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Coastline paradox

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Re: Coastline paradox

#51

Post by chrisweekly »

ilaksh wrote: post #18

I think I've heard this in reference to the difficulty of software estimation. The project details and potential problems are unknowns until you get to that specific part of the project. Even though theoretically you can see the "shape" and rough size of the project when zoomed out.

Yes, there's a classic blig post (sorry, no bookmark handy) about an analogous trip from SF to LA....

Also, (maybe counterintuitively), in software estimation the more fine-grained the estimates, the more likely they are to _underestimate_ project scope. For areas that are better-understood, the estimate will be (properly) limited in scope (reducing the overall buffer) -- which leaves less margin for error in the areas with more unknowns, where the biggest scope bloat is hiding. As a rule, software estimates should use a very broad brush. (This also helps mitigate the tendency of PHBs and product owners to mistake precision for accuracy.)

Re: Coastline paradox

#52

Post by dmonitor »

throwbabyaway wrote: post #20
bigyikes wrote: post #2

Step 1: Acquire small beachfront property Step 2: Put property on the market, listed as having a mile of beach Step 3: ??? Step 4: Profit There's no way this could backfire, unless the buyer asks how big your ruler is. But a true gentleman never questions the size of another's ruler, so you should be in the clear.

Where I'm from realtors solve this problem by declaring the length of the sea-opening (not sure of the English word, not a native speaker), the length of the straight line between two ends of the coast access. Well, this could be a problem, of course, if you are selling an island.

would be especially misleading if it’s a cove

a U shaped beach would be listed with half its effective beach area

Re: Coastline paradox

#53

Post by rootusrootus »

n_plus_1_acc wrote: post #26
tukajo wrote: post #16

Earlier quoted context omitted.

No since water boundaries like rivers are defined as the middle of the river, not as the shifting coast of either side of the river.

genuine question: how is the middle defined when both shores are fractals?

As an example, here is what is said by Oregon & Washington about the border between them. This was ratified by both states in a compact. It looks like they switched from less precise definitions like "the varying center of the main channel of the Columbia River" to a list of precise coordinates.

Washington: https://app.leg.wa.gov/rcw/default.aspx?cite=43.58&full=true

Oregon: https://oregon.public.law/statutes/ors_186.520

Re: Coastline paradox

#54

Post by paulddraper »

tedunangst wrote: post #33

Can you get a decent approximation by measuring displacement? Dump a bucket of water in the ocean, observe the level of sea rise, that tells you the volume of the island, and indirectly the area of the edge.

> the area of the edge

No, it will give you the area of the island (more precisely, the area of the sea-level cross section of the island).

Re: Coastline paradox

#55

Post by paulddraper »

School-Cotton wrote: post #9

The coastline paradox relies on the assumption that the coast is equally “jagged” at all levels. Is this actually true? I mean, if I go to the beach and look at the line where the water meets the land it doesn’t really seem like a fractal to me. The outer boundary of land masses gets smoothed out by erosion from the water, right?

If the coast is a sandy beach, then it is usually pretty smooth.

But in other cases ... https://www.nps.gov/articles/images/acad-ship-harbor-rocky-c...

Re: Coastline paradox

#56

Post by tedunangst »

rdlw wrote: post #40
tedunangst wrote: post #33

Can you get a decent approximation by measuring displacement? Dump a bucket of water in the ocean, observe the level of sea rise, that tells you the volume of the island, and indirectly the area of the edge.

Do this with Gabriel's horn and you'll observe that it has an area of pi, which does not reflect the fact that its perimeter is infinite.

Yeah, I'm not sure how I concluded you could go from volume to area.

Re: Coastline paradox

#57

Post by remram »

justinl33 wrote: post #5

Next time you go to measure your waistline, just remember: have you really put on weight, or is it just the coastline paradox?

Interestingly there is no paradox for convex shapes, like measuring tape forms.

Re: Coastline paradox

#58

Post by m4rtink »

Aachen wrote: post #48
em-bee wrote: post #39

Earlier quoted context omitted.

as the crow flies at the speed of a bullet

Do bullets fly for minutes? (Edit: to be clear, that's a genuine question. I would imagine they drop to the ground before the "three minutes from the beach" have passed no matter the firing angle, but I don't know.)

Depends on gravity of the body and its atmospheric pressure and related variables (wind speed, temperature, composition - lead bullet could meld on Venus, etc.).

Low gravity & no atmosphere- bullet reaches escape velocity and wanders off to space.

Very high atmosphere & fired high up above ground (if any - eq. gas giant) and bullet might take quite a while to fall.

Re: Coastline paradox

#59

Post by [deleted] »

bigyikes wrote: post #2

Step 1: Acquire small beachfront property Step 2: Put property on the market, listed as having a mile of beach Step 3: ??? Step 4: Profit There's no way this could backfire, unless the buyer asks how big your ruler is. But a true gentleman never questions the size of another's ruler, so you should be in the clear.

[deleted]

Re: Coastline paradox

#60

Post by DonsDiscountGas »

School-Cotton wrote: post #9

The coastline paradox relies on the assumption that the coast is equally “jagged” at all levels. Is this actually true? I mean, if I go to the beach and look at the line where the water meets the land it doesn’t really seem like a fractal to me. The outer boundary of land masses gets smoothed out by erosion from the water, right?

Rocks and boulders have all kinds of different sizes in general. If the coast/beach area is all smooth and uniform small particles (ie sand) then it would be easy to measure as long as you use a ruler larger than ~10 grains of sand. If there are ranges of particles from 1cm (pebbles) to 10 cm (rocks) to 10 meters (boulders) to 100 meters (rock outcroppings) then the effect kicks in.
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