Metric Paper

CGP Grey
26 Mar 202108:44

TLDRThe video script explores the fascinating properties of metric paper, specifically the A4 size, and its ability to be divided into identically shaped smaller sheets (A5, A6, etc.) while maintaining the same aspect ratio. This characteristic allows for efficient scaling of designs from small to large formats without distortion. The narrative then metaphorically delves into the concept of scaling down, from the observable world to microscopic and atomic levels, touching upon the complexity of life, the structure of DNA, and the fundamental particles that make up matter. It highlights the vastness of the universe, from the human scale to the cosmic, and the humbling realization of how small and interconnected everything is within the observable universe and potentially beyond.


  • 📏 The metric paper system allows for consistent scaling through a series of paper sizes (A4, A5, A6, etc.), each half the size of the previous, maintaining the same shape and aspect ratio.
  • 🔄 The concept of dividing an A4 sheet into halves creates a fascinating mathematical and practical spiral, applicable across various scales from the microscopic to the cosmic.
  • 🌐 Starting with a single A4 sheet, you can explore the exponential scaling down to the atomic and subatomic levels, illustrating the vastness of scales within our universe.
  • 🚀 The script takes us on a journey from the macroscopic scale of cities and structures down to the quantum level, highlighting the limits of human perception and understanding.
  • 🌟 It emphasizes the vastness of space and the insignificance of human achievements when compared to the cosmos, with structures becoming invisible and light from stars taking years to reach us.
  • ⚛️ The atomic and subatomic levels reveal that matter is mostly empty space, with a tiny nucleus at the center of an atom, surrounded by an electron cloud.
  • 🧬 DNA, the building block of life, is composed of atoms arranged in a hexagonal pattern, and is explored as we delve into the microscopic world.
  • 🌌 Our galaxy, along with countless others, forms a vast cosmic web, with galaxies connected by filaments of dark matter, illustrating the scale and complexity of the universe.
  • ⏱️ The speed of light sets a limit to how fast information can travel, with communication delays inherent in any interstellar communication due to the vast distances involved.
  • 🔬 The observable universe is defined by the boundary where light from objects has had time to reach us, with the unobservable universe lying beyond, possibly containing objects forever out of reach.
  • 🌍 The Earth and all human achievements are a tiny part of the cosmos, with the exploration of space being a recent and limited endeavor in the grand scheme of the universe.
  • ∞ The concept of infinite scaling, both upwards and downwards, challenges our understanding and perception, suggesting a universe that is both boundless and inconceivably complex.

Q & A

  • What is the special property of metric paper that distinguishes it from other types of paper?

    -The special property of metric paper is that when it is divided in half, each half retains the same shape and the ratio of its sides is identical to the whole. This is in contrast to origami and letter paper, which when halved, result in pieces that are half the size but different shapes.

  • What is the name of a full sheet of metric paper and how does it relate to its subsequent sizes?

    -A full sheet of metric paper is named A4. When an A4 sheet is halved, it becomes an A5, and each subsequent halving follows the same pattern, resulting in A6, and so on, with each size retaining the same shape.

  • How does the concept of metric paper relate to the design and scaling of various items, from posters to postage?

    -Metric paper allows for the design of items like posters and postage on an A4 sheet, which can then be scaled up or down perfectly without any distortion or 'fuzzing' of margins, making it a practical and mathematically satisfying system for design.

  • What is the significance of the exponential spiral in the context of the metric paper?

    -The exponential spiral refers to the process of continuously dividing the metric paper in half, which creates a series of sheets in decreasing sizes (A4 to A5 to A6, etc.), each maintaining the same shape. This concept can be extended to explore the vastness of scales, from the microscopic to the cosmic.

  • At what point does the size of the divisions of metric paper become smaller than the wavelength of visible light?

    -The size of the divisions becomes smaller than the wavelength of visible light after 39 divisions down from the original A4 sheet.

  • What is the significance of the hydrogen atom in understanding the structure of matter?

    -The hydrogen atom is significant because it is composed mostly of empty space, with a tiny nucleus containing a single proton at its center. This illustrates that most of the physical world is an illusion created by electron clouds over a void.

  • How does the concept of the observable universe relate to the process of doubling the size of a sheet of A4 paper?

    -The process of doubling the size of an A4 sheet metaphorically represents the expansion of our perspective from the personal scale to the cosmic scale. At 184 doublings, the size of the sheet metaphorically reaches the edge of the observable universe, illustrating the vastness of the cosmos.

  • What is the 'Planck length' and why is it significant?

    -The Planck length is the smallest measurable length in the universe, representing the 'reality pixel' beyond which current physical theories cannot describe or measure. It is significant as it represents the limit of our understanding of the universe at the smallest scales.

  • How does the script use the concept of doubling to illustrate the scale of human-made structures and celestial bodies?

    -The script uses the concept of doubling to show how quickly the scale of human-made structures becomes insignificant compared to the vastness of celestial bodies. It illustrates that just a few doublings after the scale of human cities, human structures become invisible, and only the light we create can be seen.

  • What is the role of DNA in the context of the script?

    -DNA is mentioned as the 'operating system of life,' highlighting its importance in the biological scale. The script explores the size of DNA strands after numerous divisions down from an A4 sheet, emphasizing the intricate and mechanical nature of life's building blocks.

  • How does the script use the metaphor of a bee's cells to illustrate the concept of life at a microscopic level?

    -The script uses the bee's cells to demonstrate that life exists at various scales, with each cell being as alive as the animal it forms. It shows that even at the level of 24 divisions down from an A4 sheet, there is a complex, living system within the bee's cells.

  • What is the significance of the electron orbital in the script's exploration of the atomic scale?

    -The electron orbital is significant as it represents the boundary within which an electron can exist around an atom's nucleus. The script uses the concept of falling through the electron orbital to metaphorically enter the interior of an atom and discover the truth that matter is mostly empty space.



📜 The Fascinating Properties of A4 Paper

This paragraph delves into the unique characteristics of metric paper, specifically the A4 size. It explains how A4 paper can be divided into halves that maintain the same shape and size ratio, unlike other paper types like origami or letter paper. The A4 size is the starting point for a series of reductions in size (A5, A6, etc.) and expansions (double A4, A3, A2, A1), all of which maintain the same shape. This property makes it ideal for designing on a single sheet and scaling it up or down without any distortion. The paragraph also explores the concept of scaling down to microscopic and even atomic levels, touching on the complexity of life at the cellular and molecular level, and the philosophical implications of the vastness and emptiness of the universe at the quantum level.


🚀 The Cosmic Journey from A4 Paper to the Observable Universe

The second paragraph takes the reader on a cosmic journey starting from a single sheet of A4 paper and scaling up through a series of doublings. It describes how quickly human-made structures become insignificant as we expand to the size of cities, countries, and eventually the entire planet. The narrative then leaps to the scale of the solar system, the position of planets, and the farthest reaches of human exploration, such as the Voyager 1 space probe. It continues to the edge of the solar system, through the Oort cloud, and into interstellar space, highlighting the vast distances between stars and galaxies. The paragraph concludes with a reflection on the observable universe and the unobservable universe beyond, emphasizing the mystery and potential infinity that lies beyond our current understanding and capabilities.



💡Metric Paper

Metric paper refers to a standard size paper system that is widely used around the world. In the context of the video, it is highlighted for its unique property of maintaining the same shape and proportions when divided into halves, which is integral to the theme of scaling and the exploration of sizes from the macroscopic to the microscopic world.

💡Exponential Spiral

An exponential spiral is a growth pattern that follows an exponential function, often seen in nature and mathematics. In the video, it is used metaphorically to describe the journey from a single sheet of A4 paper to the observable universe, scaling up and down in a manner that reflects the mathematical consistency of the metric paper system.


Origami is the Japanese art of paper folding, often used to create intricate designs and shapes from a single sheet of paper. In the video, origami is mentioned to contrast with the metric paper system, highlighting that while metric paper maintains its shape when divided, origami paper results in halves that are different in shape, emphasizing the uniqueness of the metric system.


Quantum refers to the smallest discrete amount or a fundamental understanding of physical phenomena at a very small scale, typically at the atomic and subatomic levels. In the video, quantum is used to describe the microscopic limit of the journey, where the concepts of matter and space-time are fundamentally different from our macroscopic experience.

💡Observable Universe

The observable universe is the part of the universe that we can see or detect from Earth, limited by the speed of light and the age of the universe. In the video, reaching the observable universe signifies the end of the journey, representing the furthest extent of human knowledge and exploration.

💡Bee's Organs

The organs of a bee refer to the various biological structures within the bee's body that perform specific functions necessary for its survival. In the video, the mention of bee's organs illustrates the intricate complexity at the microscopic level, emphasizing the continuity of life and the scale of biological structures.


DNA, or deoxyribonucleic acid, is a molecule that carries the genetic instructions for the development, functioning, growth, and reproduction of all known living organisms and many viruses. In the video, DNA is used to represent the fundamental building block of life, highlighting the complexity and continuity from the smallest biological entities to the larger scale of existence.

💡Electron Cloud

The electron cloud is a visual representation of the probability of finding an electron in a particular location around an atomic nucleus. It is a fundamental concept in quantum mechanics, illustrating the probabilistic nature of electrons in atoms. In the video, the electron cloud is used to convey the idea that matter is not solid as it appears, but rather composed of mostly empty space with electrons creating an illusion of solidity.

💡Quantum Abyss

The quantum abyss refers to the deep and complex realm of quantum physics, where the classical understanding of reality breaks down, and the behavior of particles is governed by the principles of quantum mechanics. In the video, it signifies the point beyond which our comprehension of the universe becomes extremely limited and abstract.

💡Light Speed

Light speed is the speed at which light travels in a vacuum, approximately 299,792 kilometers per second. It is the fastest speed at which information or matter can travel according to the current understanding of physics. In the video, light speed is used to illustrate the vastness of the universe and the limitations it imposes on communication and exploration.

💡Solar System

The solar system consists of the Sun and the objects that are gravitationally bound to it, including planets, dwarf planets, moons, asteroids, and comets. In the video, the solar system is part of the journey that starts from a sheet of A4 paper and extends to the cosmic scale, representing the scope of human exploration and knowledge.

💡Oort Cloud

The Oort Cloud is a hypothesized spherical shell of icy objects that exists in the outermost reaches of the Sun's gravitational influence. It is the source of many long-period comets. In the video, the Oort Cloud is mentioned to illustrate the extreme distances and the edge of the Sun's domain within our solar system.


Metric paper is an invitation to explore everything that exists.

Each half of the metric paper maintains the same shape and size ratio as the whole.

The A4 sheet of metric paper can be perfectly divided into A5, A6, and so on, maintaining the same shape.

Metric paper allows for precise scaling from posters to postage stamps without margin issues.

The exponential spiral of dividing A4 paper leads to the exploration of the microscopic world.

At 24 divisions, the paper size approaches the size of a bee's organs.

The division continues into the cellular level, revealing the complexity of life.

The atomic vision reveals the fundamental building blocks of life, such as DNA and hydrogen atoms.

The Planck length represents the smallest measurable unit, the reality pixel.

Doubling back from the quantum realm, the A4 paper unfolds to encompass larger scales like desks and rooms.

The paper's doubling in size can model the growth of cities and human accomplishments.

At the scale of light speed, human-made structures become invisible, and only light can be seen.

The speed of light is the宇宙速度极限, making communication across vast distances meaningfully slow.

Doublings beyond our solar system reveal the vastness of the universe and the cosmic filaments.

The observable universe, containing two trillion galaxies, is the edge of what we can know.

Beyond the observable universe lies the unobservable universe, possibly infinite and unknowable.

The journey from a single A4 sheet of paper to the edge of the universe demonstrates the vast range of scales in existence.