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How Many Holes Are There in a Straw?
- Thread starter SalixIncendium
- Start date
In a 1 dimensional universe the straw and hole become an infinitely small point.
If it had an infinite diameter wouldn't such be a two-dimensional universe?
If it had an infinite diameter everything else in the 2D universe would be in the hole.
No hole - given no length dimension?
Or 1 dimension.
RestlessSoul
Well-Known Member
How many holes here?
The straw becomes very, very dysfunctional indeed?What happens if we have an infinitely large diameter straw with zero length?
I can't see a diameter existing in one dimension.
How many holes on this straw?
exchemist
Veteran Member
That's an odd definition. I should have thought the essence of a hole would be a gap in a surface.
No - or, at least, not for any reason due to the straw.
Infinite just means "with no discernible limit". It does not mean "all-encompassing". An infinite diameter does not make such a ring a container for the whole universe.
Koch's snowflake presents a similar scenario. It has a very finite surface and exists in two dimensions with an infinitely high perimeter.
Koch snowflake - Wikipedia
One can go through the gap and down the hole
Pretty good question. I'm not sufficiently versed in topology to say with certainty, but it feels like it should be one. But it might be three.
Well I was suggesting compacting the length down as the diameter increased, so we started off with three dimensions.No - or, at least, not for any reason due to the straw.
Infinite just means "with no discernible limit". It does not mean "all-encompassing". An infinite diameter does not make such a ring a container for the whole universe.
Koch's snowflake presents a similar scenario. It has a very finite surface and exists in two dimensions with an infinitely high perimeter.
Koch snowflake - Wikipedia
en.wikipedia.org
Under the danger of being perceived as pedant, I want to remind you of an actually important matter.
Dimensions are a mathematical abstraction. Counter-intuitive as it may feel, they hold no power over the reality of observable facts, nor vice-versa.
We may build mathematical models for approaching or even fully reproducing what you describe, but whether that would resemble anything that can actually happen in the real world is a separate matter that may or may not be solvable.
RestlessSoul
Well-Known Member
And there I was ready to build an example.