Definition of a hole - not a rude question !

[Atomic12C]

Say I have a plastic cup that I use to drink water from.
I fill it up as the hole at the top allows me to do so. So one hole in the cup?
I now cut out a new hole at the bottom and the water drains out.
So does the cup now have two holes or still one hole?

Take the same cup from above, to allow the it to drain water faster I cut more holes in to the sides near the bottom.
Does the cup now have multiple holes or still one hole?

[motco]

I might question whether an 'intact' cup has any holes in it at all. The 'hole' to which you refer as being the one you fill and drink from, I would not call a hole at all. The form is that of a complete plane of material with a depression making it concave on one face and convex on the other. Once you remove material in the plane away from its boundary you have a hole - one hole.

[thebraketester]

I supposed you turned one hole into a through hole.

That’s how it would be defined if you were talking about drilling a piece of material.

[Atomic12C]

motco said:

I might question whether an 'intact' cup has any holes in it at all. The 'hole' to which you refer as being the one you fill and drink from, I would not call a hole at all. The form is that of a complete plane of material with a depression making it concave on one face and convex on the other. Once you remove material in the plane away from its boundary you have a hole - one hole.

If not a cup then would your definition change for a 'hole' in the ground?

[motco]

Atomic12C said:

motco said:

I might question whether an 'intact' cup has any holes in it at all. The 'hole' to which you refer as being the one you fill and drink from, I would not call a hole at all. The form is that of a complete plane of material with a depression making it concave on one face and convex on the other. Once you remove material in the plane away from its boundary you have a hole - one hole.

If not a cup then would your definition change for a 'hole' in the ground?

There is a wide range of possibilities from a slight depression sufficient to contain a shallow puddle, to a deep mine with the plethora of steps between. I don't know the proper answer but I suspect it is a matter of definition of 'hole'. Does a hole have to be able to be traversed between points on the surface of a figure or prism? If so what is the term for a 'blind hole'?

[Atomic12C]

motco said:

.. but I suspect it is a matter of definition of 'hole'.

Of course.

As a "hole" is something that can take numerous different forms within numerous different mediums, there are mathematical and engineering definitions but there are then conceptual alternatives that may have no widely accepted definition - or only a definition that works under restricted situations.

[JustALooseScrew]

Reminds me of the old question 'What weighs nothing but can sink a ship?'.

[StanleyT]

Remember it is the Holy Week of Easter.

Thus, no matter how many apertures are in the plastic vessel if you use holey water it will remain half full and half empty at the same time.

[Ledaig]

From an engineering perspective, you have converted a blind hole into a through hole.

[fat80b]

JustALooseScrew said:

Reminds me of the old question 'What weighs nothing but can sink a ship?'.

or

If it takes 10 minutes for one person to dig a hole, how long does it take for two people to dig half a hole?

[Derek Smith]

It reminds me of the biggest natural hole in the UK. It would appear from the reports that it had to be dug out. Before that, it was not the biggest.

[NDA]

Atomic12C said:

Say I have a plastic cup that I use to drink water from.
I fill it up as the hole at the top allows me to do so. So one hole in the cup?
I now cut out a new hole at the bottom and the water drains out.
So does the cup now have two holes or still one hole?

Take the same cup from above, to allow the it to drain water faster I cut more holes in to the sides near the bottom.
Does the cup now have multiple holes or still one hole?

It's more to do with language.

A cup is something that is made with an opening in it to pour (typically) liquid. Same as a bucket. It's form is described by 'cup' - a coherent and understood structure without holes.

A hole describes, in the context of a cup or bucket, an additional aperture - and probably not typically an aperture that was in the design.

[lazy_b]

Atomic12C said:

Say I have a plastic cup that I use to drink water from.
I fill it up as the hole at the top allows me to do so. So one hole in the cup?
I now cut out a new hole at the bottom and the water drains out.
So does the cup now have two holes or still one hole?

A topologist would say your cup doesn't have a hole in it, until you cut one in the bottom. It reminds me of the joke about the topologist who tried dunking his coffee mug in his doughnut...

[AstonZagato]

lazy_b said:

A topologist would say your cup doesn't have a hole in it, until you cut one in the bottom. It reminds me of the joke about the topologist who tried dunking his coffee mug in his doughnut...

This.

Topology is quite interesting. Mobius strips are fascinating to children - a one sided object.

https://en.wikipedia.org/wiki/Topology

[Djtemeka]

If you fill it with beer, it is no longer a cup... but a chalice