01 · Objects
Vector
A vector is an arrow: direction and length. Coordinates are a description in a basis, not the arrow itself.
In English
A vector is an arrow: which way, and how long. The numbers [x, y] are how you write it in the current grid — they are a description, not the arrow itself.
- Try this
- Drag the tip. Watch [x, y] change. The arrow is the object; the numbers are the label.
- Keep this
- Vector = arrow. Coordinates = a label in a basis.
Lab · drag the arrow
- Coordinates
- [1.4, 0.8]
- Length
- 1.61
Write v = x î + y ĵ. Those two numbers are coordinates in the standard basis. Length is independent of that description — rotate the paper and the arrow is the same object.
Volume II’s Bloch vector is this arrow on a sphere. Volume III’s state vector is this arrow with 2ⁿ components. Start here and those stop being metaphors.