Post on 2025/5/3

By Frank

Contact is an American film from 1997 based on a 1985 novel by Carl Sagan. It won the Hugo Award for Best Dramatic Presentation and two Saturn Awards, grossing over 171 million dollars worldwide. The protagonist, Dr. Ellie Arroway, is a SETI (search for extraterrestrial intelligence) scientist who first detects a mysterious signal from the star Vega, 26 light-years from Earth. Her success not only comes from her perseverance but from her gifted sensitivity to numbers.

Mathematics is often described as the “universal language.” Unlike spoken languages, numbers are not bound by culture or biology, and can be understood by all civilizations. Some may argue that humans invent numbers and define all the operations, but how do we guarantee that other orgasms can comprehend them? Granted, we cannot guarantee that extraterrestrial beings use the same symbols or count in base ten. Still, mathematics is rooted in fundamental patterns and relationships throughout the universe, also known as axioms. For instance, the addition is not defined as 1+1=2, but based on the Peano axioms and the idea of successor (which instructs in the natural number set, the first element is 0, the element after 0 is 1, and so on). Furthermore, mathematics tends to be far less ambiguous or prone to paradox than spoken language, thanks to the development of type theory. This logical consistency makes math a powerful candidate for communicating with other civilizations.

In the movie, the signal consists of a series of pulses that match the sequence of prime numbers (2, 3, 5, 7, 11…), which is highly unlikely to occur by chance in nature since most natural signals, such as those from stars or pulsars, follow simple, predictable patterns (like regular pulses, sine waves, or random noise) caused by physical phenomena, while prime numbers, are in an irregualr sequence where the patterns of distribution remain a mystery. The use of prime numbers immediately alerts the protagonist, Ellie, that the signal is not a random phenomenon but potentially a deliberate attempt at communication by an intelligent source.

Why are primes so special? The property that every prime number has no positive divisors other than one and itself prevails in any base (base-2, base-16, etc), which helps to communicate with civilization using different bases. On the other hand, the spacing of primes lacks any periodicity, and no known natural process produces such a sequence, making the appearance of primes in a radio signal extraordinarily unlikely to be a product of probability. Generating the sequence of primes requires a strong mathematical background, and only an intelligent mind can accomplish it. That’s why when Ellie detects a signal composed of prime numbers, it serves as an unmistakable indicator of an intelligent origin other than randoms.

As Ellie and her team delve deeper into the signal, they discover that the sequence of primes is only the superficial layer. The most astonishing revelation happened after decoding the data from the signal, which implies constructing a mysterious machine of unknown purpose.

The decoding process relies heavily on mathematics: from pattern recognition and cryptography to three-dimensional spatial reasoning required to interpret the alien schematics, all of which demonstrate the vital role of mathematics in various fields.

Contact thus illustrates that mathematics is more than just a tool for scientists: it is the bridge that makes communication with other intelligent life possible. The film suggests that while languages and cultures may divide us, the language of numbers, logic, and universal patterns could unite intelligent beings across the cosmos. Through mathematics, humanity discovers that we are not alone and learns how to reach out to the unknown.