Exponential Growth in Real Life: How a Court Fine Reached 2 Undecillion Rubles

When Big Numbers Escape the Textbook

Mathematics is full of mind-bogglingly large numbers — Graham’s number, Tree(3), or SCG(13). In practice, though, such figures rarely escape the realm of pure theory. Real life usually deals in smaller quantities. Usually — but not always.

Consider this headline from October 2024 (source):

The total amount of claims filed by 17 Russian TV channels against Google has reached 2 undecillion rubles, according to an RBC source familiar with the dispute. An undecillion is a one followed by 36 zeros. At a recent hearing on October 28, the judge noted that he was presiding over “a case with a great many zeros.”

2 undecillion rubles. That’s just 2,000,000,000,000,000,000,000,000,000,000,000,000.

The Mechanics of Exponential Growth in a Real Legal Case

Where did a number this large come from? The initial claims started in the tens of billions of rubles — already significant, but entirely within the range of normal finance. The key lies in the penalty structure attached to the court order.

Under the terms of the ruling, if Google fails to comply within 9 months of the decision taking effect, a fine of 100,000 rubles per day begins accruing. That daily amount doubles every week — with no cap on the total penalty.

This is exponential growth in real life, unfolding inside a courtroom. A relatively modest starting point, a fixed doubling interval, and no ceiling: the classic recipe for numbers that rapidly become incomprehensible.

A Real-Life Application of the Exponential Function

The structure of this fine is a direct real-world application of the exponential function. Each week the unpaid penalty multiplies by two, so after n weeks the daily fine is:

100,000 × 2ⁿ rubles

Doubling may sound modest at first. After one week the daily fine is 200,000 rubles. After a month, roughly 1.6 million. But the exponential function is deceptive — it accelerates slowly, then all at once. Within months the figures enter territory that no economy on Earth could service.

This is precisely why exponential growth real life examples tend to catch people off guard: human intuition is built for linear change, not geometric explosion.

Try the Math Yourself

Here is a puzzle worth solving:

Assume a conservative scenario — the penalty starts from the 2 undecillion ruble threshold, with a base rate of 100,000 rubles per day, doubling every week. When will the total fine reach the number of atoms in the observable universe (approximately 10⁸⁰)?

Hint: you won’t have to wait long.

The Modern Chessboard Problem

This case is the modern equivalent of the classic wheat-and-chessboard problem. In that ancient puzzle, a grain of wheat is placed on the first square of a chessboard, two on the second, four on the third — and by the 64th square the total exceeds all the grain ever harvested in human history.

The Google fine follows exactly the same logic. The numbers begin at a human scale, cross into the astronomical within weeks, and eventually surpass physical reality itself — the total atoms in the visible universe — before any enforcement mechanism could conceivably apply.

Exponential function real life applications are everywhere: population growth, compound interest, viral spread, radioactive decay. But few examples make the principle as viscerally clear as a court order that turned a billing dispute into a number larger than the universe.