3 ms·
> any description purely in terms of pairwise relationships would miss the fact that the three rings are connected. Here is one: A is connected to B B is con
by a333999 2y ago
> any description purely in terms of pairwise relationships would miss the fact that the three rings are connected.
Here is one:
A is connected to B
B is connected to C
C is connected to A
This is a description in terms of pairs, and from it is trivial to deduce how the rings are connected.
- defrost 2y agoBut they're not pairwise connected. In the text: If you only consider two of the rings and ignore the third, then any pair can be smoothly separated. and from looking at the diagram. Carefully looking.
- abelaer 2y agoThe pairwise description you list correspond to a different link, namely, one where each pair is actually connected. For the shown rings, the 'correct' description would be: A is not connected to B B is not connected to C C is not connected to A A, B, and C are connected This seems paradoxical, but the paradox is resolved by the 'higher-order' linkage.