The Instigator
Subutai
Con (against)
Winning
32 Points
The Contender
BornToDebate
Pro (for)
Losing
0 Points

The Shortest Distance Between Two Points Is Always a Straight Line

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Post Voting Period
The voting period for this debate has ended.
after 7 votes the winner is...
Subutai
Voting Style: Open Point System: 7 Point
Started: 7/24/2013 Category: Science
Updated: 4 years ago Status: Post Voting Period
Viewed: 9,323 times Debate No: 35906
Debate Rounds (4)
Comments (45)
Votes (7)

 

Subutai

Con

BornToDebate asks, "How can con even win wtf?" So, I challenge him to defend his assumption.

Full Resolution

The shortest distance between two points is always a straight line.

The BoP for this debate is on pro.

Definitions

The shortest distance between two points refers to a single path that has the condition that no other continuous, conceivable path would be shorter than it. Pro will be arguing that that distance is always straight, while con will argue that it is not always straight. This debate is not specific to any specific geometry.

Rules

1. A forfeit or concession is not allowed.
2. No semantics, trolling, or lawyering.
3. All arguments and sources must be visible inside this debate.
4. Debate resolution, definitions, rules, and structure cannot be changed without asking in the comments before you post your round 1 argument. Debate resolution, definitions, rules, and structure cannot be changed in the middle of the debate.

Voters, in the case of the breaking of any of these rules by either debater, all seven points in voting should be given to the other person.

Debate Structure

Round 1: Presentation all arguments by pro
Round 2: Presentation of arguments by con and rebuttal by pro
Round 3: Rebuttal by con and defense of original arguments by pro
Round 4: Defense of original argument by con and a bye round by pro (to make for even rounds; only use one line for your final post)
BornToDebate

Pro

Unless you mean that to get from A to B there might be obstacles that are too tall to jump over so you'd have to go around them I don't understand how you coul deny that the shortest distance between pont A and B is a straight line.

Any curvature of the line would require it to be a greater distance overall and therefore nto be the shortest distance from A to B.

I don't quite see how you could possibly argue this unless you will say that you have to sometimes go around things to get from one place to another, not through them.
Debate Round No. 1
Subutai

Con

I would like to thank BornToDebate for accepting this debate.

I. Lines and Euclidian Geometry

A line is the essential one-dimensional object. Between two points, there is a line that provides the shortest distance between these two points, known as a line segment. A line is essentially the extension of a line segment beyond the original two points. "A straight line is a line of zero curvature." In other words, a straight line contains no curves.[1]

Euclidian geometry relies on a two-dimensional flat plane. In such senarios, the shortest distance between two points is always a straight line as a flat plane also has zero curvature.

II. Non-Euclidian Geometry

However, Euclidian geometry is only one kind of geometry. There are other kinds of geometry that have other shapes as their base and have curvature. This means that the above postulate cannot hold true. For example, there is spherical geometry, and is basically the three-dimensional geometry of a sphere.

Here is a visual representation of spherical geometry:



[2]

Notice how, in spherical geometry, the shortest distance between two points is a so-called "great circle", which is "...obtained by taking a plane through the cente[r] of the sphere and seeing where is cuts the surface." These great circles, of course, have a curvature, and the sphere itself has a curvature of 1.[3]

Here is what some "great circles" look like:



[4]

These lines are not straight because they have a curvature.

In another form of non-Euclidian geometry, the same effect can be seen. Hyperbolic geometry has several definitions that have been interpreted over the years, but one constant truth is that the curvature of the surface is -1.

Here is an attempted visual representation of hyperbolc geometry:



[2]

In hyperbolic geometry, the shortest distance between two points is a hyperbola. Hyperbolas have a curvature, and again, hyperbolic geometry has a negative curvature.

Using the "saddle" representation of hyperbolic geometry, here is a Euclidian representation of it:



[5]

These lines are also not straight because they have a curvature.

Basically, there are non-Euclidian forms of geometry where the shortest distance between two points is a line with curvature, which cannot be straight since a "straight line" has no curvature.

Sources

[1]: http://www.thefreedictionary.com...
[2]: http://www.oswego.edu...
[3]: Gowers, Timothy. Mathematics, A Very Short Introduction.
[4]: http://spheresandsuch.wordpress.com...
[5]: http://www.josleys.com...;
BornToDebate

Pro

Evryting my opponent just said is only true if there is a physical sphere to block the straight line option. Otherwise you can just cut a straight line from A to B and it would be shorter than the curved one.

That is like saying that if there is a big stone in front of you you have to go around it instead of charging through it, it doens't change the fact that, from a bird's eye view, the straight line is the shortest distance.
Debate Round No. 2
Subutai

Con

My opponent doesn't understand the geometry here. It isn't as if there is a sphere within Euclidian space that must be gone thorugh, but as if the sphere represents geometry itself.

Further, my opponent isn't using true definition for a line. Here is the "natural" definition: "A line segment from x to y is the shortest path within the surface of the sphere." In other words, because three-dimensional geometry requires a different definition for a line because of the added depth component, a line is a one-dimensional object that lies on the surface of the sphere and not in it. Three-dimensional geometry is more two-dimensional as it deals with only the surface of the object and not the interior.[1][2]

Sources

[1]: Gowers, Timothy. Mathematics, A Very Short Introduction.
[2]: http://mathworld.wolfram.com...
BornToDebate

Pro

I'm not going to concede this debate just because my opponent puts a ton of pictures and geometric stuff.

I'm firmly sure that if you take any two points in the universe the shortest distance between them is a straight line. No sphere involved.

My opponent is just cheating by breaking their own rule of not lawyering (which means to use a ton of sources for no apparent reason just to win).

Honestly though, if you can't understand that a curve is always longer than a straight line if both begin and end at the same point then you are either mentally retarded (in the literal sense of the term retardation) or you are just a troll who actually does understand it.

I can also paste a ton of pics and links such as this: http://www.instant-analysis.com...

That doesn't make me a better debater; it makes me a loser who can't debate myself and has to use others' math equations to illustrate my point so that I don't, my self, come up with a half decent debate.

Frankly, this is just plain stupid and Con is using purely filthy tactics to win.
Debate Round No. 3
Subutai

Con

My opponent is using Ad Hominem to make his argument simply because he thinks that non-Euclidian forms of geometry do not exist. I assure you, they do, as can be seen in their applications. For example, spherical geometry is very useful in navigation around the globe, because, as you know, the Earth is roughly spherical. Take, for example, this informative picture:



[1]

As can be seen from the picture on the left, the distance from Philadelphia to Beijing (roughly on the same latitudinal line) can differ based on the path taken, and a shorter distance (by 3,400 km) can be obtained by making a "great circle" instead of making a genuine straight line. The picture on the right shows how this can be possible.

As for the accusation of lawyering, it doesn't mean that I used too many sources. First, I only used five. Three were citations for my pictures (no real "argumentative" value), one was just a proof that striaght lines have zero curvature, and the other was a definition of a "great circle". For the next round, one was just a definition for a line segment in spherical geometry and the other proved that spherical geometry only relies on the surface of a sphere. Of my sources of substance, they were all just there to prove my assumptions.

While neither of us is "mentally retarded", my opponent has obviously not been introduced to the intricates associated with non-Euclidian geometry. I understand that a straight line is the shortest distance between two points in Euclidan geometry.

Your one source is a proof that a straight line is the shortest distance between two points on a two-dimensional Cartesian coordinate system based off of Euclidian geometry, and therefore does not consider that that theorem is false when other geometries are considered.

I haven't stolen a single math equation. Everything in that argument I already knew, but I posted sources so as to prove that I had proof behind my assumptions. It's an ok thing to do.

In conclusion, here is a spherical line:


[2]

This is the shortest distance between two points, but has a positive curvature, and is obviously not a straight line.

Also, please remember, no arguments in this last round for you.

Sources

[1]: http://www.oswego.edu...
[2]: Gowers, Timothy. Mathematics, A Very Short Introduction.
BornToDebate

Pro

He expressed a curve as a straight line in the globe picture just whatever.

I don't even care about this debate anymore it's so damn stupid that pro side is just common sense tbph.

He lawyered so hardcore in round two that if you look at round one he violated his own rule and all 7 points should go to me hahaha.

Seirously this guy is a nerd and this debate is full of crap.
Debate Round No. 4
45 comments have been posted on this debate. Showing 1 through 10 records.
Posted by rajun 4 years ago
rajun
My god...this debate is having a lot of comments! thought I would add one.
By the way, CON has done a good job!
Posted by FrackJack 4 years ago
FrackJack
Subutai's pictures in R3 blew my mind.
Posted by Wocambs 4 years ago
Wocambs
Pro says: "if you take any two points in the universe the shortest distance between them is a straight line"

Is this correct?
Posted by Enji 4 years ago
Enji
DanT, Pro would have had to argue the opposite of that. A geodesic is the shortest distance between two points in spherical or hyperbolic space; Pro would have needed to argue that a geodesic is a straight line in curved space and the perception of a geodesic being curved is just an optical illusion.
Posted by DanT 4 years ago
DanT
sorry I meant pro

If I was PRO I would have argued that a straight line is not curved. Drawing a line on a sphere makes the line curved, and the perception of it being a straight line is just an optical illusion.

PRO could have done so much more with this debate, and it was very disappointing.
Posted by DanT 4 years ago
DanT
If I was con I would have argued that a straight line is not curved. Drawing a line on a sphere makes the line curved, and the perception of it being a straight line is just an optical illusion.

Con could have done so much more with this debate, and it was very disappointing.
Posted by wrichcirw 4 years ago
wrichcirw
btw, I am by no means an expert on this subject, but had I been PRO, I would simply have argued that CON was confusing the quality of a line with the quality of a geodesic, thereby equivocating on the standard definition of a line.

Interesting lesson on what not to do in a debate by PRO.
Posted by wrichcirw 4 years ago
wrichcirw
"Still, CON pretty much dropped the debate..."

Change to:

Still, PRO pretty much dropped the debate...
Posted by wrichcirw 4 years ago
wrichcirw
Hmm...CON is correct that PRO engaged in ad hominem, so conduct CON.

I don't buy the spherical geometry argument. CON also admits that such geometry predicates the impossibility of analyzing anything about the interior of the sphere, and so is not truly 3 dimensional. I side with PRO that such a concept equates to there being an object (the sphere) between what would otherwise be the shortest distance between two lines. Still, CON pretty much dropped the debate, and did not argue over the merits/demerits of spherical geometry, and so does not deserve arguments. Resorting to ad hominem as opposed to argumentation is almost always a sign of a poor debater.
Posted by Subutai 4 years ago
Subutai
That only applies in cases of Euclidian geometry. The definition of a line depends on the geometry involved.
7 votes have been placed for this debate. Showing 1 through 7 records.
Vote Placed by Magic8000 4 years ago
Magic8000
SubutaiBornToDebateTied
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Total points awarded:40 
Reasons for voting decision: Ad Hominems everywhere by Pro, so conduct to Con. Pro never answered many of Con's arguments. In the last round, he basically forfeits.
Vote Placed by DanT 4 years ago
DanT
SubutaiBornToDebateTied
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Total points awarded:70 
Reasons for voting decision: Pro might want to change his name. Pro put absolutely no effort into this debate, whereas Con obviously put allot of thought into his points. As the affirmative Pro had the BOP, which was obviously lacking. Pro provided no source, whereas Con had a plethora of sources. I hate when people don't put in any effort and still expect to win. Pro could have done so much more, and it is a damn shame he didn't.Conduct goes to con for Pro's attitude in the debate. Name calling is a pretty good indicator that someone lost. Spelling and Grammar goes to Con because Pro didn't punctuate his rants correctly.
Vote Placed by Juan_Pablo 4 years ago
Juan_Pablo
SubutaiBornToDebateTied
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Reasons for voting decision: This is a language issue. If you accept General Relativity to be true (which relies on non-Euclidean Geometry) then Con should win the debate. Like Pro though, I have hesitations about its soundness. Ultimately though I awarded the most points to Con because he used the most reliable sources and had better conduct!
Vote Placed by Piccini 4 years ago
Piccini
SubutaiBornToDebateTied
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Total points awarded:70 
Reasons for voting decision: Pro did not argue at all. Although it was indeed a difficult debate, Pro could have argued on the definition of "straight", but instead he refused to accept (or understand) the concept of non-euclidean geometry
Vote Placed by wrichcirw 4 years ago
wrichcirw
SubutaiBornToDebateTied
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Total points awarded:10 
Reasons for voting decision: see comments.
Vote Placed by Enji 4 years ago
Enji
SubutaiBornToDebateTied
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Total points awarded:40 
Reasons for voting decision: As Con argues, in curved space the shortest distance between two points is curved - hence the shortest distance between two points is not always straight. Arguments to Con. Pro, lacking an argument, resorted to attacks on Con. Conduct to Con.
Vote Placed by Sargon 4 years ago
Sargon
SubutaiBornToDebateTied
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Total points awarded:60 
Reasons for voting decision: RFD in comments.