People have this idea that when you take a measurement, you have so-and-so number of significant figures that are probably correct and the rest are just pure noise. But that's not how measurement error works. In the real world, physical measurement errors are more-or-less normally distributed (we don't have to argue about the "more-or-less" part because my argument here holds for any distribution other than a uniform…
> if your measurements are unbiased
This is a big IF which you can't actually know because its beyond your level of precision, by definition.
A lot of these kind of coordinates have no right answer anyway. They are just an abstract approximation of something else, like a parcel, address, or place to eat. And the lat/long will be completely useless for the vast majority of people. In any serious application you should have known error values and probably be using a more appropriate projection. If you need to accurately locate something you need someone trai…
They aren't approximations; you can verify this yourself. Pull up Google Maps, pick an arbitrary spot with no businesses, and click. You will get at least 6 significant digit coordinates.
No, I meant that it is an approximation or the thing in the real world that it represents. For example, consider a restraunt. Should the point be at the entrance to the building, in the middle of the building, or maybe at the door round the back where mail is delivered, or at the centroid of the parcel. In order to actually use this excessive precision you would need to know that. In the examle cases the data is not formal enough for this to matter. It is an approximation of some real world thing and never meant to be used for highly precise work.
The problem is that these lat/lon figures are not displayed with precision information at all, so we can't even know the std dev. Sig figs are a simple and clear way to communicate the precision of a measurement, but if you want to be more statistically accurate, you can use parentheses to indicate the standard deviation. In your example (if I mess this up please correct me, but I think) it would be 45.73490534578(10…
I've never seen the convention you're using and I don't think I understand it. Conventions I've seen include: * Give an error bound like 45.73490534578° (±0.00002°) and indicate in prose that this is a 2σ bound. * Put non-significant figures in parenthesis, like 45.73490(534578)° (EDIT: possibly I've misinterpreted this one when I've seen it, see logfromblammo's reply) * Put a bar over the last significant figure, li…
The parentheses show something similar to your first, where this is the +- read from the right hand side of the number. So you could write yours:
The presentation is just lazy and javascript defaults to double. No mystery.
You can use digits to indicate accuracy but if you don’t know whether the measurement stored as a double is accurate to 2, 4 or 12 decimals then you can’t really do much in presentation. The reader has to interpret the number. Usually the reader doesn’t care much about accuracy, and simply copies the numbers to another system. The coordinates with full double precision is then basically a machine readable format.
It's wrong if you ignore context -- but then, everything is. The context is that it's in a database serving up business locations. How is the geographic area owned (or occupied?) by a business reduced to a point? They don't say, so it's clearly unreasonable to expect accuracy and precision beyond, say, property boundaries, and perhaps not even that. It would be madness to infer that the extra digits denote precision…
You can click at arbitrary positions on those maps and get 6+ sig-fig values for those positions. And since the map displays a satellite representation of the property, is it really that extraordinary that people might consider it to be sufficiently precise enough to put in a fence? FWIW, the error margin for 6 significant digits is around 11 cm. Accurate enough to point at a computer mouse.
If the page in question listed something that could be construed as a property boundary, sure.
It's wrong if you ignore context -- but then, everything is. The context is that it's in a database serving up business locations. How is the geographic area owned (or occupied?) by a business reduced to a point? They don't say, so it's clearly unreasonable to expect accuracy and precision beyond, say, property boundaries, and perhaps not even that. It would be madness to infer that the extra digits denote precision…
You can click at arbitrary positions on those maps and get 6+ sig-fig values for those positions. And since the map displays a satellite representation of the property, is it really that extraordinary that people might consider it to be sufficiently precise enough to put in a fence? FWIW, the error margin for 6 significant digits is around 11 cm. Accurate enough to point at a computer mouse.
The 2D pixels in the projected satellite image will never map to a precise gps lat lng coordinate. These gps coordinates are also just a rough approximation of dead reconned coordinate systems that actually define the parcels.
You can easily try and overlay county parcel data into google earth and see how many features don’t align with the sat imagery.
People have this idea that when you take a measurement, you have so-and-so number of significant figures that are probably correct and the rest are just pure noise. But that's not how measurement error works. In the real world, physical measurement errors are more-or-less normally distributed (we don't have to argue about the "more-or-less" part because my argument here holds for any distribution other than a uniform…
> if your measurements are unbiased This is a big IF which you can't actually know because its beyond your level of precision, by definition.
This is completely knowable, by taking repeated measurements of a reference object, one which was either checked by a more precise instrument or is definitionally correct (e.g. the old reference kilogram or the Greenwich meridian)
You can click at arbitrary positions on those maps and get 6+ sig-fig values for those positions. And since the map displays a satellite representation of the property, is it really that extraordinary that people might consider it to be sufficiently precise enough to put in a fence? FWIW, the error margin for 6 significant digits is around 11 cm. Accurate enough to point at a computer mouse.
If the page in question listed something that could be construed as a property boundary, sure. It doesn't.
Every new home owner gets a "plat" that outlines the boundaries of their property, including GPS coordinates. Using a tool (like Google Maps) to overlay a coordinate with a ground feature isn't exactly absurd.
People have this idea that when you take a measurement, you have so-and-so number of significant figures that are probably correct and the rest are just pure noise. But that's not how measurement error works. In the real world, physical measurement errors are more-or-less normally distributed (we don't have to argue about the "more-or-less" part because my argument here holds for any distribution other than a uniform…
In the time it takes you to note down those extra digits, you could have improved your actual measurement by the same minuscule fraction of a bit ten times over.
You can click at arbitrary positions on those maps and get 6+ sig-fig values for those positions. And since the map displays a satellite representation of the property, is it really that extraordinary that people might consider it to be sufficiently precise enough to put in a fence? FWIW, the error margin for 6 significant digits is around 11 cm. Accurate enough to point at a computer mouse.
The 2D pixels in the projected satellite image will never map to a precise gps lat lng coordinate. These gps coordinates are also just a rough approximation of dead reconned coordinate systems that actually define the parcels. You can easily try and overlay county parcel data into google earth and see how many features don’t align with the sat imagery.
No? Then why do they appear to? Sure, a professional should "know better", but will a lay person who has the official GPS coordinates of their property lines (obtained at the time of sale)?
That's why people get concerned about this; that's why posts like this are important.