Sign Up for the BetterExplained Email List

Hi all! I’m starting an email list for BetterExplained readers and everyone interested in deep, intuitive learning. Sign up with the form below… Continue reading →

How To Understand Derivatives: The Quotient Rule, Exponents, and Logarithms

Last time… Read article we tackled derivatives with a “machine” metaphor. Functions are a machine with an input (x) and output (y) lever. The derivative, dy/dx, is how much “output wiggle” we get when we wiggle the input:

Now, we can make

How To Understand Derivatives: The Product, Power & Chain Rules

The jumble of rules for taking derivatives never truly clicked for me. The addition rule, product rule, quotient rule — how do they fit together? What are we even trying to do?

Here’s my take on derivatives:

We have

Read article

Learning To Learn: Embrace Analogies

Why do analogies work so well? They’re building blocks for our thoughts, written in the associative language of our brains.

At first, I thought analogies had to be perfect models of the idea they explained. Nope.

“All models are wrong, … Read article

Site Update: Ahas and FAQs for articles

I’ve just added a new feature to the site: an Aha / FAQ section for each article.

You can add an aha! moment or question, and vote / discuss them individually. This extends aha.betterexplained.com, making mini-posts for key ideas in an article. Continue reading →

Calculus: Building Intuition for the Derivative

How do you wish the derivative was explained to you? Here's my take.

Psst! The derivative is the heart of calculus, buried inside this definition:

But what does it mean?

Let's say I gave you a magic newspaper that listed… Read article

Vector Calculus: Understanding the Dot Product

I see the dot product as directional multiplication. But multiplication goes beyond repeated counting… Read article: it’s applying the essence of one item to another.

Normal multiplication combines growth rates: “3 x 4″ can mean “Take your 3x growth and make

Using Logarithms in the Real World

Logarithms are everywhere. Ever use any of the following phrases?

6 figures
Double digits
Order of magnitude

Read article

You’re describing numbers in terms of their powers of 10 — a logarithm. Ever mention an interest rate or rate of return? It’s

Math, Better Explained available on the Kindle Store!

Hi all, I wanted to announce that Math, Better Explained is available on the Kindle store!

If you’re looking for a digital gift this holiday season, I know just the ticket . Continue reading →

Intuition, Details and the Bow/Arrow Metaphor

My favorite analogies explain a thought and help you explore deeper truths. Here’s a metaphor that captures my stance on learning:

Rote details are arrows, intuition is the bow.

Read article

Our goal is to hunt down problems. You can use arrows