The Mathematics of Dunking a Biscuit

The perfect biscuit dunk looks like a culinary judgement call.

Underneath, it is a race between physics and structural failure.

A biscuit is a porous material: a network of tiny channels filled initially with air. Touch one end to tea and liquid begins to invade those channels through capillary action.

A useful idealization is that the penetration distance grows roughly like the square root of time:

$$L \propto \sqrt{t}.$$

That square root matters. Doubling the depth of penetration generally takes much more than twice the time.

Two clocks are ticking

While tea moves inward, another process has begun.

The biscuit is losing mechanical strength.

Dry starches and sugars that once created a rigid structure begin to soften. The wetted region becomes heavier at exactly the same time that it becomes weaker.

So the dunker is balancing two competing goals:

1. let enough tea enter to transform texture and flavour;
2. retrieve the biscuit before its wet region can no longer support its own weight.

This is not unlike many optimisation problems: the best solution lives near a boundary.

Too early and very little has happened.

Too late and everything has happened.

The Zen correction

There is, however, a flaw in turning biscuit dunking entirely into an optimisation problem.

One could imagine measuring pore size, tea temperature, biscuit thickness and tensile strength, then computing an ideal immersion time to three decimal places.

And perhaps that would be fun.

But the point of the biscuit was never merely to maximise a utility function.

There is another instrument available: attention.

Watch the surface darken. Feel the change in resistance. Notice how quickly one kind of biscuit behaves differently from another.

Physics tells us why the dunk works.

Presence tells us when to lift.