# Fourier Transforms: From Nuclear Testing to Digital Compression

## The Nuclear Age and the Role of Fourier Transforms

Have you heard of Fourier Transforms? Let’s rewind to the nuclear age in the mid-20th century. The Partial Test Ban Treaty of 1963, instead of calming the escalating nuclear arms race, simply drove it underground. In the years that followed, testers detonated over 1,500 nuclear weapons underground. By the mid-1980s, an alarming 70,000 nuclear warheads had been amassed worldwide, and both the U.S. and the Soviet Union had spent approximately \$10 trillion each throughout the 20th century.

However, things could have turned out differently. Had we rediscovered the Fast Fourier Transform (FFT), a method of analyzing frequency data, earlier, we might have had the capability to detect these underground tests remotely and stop the nuclear arms race from reaching such catastrophic proportions.

## The Forgotten Discovery

The FFT was actually conceived in 1805 by the renowned mathematician Carl Friedrich Gauss while studying asteroids Pallas, Ceres, and Juno. His discovery predated Joseph Fourier’s published work by two years. However, because Gauss wrote his method using non-standard notation in a 19th-century version of Latin, people essentially forgot it, and it only resurfaced after his death.

## FFTs and Modern Technology

Now, let’s fast-forward to the present day. The FFT has become an integral part of modern technology, from image compression algorithms to radar and sonar applications, WiFi and 5G signals, and more.

### Image Compression and FFTs

Using FFTs to transform pixel brightness values allows us to compress an image, as this process identifies the frequencies present in the image. Most real-world images yield a lot of near-zero values in their transformed form, especially those corresponding to high frequencies. By discarding these negligible values, we can achieve significant compression without substantial loss of image quality.

## The Importance of FFTs

Mathematician Gilbert Strang has rightfully called the FFT “the most important numerical algorithm of our lifetime.” The wide applications of FFTs across diverse fields and their ability to handle large-scale computations efficiently exemplify their immense value.

## A Career’s Impact and FFTs

As intriguing as the technical applications of FFTs are, the story also serves as a reminder of the unforeseen impacts our work can have on the world. Gauss, in his time, could not have foreseen the profound influence his FFT discovery would exert centuries later. Over an average career spanning 80,000 hours, we too have countless opportunities to make a significant positive impact.

### Lessons from the FFT Story

• Recognizing the value of our work: Like Gauss’s FFT, the full impact of our work might not be immediately evident but can hold immense potential.
• Learning from history: The unchecked nuclear arms race serves as a stark reminder of the need for proactive measures in global issues.

## Why Watch This Video?

The video serves as a delightful intersection of history, mathematics, and practical applications. It provides an engaging narrative that highlights the unexpected impacts of mathematical discoveries while urging viewers to ponder the potential of their life’s work.

Furthermore, the video can be an excellent educational resource for students interested in learning how abstract mathematical concepts, such as the FFT, find wide-ranging applications in everyday technologies.

From a broader perspective, the video provokes viewers to think critically about the ripple effects of our actions and innovations, serving as a potent reminder of the weight and potential our careers hold to shape the world.

## Reference

YouTube Video: The Remarkable Story Behind The Most Important Algorithm Of All Time