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How many holes does this shirt have?
Hint: you are probably wrong.
discussion of answer.
@freemo I saw the answer. Interesting, but not really relevant to how we view objects when interacting with them normally.
discussion of answer.
@Zest well how would you define a hole? just as an opening?
discussion of answer.
@freemo I think it depends on the type of thing. Like you implied, a pipe only has one hole, because it goes all the way through, but if the pipe splits and has 4 ends, I'd start thinking it has 4 holes, and that way of thinking would mean that a normal pipe with an unknown number of split paths could have 1 hole or 3, but never 2.
Which is exactly why I think the mathematical definition you're using is necessary. But still not really how we intuitively label holes.
discussion of answer.
@Zest a hole does indeed to bo all the way through but even in the case of the pipe thinking of it in the same way as the shirt. Take one of the two openings ans stretch it out really big until the pipe becomes a flat disc... you will have a disc with one hold in it. One of the openings is the hole, the other is the outside perimeter of the disc.
Now do the same with your 4-way pipe. Take an arbitrary openening and stretch it out and try to flatten the whole thing into a disc again. You're 4 way pipe has 3 holes.
The reason id say its easy to reason about is because flattening out any case to a disc will always reveal the answer.
that said i do agree you can make up your own "intuitive" definition of a hole that is wrong according to the technical one. But in all liklihood such a definition will be contradictory or break apart in many circumstances.
discussion of answer.
@freemo of course, that's also why I pointed out one big flaw in how I intuitively think about it with things like pipes.
There's another difference with what you'd intuitively call a hole too, for example if you dug a pit which was 6 feet deep and 2 feet in diameter almost anyone would agree that that's a hole. But in these geometric terms that wouldn't work at all.
discussion of answer.
@Zest you are absolutely correct.. .but in a sense if you stretch your imagination a bit you can see why...
The language could be seen as saying "a hole in the surface of the ground".. if you consider the surface of the earth as a 2d plane when when you dig a hole its sort of a hole in that plain.... yes its a bit of a cop out and a stretch and your right it isnt really a hole. But it makes some sort of linguistic sense I think.
