During those times the British were very colonial, and one of their methods of keeping power was to cause the colonised people to fight amongst themselves (as can still be seen with the Indians and Pakistanis, Israelis and Palestinians). Well, they invented a method to split the coast by first finding the angle of tangent on the point of the boarder between the countries and the sea. Take 90 degrees of the tangent, and that is the sea boarder.
While this looks good upon first glance, due to the coastline paradox, you can always find a different tangent line. That then could be the cause of conflict between countries as they try to determine the sea boarder.
If anyone knows if there is any truth to the story, I would be interested in hearing.
Alaska boundary dispute – Alaskan and Canadian claims to the Alaskan Panhandle differed greatly, based on competing interpretations of the ambiguous phrase setting the border at "a line parallel to the windings of the coast", applied to the fjord-dense region.
Arguably the same strategy exists between those who take The Sun and those who take The Economist.
At the end of the first day, a few of us tracking our progress with GPS said we had gone about 18 miles. The mapping software we had used (Gaia) had shown we had only made about 12 miles of progress on our 82 mile track.
I'm used to GPS overestimating distances since it tends to jump around on the trail a bit (and it still jumps around when you're paused) but the differences throughout the trip were much larger than I would expect.
Our 82 mile trip ended up being 104 miles, which my friends weren't really prepared for.
Examining the map closer, some of the trails we were on were pretty roughly approximated on the map (way fewer switchbacks, long straight lines, etc.)
I'm not allowed to plan our hiking trips anymore...
That said, using GPS for this task without adding an IMU for sensor fusion seems prone to measurement errors.
Unless some exchange has allowed traders to infinitely divide currency, that's doesn't seem like it could be true.
Most models of stock movement are modeled mathematically with Brownian motion which is by definition a continuous time process. You can even more trivially show that stocks are non-differentiable if you want to argue that they are fundamentally discrete time processes, in which, by definition, they are not continuous, differentiable functions.
But the argument of about "what does continuous even mean when we talk about physical systems" is another and older argument altogether.
Only if the Planck length were really a minimum possible length. But it might not be; even in a theory of quantum gravity, it might not be, since what is quantized in quantum gravity does not have to be lengths and times.
Of course, when you're zoomed in that much the concept of 'price' becomes a lot more complex. You need to distinguish between bid, ask, and last transaction price. So the whole mental model kind of falls apart.
That got me wondering if it’s generally true for any number of dimensions.
In 3D, volume converges with more perimeter points, but surface area does not.
This line of thinking leads to sampling theory. Given a noisy analog signal, digitizing it at higher and higher resolution and sample rate can yield an arbitrarily large number of data points, as you track the noise. But the area of the envelope around the waveform converges.
StandUpMaths did a great video on this recently, asking whether national land area includes elevation and which nations would gain/lose the most land area if it were/weren't: https://www.youtube.com/watch?v=PtKhbbcc1Rc
The coastline paradox and MAU effectively seem to be of the same class, i.e., change the rules for your measurement and you get different results. This hadn't occurred to me before. I wonder if there's other similar?
(Glad you're enjoying it! I absolutely loved some of the ideas - the treatment of social media, in particular)
Or a physicist for that matter - we don't have a useful theory of quantum gravity, space may or may not be quantized.