# Bobbie's Blog

## It Is Okay to Speed Up a Little

We naturally avoid making mistakes. If you were a caveman who survives by hunting, you’d try not to make mistakes that could get you killed by animals.

But in the modern days, we no longer worry about ferocious animals. We now have much safer spaces that are tolerant of our mistakes. So we can afford to make more mistakes. In fact, making mistakes is how we learn.

Yet, people avoid mistakes because it makes you “look bad.” But there is no learning without making mistakes. So how can we gain the courage to learn without worrying about the mistakes we would make?

I think math has the answer.

In numerical analysis, we design algorithms that solve problems quickly and accurately. One major task when developing such an algorithm is to combat with numerical errors. If you open any classical numerical analysis textbook, you will likely see discussions of error analysis: how to eliminate or reduce roundoff errors, and how to prevent errors from propagating and contaminating the final results.

Talking about errors can sound bad and boring. It may drive beginners away from numerical analysis before they can learn the true beauty of the subject.

In fact, mathematicians know about the bad connotations associated with “errors.” When communicating with fellow mathematicians, we don’t talk about errors as often as one would imagine. For example, instead of saying “the algorithm makes smaller errors” we like to say “the algorithm converges faster.” And instead of “the algorithm prevents error propagation” we like to say “the algorithm is stable and robust.”

“Fast convergence” and “smaller errors” mean the same thing, but the framings are completely different. “Convergence” focuses on the positive effects and makes people excited. If you ask any numerical analyst what makes them love their field, I’ll bet you no one would say they love the error analysis; rather, they would tell you about the lightning computation speeds, the simple ideas behind powerful algorithms, the unexpected connections between ideas from different fields, and more.

Likewise, “making mistakes” gets its own bad rap. I propose replacing it with “speeding up” because making more mistakes allows you to learn quicker. Whenever you are stuck and can’t make any progress because you are afraid of making mistakes, try to tell yourself “I am just going to speed up my learning a little.”

Making mistakes can be embarrassing, but embarrassment is simply the cost of entry. The embarrassment you feel only exist in your mind, learning is what can actually happen. Once you allow yourself to look stupid and take on the beginner’s mindset, learning will be unstoppable.

Make more mistakes. It is okay to speed up a little, and it feels great.