Arm-wrestling in 2D

[RQ]

Here's a confusing question: What if they had an arm wrestle? Would the greater mass (volume*density) of Bob's finger simply crush Fred, or would Fred's hand simply slice it off, because the force is concentrated on an infinitely thin line?

Interesting question. Although Bob has an extra dimension, Fred has an infinite pressure. I guess it depends on which side Bob is pushing him.

Split from "how easy it would be to kill someone in the second dimension" by BobXP.

[alkaline]

my vote's on Bob. It's not Bob wrestling a shard of metal, it is bob against a biological 2d being.

[mghtymoop]

bob could never touch fred and vice versa because fred whose matter is the derivative of bobs matter could only interact with bobs matter if it was first differentiated in which case bob would then be 2d, however you cannot differentiate real matter so fred and bob would never even be aware of each otehrs existance

[Euclid]

Disturbing, very disturbing

[jinydu]

Come to think of it, arm wrestling matches would be MUCH more difficult to win in Fred's world.

Ordinarily, when we arm wrestle in 3D, we try to pull our opponent's arm to the side. But in Fred's world, there is no "sideways". Thus, the only conceivable way to win would be to pull someone forward, so that they fall over! That would take a lot of muscle (at least for 2D people).

I think that Bob would easily win. As before, Fred's only way of winning would be to pull Bob (or rather a two dimensional slice of Bob) off his feet. On the other hand, Bob could simply pull Fred's arm sideways (out of Fred's planar home). Fred's 2D muscles are unlikely to offer any resistance, since they are only designed to move within the plane.

[Jay]

Come to think of it, arm wrestling matches would be MUCH more difficult to win in Fred's world.

Ordinarily, when we arm wrestle in 3D, we try to pull our opponent's arm to the side. But in Fred's world, there is no "sideways". Thus, the only conceivable way to win would be to pull someone forward, so that they fall over! That would take a lot of muscle (at least for 2D people).

What would a 4D match look like? Do you guys think its easier to win in 4d than in 3d?

[jinydu]

Well, there are four dimensions in tetraspace, hence four pairs of directions to pull your opponent in:

1) Up/down is definitely ruled out. Up would require fighting against gravity, while down would require trying to squash your opponent's body against the ground.

2) Forward/backward also wouldn't work. Either way woud require overcoming your opponent's entire body mass.

3) Left/right still works, like it does in 3D (I think).

4) Kata/ana should also work

Thus, it would be possible to pull your opponent in two perpendicular directions. I think that in tetraspace, arm wrestling would involve much more strategy than it does in 3D. For example, if your opponent is expending all his energy trying to pull your arm left, you could try to finish him quickly by suddenly pulling him ana.

[Geosphere]

1) You assume gravity is equivalent
2) Which is Sumo wrestling here, and possible.
3) Again, some guesses on gravity.
4) We cannot know.

[mightymrbob]

So technically arm wrestling in 2D is impossible. If you can only win by pushing sideways, and the only directions in 2D are forward and backward, then...

Fred's stuffed

[Geosphere]

Wrestling would be more like tug of war.

[Keiji]

lol yeah it would actually

[mightymrbob]

Except on a "table" (horizontal line with two vertical lines underneath). Could be interesting.

[jinydu]

There would be no gravity in that place.

[mightymrbob]

What place, 2D?

[jinydu]

On the surface of a table (which is 2D). Think about an ant walking around on a table, with no sense of height.

[PWrong]

That's the Flatland type of 2D. Ants on a table, with no gravity.

Fred's type of 4D can have gravity, because there is up and down, but not left and right. Fred probably lives on a circular planet. I prefer this version.

In an arm wrestle, how would Fred grasp his opponent's arm?

[jinydu]

That's the Flatland type of 2D. Ants on a table, with no gravity.

Fred's type of 4D can have gravity, because there is up and down, but not left and right. Fred probably lives on a circular planet. I prefer this version.

In an arm wrestle, how would Fred grasp his opponent's arm?

How about using glue?

[mightymrbob]

Yeah, but how would you get to put the glue on in 2D? :?
Oh dear...!

[jinydu]

Why would it be hard to put on glue in 2D?

[mightymrbob]

For a few reasons

1) If in 2D, you have infinite pressure because you are infinitely thin, then how would you put glue on without peircing the tube..?

2) To put the glue on, you'd have to bend your arm sideways... Uh oh! 2D limitations again!

3) Umm... wait, it'll come...


Oh, and , WOOHOO!!! Planespace! The back of that blokes' head was really annyoing...

[jinydu]

1) Pressure in 2D is only infinite from our 3D point of view. But the 2D world would have its own analogue of pressure, defined as force per unit surface length. Using this definition, pressure in 2D would have acceptable, finite values.

2) Fred would also have his own version of a glue tube. It could be shaped like a letter U. There could be 2D ways of extracting the clue. For example, the glue tube could be coated on the inside with a non-stick material. Then, Fred could slam the tube against the ground. The force would push the glue up, over the top of the container, and into Fred's hand. A bit inconvenient, but living in a plane just isn't easy (I should know. I'm a planespace citizen!)

[mightymrbob]

OK...I live in planespace too. Well, even if he did manage to get the glue into his hand, is it not against the rules of arm wrestling to use glue?!? Maybe I'm just being pedantic, but you have to take everything into account!
You'd have to jump over the back of your chair in order to sit on it 2D, wouldn't you? I suppose they could arm wrestle standing up/ kneeling down...

[jinydu]

Arm-wrestling would be even more difficult to win if the opponents were sitting down. Then, Fred would have to overcome the combined mass of both his opponent and his opponent's chair.

Thinking about it more, arm wrestling would be more of a pushing competition rather than a pulling one. Pulling is a lot more difficult without the help of a third dimension. Perhaps the most logical way for an arm wrestling match to take place would be for the opponents to glue their hands together. Then, each opponent tries to push forward, knocking his opponent over backwards. Sometimes, the rules have to be bent to take account of the situation .

[mightymrbob]

Hmm... Arm wrestling in 2D certainly would be an interesting affair!


Fred and his opponent (let's call him Jim) would have to either

a) Glue their hands together whilst standing up (by using jinydu's method) and then jumping over the backs of their chairs (whilst still glued together!!!), which would probably be extremely painful...

b) After managing to sit down, using an adapted version of the jinydu-glue technique to glue themselves together...

Then, they'd try and push each other away, which would cause even more problems. If Fred managed to push Jim away from him and Jim fell off his chair, then Fred would b slammed against the table edge if they were still stuck together...

1 / _
_O[__|/
|_ O/ ____ _ |
| | |\/\_ | | |



Fred is flying through the air after pushing jim away from him.


2
_ O
|_ O/ _____\\_ _ |
| | |\/\_ | /_ | |



Fred is slammed against the table aftre pushing jim away. (Yes I know, just imagine they are still stuck together).

Of course, there is no reason why the rules couldn't be adapted even to more, so that if you managed to push you opponent away from you and he glue seal was broken, then you won... Or something like that anyway!

(Oh, and please don't take the mickey out of my "diagrams". They took me ages).

P.S. I just previewed my message and the diagrams got made all wonky. You'll have to do with the written explanation for the 2nd one. Sorry!

[RQ]

Although I agree with mightymoop that they wouldn't be aware of their existences, I put my vote on Bob, because, I don't know I have a feeling like he's bigger, you know with the extra dimension and stuff.
Oh by the way, 2D arm-wrestling should be the two players, one on top of the other and pushing left or right, whichever direction the player has to push in to win.
Maybe they should pull each other, instead of push to the side.

[koyaanmaster]

It still seems impossible (improbable ?) for two forms of matter of different physical dimensions to physically interact (i.e. 2D being arm wrestling a 3D being). The "hand" of a 2D being would simply glide through 3D matter, as the "hand" would have a thickness of nothing. Yet then as the 2D "hand" is passing through 3D matter with a thickness of 0, its length and height would be taking up space.

Thus it would be an object, both existing (in two dimensions) and not existing (in the third dimension) at the same time. This paradox seems to bring doubt as to whether 2D matter could simultaneously exist with 3D matter.

Or then again, maybe not. Hhmmm . . .

[RQ]

Yes, they would be "ignorant" of each other, and they would never intersect, and that's why I said ignoring the fact that this cannot happen, I put my vote on Bob.(man every time I leave the logic someone corrects me)

[koyaanmaster]

Now that I will explore the boundaries outside of logic, I am going to bet that new player could win the arm wrestling match: Ted.

Ted does not live in Lineland or Flatland, or realmspace or tetraspace. Ted is not in any spatial dimensions. Rather, Ted lives in one (or two?) temporal dimensions. Ted is a citizen of Timeland.

So, if the Timeland citizen, Ted (who is 1T or 2T), were to arm wrestle a 2D or a 3D Bob or Fred, Ted would always win. Able to travel freely through time, he would outlast any opponent. Although Ted has no physical strength, he has temporal strength.

As JFK once said, "We must use time as a tool, not as a crutch." Ted would certainly have total control over his time.

[elpenmaster]

well, second temporal dimensions would allow Ted to be in two places at the same time (if he lived in 2T. if he lived in 10T, he could be in ten places at once)

to him it would appear as if he was moving while the dude he wwas arm wrestling was staying still, but to the dude he was arm wrestling he would appear to be in two places at once (i think)

so he could seem to be in two places at once. i dont think that this would give him any extra strength, though. but he would be very agile!!! :wink:

[jinydu]

Ted is not in any spatial dimensions.

Then he would definitely lose, because he wouldn't have any arms! Arms need some physical size. Without any spatial dimensions, he would just be a point.