In my last post, Artificial Intelligence and the Shape of Reality, I jumped off the deep end and explored an idea that surprised even me as I wrote it—that the high-dimensional space in which large ...

Two vectors close vectorA vector quantity has both direction and magnitude (size). are parallel if they have the same (or opposite) directions. Their magnitude can be different. In the image to the ...

Symplectic geometry is a relatively new field with implications for much of modern mathematics. Here’s what it’s all about. In the early 1800s, William Rowan Hamilton discovered a new kind of ...