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Klein Tunnel
Klein based Super-/Subway - And you thought the Circle and District Line was cool! | |
Metropolitan Mass Transit system based on Klein Tunnels - If you stay on the train for long enough you visit all mainline and sub-terrain stations.
Inspired by xenzag's comment on Exit Photos
Exit_20Photos
[Dub, Dec 09 2005]
3D representation of a Klein Bottle
http://sodwana.uni-...mg/klein_bottle.jpg
Two points:
a) A Klein bottle is actually a four dimensional object.
b) If you went on a subway train down a real Klein tunnel, you would come back inside out. [DrCurry, Dec 09 2005]
Kingston Trio MTA Lyrics
http://web.mit.edu/.../www/t/charlie.html
How Charlie [possibly Felix Klein's grandson] became "the man who never returned", circa 1959. [jurist, Dec 12 2005, last modified Dec 14 2005]
The Manhattan Transfer - TWILIGHT TONE -
http://www.tmtfanclub.com/extens.html
Song about //Mr Miller// one of the many songs about the subject (American Pie's another one, unless I'm wrong!) [Dub, Dec 12 2005]
Buy a Klein Bottle
http://www.kleinbottle.com/
Fairly inexpensive too. I've been after one for a while. [wagster, Dec 12 2005]
(???) Ian's Underwear question...?
Mobius_20Strip_20Underwear
(Comment dated today) [Dub, Dec 12 2005]
Klein Tunnel
Klein_20Tunnel
(Watch it, when you use this link... Count how many times you press it. It'll be useful information later) [Dub, Feb 03 2006]
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Someone wrote a sci fi story once where the Boston subway turned into a Mobius strip (I guess that was before the days of Klein bottles), and some trains got lost permanently. |
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I was thinking of implementing it as a map - I.e. throw away the current Tube network map (obviously keep they style, format and layout! - but throw away the Northern Line/Bakerloo line... etc) and re-render it on a Klein bottle - and then (with some engineering, anyway) ensure that a tube train you get on at Morden ends up at Morden having first visited the other stations - e.g. at Balham it might go overground to Clapham Junction and then Pop back underground at Waterloo etc... I haven't really thought it through very much, I must admit. |
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You could possibly make all the lines figures of eight. It would certainly address the poor service the outer boroughs/boros receive. |
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Yes, figure-8 but sur-/sub-terrain. |
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//...subway turned into a Mobius strip...and some trains got lost permanently//
How can you get lost on a Mobius strip? |
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That part was not adequately explained - it was a science fiction story, after all. |
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Well, the Kennedys did figure out how to make billions of dollars dissapear into those tunnels -- does that count, DrCurry? |
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Can someone explain to me, and possibly a large amount of readers who don't post here, what the fuck a Klein tunnel is? |
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I'm not trying to be hostile, but I find that the addage of profane comments adds a bit a certain kind of humor I like. =D |
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[Evil Pickels] Just a tip, but you might just try googling "Klein bottle" next time before profanely expressing easily fixable ignorance. Works for me. |
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He did, but one of the hyperlinks off the page was to //Recursion//, and that had a tail-recursive self-reference, and he got stuck / his stack crashed. |
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[Dub], that's a good "inside" joke...infinitely inside/outside perhaps.... |
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Sorry, I couldn't help myself. |
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So the only thing stopping us implementing this is to find a way to tunnel in 4 dimensions? Surely this is not insurmountable? Can anyone think of a way of doing this? |
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slip acid drops in all the construction workers' choc-milks. |
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//And you thought the Circle and District Line was cool// Are you quite sure you're not a (Tube) trainspotter, [dub]? |
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You can buy Klein bottles - would a tunnel not just be an
elongated version? |
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What would happen if the entrance to the Klien bottle
was on the lid of Schrödinger's cat box? Would the box
still be a box? etc etc |
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Didn't the Kingston Trio address this issue in 1959? [link] |
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[DrCurry][Link] Perfect! - If the tunnels are arranged correctly, and you're standing on the right place in the platforms, you'll automagically 'enter' the train at your start and 'exit' at the destination! Doors become just one more problem you don't have to think about - And there'd be no need for the //Mind The Gap// warnings anymore! |
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[jurist] Could be. Kendall Square, isn't that where Thinking Machines used to be? - Right near MIT. And I guess he's called Charlie after the river - I guess the fares would be tricky to calculate, what with moving in 5D space (4D+Time) - Some clever new 'Zones' would have to be dreamt-up - Tooting Bec/Broadway would be in the Twilight Zone. - Perhaps //The Manhattan Transfer// will write lyrics about it one day too (cf "Twilight Tone"). |
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[AbsintheWithoutLeave] Of course - And you don't need an anorak down/up/in/out there (of course a clipboard and thermos are still de rigeur) |
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[xenzag] Excellent, too! - The cats would sort-out the Tube's long running Schrödinger's Mouse problems - Ow, I'm getting sooo excited about the idea now! |
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Tooting would be in the Benighted Zone. |
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Trains delayed by Fractal Ferns on the (Möbius strip) rails |
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[Copro] Tooting is twinned with both The Twighlight Zone and "Your Darkest Thought" |
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[wagster]Wow, that vessel with Green/Yellow liquid in it's amazing!... |
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Ah, but is it half yellow, half full, half empty or half green? |
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I'm starting to suspect there's a joke hovering about Bakerloo... but nah! |
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/How can you get lost on a Mobius strip?/
By falling off, of course. |
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/And there'd be no need for the //Mind The Gap// warnings anymore!/
Mind The Singularity |
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Ignorance check (for exoneration of [EvilPickels]): I searched for "Klein tunnels" on Teoma, and it took me right back to this Halfbakery page. |
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If the idea mentioned "Klein bottle" maybe I would have recognized it as the 4-dimensional object/surface. |
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// I searched for "Klein tunnels" on Teoma, and it took me right back to this Halfbakery page.// |
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Haha! MY MONSTER LIVES!!!! - Hundreds will be trapped here! |
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//entrance to the Klien bottle was on the lid of Schrödinger's cat box?// The cat would remain in an indeterminate state, neither inside nor outside the box. |
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