A little illustration showing my take on einstein's quote. What we know we dont know is simply a small, ever growing line between what we know and what we don't know we know...,

“As our circle of knowledge expands, so does the circumference of darkness surrounding it.” -- Albert Einstein

#einstein #quote #science #knowledge #philosophy

@freemo this strikes me as a peculiar analogy. It is mathematically flawed in two respects For one, Mr. Einstein clearly confused a geometric circle, which has measure zero in the plane, with an open ball. Secondly, the area outside of the ball, the set complement, can never increase as long as the radius increases monotonically.

@hector That seems to misrepresent what he said.. he never said the area outside of the circle or sphere but rather its circumference. So the area outside the circle is not what he referenced.

My own illustration takes it further, the area outside the circle will decrease as the circle grows (assuming it isnt infinite, and it might be).

@freemo a circle is ONLY the points on the circumference, which are all equidistant from the center point. The circle and the circumference are one and the same.

@hector sort of, but not really... regardless this isnt in contradiction with what einstein said either way.

First off circumference is not the same as the circle.

A circle is, as you said, a set of points which lie equal distance from a central point, yes. A circumference however is something very different. It is not a shape or a set of points, it is a distance, a number. A circle is **not** its a circumference, the circumference is simple one, among many, properties of a circle.

Saying a circle is it's circumference is like say a line is it's length, it is not.

@freemo I know that the term "circumference" usually refers to a length measure, of course. Yet that does not fit with the wording of the quotation. It describes the circumference as "surrounding" the circle, which, as we have established, does not fit either a meaning of length or a meaning of a set of points for circumference.

@hector Technically it fits both. The enclosing boundary of a circle would be the set of points themselves. This is called an "Edge Boundary" in technical language (rather than circumference). The edge boundary of a circle is the circle itself, though due to this redundancy no one would feel the need to use such language as it offers no new information.