NationStates Jolt Archive

Explain this: "Klein bottle for rent--inquire within." :D

42!!!

Explain this: "Klein bottle for rent--inquire within." :D

Looks like the Ginny wants to rent out the bottle. :)

42!!!

I agree

Ha!

I get it. ;)

[Should I spoil it for everyone else, I wonder?]

Ehmmmmmmmmm... love?

Ehmmmmmmmmm... love?

*euht* wrong answer... Hehe this is fun.

Oh! I get it! Hahaha!

...What do I get? :confused:

A klein bottle is a one-sided shape, isn't it?

Ha!

I get it. ;)

[Should I spoil it for everyone else, I wonder?]

I must be with Will Robinson, Robbie the Robot, and Dr. Smith. I haven't a clue. :confused:..and old.

Ok, so I went and looked up klein bottle and y'all explained 42. Cute E very cute. :D

...What do I get? :confused:

No love. No sleep at night.

This isn't so much an IQ question, but more one about trivia and just happening to know what a Klein bottle is.

This isn't so much an IQ question, but more one about trivia and just happening to know what a Klein bottle is.

You are 100% correct.

42!!!
I've seen 42 so many times but I don't know what it means...

hint: Is it near the back side of the Mobius Strip Club?

I've seen 42 so many times but I don't know what it means...

Read 'The Hitchhikers Guide to the Galaxy'. 42 is the answer to the ultimate question of life the universe and everything.

I've seen 42 so many times but I don't know what it means...
42 is the supposed answer for Life, the Universe and Evrything, at least according to the Hitchhikers guide to the Galaxy, by Douglas Adams.

I've seen 42 so many times but I don't know what it means...
It's the answer to life, the universe and everything.

Read "The Hitchhikers Guide to the Galaxy" by Douglas Adams, and all will be revealed. Or if you're lazy you could go and watch the movie.

So the answer might be 42, but what is the question then? Some sort of equation? Some silly number like that means nothing. I could say 'pi', and we'd all know that there's only one fundamental question leading to that answer. So, what about this '42' you keep mentioning?

So the answer might be 42, but what is the question then? Some sort of equation? Some silly number like that means nothing. I could say 'pi', and we'd all know that there's only one fundamental question leading to that answer. So, what about this '42' you keep mentioning?

ah, now THAT is what the earth is for...

ah, now THAT is what the earth is for...

It all makes sense now :p

ah, now THAT is what the earth is for...
Actually (in the books) WAS for...

Actually (in the books) WAS for...

true

So the answer might be 42, but what is the question then? Some sort of equation? Some silly number like that means nothing. I could say 'pi', and we'd all know that there's only one fundamental question leading to that answer. So, what about this '42' you keep mentioning?

A nice resource on the subject: http://en.wikipedia.org/wiki/The_Answer_to_Life,_the_Universe,_and_Everything

So the answer might be 42, but what is the question then? Some sort of equation? Some silly number like that means nothing. I could say 'pi', and we'd all know that there's only one fundamental question leading to that answer. So, what about this '42' you keep mentioning?
Aye, I believe the closest thing they ever got to an answer to what the question is was 6*9, but there's questions as to whether that's correct, because Arthur was only a piece of the giant supercomputer known as the Earth.

Actually (in the books) WAS for...

No...actually, in the books it did get recreated like in the film But it gets destroyed (AGAIN) later (in another one of the books). And then in the 5th book ("Don't Panic") he decides to go with multiple universes or "the mish mash?" and it exists in some universes, but not others??


I think...it's a long time since i read them.

Aye, I believe the closest thing they ever got to an answer to what the question is was 6*9, but there's questions as to whether that's correct, because Arthur was only a piece of the giant supercomputer known as the Earth.

6*9 = 54

6*9 = 54
That's the beauty of it.
Arthur draws random pieces from the Scrabble bag to try and spell out the Question, and what he draws is "Whatdoyougetwhenyoumultiplysixbynine". I forget which book it was in.

So the answer might be 42, but what is the question then? Some sort of equation? Some silly number like that means nothing. I could say 'pi', and we'd all know that there's only one fundamental question leading to that answer. So, what about this '42' you keep mentioning?

***SPOILERS****

In the Hitchhiker's Guide series of books (a comic farce) a super intelligent race programed a computer to answer the meaning of "life, the universe, and everything". The computer spat out "42". They then had to construct another computer (Earth) to figure out the question. The earth was destroyed befdore it finished computing, but the question was (possibly and open to argument) "What's 6x9?".

Remember, it's farce.

Explain this: "Klein bottle for rent--inquire within." :D



you cant because a klein bottle has no "inside" as such seeing as its a non orientable object, much like a mobius band only one dimension up

6*9 = 54

Only in base 10, I heard somewhere that 6x9 equals 42 in base 13

6*9 = 54 Which is why Arthur says, when he sees the supposed question; "I've always though there was something fundamentally wrong with the universe."

Only in base 10, I heard somewhere that 6x9 equals 42 in base 13
If I'm doing my math right, you are correct.

lol. How much the topic has changed...

I myself have the 4 part trilogy omnibus. Great if you're a particularly random person btw.

6*9 =42 in Base 13 though...

So long, and thanks for all the fish!

you cant because a klein bottle has no "inside" as such seeing as its a non orientable object, much like a mobius band only one dimension up

Yah, boohoo - now you've spoiled it! No matter, cuz the rest of the posters here seem to have gone off-topic anyway.

Explain this: "Klein bottle for rent--inquire within." :DThe thing to remember about Klein Bottles is that they're two-dimensional surfaces curved into a four-dimensional shape*. A true Klein bottle does not intersect itself, so a true Klein Bottle cannot exist in a three-dimensional universe. In a four-dimensional space, a two-dimensional curved surface (like a klein Bottle) is incapable of completely encapsulating a four-dimensional space; you would need a three-dimensional surface curved into a four-dimensional space to encapsulate anything.

So, saying "Klein bottle for rent--inquire within" in a four-dimensional universe makes about as much sense as saying "Hula-hoop for rent--inquire within" in our universe. A hula-hoop is not going to encapsulate anyting.

You could claim that a Klein Bottle is resting partly within and partly outside our universe. However, such a thing would look like it had holes in the wall as a Klein Bottle would have to "lift up" outside our universe somewhere... kinda like a bridge has to "lift up" off of the ground.

* For comparison, an ordinary sphere such as a beach ball is a two-dimensional surface curved into a three-dimensional shape. A Moebius Strip is also a two-dimensional surface curved into a three-dimensional shape. A ball of string is a one-dimensional object curved into a three-dimensional shape.

--The Democratic States of Cogitation
"Think about it for a moment."
Founder and Delegate of The Realm of Ambrosia

The thing to remember about Klein Bottles is that they're two-dimensional surfaces curved into a four-dimensional shape*. A true Klein bottle does not intersect itself, so a true Klein Bottle cannot exist in a three-dimensional universe. In a four-dimensional space, a two-dimensional curved surface (like a klein Bottle) is incapable of completely encapsulating a four-dimensional space; you would need a three-dimensional surface curved into a four-dimensional space to encapsulate anything.

So, saying "Klein bottle for rent--inquire within" in a four-dimensional universe makes about as much sense as saying "Hula-hoop for rent--inquire within" in our universe. A hula-hoop is not going to encapsulate anyting.

You could claim that a Klein Bottle is resting partly within and partly outside our universe. However, such a thing would look like it had holes in the wall as a Klein Bottle would have to "lift up" outside our universe somewhere... kinda like a bridge has to "lift up" off of the ground.

* For comparison, an ordinary sphere such as a beach ball is a two-dimensional surface curved into a three-dimensional shape. A Moebius Strip is also a two-dimensional surface curved into a three-dimensional shape. A ball of string is a one-dimensional object curved into a three-dimensional shape.

--The Democratic States of Cogitation
"Think about it for a moment."
Founder and Delegate of The Realm of Ambrosia

What Cog said.

*Nod*

The thing to remember about Klein Bottles is that they're two-dimensional surfaces curved into a four-dimensional shape*. A true Klein bottle does not intersect itself, so a true Klein Bottle cannot exist in a three-dimensional universe. In a four-dimensional space, a two-dimensional curved surface (like a klein Bottle) is incapable of completely encapsulating a four-dimensional space; you would need a three-dimensional surface curved into a four-dimensional space to encapsulate anything.

So, saying "Klein bottle for rent--inquire within" in a four-dimensional universe makes about as much sense as saying "Hula-hoop for rent--inquire within" in our universe. A hula-hoop is not going to encapsulate anyting.

You could claim that a Klein Bottle is resting partly within and partly outside our universe. However, such a thing would look like it had holes in the wall as a Klein Bottle would have to "lift up" outside our universe somewhere... kinda like a bridge has to "lift up" off of the ground.

* For comparison, an ordinary sphere such as a beach ball is a two-dimensional surface curved into a three-dimensional shape. A Moebius Strip is also a two-dimensional surface curved into a three-dimensional shape. A ball of string is a one-dimensional object curved into a three-dimensional shape.

--The Democratic States of Cogitation
"Think about it for a moment."
Founder and Delegate of The Realm of Ambrosia

That's telling them Cog! :confused:

you cant because a klein bottle has no "inside" as such seeing as its a non orientable object, much like a mobius band only one dimension up
Yup! You have an IQ in the 120-140 range! :)

The thing to remember about Klein Bottles is that they're two-dimensional surfaces curved into a four-dimensional shape*. A true Klein bottle does not intersect itself, so a true Klein Bottle cannot exist in a three-dimensional universe. In a four-dimensional space, a two-dimensional curved surface (like a klein Bottle) is incapable of completely encapsulating a four-dimensional space; you would need a three-dimensional surface curved into a four-dimensional space to encapsulate anything.

So, saying "Klein bottle for rent--inquire within" in a four-dimensional universe makes about as much sense as saying "Hula-hoop for rent--inquire within" in our universe. A hula-hoop is not going to encapsulate anyting.

You could claim that a Klein Bottle is resting partly within and partly outside our universe. However, such a thing would look like it had holes in the wall as a Klein Bottle would have to "lift up" outside our universe somewhere... kinda like a bridge has to "lift up" off of the ground.

* For comparison, an ordinary sphere such as a beach ball is a two-dimensional surface curved into a three-dimensional shape. A Moebius Strip is also a two-dimensional surface curved into a three-dimensional shape. A ball of string is a one-dimensional object curved into a three-dimensional shape.

--The Democratic States of Cogitation
"Think about it for a moment."
Founder and Delegate of The Realm of Ambrosia
Excellent elucidation, Euclid! :D

Now, for the next question: "Define a four-dimensional super-cube!" :)

But surely the question is a general knowledge question, as it requires prior knowledge. A true IQ test wouldn't have a question such as this right?

Excellent elucidation, Euclid! :D

Now, for the next question: "Define a four-dimensional super-cube!" :)I begin with two fixed points separated by finite arbitrary distance (which I shall call "L") and draw the line segment connecting them.

I then draw two new line segments of length L parallel to each other such that one new segment starts at each of one of the two fixed points AND such that the two new line segments are perpendicular to the original line segment AND such that the new line segments are on the same side of the original line segment. This results in defining two new fixed points, between which the distance is necessarily L (I could supply a proof of this if absolutely necessary, but I have to cut this short due to real life time limitations). I draw a line segment between the two nex fixed points. This set of points and line segments, and the 2-dimensional space enclosed within them, is a square.

I then draw four new line segments of length L parallel to each other such that one new segment starts at each of one of the four corners of the square AND such that the four new line segments are perpendicular to the square AND such that the new line segments are on the same side of the square. This defines four new fixed points, which between them necessarily share four new line segments of length L. (The proof needed for this would logically follow from the proof needed for the above square.) I draw those line segments. This set of points and line segments, and the 3-dimensional space enclosed within them, is a cube.

I then draw eight new line segments of length L parallel to each other such that one new segment starts at each of one of the eight corners of the cube AND such that the eight new line segments are perpendicular to the cube AND such that the new line segments are on the same side of the cube. This defines eight new fixed points, which between them necessarily share twelve new line segments of length L (yes, twelve, because that's how many edges there are in a cube). (The proof needed for this would logically follow from the proof needed for the above square and cube.) I draw those line segments. This set of points and line segments, and the 4-dimensional space enclosed within them, may be called a 4-dimensional hypercube or a 4-dimensional supercube.

This may be extended to supercubes of higher dimensions, as desired.

But surely the question is a general knowledge question, as it requires prior knowledge. A true IQ test wouldn't have a question such as this right?Probably correct, though you could attempt to rectify this by explaining what a Klein Bottle is as part of the question.

--The Democratic States of Cogitation
"Think about it for a moment."
Founder and Delegate of The Realm of Ambrosia

I could sit here all day and watch Cog say stuff like this.

*sports her "Big Brained Guys Rock" t-shirt*

The thing to remember about Klein Bottles is <snip>

hahahahaa ... you nerd. :D

6*9 = 54

Not in base 13.

I begin with two fixed points separated by finite arbitrary distance (which I shall call "L") and draw the line segment connecting them.

I then draw two new line segments of length L parallel to each other such that one new segment starts at each of one of the two fixed points AND such that the two new line segments are perpendicular to the original line segment AND such that the new line segments are on the same side of the original line segment. This results in defining two new fixed points, between which the distance is necessarily L (I could supply a proof of this if absolutely necessary, but I have to cut this short due to real life time limitations). I draw a line segment between the two nex fixed points. This set of points and line segments, and the 2-dimensional space enclosed within them, is a square.

I then draw four new line segments of length L parallel to each other such that one new segment starts at each of one of the four corners of the square AND such that the four new line segments are perpendicular to the square AND such that the new line segments are on the same side of the square. This defines four new fixed points, which between them necessarily share four new line segments of length L. (The proof needed for this would logically follow from the proof needed for the above square.) I draw those line segments. This set of points and line segments, and the 3-dimensional space enclosed within them, is a cube.

I then draw eight new line segments of length L parallel to each other such that one new segment starts at each of one of the eight corners of the cube AND such that the eight new line segments are perpendicular to the cube AND such that the new line segments are on the same side of the cube. This defines eight new fixed points, which between them necessarily share twelve new line segments of length L (yes, twelve, because that's how many edges there are in a cube). (The proof needed for this would logically follow from the proof needed for the above square and cube.) I draw those line segments. This set of points and line segments, and the 4-dimensional space enclosed within them, may be called a 4-dimensional hypercube or a 4-dimensional supercube.

This may be extended to supercubes of higher dimensions, as desired.

Probably correct, though you could attempt to rectify this by explaining what a Klein Bottle is as part of the question.

--The Democratic States of Cogitation
"Think about it for a moment."
Founder and Delegate of The Realm of Ambrosia
You win this year's Pythagoras Award! Yayyyy! :D

hahahahaa ... you nerd. :D
ROFLMAO!!! Tsk! :D

smash it

smash it
[ Smacks LP upside da head wid a copy of Principia Mathematica! ] Hush! :p

[ Smacks LP upside da head wid a copy of Principia Mathematica! ] Hush! :p
Did i win?

Explain this: "Klein bottle for rent--inquire within." :D


I saw that website...read that,and laughed. I'm such a nerd.

Oh, and Cogitation is now my favourite mod for their posts..lol.

Explain this: "Klein bottle for rent--inquire within." :D

Why did the chicken cross the Moebius strip?

Not in base 13.

Which has absolutely nothing to do with the reason why Adams chose the number.

Why did the chicken cross the Moebius strip?
Um ... to get to the same side? :D

I've seen 42 so many times but I don't know what it means...Hitchhiker's Guide to the Galaxy, "What is the meaning of life, the universe, and everything, etc."

Did i win?
Nope. I just wanted you to shut up! :D

<snip>Wow, there are actually educated people on General.*

Good job Cog, keep up the mathematics. :D

* Wait, Cog's a mod, does he count?

~Czardas, Supreme Ruler of the Universe

Which has absolutely nothing to do with the reason why Adams chose the number.Why did he choose the number, anyway? I know for sure that it's not the answer.

The correct answer is: 49

:D


~Czardas, Supreme Ruler of the Universe

Why did he choose the number, anyway?

From Usenet:

Newsgroups: alt.fan.douglas-adams
From: ada...@nic.cerf.net (Douglas Adams) -
Date: Wed, 3 Nov 93 07:51:46 GMT
Local: Wed,Nov 3 1993 7:51 am
Subject: Re: Why 42 ?In Article <2b4asr$...@syzygy.socs.uts.edu.au>, mjche...@socs.uts.EDU.AU

(Mark J Cherkas) wrote:

>I am new to this group so bear with this beginners question:
>Why is the answer 42 ?
>Has Douglas Adams ever explained this ?

The answer to this is very simple. It was a joke. It had to be a number, an ordinary, smallish number, and I chose that one. Binary representations, base thirteen, Tibetan monks are all complete nonsense. I sat at my desk, stared into the garden and thought '42 will do' I typed it out. End of story.

Best,

Douglas Adams


London, UK | d...@dadams.demon.co.uk (dormant)
Currently in Santa Fe, NM | ada...@nic.cerf.net (current)

Ah. He made it up. No wonder he didn't get the right answer.

~Czardas, Supreme Ruler of the Universe

Google knows the answer to life the universe and everything (Not kidding):

Look:

http://www.google.com/search?hl=en&q=answer+to+life+the+universe+and+everything&btnG=Google+Search

I begin with two fixed points separated by finite arbitrary distance (which I shall call "L") and draw the line segment connecting them.

<snip>

You never mentioned how a fellow Deutschman invented it (Felix Klein)! Us Germans know the answer to life the universe and everything! ;)

Which has absolutely nothing to do with the reason why Adams chose the number.
This is interesting, its in the Wiki article linked earlier...

There is a joke amongst computer programmers that Deep Thought may have had some order of operations issues. The following code in the C programming language defines the macros SIX as "1 + 5" and NINE as "8 + 1", and then performs the computation "SIX * NINE". It returns the answer "42", because "SIX * NINE" is expanded by the computer to "1 + 5 * 8 + 1", and the multiplication takes precedence over the additions. (This occurs because the macro expansion is textual, not logical.)

"#include <stdio.h>
#define SIX 1 + 5
#define NINE 8 + 1

int main(void)
{
printf( "What you get if you multiply six by nine: %d\n", SIX * NINE );
return 0;
}"
Assuming that this is indeed correct, that means that the meaning of life, the universe and everything would be 42.

I could sit here all day and watch Cog say stuff like this.

*sports her "Big Brained Guys Rock" t-shirt*hahahahaa ... you nerd. :D
/me bows: "Thank you. I try."Wow, there are actually educated people on General.*

Good job Cog, keep up the mathematics. :D

* Wait, Cog's a mod, does he count?Well, since I don't have to be a NationStates Moderator to explain higher-dimensional geometry (I think a few of the other Mods would balk at that requirement), I'd say that I do count as an educated person on "General". ;)

Why did the chicken cross the Moebius strip?It's a shortcut to another point on the same side.

[edit #2] Bah! I was just looking at a Wikipedia article on the subject (http://en.wikipedia.org/wiki/Tesseract) when I figured out a simpler way to define supercubes.

An N-dimensional supercube is the space enclosed by a set of 2^N distinct points, which are spaced out from each other such that each point is connected to N other points by N mutually-perpendicular line segments of equal length.

This is a much more concise definition than what I posted above* and loses no information; for a given integer N, there is only one way to arrange the points such that the definition is satisfied (though, again, I don't have a rigorous proof for this).

* ...though the above definition may or may not make for a more understandable explanation. [/edit #2]

--The Democratic States of Cogitation
"Think about it for a moment."

Which has absolutely nothing to do with the reason why Adams chose the number.

I didn't say it was.

It was, however, ONE of the many explanations he gave, over the years, for the reasoning behind '42'... and my personal favourite - since it plays on the fact that people always make assumptions.

I then draw eight new line segments of length L parallel to each other such that one new segment starts at each of one of the eight corners of the cube AND such that the eight new line segments are perpendicular to the cube AND such that the new line segments are on the same side of the cube. This defines eight new fixed points, which between them necessarily share twelve new line segments of length L (yes, twelve, because that's how many edges there are in a cube). (The proof needed for this would logically follow from the proof needed for the above square and cube.) I draw those line segments. This set of points and line segments, and the 4-dimensional space enclosed within them, may be called a 4-dimensional hypercube or a 4-dimensional supercube.

OK, that makes sense in a purely mathematical manner but isn't this all overextending the principles of geometry? How can a line be perpedicular to a cube without overlapping the lines already present from the construction of the cube?

:confused:

OK, that makes sense in a purely mathematical manner but isn't this all overextending the principles of geometry? How can a line be perpedicular to a cube without overlapping the lines already present from the construction of the cube?

:confused:

The 4D-hypercube can only 'exist' in a (eucledian) space E with dim(E)>=4.
Because dim(E)>=4, we can at least find 4 vectors vi for which <vi|vj> = delta(i,j). This means that we can find 4 vectors that are perpendicular to eachother so we can draw 4 perpendicular lines through one point.