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Comment by CogitoCogito | Hacker News Reader

What about a permeable membrane? I.e. an organism absorbing nutrients through a wall that still maintains structure?

The whole concept of a permeable membrane, i.e. essentially stuff that has holes but still is "one piece" (something like a sieve or strainer or colander or net or anyhing of the kind), is something that IMHO requires 3+ dimensions. In two dimensions if a membrane has two or more holes then it's not a single membrane anymore.

> The whole concept of a permeable membrane, i.e. essentially stuff that has holes but still is "one piece" (something like a sieve or strainer or colander or net or anyhing of the kind), is something that IMHO requires 3+ dimensions. In two dimensions if a membrane has two or more holes then it's not a single membrane anymore.

By what reasoning would it not be a single membrane in two dimensions, but it would be in three dimensions? As far as I can tell your only support/reasoning is found when you write "IMHO"...

In 3 dimensions, the sieve/strainer/colander is an object that's connected with itself despite having holes. There's material that goes around the holes.

In 2 dimensions, the membrane is essentially a line (or a linear sequence of objects) - if that line is interrupted in one space to let stuff through, then it's not connected anymore, it's two separate lines with nothing linking them, it's broken with no possibility to connect "around the hole" because any connection around the hole requires the third dimension, and any connection through the hole closes that hole.

Thanks for the clarification that makes sense.

It actually doesn't make sense. A circle with a 1D point missing from its edge is the same as a sphere with a 2D hole in it. Both have material connected "around" it in another dimension. For a sphere the connection wraps around the hole and for a circle the connection wraps around the point (comprising the entirety of the circle's edge).

This fails with more than one hole (as I said in the inital comment, two or more). A circle with two 1D points missing breaks apart, a sphere can have an arbitrary number of 2d holes and still be fully connected.

Yes! Like this: https://youtu.be/gaFKqOBTj9w

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