Is a Sauce Replenished for 100 Years Really 100 Years Old?

There is a phrase you often hear at long-established yakitori and grilled eel restaurants in Japan:

“Our secret sauce has been preserved by continuously replenishing it since the restaurant was founded.”

It sounds impressive.

You imagine that some of the sauce made by a craftsman a century ago still remains in the pot, with each generation of owners adding another layer of flavor.

Mathematically, however, the reality is rather less romantic.

Every time the sauce is used, some of it disappears and fresh sauce is added to replace it. Naturally, the proportion of the old sauce becomes smaller and smaller.

In a model where a fixed percentage is replaced each time, the original sauce decreases exponentially. The speed depends on how the restaurant uses it, but after several months, the original contents may have effectively been replaced.

In other words, a sauce that has been replenished for 100 years does not necessarily contain sauce from 100 years ago.

That takes some of the magic out of the story.

Does That Mean Replenishing the Sauce Is Pointless?

It does not follow that making a completely new batch every morning would produce the same result.

As the sauce is repeatedly used and replenished, fat and savory flavor from the grilled meat or fish enter the mixture. Its character develops through the daily cycle of use and renewal.

What matters may not be whether molecules from a century ago remain. It is that today’s sauce inherits yesterday’s sauce, and tomorrow’s sauce will inherit today’s.

There is never a day when it is completely reset.

That is a curious idea when you stop to think about it.

The sauce from 100 years ago is no longer there. Whether any of it survives even at the molecular level is doubtful.

And yet the sauce has undeniably continued for 100 years.

Is This the Ship of Theseus?

This brings to mind the famous philosophical thought experiment known as the Ship of Theseus.

Imagine a ship that has been used for many years. Whenever one of its wooden planks deteriorates, it is replaced with a new one.

Eventually, none of the original planks remain.

Is it still the same ship?

A continuously replenished sauce presents much the same question.

Soy sauce is added. Sugar is added. Some of the mixture is used. Then more ingredients are added.

After 100 years, virtually none of the original ingredients remain. The restaurant still calls it the same sauce it has used since opening.

As matter, it is something different.

As history, it forms one unbroken line.

Apparently, when we call something “the same,” we do not judge its identity by its physical material alone.

We Do Not Taste with the Tongue Alone

The effect on taste is even more interesting.

Imagine being served the same dish with one of two explanations:

“This is our secret sauce, replenished for 100 years.”

“We made this sauce in the kitchen a few minutes ago.”

Even if the flavor were identical, the two dishes would probably leave very different impressions.

We do not experience food with the tongue alone.

There is the old restaurant building, the craftsperson grilling the food, and the pot passed down through generations. When someone tells us that its sauce has been replenished for a century, that history becomes part of the flavor.

A scientific analysis would not identify history as a flavor compound.

But for human beings, deliciousness is not determined entirely by the numbers in a chemical analysis.

If that history affects the experience, perhaps it too is part of the dish.

What Has Actually Survived for 100 Years?

In the end, asking how much century-old sauce remains in a century-old pot may be the wrong question.

What remains is not the physical substance.

It is the method, the daily practice of using and replenishing the sauce, and the continuity created by passing that practice from one person to the next.

Companies, cities, and cultures work in much the same way.

Even our bodies are not composed entirely of the same cells they once were. We still do not regard yesterday’s self and today’s self as two different people.

Seen this way, laughing that the sauce is “not the same thing it was 100 years ago” may be the more simplistic view.

Of course, grilled eel tastes good even without the philosophy.

And it will probably taste better if you do not ask the owner whether any of the original century-old molecules are still in the pot.