Somewhat counterintuitively, all knots are homeomorphic to each other.

Only because "homeomorphic" is a highly technical term that most people don't even know the definition of, let alone have an intuition for, and because "knot" in math is a closed loop, unlikely "knot" in common language.

Once you know the definitions and have learned to tie your shoes, it's quite intuitive. Even a small child can easily constructively prove that knots are homeomorphic.

	▲	bmitc 7 months ago \| parent [-]
		Homeomorphic is also interesting because it's a very fancy sounding word for a concept that has very few requirements to be met. It's usually a basic requirement for concepts in topology, but it does very little to distinguish topological spaces. It's essentially a highfalutin word for "these things are basically the same thing in a very basic way".

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xanderlewis 7 months ago | parent | prev [-]

If you regard two spaces being homeomorphic as meaning — roughly — that if you lived in either space you’d not notice a difference, it makes sense. To a one-dimensional being (that has no concept of curvature or length, since we’re talking about topology here), they’d all feel like living in a circle.