A Tale of Affine Scaling

David Kanenwisher • May 15, 2023

The Geometer stands with a vast space before them. They needed to both make objects larger and smaller at the point just in front of them. Each time they scaled the space the objects either move toward the origin or push away from the origin.

They rested their head on their hand and contemplated. If the objects wanted to scale in relation to the origin, was it possible to move the origin?! The thought seemed absurd. If the origin moved everything would move away from them. Could it be possible to move it right back though? If you did it would be as if everything was where it had been. Then if you changed the size it would be as if it had been but bigger or smaller! Could this work!?

The Geometer used their great power to move the origin to the place where they stand. Then with a great stretch of their hands the objects grower larger. Then again they applied their great power to move the origin to where it had been. They had done it the objects were larger and exactly where they had been.