Art inspired by mathematics | Michael Naylor | TEDxTrondheim

TEDx Talks
4 Dec 202018:28
EducationalLearning
32 Likes 10 Comments

TLDRThe artist in the transcript explores the intersection of mathematics and creativity, using the Towers of Hanoi puzzle as a starting point to demonstrate how mathematical patterns can inspire various forms of art. The script details the artist's journey from solving the puzzle to creating art, music, poetry, and literature, all stemming from the discovery of a pattern they term the 'abba cabba' pattern. This pattern is represented in different ways, such as doubling lengths, English ruler patterns, and binary numbers, each leading to unique and organic shapes found in nature. The artist's work extends to creating a decision tree poem, a children's story, a musical piece, and even a mechanical music box that plays the pattern. The exploration of binary numbers also leads to visual art pieces and a fantasy novel set on a mathematically inspired planet. The transcript concludes with an encouragement to engage with patterns and mathematics as a source of inspiration for creativity.

Takeaways
  • 🎨 Mathematics and art are deeply connected: The artist uses mathematical patterns to inspire various forms of art, showing that math is not just about numbers but also about life, beauty, and connections.
  • 🧩 The Tower of Hanoi puzzle: The artist's journey begins with this puzzle, which is full of patterns that can be used to create art, music, and poetry.
  • 📊 Patterns in numbers: The artist represents the sequence of moves in the Tower of Hanoi puzzle as lengths that double, creating shapes and patterns that resemble landscapes and trees.
  • 🌳 Nature-inspired art: The patterns found in the puzzle resemble those found in nature, such as family trees and the branching structures seen in plants.
  • 📜 Decision Tree poem: The artist creates a poem that explores the concept of decision-making and its consequences, structured in a way that reflects the binary nature of choices.
  • 🎼 Music from patterns: The artist translates the pattern into musical notes, creating a structured yet harmonious song that can be played on a piano.
  • 🤖 The Abba Kaba Music Machine: A physical device built to play the song based on the mathematical pattern, demonstrating the tangible connection between math and music.
  • 🔢 Binary and patterns: The artist explores binary numbers and discovers patterns within them, which are then used to create visual art and further inspire creative projects.
  • 🐟 Pisces artwork: Binary patterns are used to create an artwork filled with fish shapes, showcasing the aesthetic potential hidden in mathematical structures.
  • 🧊 3D art and architecture: The artist extends the pattern to three dimensions, creating sculptures and models that resemble steps or a futuristic landscape.
  • ✍️ Literature and world-building: The patterns inspire a fantasy novel set on a planet where the mathematical pattern is integral to the world's design and narrative.
  • 🌐 Sharing resources: The artist has made resources available online for others to explore and be inspired by the connection between mathematics and creativity.
Q & A

  • What is the artist's perspective on the relationship between mathematics and life?

    -The artist sees mathematics as deeply connected to life, emphasizing that it is about life, beauty, patterns, and connections, which are some of the most inspiring aspects of existence.

  • What is the Towers of Hanoi puzzle?

    -The Towers of Hanoi is a mathematical puzzle consisting of a stack of discs on some pins. The goal is to move the entire stack to one of the other two locations by moving one disc at a time, without placing a larger disc on top of a smaller one.

  • How did the artist use the Towers of Hanoi puzzle to create art?

    -The artist represented the moves of the puzzle as lengths that doubled, creating shapes and patterns that inspired various forms of art, including landscapes, family trees, and decision trees.

  • What is the 'abba cabba' pattern?

    -The 'abba cabba' pattern is a sequence created by doubling a letter (starting with 'a') and inserting the next letter of the alphabet in between the duplicates. It's a playful and creative way to transform numerical patterns into a linguistic structure.

  • How did the artist use the 'abba cabba' pattern to create a children's story?

    -The artist wrote a story called 'Maggie and the Abba Cabbage Genies,' where a young girl has to say increasingly complex genie names based on the 'abba cabba' pattern to call more powerful genies.

  • What is the significance of the binary system in the artist's work?

    -The binary system is used to explore patterns and structures in mathematics. The artist found 'abba cabba' patterns within binary numbers and used these patterns to create visual art, including a piece called 'Pisces' that represents fish made from binary numbers.

  • How did the artist transform the 'abba cabba' pattern into music?

    -The artist used the pattern to create a musical sequence where each letter corresponds to a musical note, and the pattern is repeated and extended across the musical scale, resulting in a structured yet harmonious piece of music.

  • What is the 'Abba Kaba Music Machine'?

    -The 'Abba Kaba Music Machine' is a physical device built by the artist that plays the 'abba cabba' pattern by dropping balls onto a xylophone. It incorporates a simple mechanism to demonstrate the pattern musically.

  • How did the artist use the 'abba cabba' pattern to inspire a fantasy novel?

    -The artist created a fantasy world and novel called 'Abba Qabex,' where the 'abba cabba' pattern is a central theme. The novel is set on a planet with landscapes, people, monsters, and magic all connected to the pattern.

  • What resources are available for those interested in exploring the 'abba cabba' pattern further?

    -The artist has made various resources available on abacabba.org, where people can view more art, listen to music, download activities or games, and explore the 'abba cabba' pattern further.

  • What is the overarching message the artist hopes to convey through their work with the 'abba cabba' pattern?

    -The artist aims to demonstrate that mathematics is a source of inspiration and creativity, and that by playing with patterns and ideas, one can create a wide range of artistic expressions, from visual art to literature.

Outlines
00:00
🎨 The Artistic Fusion of Mathematics and Life

The speaker, an artist inspired by mathematics, challenges the common perception of math as dull and unrelated to life. They aim to demonstrate how mathematical patterns can inspire various forms of art, including music, poetry, and literature. The narrative begins with the Towers of Hanoi puzzle, which, despite its simplicity, reveals intricate patterns that the artist uses to create visual representations, such as landscapes and family trees. These patterns are then connected to broader concepts like decision-making and the metaphorical 'tree of life,' leading to a multifaceted exploration of the beauty and interconnectedness found within mathematical structures.

05:01
📚 The 'Abba Cabba' Pattern and Its Creative Evolution

The artist introduces the 'Abba Cabba' pattern, a sequence derived from the Towers of Hanoi puzzle, and explores its potential for creative expression. By assigning letters to numbers and expanding the pattern, the artist creates a lengthy, magical word that serves as the basis for a children's story and a musical composition. The pattern also inspires the construction of a mechanical music box, the 'Abba Kaba Music Machine,' which plays the pattern using a system of gates and balls. The artist further delves into the pattern's mathematical properties, such as its connection to binary numbers and its potential for visual representation, leading to the creation of a piece of op art and a 3D pop-up card.

10:01
🎼 The Melodic and Structural Beauty of 'Abikabha'

The artist explores the musical implications of the 'Abba Cabba' pattern by translating it into a sequence of musical notes, creating a composition that sounds harmonious despite its structured nature. This leads to the idea of building a machine to play the song automatically, resulting in the 'Abba Kaba Music Machine.' The artist also discusses the pattern's presence in binary numbers and how it can be visualized in a creative and engaging way, leading to the creation of a symmetrical artwork filled with fish shapes, titled 'Pisces,' which also has an upside-down symmetry in its name.

15:03
🌌 The 'Abba Qabex' Universe: A Mathematical Fantasy

The artist extends the 'Abba Cabba' pattern into three dimensions, creating a series of interconnected steps that form a 3D structure. This structure is further developed into a fantasy novel called 'Abba Qabex,' set on a planet where the pattern is a central element. The novel incorporates people, monsters, magic, and mathematics, all connected to the 'Abba Kaba' pattern. The artist emphasizes the magical qualities of mathematics and encourages others to explore patterns and ideas, suggesting that they may discover their own beautiful creations through this process. Resources related to the pattern and its applications are made available on the website abacabba.org.

Mindmap
Keywords
💡Towers of Hanoi
The Towers of Hanoi is a mathematical puzzle that consists of three pegs and a number of disks of different sizes which can slide onto any peg. The puzzle starts with the disks in a neat stack in ascending order of size on one peg, the smallest at the top, thus making a conical shape. The objective of the puzzle is to move the entire stack to another peg, obeying the rule that only one disk can be moved at a time and no larger disk may be placed on top of a smaller disk. In the video, the artist uses this puzzle to demonstrate how mathematical patterns can inspire creativity, leading to the creation of art, music, and poetry.
💡Mathematical Patterns
Mathematical patterns refer to the regularity and repetition of numbers or shapes in mathematics. In the context of the video, the artist explores how these patterns can be found in various forms of art and creativity. The artist uses the pattern from the Towers of Hanoi puzzle to create visual representations, music, and even literature, showcasing the beauty and interconnectedness inherent in mathematics.
💡Abba Cabba Pattern
The Abba Cabba pattern is a specific sequence created by the artist, which starts with the letter 'a' and successively adds the next letter of the alphabet in the middle of the doubled sequence. For example, 'a' becomes 'abba', then 'abba cabba', and so on. This pattern is used to create a long, magical word that the artist turns into a children's story and a musical composition. It serves as a central theme in the video, illustrating how a simple mathematical concept can be transformed into various forms of art.
💡Binary System
The binary system is a method of representing numeric values using two symbols, typically 0 and 1. It is the foundation of all digital computing. In the video, the artist uses binary to create visual patterns and to explore the connection between numbers and their representation in a different base system. The binary patterns are also used to create a unique piece of art that resembles a tree, demonstrating the aesthetic potential of mathematical concepts.
💡Decision Tree
A decision tree is a diagram used to represent a flow of decisions and their possible consequences. In the video, the artist uses the concept of a decision tree to create a poem that explores different outcomes based on choices. The poem is structured in a way that reflects the branching nature of a decision tree, with each choice leading to a different verse and emotional outcome, thus connecting the mathematical concept with human emotions and decision-making.
💡Fibonacci Sequence
Although not explicitly mentioned in the transcript, the Fibonacci sequence is a series of numbers where each number is the sum of the two preceding ones, usually starting with 0 and 1. This sequence often appears in natural patterns and is closely related to the patterns the artist explores. The artist's use of doubling lengths and the progression of shapes and notes in the video can be associated with the Fibonacci sequence, which is a key concept in understanding the beauty and structure found in nature and mathematics.
💡Nature and Mathematics
The video emphasizes the connection between nature and mathematics, suggesting that mathematical patterns are not only abstract concepts but are also found in the natural world. The artist points out that patterns such as the family tree and the growth patterns in nature are inherently mathematical. This connection is used to inspire art that reflects the beauty and structure observed in nature.
💡Art and Mathematics
The video explores the intersection of art and mathematics, showing how mathematical concepts can inspire various forms of artistic expression. From visual art that represents mathematical patterns to music and literature that are structured around mathematical principles, the artist demonstrates that mathematics is a rich source of creativity and inspiration.
💡Music and Mathematics
The artist uses mathematical patterns to create music, specifically by translating the Abba Cabba pattern into a musical composition. This demonstrates the harmony between mathematics and music, as both rely on structure and patterns. The video shows how mathematical sequences can be used to create melodies and rhythms, highlighting the interconnectedness of these two domains.
💡Literature and Mathematics
The artist creates a piece of literature, a poem called 'Decision Tree,' which is structured around the concept of a decision tree, a mathematical model. The poem explores different outcomes based on decisions, reflecting the branching structure of a decision tree. This piece illustrates how mathematical ideas can be used to craft narratives and evoke emotions, bridging the gap between the abstract world of numbers and the expressive world of literature.
💡3D Modeling and Mathematics
The artist extends the 2D patterns into three-dimensional models, creating a fantasy world inspired by mathematical patterns. This process involves using mathematical concepts to design landscapes and structures, demonstrating how mathematics can be a foundation for imaginative and creative design. The 3D models and the fantasy novel 'Abba Qabex' that the artist writes are based on these mathematically inspired designs, showing the depth and versatility of mathematical concepts in creative storytelling.
Highlights

The artist uses mathematics as a source of inspiration for their art, demonstrating the connection between math and beauty.

The Towers of Hanoi puzzle is used to showcase the interesting patterns and structures found within mathematics.

The artist represents the puzzle's solution as lengths that double, creating shapes and patterns that resemble landscapes and mountains.

The pattern from the puzzle is connected to an English ruler, revealing a fractal tree shape that is found in nature and family trees.

The fractal tree inspires a picture using actual people to represent the interconnectedness of generations.

The concept of decision-making and its impact on life is explored through a poem called 'Decision Tree', which has 16 variations.

The poem structure suggests that happiness in life, like in mathematics, comes from consistency between our actions and our rules.

The artist introduces the 'abba cabba' pattern, a creative way to convert numerical sequences into a word pattern.

The 'abba cabba' pattern is extended to create the world's longest published word, consisting of over 67 million letters.

The artist wrote a children's story called 'Maggie and the Abba Cabbage Genies', inspired by the 'abba cabba' pattern.

Musical notes are associated with letters to create a structured yet pleasing melody that can be played on a piano.

The artist built an 'Abba Kaba Music Machine' that plays the pattern by dropping balls onto a xylophone.

Binary numbers are used to create visual patterns that resemble trees and fish, showcasing the aesthetic in mathematical structures.

The artist explores three-dimensional representations of the pattern, creating a pop-up card and a fantasy world for a novel.

The fantasy novel 'Abba Qabex' incorporates people, monsters, magic, and mathematics, all connected to the 'abba kaba' pattern.

The artist emphasizes the potential for mathematical patterns to inspire a wide range of creative disciplines.

Resources and activities related to the 'abba cabba' pattern are made available on abacabba.org for further exploration.

Transcripts

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Mathematical ArtTowers of HanoiCreative InspirationPattern RecognitionDecision TreesBinary NumbersMusical NotesNature PatternsFantasy NovelInteractive ArtEducational Resource