# ­xkcd thread **URL:** \ **Category:** Cafe Society\ **Tags:** comic-strips\ **Created:** [May 28, 2020, 12:57am UTC](https://boards.straightdope.com/t/xkcd-thread/854574 "2020-05-28T00:57:03Z")\ **Posts on this page:** 20\ **Page:** 143
**Author:** ![LSLGuy](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/lslguy/32/5813_2.png) [@LSLGuy](https://boards.straightdope.com/u/LSLGuy)\ **Post date:** [March 20, 2024, 7:58pm UTC](https://boards.straightdope.com/t/xkcd-thread/854574/2843 "2024-03-20T19:58:39Z")
And of course resolves the problem of implementing that moon armor idea from yesterday. ---
**Author:** ![Lumpy](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/lumpy/32/446_2.png) [@Lumpy](https://boards.straightdope.com/u/Lumpy)\ **Post date:** [March 20, 2024, 8:54pm UTC](https://boards.straightdope.com/t/xkcd-thread/854574/2844 "2024-03-20T20:54:33Z")
I dunno, ladders don’t have a good record for space exploration (SFW): (page 1) [Ladder 1](https://www.oglaf.com/ladder1/) (page 2)[Ladder 1](https://www.oglaf.com/ladder1/2/) ---
**Author:** ![dtilque](https://avatars.discourse-cdn.com/v4/letter/d/d6d6ee/32.png) [@dtilque](https://boards.straightdope.com/u/dtilque)\ **Post date:** [March 24, 2024, 12:44am UTC](https://boards.straightdope.com/t/xkcd-thread/854574/2845 "2024-03-24T00:44:45Z")
> **[The Wreck of the Edmund Fitzgerald](https://xkcd.com/2910/)** > > You know that asteroid that almost destroyed Earth in the 90s? Turns out the whole thing was secretly created by Michael Bay, who then PAID Bruce Willis and Ben Affleck to look heroic while blowing it up! ---
**Author:** ![dtilque](https://avatars.discourse-cdn.com/v4/letter/d/d6d6ee/32.png) [@dtilque](https://boards.straightdope.com/u/dtilque)\ **Post date:** [March 25, 2024, 10:27pm UTC](https://boards.straightdope.com/t/xkcd-thread/854574/2846 "2024-03-25T22:27:20Z")
> **[Greenland Size](https://xkcd.com/2911/)** > > The Mercator projection drastically distorts the size of almost every area of land except a small ring around the North and South Poles. ---
**Author:** ![Dr.Strangelove](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/dr.strangelove/32/6613_2.png) [@Dr.Strangelove](https://boards.straightdope.com/u/Dr.Strangelove)\ **Post date:** [March 25, 2024, 10:36pm UTC](https://boards.straightdope.com/t/xkcd-thread/854574/2847 "2024-03-25T22:36:07Z")
The rare xkcd that I only understood after reading the alt-text. And then a sensible chuckle. ---
**Author:** ![LSLGuy](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/lslguy/32/5813_2.png) [@LSLGuy](https://boards.straightdope.com/u/LSLGuy)\ **Post date:** [March 25, 2024, 10:51pm UTC](https://boards.straightdope.com/t/xkcd-thread/854574/2848 "2024-03-25T22:51:06Z")
Now _that’s_ funny. Your comment I mean. I got the idea of the dialog instantly, before I even got to the last word, but had to puzzle for awhile to get the point of the hover-text. Brains are weird. And evidently idiosyncratic. ---
**Author:** ![Dr.Strangelove](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/dr.strangelove/32/6613_2.png) [@Dr.Strangelove](https://boards.straightdope.com/u/Dr.Strangelove)\ **Post date:** [March 25, 2024, 10:56pm UTC](https://boards.straightdope.com/t/xkcd-thread/854574/2849 "2024-03-25T22:56:31Z")
> [@LSLGuy](#): > > And evidently idiosyncratic. Yep. For me, the idea of map projection problems being about the _ratio_ of area scaling was just too ingrained for the original comic to hit immediately. But somehow the idea in the alt-text of “well yes, that’s the only place where you get a true 1:1 scale” explained the original comic retroactively. ---
**Author:** ![Pleonast](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/pleonast/32/1183_2.png) [@Pleonast](https://boards.straightdope.com/u/Pleonast)\ **Post date:** [March 25, 2024, 11:00pm UTC](https://boards.straightdope.com/t/xkcd-thread/854574/2850 "2024-03-25T23:00:19Z")
Must resist urge to compute the width of the ring… ---
**Author:** ![Dr.Strangelove](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/dr.strangelove/32/6613_2.png) [@Dr.Strangelove](https://boards.straightdope.com/u/Dr.Strangelove)\ **Post date:** [March 25, 2024, 11:21pm UTC](https://boards.straightdope.com/t/xkcd-thread/854574/2851 "2024-03-25T23:21:55Z")
Well, it’s not too hard. If the map is a meter across, then the scale ring is a meter in circumference. The thickness of the ring depends on what you consider “drastically,” but if you want 10% error, then the ring would have an inner circumference of 0.9 m and an outer of 1.1, which works out to a width of 3.2 cm. ---
**Author:** ![Chronos](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/chronos/32/134_2.png) [@Chronos](https://boards.straightdope.com/u/Chronos)\ **Post date:** [March 26, 2024, 12:24am UTC](https://boards.straightdope.com/t/xkcd-thread/854574/2852 "2024-03-26T00:24:37Z")
> [@Dr.Strangelove](#): > > The thickness of the ring depends on what you consider “drastically,” but if you want 10% error, then the ring would have an inner circumference of 0.9 m and an outer of 1.1, which works out to a width of 3.2 cm. I don’t think that’s correct… Remember, we’re in a hugely nonlinear regime, here. The y coordinate of a Mercator projection map is proportional to the tangent of the latitude. Even a micron-wide band inside the perfect-fit ring would result in an area on the map much greater than the area of the entire circular cap on the real Earth. Oh, and speaking of which, a Mercator projection isn’t actually rectangular. It’s infinitely tall. ---
**Author:** ![Dr.Strangelove](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/dr.strangelove/32/6613_2.png) [@Dr.Strangelove](https://boards.straightdope.com/u/Dr.Strangelove)\ **Post date:** [March 26, 2024, 12:43am UTC](https://boards.straightdope.com/t/xkcd-thread/854574/2853 "2024-03-26T00:43:28Z")
Locally, it’s still quite linear. That’s one of the biggest advantages to the Mercator projection: you can zoom in anywhere, and squares always look like squares (the aspect ratio stays 1:1). So relatively small amounts of error will have the same magnitude in the projection vs. not. It gets more dicey if “drastically” means like 1000% vs. 110%. Which is why I didn’t assume that 🙂 . ---
**Author:** ![Pleonast](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/pleonast/32/1183_2.png) [@Pleonast](https://boards.straightdope.com/u/Pleonast)\ **Post date:** [March 26, 2024, 12:53am UTC](https://boards.straightdope.com/t/xkcd-thread/854574/2854 "2024-03-26T00:53:15Z")
> [@Chronos](#): > > a Mercator projection isn’t actually rectangular. It’s infinitely tall. Yes, that’s the difficulty. To compute the width accurately, we need to take into account the distance on the map of the ring from the equator. ---
**Author:** ![Chronos](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/chronos/32/134_2.png) [@Chronos](https://boards.straightdope.com/u/Chronos)\ **Post date:** [March 26, 2024, 12:56am UTC](https://boards.straightdope.com/t/xkcd-thread/854574/2855 "2024-03-26T00:56:48Z")
Any sufficiently-small square still looks like a square. But up that close to the pole, “sufficiently small” is very small indeed. ---
**Author:** ![Dr.Strangelove](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/dr.strangelove/32/6613_2.png) [@Dr.Strangelove](https://boards.straightdope.com/u/Dr.Strangelove)\ **Post date:** [March 26, 2024, 1:27am UTC](https://boards.straightdope.com/t/xkcd-thread/854574/2856 "2024-03-26T01:27:51Z")
> [@Chronos](#): > > But up that close to the pole, “sufficiently small” is very small indeed. And 3.2 cm is very small indeed compared to the circumference of Earth. The equation for the y coordinate is y=R\ln[\tan(\frac{\pi}{4} + \frac{\phi}{2})], where \phi is latitude. R is the radius of the globe, so for a 1 m circumference it comes to 0.16. If the ring’s centerline radius is at 0.16 m, then I claim the outer radius for 10% error is at 0.176 m. The latitudes for those are 1.57079632279 and 1.57079632239 respectively. That comes to y-values of 3.0937 and 3.0784 meters. The difference is 0.0153 m, which is very close to the 0.016 m I added in physical space. I’m actually mildly surprised we only get a 6 meter tall map here, but that ln is doing a lot of work. ---
**Author:** ![digs](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/digs/32/14889_2.png) [@digs](https://boards.straightdope.com/u/digs)\ **Post date:** [March 26, 2024, 1:31am UTC](https://boards.straightdope.com/t/xkcd-thread/854574/2857 "2024-03-26T01:31:03Z")
I’m reminded of Steven Wright’s deadpan line: > I bought a map of the world. Full-size, one inch equals one inch. > > Here, I’ll unfold it… ---
**Author:** ![smithsb](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/smithsb/32/12107_2.png) [@smithsb](https://boards.straightdope.com/u/smithsb)\ **Post date:** [March 26, 2024, 1:40am UTC](https://boards.straightdope.com/t/xkcd-thread/854574/2858 "2024-03-26T01:40:18Z")
Stop pandering to those nutso flat earthers with this projection map stuff. We’re on a globe, an oblate sphereoid dammit. /unhinged rant off ---
**Author:** ![Mollie\_Magill](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/mollie_magill/32/20882_2.png) [@Mollie\_Magill](https://boards.straightdope.com/u/Mollie_Magill)\ **Post date:** [March 26, 2024, 4:35am UTC](https://boards.straightdope.com/t/xkcd-thread/854574/2859 "2024-03-26T04:35:53Z")
I would imagine that the biggest problem isn’t how big the circle is, but rather exactly _where_ it is. ---
**Author:** ![LSLGuy](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/lslguy/32/5813_2.png) [@LSLGuy](https://boards.straightdope.com/u/LSLGuy)\ **Post date:** [March 26, 2024, 12:27pm UTC](https://boards.straightdope.com/t/xkcd-thread/854574/2860 "2024-03-26T12:27:06Z")
> [@digs](#): > > I’m reminded of Steven Wright’s deadpan line: > > > I bought a map of the world. Full-size, one inch equals one inch. > > > > Here, I’ll unfold it… The funny thing is that if we ignore the spherical / flat conversion issue, it would only take 39 folds in half to reduce the area of the folded map to 1m square. So something a human could easily carry. _If_ we ignore its immense weight and thickness. And the ~~difficulty~~ near impossibility of folding anything in half that many times. 🙂 ---
**Author:** ![TroutMan](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/troutman/32/6721_2.png) [@TroutMan](https://boards.straightdope.com/u/TroutMan)\ **Post date:** [March 26, 2024, 2:56pm UTC](https://boards.straightdope.com/t/xkcd-thread/854574/2861 "2024-03-26T14:56:40Z")
I get 49 folds. The surface area of the earth is 510 trillion m2, so 39 folds will get you down to 928 m2, and 49 folds to 0.9 m2. The Mercator projection is about 3x the area, so you’d need 50-51 folds to get to 1 m2. A quick google says the thinnest paper is 0.02 mm thick and 70 g per m2, so at 49 “folds” it would be 11.3 million km thick – 30x the distance to the moon – and weigh 35.7 trillion kg. Exponential growth is a beast. ---
**Author:** ![N9IWP](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/n9iwp/32/3154_2.png) [@N9IWP](https://boards.straightdope.com/u/N9IWP)\ **Post date:** [March 26, 2024, 3:06pm UTC](https://boards.straightdope.com/t/xkcd-thread/854574/2862 "2024-03-26T15:06:41Z")
I get log (510\*10^9)/log(2)\approx 39 Brian [Previous page](https://boards.straightdope.com/t/xkcd-thread/854574.md?page=142) [Next page](https://boards.straightdope.com/t/xkcd-thread/854574.md?page=144)