Math is the hidden secret to understanding the world | Roger Antonsen

TED

13 Dec 201617:04

EducationalLearning

32 Likes 10 Comments

TLDRThe speaker explores the concept of understanding, positing that true comprehension hinges on the ability to change perspectives. Using mathematics as a lens, the talk delves into the essence of the subject, highlighting its foundational role in identifying patterns and creating languages to represent these patterns. From the structure of tie knots to the volume of a sphere, the presentation illustrates how varying viewpoints enrich our understanding, advocating for a flexible mindset akin to water, open to new insights.

Takeaways

🧠 Understanding is linked to the ability to change perspectives and view things from different angles.
🔢 Mathematics is defined as the search for patterns, their representation through language, and the exploration of assumptions.
📚 The essence of mathematics is not just arithmetic operations but the identification of patterns and structures in various forms.
👔 The concept of patterns extends to everyday objects like tie knots, which can be mathematically analyzed and represented.
🎵 Mathematics is used to represent and analyze phenomena in nature, such as the motion of objects, through invented notations.
💃 Representation in mathematics is not limited to numbers; it also includes visual and auditory elements, like dance notations and sounds.
📉 The script demonstrates that patterns can emerge from simple actions, like drawing straight lines, which can form complex shapes like a parabola.
🎼 The number four-thirds is explored in various contexts, showing how changing the base or perspective can alter its representation.
📐 Geometry and spatial reasoning are highlighted through the manipulation of shapes to form three-dimensional structures like pyramids and octahedra.
🌐 Perspective-taking is a fundamental human ability that is crucial for empathy and is analogous to the process of gaining mathematical understanding.
🌊 The script concludes that true understanding requires the flexibility of thought to view a subject from multiple perspectives, akin to immersing oneself in different experiences.

Q & A

What is the speaker's main claim about understanding?
-The speaker claims that understanding is closely related to the ability to change one's perspective. Without this ability, true understanding cannot be achieved.
How does the speaker define the essence of mathematics?
-The speaker defines the essence of mathematics as being about finding patterns, representing these patterns with language, making assumptions, and doing 'cool stuff' with these patterns.
What is an example of a pattern in everyday life that the speaker mentions?
-The speaker mentions tie knots as an example of a pattern in everyday life, which can be analyzed mathematically and has its own language for different types of knots.
What are some other examples of patterns mentioned by the speaker?
-The speaker also discusses patterns in nature, like the spiral shapes of shells and galaxies, and how these patterns can be observed and studied.

Outlines

00:00

🔍 The Essence of Understanding and Mathematics

The speaker introduces the concept of understanding as the ability to change one's perspective, using mathematics as a lens to explore this idea. They define mathematics as the search for patterns, the creation of a language to represent these patterns, and the exploration of assumptions. The speaker illustrates this with examples such as tie knots, shoelace patterns, and historical mathematical notations. They emphasize the importance of representation in mathematics, from Leibniz's notation to a tap dancing notation system, and even the representation of words through symbols and sounds.

05:01

📚 Patterns and Representations in Mathematics

This paragraph delves deeper into the nature of patterns and their representation in mathematics. The speaker uses the equation x + x = 2 • x to demonstrate how equations are metaphors that allow us to view the same thing from different perspectives. They explore the number four-thirds, showing how it can be represented in various forms, such as binary, decimal, and fraction, and even visualized through geometric shapes and musical notes. The speaker also discusses the importance of changing perspective in understanding, using the example of a rotating circle to illustrate how different viewpoints can lead to new insights.

10:03

🎶 Exploring Perspectives in Numbers and Sound

The speaker continues to explore the concept of perspective by examining the number four-thirds in the context of sound and rhythm. They demonstrate how multiplying a base frequency by different ratios can produce musical intervals like the perfect fifth and the perfect fourth. The paragraph also introduces the idea of changing perspective through physical representations, such as folding triangles to form a three-dimensional pyramid and combining them to create an octahedron, one of the five platonic solids. The speaker uses these examples to argue that understanding is achieved by viewing things from multiple perspectives.

15:05

🌊 The Power of Perspective in Understanding

In the final paragraph, the speaker concludes the discussion by emphasizing the fundamental role of perspective in understanding. They use the metaphor of the ocean to illustrate how different perspectives—close-up, from the shore, or from within the water—enrich our understanding of the subject. The speaker suggests that imagination is a key component in changing perspective, and they draw a connection between this ability and empathy, the act of understanding others' experiences. They conclude by encouraging the audience to embrace the flexibility of thought that comes with changing perspectives, likening a mind open to new ideas to water.

Mindmap

Keywords

💡Understanding

Understanding, in the context of the video, refers to the cognitive process of grasping the meaning or essence of something. The video argues that true understanding is not just about knowing facts but also about being able to change one's perspective to see things from different angles. For example, the video discusses how understanding in mathematics involves recognizing patterns and being able to represent and manipulate them in various ways.

💡Perspective

Perspective is the viewpoint or way of considering things. The video emphasizes the importance of changing one's perspective to achieve a deeper understanding. It suggests that by viewing a concept from different angles, one can learn new insights and make novel connections. The script uses the metaphor of rotating a 3D shape to illustrate how changing perspective can reveal new aspects of the same object.

💡Mathematics

Mathematics, as presented in the video, is not just about arithmetic operations but is fundamentally about finding and representing patterns. The video defines mathematics as the process of identifying patterns, creating a language to describe them, making assumptions, and exploring the consequences of those assumptions. It uses various examples, such as tie knots and tap dancing notation, to show how mathematics is about finding structure and regularity in diverse phenomena.

💡Patterns

Patterns are recurring structures or regularities that can be found in various phenomena. The video claims that mathematics is intrinsically about discovering these patterns and represents them using a language. Patterns are illustrated through examples such as the geometric patterns created by drawing circles, the patterns in music, and the mathematical representation of physical motion.

💡Representation

Representation in the video is the act of expressing patterns or concepts using a language or symbolic system. It is a crucial aspect of mathematics, allowing for the communication and manipulation of ideas. The script provides examples like Leibniz's notation for calculus and the representation of dance moves, emphasizing how representation can enable new insights and applications.

💡Assumptions

Assumptions are the starting points or premises from which reasoning or calculations are made. In the context of the video, making assumptions is part of the mathematical process, where one explores the implications of these assumptions to see what new patterns or insights emerge. The video suggests that playing around with assumptions is a way to deepen understanding and discover new mathematical relationships.

💡Metaphor

A metaphor is a figure of speech that describes one thing in terms of another, often to reveal a deeper meaning or to make abstract concepts more tangible. The video uses the concept of metaphor to explain how mathematical equations can be seen as analogies between different perspectives of the same concept, thus aiding in understanding by drawing connections between seemingly disparate ideas.

💡Empathy

Empathy is the ability to understand and share the feelings of another. The video draws a parallel between empathy and the process of changing one's perspective in mathematics and computer science. It suggests that by imagining the world from another's point of view, one can gain a deeper understanding, which is a fundamental aspect of both empathy and scientific inquiry.

💡Imagination

Imagination is the faculty or action of forming new ideas or images or concepts of external objects not present to the senses. The video posits that imagination is essential for changing one's perspective and for gaining a deeper understanding. It is highlighted as a key component in the process of viewing a concept from different angles, which is likened to viewing oneself from the outside.

💡Flexibility

Flexibility, in the context of the video, refers to the mental ability to adapt and adjust one's thinking to different viewpoints or situations. The speaker suggests that practicing changing perspectives, as one does in mathematics, can make the mind more flexible, open to new ideas, and better able to understand complex concepts.

💡Pi and Platonic Solids

Pi (π) and Platonic solids are mathematical concepts that the video uses to illustrate the beauty and depth of mathematics. Pi is an irrational number representing the ratio of a circle's circumference to its diameter, while Platonic solids are three-dimensional shapes with congruent faces and vertices. The video uses these concepts to show how mathematics can be both a rigorous discipline and a source of aesthetic pleasure.

Highlights

Understanding is linked to the ability to change one's perspective.

Mathematics is defined as finding patterns, representing them with language, making assumptions, and doing innovative work.

Patterns can be found in everyday objects like tie knots and are given specific mathematical language.

The mathematics of shoelaces is explored at a university level due to the complexity of patterns involved.

Leibniz's notation from 1675 was a language for patterns in nature, particularly the motion of objects.

Dance notation is a system for representing movement patterns in tap dancing.

The importance of representation in communication, using dots, symbols, and sounds to convey the word 'mathematics'.

Experiments with straight lines reveal patterns that form a parabola, demonstrating the discovery of patterns through simple actions.

Changing perspective can lead to new insights, as shown by rotating a pattern to reveal its true nature.

The equation x + x = 2 • x is used to illustrate the concept of viewing patterns from different mathematical perspectives.

The number four-thirds is explored through various representations, including binary, decimal, and fraction forms.

Visualizing numbers through geometric shapes, such as the relationship between a sphere's volume and a cylinder.

Sound can be mathematically manipulated to demonstrate relationships, such as multiplying a frequency by four-thirds to produce a musical interval.

Rhythms can embody mathematical ratios, as shown by playing beats in multiples of four-thirds.

Understanding is achieved by viewing objects from multiple perspectives, as demonstrated with the octahedron and its rotations.

Imagination is crucial for changing perspective and is a key component in both mathematics and computer science.

Empathy is related to perspective-taking and is a human application of the same cognitive process used in mathematics.

The conclusion that deep understanding is achieved through the ability to change one's perspective is emphasized.

The speaker encourages the audience to adopt a flexible mindset like water, embracing new perspectives for deeper understanding.

Transcripts

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