# Spatial Question
**URL:** https://boards.straightdope.com/t/spatial-question/342686
**Category:** Factual Questions
**Created:** [February 2, 2006, 5:10pm UTC](https://boards.straightdope.com/t/spatial-question/342686 "2006-02-02T17:10:05Z")
**Posts on this page:** 8
**Page:** 1
### Author:  [@agander](https://boards.straightdope.com/u/agander)
#### Post date: [February 2, 2006, 5:10pm UTC](https://boards.straightdope.com/t/spatial-question/342686/1 "2006-02-02T17:10:05Z")
My question began when we were graphing parabolas (or some such form) in my high school trig class. The teacher would constantly insist that while the line would get closer and closer to the x or y axis, it would never actually touch it. While I didn’t like the sound of that, I could see why it was true.
I then took that notion and started to wonder, using that same kind of logic, if it would be possible for one object to ever touch another object. On the surface that seems totally absurd, that one object could never touch another object, but please listen to me. First, what would be the distance between two objects if they were touching? I would say the distance would be zero. Now imagine that we had some sort of highly accurate measuring device that measured distances between two objects and could go out to an infinite number of decimal places. Theoretically, when that measuring device displayed 0, the two objects would be touching. Now imagine the two objects are sitting one inch apart. The device reads 1. Then they get a little closer and the device now reads .5. They again get closer and it reads .1. Now we are at one tenth of an inch apart. Say they get a little closer, the device, since it is the most accurate measuring device ever created, does not go to 0, but then goes to .09. It continues to get smaller as the two objects get closer together until it is now down to .01. Again, we have an infinite number of decimal places, so after .01 it goes to .009. This continues on an on, but never reaches 0, or when the two objects would actually touch.
This is interesting, but we can obviously see that objects touch. We can also see that two objects can pass one another, which would be impossible if you could never even get to another object. My question would be, what is going on here? Have I stumpled upon the demise of math? Am I missing something obvious? Should I just accept that things can get pretty close and then just say that they are touching?
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### Author:  [@RandomLetters](https://boards.straightdope.com/u/RandomLetters)
#### Post date: [February 2, 2006, 5:18pm UTC](https://boards.straightdope.com/t/spatial-question/342686/2 "2006-02-02T17:18:01Z")
Seems like you came up with a varient of [Zeno’s paradox.](http://en.wikipedia.org/wiki/Zeno's_paradoxes)
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### Author:  [@ultrafilter](https://boards.straightdope.com/u/ultrafilter)
#### Post date: [February 2, 2006, 5:32pm UTC](https://boards.straightdope.com/t/spatial-question/342686/3 "2006-02-02T17:32:47Z")
This is the difference between the abstract and the physical. Note that on a graph, two curves may be asymptotic, or they may actually intersect (or do something else). In the real world, there are no asymptotes.
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### Author:  [@panache45](https://boards.straightdope.com/u/panache45)
#### Post date: [February 2, 2006, 5:38pm UTC](https://boards.straightdope.com/t/spatial-question/342686/4 "2006-02-02T17:38:18Z")
> [@agander](#):
>
> . . . if it would be possible for one object to ever touch another object.
Or even **itself** , for that matter. There’s space separating molecules, atoms, subatomic particles, etc.
This is similar to the 0.999…=1 question, which we’ve already covered in a few threads.
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### Author:  [@Thudlow\_Boink](https://boards.straightdope.com/u/Thudlow_Boink)
#### Post date: [February 2, 2006, 5:38pm UTC](https://boards.straightdope.com/t/spatial-question/342686/5 "2006-02-02T17:38:35Z")
You guys beat me to it.
Yes, read up on Zeno’s Paradoxes. And yes, mathematics and the Real World can only approximate each other. In math, distances can get as small as you want, but in the real world, when you get down to the molecular or sub-molecular level, things aren’t as smooth and continuous as in the theoretical x-y plane.
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### Author:  [@agander](https://boards.straightdope.com/u/agander)
#### Post date: [February 2, 2006, 5:50pm UTC](https://boards.straightdope.com/t/spatial-question/342686/6 "2006-02-02T17:50:06Z")
Sweet. To think, this has been in my mind for 15 years now, and all of the sudden on a slow day at work I decide to put it on here and I have an answer in 15 minutes. Thanks a lot.
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### Author:  [@Mathochist](https://boards.straightdope.com/u/Mathochist)
#### Post date: [February 3, 2006, 1:57pm UTC](https://boards.straightdope.com/t/spatial-question/342686/7 "2006-02-03T13:57:01Z")
> [@panache45](#):
>
> Or even **itself** , for that matter. There’s space separating molecules, atoms, subatomic particles, etc.
>
> This is similar to the 0.999…=1 question, which we’ve already covered in a few threads.
DON’T SAY THAT…
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### Author:  [@Strinka](https://boards.straightdope.com/u/Strinka)
#### Post date: [February 3, 2006, 2:05pm UTC](https://boards.straightdope.com/t/spatial-question/342686/8 "2006-02-03T14:05:28Z")
You’re talking about hyperbolas in the OP, not parabolas.