# Listen closely, people: parallel lines NEVER intersect!

**URL:** https://boards.straightdope.com/t/listen-closely-people-parallel-lines-never-intersect/121484
**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:** 1
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### 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")

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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!

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