# ­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:** 144
**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, 4:26pm UTC](https://boards.straightdope.com/t/xkcd-thread/854574/2863 "2024-03-26T16:26:41Z")
510x109 is 510 billion. Earth surface area is 510 _trillion_. ---
**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, 4:48pm UTC](https://boards.straightdope.com/t/xkcd-thread/854574/2864 "2024-03-26T16:48:41Z")
Yep log(510\*10^{12})/log(2) \approx 49 Only off by a factor of 1000 😉 Brian ---
**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 26, 2024, 5:11pm UTC](https://boards.straightdope.com/t/xkcd-thread/854574/2865 "2024-03-26T17:11:09Z")
I completely misinterpreted the cartoon until just a moment ago. I thought it was joking about the distortions the Mercator projection introduces; I was completely whooshed by the joke that it was talking about the literal physical size of the map on the wall. 🤦 ---
**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, 6:25pm UTC](https://boards.straightdope.com/t/xkcd-thread/854574/2866 "2024-03-26T18:25:01Z")
@TroutMan … I did it in SI, not US customary units, but in hindsight I realize I converted km^2 to m^2 with a factor of 1000, not 1000000. Oops. So yeah, 10 more folds = 49 total to reduce the map to ~ 1m^2. ---
**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, 9:20pm UTC](https://boards.straightdope.com/t/xkcd-thread/854574/2867 "2024-03-26T21:20:42Z")
> [@Dr.Strangelove](#): > > The equation for the y coordinate is y=R\ln[\tan(\frac{\pi}{4} + \frac{\phi}{2})], where \phi is latitude. …Huh. So it is. So why the heck does everything written about the Mercator projection always show the diagram where y = R\tan(\phi) ? ---
**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, 9:25pm UTC](https://boards.straightdope.com/t/xkcd-thread/854574/2868 "2024-03-26T21:25:42Z")
Even if you made the map of graphene–a single layer of carbon atoms–the resulting “folded” map would be 170 kilometers thick. The folding is gonna be a trick, though. I suppose you could have a really thin map that spirals around the Earth, like what you get from an apple peeler. Then you can fold it in a zig-zag fashion and not have the problems you get when repeatedly halving it. ---
**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, 9:39pm UTC](https://boards.straightdope.com/t/xkcd-thread/854574/2869 "2024-03-26T21:39:52Z")
> [@Chronos](#): > > So it is. So why the heck does everything written about the Mercator projection always show the diagram where y = R\tan(\phi)? Dunno. Maybe confusion between different cylindrical projections? They all have the same sort of problem where things go divergent at the poles. But that \ln makes things a little less extreme. I see that Encyclopedia Britannica has this image: [![Imgur](https://i.imgur.com/TyElWb0.png "imgur.com") ](https://imgur.com/TyElWb0) It confused me too at first glance, but they’re differentiating between a “simple cylindrical projection” and Mercator. Mercator rescales the lines of latitude to preserve shape. ---
**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, 10:21pm UTC](https://boards.straightdope.com/t/xkcd-thread/854574/2870 "2024-03-26T22:21:47Z")
> [@Dr.Strangelove](#): > > I suppose you could have a really thin map that spirals around the Earth, like what you get from an apple peeler. Then you can fold it in a zig-zag fashion and not have the problems you get when repeatedly halving it. That’s a fun idea. Thank you I have a nagging memory that we had a thread back around 2005 or so about a young woman who had recently broken the record for most halving folds in a piece of paper. IIRC @Chronos was prominent in the thread. Or else it was the similarly esteemed and now sadly late @Q.E.D. I don’t have quite enough memory tendrils to successfully search up the thread now. Does that ring a bell with anyone? It would be interesting to compare the most folds ever achieved with the number required to make our 1 m^2 folded 1:1 scale Mercator. ---
**Author:** ![SpoilerVirgin](https://avatars.discourse-cdn.com/v4/letter/s/4491bb/32.png) [@SpoilerVirgin](https://boards.straightdope.com/u/SpoilerVirgin)\ **Post date:** [March 26, 2024, 10:31pm UTC](https://boards.straightdope.com/t/xkcd-thread/854574/2871 "2024-03-26T22:31:00Z")
> [@LSLGuy](#): > > I have a nagging memory that we had a thread back around 2005 or so about a young woman who had recently broken the record for most halving folds in a piece of paper. Here is the original thread. There have also been several interesting discussions of paper folding since then. > [@Fold in half 12 times!](https://boards.straightdope.com/t/fold-in-half-12-times/331381): > > I didn’t see this here, but thought people may be interested: Britney Gallivan has solved the Paper Folding Problem. This well known challenge was to fold paper in half more than seven or eight times, using paper of any size or shape. [http://pomonahistorical.org/12times.htm](http://pomonahistorical.org/12times.htm) ---
**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, 10:36pm UTC](https://boards.straightdope.com/t/xkcd-thread/854574/2872 "2024-03-26T22:36:46Z")
Maybe one of these? > [@Paper folding math](https://boards.straightdope.com/t/paper-folding-math/740397): > > I hesitate to even ask this due to the source (quora), but they claim that: “2. If you could fold a piece of paper in half on itself 100 times, the height of the resulting folded paper would not fit within the current known universe.” That seems incredible. Is it even remotely true? Link: [https://www.quora.com/?digest\_story=1287380](https://www.quora.com/?digest_story=1287380) > [@Folding paper in half](https://boards.straightdope.com/t/folding-paper-in-half/402040): > > I was always lead to believe that it was impossible to fold paper in half more than 7 times but a friend of mine maintains that some girl has managed to fold it 12 times. I can’t find anything about this, anyone any knowledge? Or maybe this column by Cecil. > **[Can a piece of paper be folded in half no more than seven times?](https://www.straightdope.com/21342035/can-a-piece-of-paper-be-folded-in-half-no-more-than-seven-times)** ---
**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, 10:40pm UTC](https://boards.straightdope.com/t/xkcd-thread/854574/2873 "2024-03-26T22:40:12Z")
> [@Dr.Strangelove](#): > > > [@Chronos](#): > > > > y = R\tan(\phi)? > > Dunno. Maybe confusion between different cylindrical projections? They all have the same sort of problem where things go divergent at the poles. Surely, the simplest cylindrical projection is the one with y=R\phi, and the one with y=R\sin\phi (i.e., the Peters projection) is at least as “simple” as the one with y = R\tan\phi . Those both still have a coordinate singularity at the poles (indeed, any flat map projection will have a coordinate singularity somewhere), but they at least map the poles to lines a finite distance from the Equator. And yeah, I’m a big fan of any middle-schooler who not only recognizes that a mathematical problem can be solved, but then does so, very thoroughly, and then also puts it to the experimental test. ---
**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, 10:49pm UTC](https://boards.straightdope.com/t/xkcd-thread/854574/2874 "2024-03-26T22:49:31Z")
Well, the formulas look easier in those cases, but I’d say the light-projection version is the simplest in an intuitive sense, and something you can actually perform in real life. It makes the singularities apparent since the cylinder has no top or bottom, so a beam of light going in those directions must necessarily miss the map. But you’re right–there are lots of cylindrical projections with no singularity. ---
**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, 11:01pm UTC](https://boards.straightdope.com/t/xkcd-thread/854574/2875 "2024-03-26T23:01:01Z")
> [@SpoilerVirgin](#): > > Here is the original thread. There have also been several interesting discussions of paper folding since then. Bingo! Thank you! And honorable mention to @TroutMan just below. I did get the timeframe right (2005), but flubbed the dub on @Chronos or @Q.E.D ---
**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, 11:08pm UTC](https://boards.straightdope.com/t/xkcd-thread/854574/2876 "2024-03-26T23:08:38Z")
> [@Dr.Strangelove](#): > > Well, the formulas look easier in those cases, but I’d say the light-projection version is the simplest in an intuitive sense, and something you can actually perform in real life. The tangent one projects out from a single point; the sine one projects out perpendicular to the axis. It might be easier to build a physical light projector for the tangent one, but I think that conceptually, it’s about a tie. ---
**Author:** ![Andy\_L](https://avatars.discourse-cdn.com/v4/letter/a/c67d28/32.png) [@Andy\_L](https://boards.straightdope.com/u/Andy_L)\ **Post date:** [March 26, 2024, 11:09pm UTC](https://boards.straightdope.com/t/xkcd-thread/854574/2877 "2024-03-26T23:09:12Z")
> [@N9IWP](#): > > Yep log(510_10^{12})/log(2) \approx 49log(510∗1012)/log(2)≈49log(510_10^{12})/log(2) \approx 49 > > Only off by a factor of 1000 😉 Another reminder that 2^10 is darn close to 1000. If you approximate 510 as 512 (2^9) and a trillion = 10^12 ~ 2^40, you get 49 folds without having to do the actual logs. ---
**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 27, 2024, 12:38am UTC](https://boards.straightdope.com/t/xkcd-thread/854574/2878 "2024-03-27T00:38:17Z")
Yeah, since 2 ≈ 10.301, binary and decimal exponents remain close to 10/3 up to pretty high values; you’d have to go up to about 1090 before 2299 would be a better approximation than 2300. ---
**Author:** ![dtilque](https://avatars.discourse-cdn.com/v4/letter/d/d6d6ee/32.png) [@dtilque](https://boards.straightdope.com/u/dtilque)\ **Post date:** [March 28, 2024, 6:57am UTC](https://boards.straightdope.com/t/xkcd-thread/854574/2879 "2024-03-28T06:57:52Z")
> **[Cursive Letters](https://xkcd.com/2912/)** > > 𝓘 𝓽𝓱𝓲𝓷𝓴 𝓬𝓪𝓹𝓲𝓽𝓪𝓵 𝓛 𝓲𝓼 𝓹𝓻𝓸𝓫𝓪𝓫𝓵𝔂 𝓽𝓱𝓮 𝓶𝓸𝓼𝓽 𝓯𝓾𝓷 𝓽𝓸 𝔀𝓻𝓲𝓽𝓮, 𝓽𝓱𝓸𝓾𝓰𝓱 𝓵𝓸𝔀𝓮𝓻𝓬𝓪𝓼𝓮 𝓺 𝓲𝓼 𝓪𝓵𝓼𝓸 𝓪 𝓼𝓽𝓻𝓸𝓷𝓰 𝓬𝓸𝓷𝓽𝓮𝓷𝓭𝓮𝓻. ---
**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 28, 2024, 7:51am UTC](https://boards.straightdope.com/t/xkcd-thread/854574/2880 "2024-03-28T07:51:07Z")
I think all cursive letters look lame. There’s only one cool letter and that’s the Cool S: [![](https://upload.wikimedia.org/wikipedia/commons/thumb/7/71/S-cool.svg/272px-S-cool.svg.png) ](https://upload.wikimedia.org/wikipedia/commons/thumb/7/71/S-cool.svg/272px-S-cool.svg.png) ---
**Author:** ![Andy\_L](https://avatars.discourse-cdn.com/v4/letter/a/c67d28/32.png) [@Andy\_L](https://boards.straightdope.com/u/Andy_L)\ **Post date:** [March 28, 2024, 4:10pm UTC](https://boards.straightdope.com/t/xkcd-thread/854574/2881 "2024-03-28T16:10:25Z")
It’s a cool letter but it doesn’t put on airs; judging from the desks I’ve seen, cool S is not too cool for school ---
**Author:** ![Slow\_Moving\_Vehicle](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/slow_moving_vehicle/32/291_2.png) [@Slow\_Moving\_Vehicle](https://boards.straightdope.com/u/Slow_Moving_Vehicle)\ **Post date:** [March 28, 2024, 4:59pm UTC](https://boards.straightdope.com/t/xkcd-thread/854574/2882 "2024-03-28T16:59:10Z")
> [@Lumpy](#): > > I completely misinterpreted the cartoon until just a moment ago. I thought it was joking about the distortions the Mercator projection introduces; I was completely whooshed by the joke that it was talking about the literal physical size of the map on the wall > 🤦 Me too. I’m not smart enough for every xkcd. [Previous page](https://boards.straightdope.com/t/xkcd-thread/854574.md?page=143) [Next page](https://boards.straightdope.com/t/xkcd-thread/854574.md?page=145)