Well, one of the mysteries of life.  And don’t go googling it and show me that everyone else already knew this.  Don’t care.

It is widely acknowledged that a tube of toothpaste will be half empty in a week, but then the remaining half will last a month.  Unpossible, right?

Probably most of us have a nagging sense that this is not really so, it’s just a perception of an average human being who is generally not quite awake most of the time it’s noticing this.

But it is so.  I will now explain.

Here we have a cross-section of a tube of toothpaste:

Or a sideways view.  Whatever LEAVE ME ALONE.

You may have seen some television program on how they make these things, but essentially, it is a tube that is crimped at the bottom.  In other words, an uncrimped tube would look like the blue square below:

From here, we can easily see what happens if we look at the two “halves” of the tube:

When we say that “half” the tube is gone in a week, it’s because we’re looking at the rectangle of the crimped tube (as viewed from the top) and dividing it in half visually.  By volume, clearly, that lower half is not even close to being half the contents and is therefore used up fairly quickly.  What’s left is the majority of the toothpaste, and of course that takes a lot longer to use up.   We could go all Euclidean on the topic and prove it with MATH, but I’m content to leave that work to future generations.

And now you know.  Unless you already knew.  Whatever LEAVE ME ALONE.