The Truth About a Ball of Yarn

Quick Question. How many dimensions does a ball of yarn have? If you answered 3, your wrong! Or right... depending on the context.

A ball of yarn at an arms length has a visible height, width, and depth. However at 100 yards away, it appears at a dot (0 dimensions). 100 miles away you can't even see it so the question of it's dimensionality is moot.

Let's zoom in the other direction. As you get the ball of yarn scrunched into your face, it a series of 3 dimensionally arranged strings that locally appear as straight 1-dimensional lines. Of course as you zoom in further, the lines get thicker and thus appear 3 dimensional again. That is until you zoom in far enough to see individual threads and then it collapses down to a series of 1 dimension lines (locally) albeit they twist and turn 3 dimesionally.

Then you get to the atoms and, if you believe an electron microscope, we 'perceive' 3dimensions again as an effect of shooting electrons and watching their deflection or scattering as they bounce off the individual atoms making up the ball of yarn. So that atom itself is again, 3 dimesional. Of course if you zoom in deeper, quantum physics will say the atoms are not actual physical objects but merely waves of probability. So it's 3 dimensional if you look at it classically or physically and a 3D distributions of probability if you look at it with a more refined model.

Zoom in further and you get into sub particles and virtual parties where the parts and sub parts that make up an atom itself are winking in and out of existence countless times per second. But have no fear, the string theorists will tell you that there really is 11 dimensions going on, but we simply perceive 3 of them.

Summarizing:

Starting 100 yards away we have 0 dimensions, then 3 dimensions, then a collection of 3 or 1 dimensional objects, then 3 dimensions again, then 1 dimension again made of a series of 3 dimensional objects, which turn out to be 3 dimensional probabilities which turn out to be 11 dimensional mathematical constructs.

So how many dimensions does a ball of yarn have? It depends on the context. But if you're on Jeopardy or at a bar playing trivia night, go with 3.