# How many probable universes are there

**URL:** <https://boards.straightdope.com/t/how-many-probable-universes-are-there/290463>\
**Category:** Factual Questions\
**Created:** [February 17, 2005, 2:03am UTC](https://boards.straightdope.com/t/how-many-probable-universes-are-there/290463 "2005-02-17T02:03:26Z")\
**Posts on this page:** 8\
**Page:** 2

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**Author:** ![robby](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/robby/32/11048_2.png) [@robby](https://boards.straightdope.com/u/robby)\
**Post date:** [February 18, 2005, 8:38pm UTC](https://boards.straightdope.com/t/how-many-probable-universes-are-there/290463/21 "2005-02-18T20:38:42Z")

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As I understand it, the mathematical answer in modern physics is almost always zero, one, or infinity, regardless of the question being asked.

So as to the number of universes, take your pick.

If I had to guess, I’d go with zero. You’re all a figment of my imagination! 😃

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**Author:** ![Mathochist](https://avatars.discourse-cdn.com/v4/letter/m/c89c15/32.png) [@Mathochist](https://boards.straightdope.com/u/Mathochist)\
**Post date:** [February 19, 2005, 12:36am UTC](https://boards.straightdope.com/t/how-many-probable-universes-are-there/290463/22 "2005-02-19T00:36:38Z")

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> [@Chronos](#):
>
> Can’t you treat a point as a degenerate case of a circle, with radius 0?

That’s definitely a singularity. A regular fibration is pretty specific about what’s allowed as a fiber.

Really, what we’ve got here is an orbifold, as I’m sure **Orbifold** can tell you.

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**Author:** ![RancidYakButterTeaParty](https://avatars.discourse-cdn.com/v4/letter/r/53a042/32.png) [@RancidYakButterTeaParty](https://boards.straightdope.com/u/RancidYakButterTeaParty)\
**Post date:** [February 19, 2005, 1:32am UTC](https://boards.straightdope.com/t/how-many-probable-universes-are-there/290463/23 "2005-02-19T01:32:32Z")

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> [@SentientMeat](#):
>
> How many circles do you have to stack together to make a sphere?

Small town idiot checking in here. My limited spacial intelligence tells me that a circle is defined as being 2-d, meaning it would have a height of “zero”. How then are we stacking these heightless shapes?

Remember, I’m none too smart, so take it easy on the vocab. if you don’t mind.

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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:** [February 19, 2005, 1:35am UTC](https://boards.straightdope.com/t/how-many-probable-universes-are-there/290463/24 "2005-02-19T01:35:33Z")

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> [@RancidYakButterTeaParty](#):
>
> Small town idiot checking in here. My limited spacial intelligence tells me that a circle is defined as being 2-d, meaning it would have a height of “zero”. How then are we stacking these heightless shapes?

It’s the same as integration, really. Remember, the integral of a function over a single point is zero, but the integral over an interval may be non-zero.

The trick is that you’re dealing with measures here, and measures are only guaranteed to be countably additive.

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**Author:** ![RancidYakButterTeaParty](https://avatars.discourse-cdn.com/v4/letter/r/53a042/32.png) [@RancidYakButterTeaParty](https://boards.straightdope.com/u/RancidYakButterTeaParty)\
**Post date:** [February 19, 2005, 1:38am UTC](https://boards.straightdope.com/t/how-many-probable-universes-are-there/290463/25 "2005-02-19T01:38:44Z")

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Do you mind providing an example?

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**Author:** ![Mathochist](https://avatars.discourse-cdn.com/v4/letter/m/c89c15/32.png) [@Mathochist](https://boards.straightdope.com/u/Mathochist)\
**Post date:** [February 19, 2005, 1:56am UTC](https://boards.straightdope.com/t/how-many-probable-universes-are-there/290463/26 "2005-02-19T01:56:33Z")

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> [@RancidYakButterTeaParty](#):
>
> Small town idiot checking in here. My limited spacial intelligence tells me that a circle is defined as being 2-d, meaning it would have a height of “zero”. How then are we stacking these heightless shapes?
> 
> Remember, I’m none too smart, so take it easy on the vocab. if you don’t mind.

Firstly, a circle is _one_-dimensional. A _disk_ is 2-d.

Now to your question, consider a unit square: the points in the plane with x- and y-coordinates both between 0 and 1. This is the union of a bunch of line segments. For every number x[sub]0[/sub] between 0 and 1, the segment l[sub]x[sub]0[/sub][/sub] = {(x[sub]0[/sub],y)| 0\<=y\<=1} is in the square, and the collection of all these (infinitely many) line segments makes up the square.

Now, consider the unit sphere. The naive way of chopping it up is (after removing the north and south poles) to break it into circles, each of which consists of the points at the same latitude. The problem is that those points at the poles aren’t circles, and they’re left out. The question is whether there’s a way of breaking the sphere into circles which _doesn’t_ leave out any points, which it turns out can’t be done.

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**Author:** ![RancidYakButterTeaParty](https://avatars.discourse-cdn.com/v4/letter/r/53a042/32.png) [@RancidYakButterTeaParty](https://boards.straightdope.com/u/RancidYakButterTeaParty)\
**Post date:** [February 19, 2005, 2:25am UTC](https://boards.straightdope.com/t/how-many-probable-universes-are-there/290463/27 "2005-02-19T02:25:52Z")

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> [@Mathochist](#):
>
> Firstly, a circle is _one_-dimensional. A _disk_ is 2-d.
> 
> Now to your question, consider a unit square: the points in the plane with x- and y-coordinates both between 0 and 1. This is the union of a bunch of line segments. For every number x[sub]0[/sub] between 0 and 1, the segment l[sub]x[sub]0[/sub][/sub] = {(x[sub]0[/sub],y)| 0\<=y\<=1} is in the square, and the collection of all these (infinitely many) line segments makes up the square.
> 
> Now, consider the unit sphere. The naive way of chopping it up is (after removing the north and south poles) to break it into circles, each of which consists of the points at the same latitude. The problem is that those points at the poles aren’t circles, and they’re left out. The question is whether there’s a way of breaking the sphere into circles which _doesn’t_ leave out any points, which it turns out can’t be done.

Thanks for the chopping up the sphere talk, that makes plenty of sense.

To continue the hijack…

Have patience with me on this circle thing, but I really do want to make sure I learn the correct definition.

About the 1-d circle, am I wrong in stating that all polygons are 2-d? What then causes the circle to be considered 1-d? The only difference I can see is that polygons must be made up of line segments.

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<div class="post-metadata">

**Author:** ![Mathochist](https://avatars.discourse-cdn.com/v4/letter/m/c89c15/32.png) [@Mathochist](https://boards.straightdope.com/u/Mathochist)\
**Post date:** [February 19, 2005, 2:30am UTC](https://boards.straightdope.com/t/how-many-probable-universes-are-there/290463/28 "2005-02-19T02:30:19Z")

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> [@RancidYakButterTeaParty](#):
>
> About the 1-d circle, am I wrong in stating that all polygons are 2-d? What then causes the circle to be considered 1-d? The only difference I can see is that polygons must be made up of line segments.

You’re thinking of the interior of a circle: a disk. The circle is properly the edge of the disk.

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