Calculus unlocks the mysteries of the universe and the mysterious power to reshape civilization

"Without calculus, we wouldn't have cell phones, computers, and microwave ovens, and we wouldn't have radios, televisions, ultrasounds for pregnant women, and GPS (Global Positioning System) for navigating lost travelers. We won't be able to get atoms, crack the human genome, or send astronauts to the moon, and we may even miss the Declaration of Independence.

There is a rare and interesting historical view that the world was completely changed by a mysterious branch of mathematics. How did a theory that was originally associated with shapes end up reshaping civilization?

The answer to this question can be gleaned in a witty quote by physicist Richard Feynman, who spoke during his discussion of the Manhattan Project with Herman Walker. At the time, Walker was researching a long-form he was planning to write about World War II, and he went to Caltech to interview physicists who had worked on the atomic bomb, and Feynman was one of them. At the end of the interview, Feynman asked Walker if he knew calculus. Walker admits he doesn't know, so Feynman says, "You'd better learn calculus, it's the language of God." ”[1]

The universe is highly mathematical,[2] but the reason is unknown. This may be the only viable way for the universe that includes us, because the non-mathematical universe cannot shelter intelligent beings who can ask this question. In any case, it is a mysterious and uncanny fact that the laws of nature that our universe follows can always be expressed in the language of calculus and in the form of differential equations. This type of equation describes the difference between something at one moment and the next, or between something at one point and at the next point infinitely close to that point. Although the details will vary depending on what we have, the structure of the laws of nature is always the same. This astonishing statement can also be expressed as the fact that there seems to be something akin to the cosmic code, that is, an operating system that allows everything to change all the time. Calculus takes this rule and formulates it.

Isaac Newton was one of the first to catch a glimpse of this cosmic mystery. He discovered that the orbits of the planets, the rhythm of the tides, and the ballistics of the cannonballs could all be described, explained, and ** by a set of differential equations. Nowadays, we refer to these equations as Newton's laws of motion and the laws of gravitation. Since Newton, every time a new mystery of the universe is revealed, we find that the same pattern has been in effect. From the ancient earth, air, fire, and water elements to the more recent electrons, quarks, black holes, and superstrings, all inanimate things in the universe obey the rules of differential equations. I bet that's what Feynman was trying to convey when he said "calculus is God's language." If there's one thing that can be called the mystery of the universe, it's calculus.

Humans inadvertently discovered this strange language (first in the hidden corners of geometry, and later in the cosmic code), then learned to use it skillfully, and deciphered its idioms and subtleties, and finally used its ** ability to reconstruct the world.

This is the central thesis of the book.

If this argument is correct, then it means that the answer to the ultimate question about life, the universe, and all things[3] is not 42, for which I apologize to Douglas Adams and fans of The Hitchhiker's Guide to the Galaxy. But Deep Thought, a supercomputer in The Hitchhiker's Guide to the Galaxy, is the right thing to do, because the mysteries of the universe are indeed a series of mathematical problems. ”

Excerpt from The Power of Calculus, Steve Storgats.

Calculus and technological advances

First of all, the advent of calculus is undoubtedly a major milestone in the history of science. Isaac Newton and Gottfried Leibniz invented calculus almost simultaneously but independently, laying the foundation for later scientific research. From physics to engineering to economics and biology, calculus has become the universal language for describing change and dealing with dynamic processes in complex systems.

For example, Newton used calculus to discover the laws of planetary motion, which not only overturned the millennial concept of celestial motion, but also provided a theoretical basis for later space exploration. Today, everything from architectural design to medical imaging to GPS positioning systems in our mobile phones is the result of calculus applications.

Calculus and the understanding of the universe

The reason why calculus is so widely used in scientific research and technological development is rooted in its ability to accurately describe the laws of change in nature. As mentioned in the excerpt, the laws of nature that the universe follows can always be expressed in the language of calculus and in the form of differential equations. This means that both macroscopic galaxies and microscopic particle behavior can be understood through calculus.

This ability has allowed humans to delve deeper into the mysteries of the natural world, from the atom to the universe, from the origin of life to the structure of the universe, in which calculus plays a key role. Not only has it helped us answer many long-standing questions, but it has also pushed us into uncharted territory.

Conclusion

Therefore, it can be said that calculus is not only a branch of mathematics, but also a powerful tool that allows human beings to deeply understand and transform the world. Its development has promoted the rapid progress of science and technology, changed our way of life, and even changed our understanding of the universe. The importance of calculus is not only reflected in its mathematical aesthetics, but more importantly, its great value in practical applications. From this perspective, calculus can indeed be seen as a "language of God" that reveals the fundamental laws of how the universe works, becoming the key to understanding and exploring the natural world.