The Nagual has the following fleeting properties:

• It cannot be reasoned about
• It can only be described by its effects
• It can be percieved
• It can be handled
• It is never an objekt on the Island of Tonal
• It is much bigger than the Tonal

Castaneda splits the Nagual into the Knowable and the Unknowable. The Unknowable is utterly beyond our capabilities as humans, while the Knowable is at least possible to know something about, and explore.

The size of Tonal and Nagual can be described by the Metaphor of the Line and the Plane. A line may be infinitely long, and thus there are no measure which can measure it. Choose any length, the width of the universe a thousand times or a billion billion billion times and it is still not even close in length of the infinite line. The infinite line is always the longest line there is.

Then look at the infinite plane. It is like a infinite sheet of infinitely thin paper, it has infinite length and infinite width. One can now see that the Plane is infinitely larger than the line! No matter how many billions of billions of billions (etc) of infinite lines we take, they would not measure a single square micrometer of the infinite plane... How can this be when they are both infinite? The answer is left as an exercise to the reader.

This is just an allegory to show how something infinite may be bigger than something else that is also infinite, the above example has otherwise little to do with reality. Castaneda says that the Nagual is bigger than the Tonal, that is, the irrational is larger than the rational, what cannot be rationally understood is more than what can be rationally understood. It is common for all people of all cultures of all times to think otherwise...