We are leaving the Bay of Rainbows. behind us the "Golden Handle" that perfect polynomial curve is fading.
We are heading South-West, down into the largest basin on the moon: Oceanus Procellarum, The Ocean of Storms.
Why? Because we have a problem.
The smooth curves of Chapter 2 are too "heavy" for us. They rely on real numbers : decimals that stretch to infinity.
But our computers are finite, in the digital world, we cannot handle infinity, and we cannot afford the inaccuracy of rounding down.
Fortunately, we are on the Moon.
If you travel West across the Ocean of Storms and keep going, you don't vanish into infinity. Eventually you wrap around the sphere that is the Moon and return to where you started. The surface of the Moon is a closed loop.
In Chapter 3 we will apply this "closed loop" logic to our mathematics. We will leave the rocky terrain of standard integers where division often fails.
We are moving to a Finite Field.
A Field is a mathematical landscape where you can add, subtract, multiply and divide freely without ever falling off the map.
It is a closed system that allows us to have the complexity of curves with the absolute precision of integers.
We are heading to the Ocean of Storms because we need an ocean to freely sail on, a place where math works in every direction.
But be warned, when you force a smooth curve into a closed loop it shatters. The Golden Handle is about to turn into stardust.
Top comments (1)
very good news!