# Listen closely, people: parallel lines NEVER intersect! **URL:** \ **Category:** The BBQ Pit\ **Created:** [July 30, 2002, 4:13am UTC](https://boards.straightdope.com/t/listen-closely-people-parallel-lines-never-intersect/121484 "2002-07-30T04:13:14Z")\ **Posts on this page:** 20\ **Page:** 1
**Author:** ![ultrafilter](https://avatars.discourse-cdn.com/v4/letter/u/3d9bf3/32.png) [@ultrafilter](https://boards.straightdope.com/u/ultrafilter)\ **Post date:** [July 30, 2002, 4:13am UTC](https://boards.straightdope.com/t/listen-closely-people-parallel-lines-never-intersect/121484/1 "2002-07-30T04:13:14Z")
All right, this may be the single geekiest rant ever, but the subject in question bugs me enough that I’m gonna post it anyway. Very often, people want us to imagine a world vastly different from our own, or a new scientific theory based on a completely different set of assumptions. One of the popular methods of differentiating these from existing worlds/theories is to postulate that we’ve got something where parallel lines intersect. Well, that’s different all right. But not like they think: it’s different cause it’s impossible, and it’s impossible cause people seem to misunderstand the force of a definition. These people aren’t stupid, mind you; they just seem to be thinking sloppily at that moment. A definition is shorthand, and nothing else. Parallel lines are lines that don’t intersect. Any time you see “Line _l_ is parallel to line _m_,” you may replace that with “Line _l_ does not intersect line _m_,” which you may in turn replace with “There is no point P such that line _l_ passes through point P and line _m_ passes through point P.” See why lines _l_ and _m_ can’t intersect if they are parallel? Isn’t it simple? So let’s hope this has been put to rest. The next time you want a weird world, assume that there are no infinite sets, or that there is some set whose powerset doesn’t exist. If you want a bizarre scientific theory, imagine that **F** = m **a** [sup]2[/sup], or that gravity is inversely proportional to the cube of the distance between two objects. But for the sake of Pete, lay off the parallel lines! ---
**Author:** ![Duck\_Duck\_Goose](https://avatars.discourse-cdn.com/v4/letter/d/50afbb/32.png) [@Duck\_Duck\_Goose](https://boards.straightdope.com/u/Duck_Duck_Goose)\ **Post date:** [July 30, 2002, 4:23am UTC](https://boards.straightdope.com/t/listen-closely-people-parallel-lines-never-intersect/121484/2 "2002-07-30T04:23:16Z")
Okay, now that you got that off your chest, can this be a thread for “weird world” requests? I mean, as long as nobody wants a weird world in which parallel lines intersect? I’d like a weird world in which there’s no such thing as “algebra”. Is that too weird? ---
**Author:** ![Giraffe](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/giraffe/32/129_2.png) [@Giraffe](https://boards.straightdope.com/u/Giraffe)\ **Post date:** [July 30, 2002, 4:26am UTC](https://boards.straightdope.com/t/listen-closely-people-parallel-lines-never-intersect/121484/3 "2002-07-30T04:26:15Z")
My sister’s boyfriend once saw a guy who could make parallel lines intersect. He said it was really trippy. ---
**Author:** ![Squish](https://avatars.discourse-cdn.com/v4/letter/s/8797f3/32.png) [@Squish](https://boards.straightdope.com/u/Squish)\ **Post date:** [July 30, 2002, 4:26am UTC](https://boards.straightdope.com/t/listen-closely-people-parallel-lines-never-intersect/121484/4 "2002-07-30T04:26:18Z")
They can if you’ve taken enough LSD. ---
**Author:** ![Speleophile](https://avatars.discourse-cdn.com/v4/letter/s/898d66/32.png) [@Speleophile](https://boards.straightdope.com/u/Speleophile)\ **Post date:** [July 30, 2002, 4:29am UTC](https://boards.straightdope.com/t/listen-closely-people-parallel-lines-never-intersect/121484/5 "2002-07-30T04:29:57Z")
Well, that’s the very definition of parallel lines - two line (typically by definition coplanar) that have no point of intersection. No mathmatician will suggest that parallel lines ever do intersect. The real fun comes not from contradicting your definition, but from asking a simple question. Given a point not on a line, how many line through the point, and lying the plane determined by the point and the original line, are parallel to the given line? Euclid’s 5th postulate says exactly one, but perfectly consistent geometries follow from answering zero or infinitely many. In non-of these systems do parallel lines intersect. Indeed if the answer is zero, then in that geometry parallel lines simply don’t exist. (I’ve never heard of a geometry based on a fixed quantity greater than one, but I suppose that would lead to an equally self-consistent set of theorems as well). ---
**Author:** ![NightRabbit](https://avatars.discourse-cdn.com/v4/letter/n/bbce88/32.png) [@NightRabbit](https://boards.straightdope.com/u/NightRabbit)\ **Post date:** [July 30, 2002, 4:30am UTC](https://boards.straightdope.com/t/listen-closely-people-parallel-lines-never-intersect/121484/6 "2002-07-30T04:30:34Z")
“Heh yeah baby, let’s go make some of our parallel lines intersect, catch my drift?” Worst-pickupline-ever 😃 ---
**Author:** ![Gozu\_Tashoya](https://avatars.discourse-cdn.com/v4/letter/g/7993a0/32.png) [@Gozu\_Tashoya](https://boards.straightdope.com/u/Gozu_Tashoya)\ **Post date:** [July 30, 2002, 4:31am UTC](https://boards.straightdope.com/t/listen-closely-people-parallel-lines-never-intersect/121484/7 "2002-07-30T04:31:22Z")
Wow, now that’s one heck of a simulpost. ---
**Author:** ![Gozu\_Tashoya](https://avatars.discourse-cdn.com/v4/letter/g/7993a0/32.png) [@Gozu\_Tashoya](https://boards.straightdope.com/u/Gozu_Tashoya)\ **Post date:** [July 30, 2002, 4:32am UTC](https://boards.straightdope.com/t/listen-closely-people-parallel-lines-never-intersect/121484/8 "2002-07-30T04:32:26Z")
Referring to Giraffe and Squish, of course. (I swear the two intervening posts weren’t there when I posted…) ---
**Author:** ![Captain\_Amazing](https://avatars.discourse-cdn.com/v4/letter/c/6de8d8/32.png) [@Captain\_Amazing](https://boards.straightdope.com/u/Captain_Amazing)\ **Post date:** [July 30, 2002, 4:40am UTC](https://boards.straightdope.com/t/listen-closely-people-parallel-lines-never-intersect/121484/9 "2002-07-30T04:40:23Z")
They can if you define a non-Euclidian geometry where parallel lines intersect. Lets say you and I both start out on the equator, you’re on the prime meridian, and I’m at 30 degrees west, and we both decide we’re going to walk north. We’re walking parallel to each other, but eventually we’re going to meet. They don’t meat in Euclidian planar geometry, though. ---
**Author:** ![Miller](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/miller/32/481_2.png) [@Miller](https://boards.straightdope.com/u/Miller)\ **Post date:** [July 30, 2002, 4:41am UTC](https://boards.straightdope.com/t/listen-closely-people-parallel-lines-never-intersect/121484/10 "2002-07-30T04:41:29Z")
What, exactly, goes on in your life that this is common enough for you to need to rant about it? Are you president of the Edwin Abbott fan club or something? ---
**Author:** ![The\_Flying\_Dutchman](https://avatars.discourse-cdn.com/v4/letter/t/9fc348/32.png) [@The\_Flying\_Dutchman](https://boards.straightdope.com/u/The_Flying_Dutchman)\ **Post date:** [July 30, 2002, 5:54am UTC](https://boards.straightdope.com/t/listen-closely-people-parallel-lines-never-intersect/121484/11 "2002-07-30T05:54:23Z")
Listen closely **ultrafilter** Of course parallel lines can intersect, but it takes at least 4 lines. That is 2 parallel lines can intersect with two other parallel lines provided the two _sets_ of parallel lines are not parallel. ---
**Author:** ![John\_Kentzel-Griffin](https://avatars.discourse-cdn.com/v4/letter/j/ccd318/32.png) [@John\_Kentzel-Griffin](https://boards.straightdope.com/u/John_Kentzel-Griffin)\ **Post date:** [July 30, 2002, 6:07am UTC](https://boards.straightdope.com/t/listen-closely-people-parallel-lines-never-intersect/121484/12 "2002-07-30T06:07:45Z")
> [@](#): > > \*Originally posted by \*\*\*Captain Amazing \*\* > > They can if you define a non-Euclidian geometry where parallel lines intersect. No. They can’t. Unless you change the definition of parallel. Parallel lines do _not_ intersect. Parallel lines do not exist in positively curved space. **ultrafilter** is correct. ---
**Author:** ![kniz](https://avatars.discourse-cdn.com/v4/letter/k/c37758/32.png) [@kniz](https://boards.straightdope.com/u/kniz)\ **Post date:** [July 30, 2002, 6:14am UTC](https://boards.straightdope.com/t/listen-closely-people-parallel-lines-never-intersect/121484/13 "2002-07-30T06:14:18Z")
> [@](#): > > _Richard Barrans, Jr - PhD_ > Well, the whole difference between Euclidean and other geometries is their > treatment of parallel lines. In Euclidean (plane) geometry, parallel lines > never meet, and they are always separated by the same distance. In > Riemannian (elliptical) geometry, there are no parallel lines, as any two > straight lines will always meet somewhere. This is similar to what happens > to longitude lines on the earth’s surface. The longitude lines on the > earth are not parallel; they are sections describing the intersection of > the earth’s surface with planes that all intersect at the earth’s axis. In > Lobachevskyan (hyperbolic) geometry, non-intersecting straight lines can > exist, and they will not always be the same distance from each other. > There will be some points that are closest to each other, and the lines > will ever diverge away from those points. ---
**Author:** ![SPOOFE](https://avatars.discourse-cdn.com/v4/letter/s/c5a1d2/32.png) [@SPOOFE](https://boards.straightdope.com/u/SPOOFE)\ **Post date:** [July 30, 2002, 6:29am UTC](https://boards.straightdope.com/t/listen-closely-people-parallel-lines-never-intersect/121484/14 "2002-07-30T06:29:00Z")
> [@](#): > > parallel lines NEVER intersect! Unless you’re in an episode of Star Trek. Cracks in event horizons, anyone? ---
**Author:** ![Squish](https://avatars.discourse-cdn.com/v4/letter/s/8797f3/32.png) [@Squish](https://boards.straightdope.com/u/Squish)\ **Post date:** [July 30, 2002, 8:13am UTC](https://boards.straightdope.com/t/listen-closely-people-parallel-lines-never-intersect/121484/15 "2002-07-30T08:13:26Z")
> [@](#): > > \*Originally posted by KKBattousai \* > \*\*Wow, now that’s one heck of a simulpost. \*\* Uh…altered minds think alike, I guess? 😉 ---
**Author:** ![Liberal](https://avatars.discourse-cdn.com/v4/letter/l/848f3c/32.png) [@Liberal](https://boards.straightdope.com/u/Liberal)\ **Post date:** [July 30, 2002, 9:26am UTC](https://boards.straightdope.com/t/listen-closely-people-parallel-lines-never-intersect/121484/16 "2002-07-30T09:26:03Z")
> [@](#): > > _Nicolai Lobachevsky, founder of non-Euclidean geometry in which Euclid’s Fifth Postulate does not hold_ > “Parallel lines meet each other at a point of infinity” Riemann geometry is not the only non-Euclidean geometry. ---
**Author:** ![jjimm](https://avatars.discourse-cdn.com/v4/letter/j/ba8739/32.png) [@jjimm](https://boards.straightdope.com/u/jjimm)\ **Post date:** [July 30, 2002, 9:35am UTC](https://boards.straightdope.com/t/listen-closely-people-parallel-lines-never-intersect/121484/17 "2002-07-30T09:35:31Z")
How about a universe where the _logic_ of the definition of ‘parallel’ is incorrect, not necessarily the physics? In that respect the statement “parallel lines intersect” is not incorrect, it’s simply beyond our comprehension. ---
**Author:** ![SPOOFE](https://avatars.discourse-cdn.com/v4/letter/s/c5a1d2/32.png) [@SPOOFE](https://boards.straightdope.com/u/SPOOFE)\ **Post date:** [July 30, 2002, 9:38am UTC](https://boards.straightdope.com/t/listen-closely-people-parallel-lines-never-intersect/121484/18 "2002-07-30T09:38:42Z")
But, jjimm, using that line of thinking, we’re really left with a completely undefineable universe. “It’s not incorrect to say red is blue, it’s just beyond our comprehension.” ---
**Author:** ![jjimm](https://avatars.discourse-cdn.com/v4/letter/j/ba8739/32.png) [@jjimm](https://boards.straightdope.com/u/jjimm)\ **Post date:** [July 30, 2002, 9:42am UTC](https://boards.straightdope.com/t/listen-closely-people-parallel-lines-never-intersect/121484/19 "2002-07-30T09:42:51Z")
Precisely. ---
**Author:** ![sailor](https://avatars.discourse-cdn.com/v4/letter/s/a587f6/32.png) [@sailor](https://boards.straightdope.com/u/sailor)\ **Post date:** [July 30, 2002, 9:47am UTC](https://boards.straightdope.com/t/listen-closely-people-parallel-lines-never-intersect/121484/20 "2002-07-30T09:47:38Z")
How do you know they don’t intersect? Did anyone go all the way to the end? How do you know they don’t intersect when you are not looking? How do you know scientist cannot invent a way to make them intersect? Just because it has not been done in the past does not mean it cannot be done in the future. Remember Galileo. There are many questions which have not been answered yet. [Next page](https://boards.straightdope.com/t/listen-closely-people-parallel-lines-never-intersect/121484.md?page=2)