. Over a couple of decades, the discrepancy between a static datum and the dynamic frame can exceed a meter.
If you're working with coordinates at eight decimal places, roughly millimeter precision, you're not just making a measurement. You're making a measurement at a specific moment in time, in a specific reference frame, with a known velocity relative to the tectonic plate you're standing on. The coordinate is a four-dimensional data point.
And tools exist to handle this. There's the U. Plate Motion Calculator, where you can input a latitude and longitude, select a plate motion model, and it'll spit out the velocity vector at that location. services like G. automatically update base stations to the latest W. eighty-four slash I. frames, which is how you get one-centimeter R. But all of this machinery is invisible to someone just opening Google Maps.
This is where I want to push on the philosophical limit Daniel's asking about. He asked if there's a precision limit due to planetary physics, and I think the answer is yes, but it's not one limit. It's a stack of them. You mentioned the ionosphere. There's also the fact that the solid Earth itself has tides. The ground bulges about thirty centimeters twice a day due to lunar gravity. That's Earth tides, not ocean tides. The rock you're standing on is moving up and down by a noticeable amount.
If you're trying to locate something to sub-centimeter precision, you need to know what time of day you measured it, because the ground was in a different position at high tide versus low tide. Then you add groundwater extraction causing local subsidence, seasonal soil expansion and contraction, and eventually at the atomic scale you hit Brownian motion where everything is jiggling randomly. The question "what does it mean to locate a point on Earth to one-millimeter precision" gets surprisingly deep.
It also connects to the datum ambiguity problem. At five or more decimal places, you have to specify which geodetic datum you're using. eighty-four, N. eighty-three, I. Otherwise your coordinates are ambiguous by up to several meters. Most people outside G. never think about this. They assume latitude and longitude are absolute.
They're not. They're relative to a model of the Earth's shape, which is itself an approximation. gives you ellipsoidal heights, meaning height above a mathematical ellipsoid. But if you want actual orthometric height, height above mean sea level, you need a geoid model. The geoid deviates from the reference ellipsoid by up to a hundred meters in places. That's not a small correction. And geoid models are continuously refined as we get better gravity data from satellites like G.
Even the "up" direction is contested. Let's shift to the other part of Daniel's question, because the notation systems beyond D. and decimal are where things get practical for people doing mapping work. He mentioned U. and municipal X. systems in Israel.
, Universal Transverse Mercator, is a projected coordinate system. This is the key distinction. Decimal degrees and D. are geographic coordinate systems. They describe positions on a sphere or ellipsoid. projects that curved surface onto a flat plane. It divides the Earth into sixty zones, each six degrees of longitude wide. Within each zone, coordinates are in meters. Easting is the X coordinate, northing is the Y coordinate. The central meridian of each zone gets a false easting of five hundred thousand meters, so you never have negative numbers. In the southern hemisphere, there's a false northing of ten million meters for the same reason.
Why meters instead of degrees?
Because once you're on a flat plane, you want units that make sense for measuring distance and area. If you're calculating the area of a parcel of land or the distance between two points, doing that in degrees is messy because a degree of longitude changes width depending on your latitude. At the equator it's about a hundred and eleven kilometers. Near the poles it shrinks to zero. in meters avoids that. Distortion is minimized near the central meridian of each zone, and it increases toward the zone edges, but within a zone it's manageable for most applications.
If I'm a municipal planner in Tel Aviv and I need to know exactly how large a building plot is, I'm working in U. or something like it, not in decimal degrees.
And this brings us to Israel's specific systems, which is a fascinating case study in national G. Israel uses the Israeli Transverse Mercator, or I. , also called the New Israel Grid. It's been the official projected coordinate system since nineteen ninety-eight, E. code twenty thirty-nine. Its central meridian runs through Jerusalem, at about thirty-five point two zero degrees east. The latitude of origin is about thirty-one point seven three degrees north. The false easting is two hundred nineteen thousand, five hundred twenty-nine point five eight four meters, false northing is six hundred twenty-six thousand, nine hundred seven point three nine meters.
They deliberately placed the central meridian through Jerusalem.
And this is something many countries do. The British national grid, O. , has its origin off the southwest coast of Cornwall. The Australian G. system is optimized for the Australian continent. These national grids are partly about local optimization, minimizing distortion over the country's territory, and partly about sovereignty. Having your own coordinate system is a statement that you control your own spatial data infrastructure.
Daniel also mentioned that Israel has older systems still floating around. Hiking guides, legacy maps, some navigation software still use the Israeli Cassini Soldner system, I. , which predates I. It uses a different projection, Cassini-Soldner instead of Transverse Mercator, and different false easting and northing values. So if you're pulling coordinates from an older source, you might be in a different system entirely.
There have been more recent refinements too. Israeli Grid zero five from twenty fourteen, E. sixty-nine eighty-four, and Israeli Grid zero five slash twelve, E. sixty-nine ninety-one, provide minor updates for cadastral and topographic use. They're coincident with I. at roughly the one-meter level, so for most purposes they're interchangeable, but if you're doing high-precision survey work you need to know which one you're in.
How does someone actually work with all these in practice? Daniel specifically asked about GeoPandas.
GeoPandas handles this beautifully. The core idea is that every GeoDataFrame has a coordinate reference system attribute. You can transform between systems with the to underscore C. So if you have a GeoDataFrame in W. eighty-four, E. forty-three twenty-six, and you want to project it to the appropriate U. zone, you can call gdf dot estimate underscore utm underscore crs and it'll automatically detect the correct zone from your data's bounding box and return the right E. Then you pass that to to underscore C. and you're done.
For Israel's I.
You create a GeoDataFrame with geometry from your easting and northing values, specifying the C. twenty thirty-nine. Then to get W. eighty-four coordinates, you call gdf dot to underscore C. forty-three twenty-six. Under the hood, GeoPandas uses pyproj, which handles the datum transformations. One important gotcha from the pyproj documentation is that you should use the Transformer class rather than the older Proj class to ensure proper datum shifts are applied. The older approach can silently drop the datum transformation and give you coordinates that are off by meters.
That's the kind of silent failure that would drive someone insane. Your code runs, it produces numbers, everything looks fine, and your points are systematically shifted by a meter and a half.
You'd only catch it if you validated against known ground control points. This is why G. work requires a certain paranoia about coordinate systems. I've seen datasets where half the points were in I. and half in I. because someone merged files from different eras without checking. The resulting map had buildings floating in the Mediterranean.
That would be a very short-lived building. So let me try to synthesize the precision question, because I think there's something counterintuitive here. The more decimal places you add, the less the coordinate is about "where" and the more it's about "when." At four decimal places, you're locating a house. The house isn't moving in any meaningful way, so the coordinate is stable. At eight decimal places, you're locating a specific millimeter on a patio stone, and that millimeter is drifting at several centimeters per year due to tectonics, bobbing up and down thirty centimeters twice daily from Earth tides, and vibrating from every truck that drives past. The coordinate becomes a time series.
That's before you even get to the relativistic corrections in the G. The satellites are moving fast enough that special relativity would cause their clocks to lose about seven microseconds per day. But they're also higher in Earth's gravity well, so general relativity causes them to gain about forty-five microseconds per day. The net effect is about thirty-eight microseconds per day faster than ground clocks. If you didn't correct for that, your position error would accumulate at about ten kilometers per day.
Ten kilometers of error per day from relativity alone.
So the satellites' atomic clocks are deliberately set to run slightly slow before launch, so that in orbit they tick at the correct rate relative to ground stations. A one-nanosecond clock error produces about thirty centimeters of positioning error. The entire G. system is a working demonstration of general relativity.
Which means that when you open your phone's map app and it shows your location, you are personally benefiting from a chain of corrections that includes Einstein's field equations, ionospheric modeling, and tectonic plate velocity vectors. And all of that collapses into a blue dot.
The blue dot is a lie, but it's an extraordinarily well-engineered lie.
Let me pull on one more thread from Daniel's question. He mentioned that four decimal places is the gold standard for geolocation. I think that's worth defending as a practical convention. Four decimal places gives you about eleven meters of precision at the equator. That's enough to distinguish which side of a street you're on, which building entrance, but not so precise that you're claiming false accuracy. It matches the actual performance of consumer G. under good conditions. And it's compact enough to store efficiently.
Five decimal places gets you to about one point one meters, which starts to exceed what consumer G. can reliably deliver, but it's useful for survey-grade work. Six decimal places, eleven centimeters, you're into R. Seven decimal places, about eleven millimeters, you're doing precision agriculture or construction staking. Eight decimal places, one point one millimeters, you're monitoring tectonic deformation or structural movement on bridges and dams.
Each step requires a whole additional layer of corrections and metadata. Datum specification, epoch, velocity model, geoid model, tide correction. The precision isn't free.
One thing I want to note about Israel's system specifically, because Daniel brought it up and it's a good example of how national grids evolve. The Survey of Israel and the Israel Lands Authority have been working since two thousand nine on modernizing toward a fully coordinate-based cadastre. Historically, land registration was done with textual descriptions and parcel maps that weren't always geometrically consistent. Moving to a coordinate-based system means every property boundary is defined by coordinates in I. , which eliminates ambiguity about where boundaries actually are.
Which presumably also means that if the coordinate system gets updated, as it did with Israeli Grid zero five and zero five slash twelve, every boundary definition needs to be checked for consistency.
It does, and that's part of why these transitions take years. You can't just shift a national coordinate system and tell everyone to update their databases. Property boundaries, infrastructure maps, environmental monitoring stations, they all have legal and operational dependencies on specific coordinate values.
What should someone actually do with all this? If a listener is working with geospatial data and wants to handle these coordinate systems correctly, what's the practical checklist?
First, know what C. your data is actually in. Don't assume. Check the metadata, check with the data provider, and if there's any doubt, validate against known locations. Second, when you're transforming between systems, use established libraries like GeoPandas with pyproj's Transformer class, not older approaches that might drop datum shifts. Third, if you're working at better than five-meter precision, you need to know which realization of W. eighty-four or I. you're using and what epoch it's referenced to. Fourth, if you're merging datasets from different eras in Israel, verify whether you're dealing with I. They are not interchangeable.
If you're displaying coordinates to users, don't show more decimal places than your measurement accuracy supports. If your G. is accurate to seven meters, showing eight decimal places is misleading. Five decimal places is already pushing it.
The xkcd comic really is the best teaching tool for this. I've used it to explain precision versus accuracy to people who've never touched a G. The visual of Waldo on a page at seven decimal places, and then the Planck length at forty, it makes the concept intuitive.
The other thing I'd add is that coordinate systems are not just technical choices. They're political and historical artifacts. Israel putting its central meridian through Jerusalem, Britain putting its origin off the coast of Cornwall, the U. maintaining multiple state plane coordinate systems. Each of these reflects decisions about what matters, what's worth optimizing for, and who gets to define the reference frame.
The global systems like W. eighty-four and I. are themselves the product of international cooperation and sometimes tension. Who maintains the reference frame, which stations are included, how often it's updated, these are negotiated among national mapping agencies and international geodetic organizations. The coordinates on your phone are the output of a global infrastructure that most people never think about.
To circle back to Daniel's original question about the precision limit from planetary physics. I think the answer is that there isn't a single hard limit. It's a cascade of corrections that become necessary at different scales. At the meter level, you need differential G. At the centimeter level, you need tectonic corrections and atmospheric modeling. At the millimeter level, you need Earth tide corrections and local deformation monitoring. At the atomic level, you hit quantum uncertainty. And at the Planck length, the concept of location stops meaning anything at all.
Which is a satisfying endpoint for a discussion about coordinates. You can keep adding decimal places, but eventually you're trying to locate a point more precisely than the universe allows.
Now: Hilbert's daily fun fact.
There's a species of jellyfish called Turritopsis dohrnii that can revert its cells to an earlier developmental stage when stressed, effectively making it biologically immortal.
For someone working with geospatial data, here's what I'd say. Learn the difference between geographic and projected coordinate systems. Know which one your data uses. Use GeoPandas or equivalent tools that handle transformations correctly. Don't trust decimal places you haven't earned. And if you're working in Israel, check whether you're in I. before you do anything else.
I'd also recommend playing with the U. plate motion calculator. It's genuinely illuminating to plug in your own coordinates and see how fast the ground under your feet is moving. For Jerusalem, it's something like two to three centimeters per year north-northeast. In a decade, that's twenty to thirty centimeters. Your house is not where it was when you bought it.
The ground is a conveyor belt and we're all just riding it. One thing I'm left wondering about is what happens as augmented reality and autonomous navigation push precision requirements further. If self-driving cars need centimeter-level lane positioning, and they're operating in areas with different tectonic regimes, do their maps need epoch tags and velocity models baked in?
They already do. High-definition maps for autonomous vehicles typically include not just the coordinates but the reference frame and epoch. When the car localizes itself using G. and inertial sensors, it's matching against a map that's tied to a specific realization of a dynamic datum. The car is doing plate tectonics math in real time.
Which means every self-driving car is a mobile geodetic observatory. The future is weird. Thanks to Hilbert Flumingtop for producing, and thanks to Daniel for the prompt. This has been My Weird Prompts. Find us at myweirdprompts dot com or wherever you get your podcasts.
If you enjoyed this, leave us a review. It helps other people find the show, and it makes Corn feel validated.
I don't need validation. I have eight decimal places of self-confidence.
