Measuring Coastline - Numberphile

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NUMBERPHILE

Videos by Brady Haran

Apologies for misspelling Mandelbrot - re-editing and uploading a new video causes more problems than it is worth.

[Zaskar]

Bwahaha, "The B. stands for Benoit B. Mandelbrodt", the first mathematical joke i instantly got!!

[jeffreybernath]

"The 'B' stands for Benoit B. Mandelbrot." I have not laughed this hard in YEARS! Thank you Brady and Steve!

[IRONMANAustralia]

I think the solution to this problem is simply to get the British population out there with a bunch of shovels to fill in all the little gaps and make the British Isle a square.

Fix'd.

[FoxDren]

Surely you measure it in Planck lengths.

[MrAidanFrancis]

6:17 is, hands down, my absolute favorite math joke.

[kwinvdv]

Even if the coastline would be smooth at some level, how would you define it? Because due to waves, tides (and other phenomena) there will be fluctuations in where the sea stops and the mainland starts. And what about a river flowing into the sea, where does the coastline of the sea transit into the coastline of the river. If you would somehow take the average of the fluctuation of coastline it should become smooth at some level.

[gabiotta]

How do you measure a coastline?

Sack the mathematician and employ an engineer. 

[Wanderlust]

this reminds me of how archimedes found the circumference of a circle by inscribing it in polygons with more and more sides as if he was using smaller and smaller units or rulers

[energysage]

"The 'B' stands for Benoit B. Mandelbrot."
Laughed way too hard at this.

[markchadwick]

I ran into this same issue when attempting to calculate total elevation gain for a bicycle route. Different sources reported vastly different values.

[numberphile]

Get the paper from this video (and others)

[Adamantium]

The usefulness of the coastline measurement is in the knowledge of how much time it would take to travel it (or some equivalent formulation of the same). Therefore, I advocate a 1m ruler, as a nice round number that is close to the length of a human stride.

[tadashimori]

When I want to know the length of a coastline, I'm asking how much I have to run to get to the other side of the coastline.

[LimeGreenTeknii]

I'd say the ideal resolution would be the length of the average person's stride, or maybe the average stride of the shortest 5% of people or something, because if you're walking the coast, that's the highest resolution you'll really need, and I can't think of any need for a smaller resolution.

[altruistical]

I studied Fractals for my senior thesis and loved them!  Thanks for this trip down memory lane!

[AaronSherman]

In practice, what we do is to measure a smooth curve between the high and low tide marks. This eliminates any complexity that cannot be practically relied upon.

[Tupster]

Why is it that every time this channel talks about infinity there are countless responses trying to rationalize infinity back down to something more like what people learn in primary school.

Infinity follows a set of rules that are not that complicated and make working with it a lot simpler than trying to shove it into a naive mathematical intuition developed when one was 7.

[josie]

The filming locations of Numberphile vids greatly amuse me.

[frisianmouve]

The real answer is that britain has no coastline because there's no land touching water, when you get down to the molecular level

[ArmgddnX]

I guess the main difficulty here is you can calculate the average fractalness of a coastline, but not the average bumpiness.  If you knew the average bumpiness, you could use a sinusoidal circle or something of equal bumpiness and total volume was equal and calculate the circumference from there.