Directions you cannot picture

And here the picture runs out. You can picture the box. You cannot picture the fourth direction, because there isn't one to picture. Nothing in the room you are sitting in points that way. Three is where your eyes stop, and meaning has already asked for more.

But nothing breaks at four. The picture stops working, and the arithmetic carries on exactly as before. Two numbers per word, then three, then four, then three hundred, and every step is the same step. A word's position is just its list of numbers, and "close" just means the lists are similar. None of that needs a direction you can point at.

Each number in that list is called a . It is a heavier word than the idea deserves. A dimension is one more direction things are allowed to differ in, one more entry in the list, one more question the numbers get to answer about a word.

So the list can be as long as it needs to be. The remaining question is not how to picture it. It is what the numbers should say about each word, and how anyone could choose them.

>did you know?

# did you know?

:close

People who work with embeddings do look at them, using a tool like the TensorFlow Embedding Projector: a cloud of real words you can spin and zoom, where clicking one lights up its nearest neighbours.

It is a shadow, not the thing itself. Squashing three hundred directions down to three has to lose something, so words can land next to each other in the picture without being neighbours in the real space.