i hate the coastline ‘paradox’ and every other ‘paradox’ that’s just a missing variable. “if we measure with a big resolution it’s a smaller number of units and a small resolution is a bigger number!?” that’s not a paradox. that’s just how that variable works always. it’s not confusing or interesting at all.
Jeopardy wall calendar pretending that the coastline paradox doesn't exist
Submitted 7 hours ago by GraniteM@lemmy.world to mildlyinfuriating@lemmy.world
https://lemmy.world/pictrs/image/ecfd3de2-68ce-49ee-a1bf-fc1b1979ef69.jpeg
Comments
nublug@piefed.blahaj.zone 4 hours ago
scott@lem.free.as 4 hours ago
But if you shrink the “yardstick” down to an infinitesimally small size, the length, effectively, becomes infinite… and it’s the same for all coastlines. They’re all infinitely long.
… but some are longer than others. ;)
Fredthefishlord@lemmy.blahaj.zone 1 hour ago
Literally no
MrPoopyButthole@lemmy.world 2 hours ago
Max Planck says no…
Lemming6969@lemmy.world 2 hours ago
Didn’t calculus solve this stuff?
theunknownmuncher@lemmy.world 7 hours ago
Not all infinities are equal, friend. Asia does have more infinite coastline than other continents.
BetterDev@programming.dev 2 hours ago
Its true that not all intinities are equal, but the way we determine which infinities are larger is as follows
Say you have two infinite sets: A and B A is the set of integers B is the set of positive integers
Now, based on your argument, Asia has the largest infinite coastline in the same way A contains more numbers than B, right?
Well that’s not how infinity works. |B| = |A| surprisingly.
The test you can use to see if one infinity is bigger than another is thus:
Can you take each element of A, and assign a unique member of B to it? If so, they’re the same order of infinity.
As an example where you can’t do this, and therefore the infinite sets are truely of different sizes, is the real numbers vs the integers. Go ahead, try to label every real number with an integer, I’ll wait.
theunknownmuncher@lemmy.world 2 hours ago
Go ahead, try to label every real number with an integer, I’ll wait.
Why would I be trying to do this though? You’ve got the argument backwards.
cattywampas@midwest.social 2 hours ago
Unless they’re assuming a certain resolution of measurement.
Diddlydee@feddit.uk 6 hours ago
It’s correct, though. You’d apply the same scale of measurements to all coastlines, and using a standard of 1km or 0.5km plot points, Asia wins.
bryndos@fedia.io 2 hours ago
My new years resolution will be to solve this paradox.
BedbugCutlefish@lemmy.world 7 hours ago
Nah, that’s silly. Asia obviously has the longest coastline.
Sure, based on that paradox, the specific measurement of a given coastline will differ. But if you pick a standard (i.e., 1km straight lines), Asia is easily the longest. Doesn’t matter what standard you pick.
TropicalDingdong@lemmy.world 6 hours ago
Some infinites are larger than other infinites.
cynar@lemmy.world 3 hours ago
It’s not a true fractal, so the length has some finite bounding. It’s just stupidly large, since you are tracing the atomic structure.
GraniteM@lemmy.world 6 hours ago
That’s a fair point. I forgot that some infinites are larger than other infinites.
SmoothOperator@lemmy.world 2 hours ago
Isn’t it a bit like saying “there’s obviously more real numbers between 0 and 2 than between 0 and 1”? Which, to my knowledge, is a false statement.
AnarchoEngineer@lemmy.dbzer0.com 12 minutes ago
The cardinality of the two intervals [0,1] and [0,2] are equivalent. E.g. for every number in the former you could map it to a unique number in the latter and vice versa. (Multiply or divide by two)
However in statistics, if you have a continuous variable with a uniform distribution on the interval [0, 2] and you want to know what the chances are of that value being between [0,1] then you do what you normally would for a discrete set and divide 1 by 2 because there are twice as many elements in the total than there are in half the range.
In other words, for weird theoretical math the amount of numbers in the reals is equivalent to the amount of any elements in a subset of the reals, but other than those weird cases, you should treat it as though they are different sizes.
clay_pidgin@sh.itjust.works 2 hours ago
If between 0 and 1 are an infinite number of real numbers, then between 0 and 2 are twice infinite real numbers, IIRC my college math. I probably don’t.
bryndos@fedia.io 2 hours ago
Funny that so many uses of maths depends on measurement, and yet so many pure mathematicians seem to be clueless about how we actually measure things and why its useful. It doesn't even matters about all this bullshit about infinities , were talking about the real world. It's all about the precision of the tape measure. Here's a true story from back in the day:
English Mathematician: You'll need an infinite number of bricks to build a wall around any island's coastline.
French guy: come on over and see Mont Saint Michel it's vraiment genial!
English Mathematician: Oh that wall is infinitely far away from the true coastline, those bricks are not regulation infinitesimal length. If they'd started from the other corner they'd have got a different shape, and for sure needed infinite number of infinitesimal bricks to actually build that wall. Sloppy french masons. I can prove it I'll blast them all away with cannon fire until the glorious mathematical truth is revealed underneath.
One year later
French inhabitants: fuck off english maths whore!
Ten years more laterer
Hi french dudes! I'm back with a greater number of even bigger state of the art truth seeking cannon. I will prove this if its the last thing i do.
One year later . . .