[seanhunter]

Totally agree. I really enjoyed the article, and the illustrations are really cool but scale is just something I don’t even consider. Even the very first question baffled me, when it said “Picture a torus. Is it big or small?”

I answered an unambiguous “yes”.

Also, we haven’t defined measure yet here have we? What does it even mean for something to have scale without measure?

[Telemakhos]

This is one of those places where Plato really is worth reading. Plato has levels of reality that correspond to numbers. The first level, forms (also called "the monad"), is what the statement "Picture a torus" engages: contemplate an ideal torus. That torus won't have a particular color or texture or any accidental quality, just the essence of a torus, which is its shape (because torus is a shape). Size is one of those accidental qualities, and those live in the second level, which Plato calls "the bigger and smaller"—exactly what the question asks you to imagine—or "the dyad."

So, the instructions for Plato boil down to an absurdity: "contemplate the monad; what dyad do you see?" The two sentences should have nothing to do with each other in Platonic terms.

[mkl]

Right, I immediately saw a torus - it was light blue (that's trivial to change, but I can't have no colour if it's visual) - but it could have been the size of a bacterium or the size of a galaxy. Without any context or application, the size is undefined.

[red75prime]

When you've mentioned that, I've noticed that by default I imagine just a shape devoid of color and texture. But I can imagine a donut, or a blue torus, but I need to explicitly think the word "blue".

[Pay08]

> Also, we haven’t defined measure yet here have we?

Kilograms, obviously.