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Tadashi Tokieda - Magic with a ribbon, paperclips, rubber bands

Simons Center for Geometry and Physics・50 minutes read

Tadashi Tokieda uses everyday objects to explain mathematical concepts, emphasizing a deeper understanding beyond calculations and formulas. He showcases a magic trick with paper clips and rubber bands to demonstrate nature's simplicity and the importance of careful observation in science.

Insights

  • Tadashi Tokieda, a mathematician, uses everyday objects to teach math beyond numbers and formulas, emphasizing observation and guessing in problem-solving.
  • The concept of Borromean links, showcased through paper clips and rubber bands, highlights the unexpected outcomes in linking objects, emphasizing the importance of orientation and caution in assuming safety through more connections.

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Recent questions

  • What does Tadashi Tokieda specialize in?

    Mathematics

  • How does Tadashi Tokieda explain mathematical concepts?

    Using everyday objects

  • What is the significance of observation in science?

    Identifying subtle differences

  • What is the Borromean link concept?

    Interlocked rings

  • How does Tadashi Tokieda emphasize the importance of orientation in linking objects?

    Orientation affects linking ability

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Summary

00:00

"Mathematician uses everyday objects to teach"

  • Tadashi Tokieda, a renowned mathematician, is the director of mathematical studies at Trinity Hall, Cambridge, and a visiting professor at Stanford University.
  • Tokieda is known for using everyday objects and toys to explain mathematical principles in engaging talks.
  • He emphasizes that mathematics is not just about numbers and formulas but involves a deeper understanding beyond calculations.
  • Tokieda demonstrates a magic trick involving paper clips and a strip of paper to showcase mathematical concepts.
  • The trick involves bending the paper strip and fixing it with paper clips, leading to a surprising link between the clips when pulled.
  • The trick was discovered by someone in the 1950s and has variations involving rubber bands and different configurations.
  • Tokieda highlights the importance of observation in science, pointing out subtle differences in seemingly similar setups.
  • He demonstrates variations of the trick, showing how the position of the rubber band affects whether it stays on the paper or falls off.
  • Tokieda explains the scientific reasoning behind the trick, focusing on the interaction between the paper clips and rubber bands.
  • The audience is encouraged to guess the outcome of combining different versions of the trick, emphasizing the importance of guessing in problem-solving and learning.

16:32

"Nature's Simplicity: Rubber Band Magic Trick"

  • Nature is simple and straightforward, unlike human interactions where second-guessing is common.
  • Demonstrating a magic trick with rubber bands and paper clips to showcase nature's simplicity.
  • Performing the calculation of one plus two, resulting in a long chain of rubber bands and paper clips.
  • Explaining the significance of the rubber bands' connection to the paper in the trick.
  • Performing the calculation of one plus one, showcasing two copies of the same rubber band linked to the paper.
  • Soliciting audience guesses on the outcome of one plus one, leading to a suspension bridge-like configuration of rubber bands and paper clips.
  • Performing the calculation of two plus two, setting up two rubber bands unlinked to the paper.
  • Audience predictions for two plus two, with most expecting the rubber bands to fall off the paper.
  • Revealing the unexpected outcome of two plus two, where the rubber bands form a Borromean link, interlocked and preventing each other from falling.
  • Explaining the Borromean link concept, its historical significance, and its presence in various cultures, including the Miwa Shrine in Japan.

32:51

"Linking and Unlinking Objects: A Scientific Approach"

  • Shinto shrines have a unique layout with multiple gates and buildings before reaching the main worship area, which is actually the forest and mountain.
  • The coat of arms of a specific shrine is a Borromean link, symbolizing three rings, with examples of similar objects available for purchase.
  • A wooden object made of three pieces can be manipulated to appear as if two pieces can be separated when one disappears.
  • A demonstration with two loops shows how they can be linked and unlinked by exchanging positions, showcasing the concept of Borromean links.
  • Carabiners, used in mountaineering, are designed for easy linking but deliberate unlinking, emphasizing that more links do not always mean increased safety.
  • The concept of Borromean links in safety equipment highlights the potential dangers of assuming increased links equate to enhanced security.
  • A demonstration with paper clips and rubber bands showcases how topology can lead to unexpected results when attempting to link or unlink objects.
  • The importance of orientation in linking objects is highlighted, with a demonstration showing how the orientation of paper clips can affect their ability to be linked or unlinked.
  • The speaker introduces the idea of subtracting paper clips by carefully orienting them to link and unlink them, emphasizing the significance of orientation in the process.
  • The speaker concludes by emphasizing the scientific approach to understanding complex concepts through experimentation and observation, highlighting the importance of careful attention to detail in linking and unlinking objects.

48:15

"Paper clip trick surprises scientists"

  • Paper clips are linked tightly to avoid tearing the paper.
  • Failure in orientation choice can lead to bending or tearing of paper clips.
  • Anecdote about George Bernard Shaw and Winston Churchill's teasing friendship.
  • Scientific research involves finding surprises and developing them.
  • Majority of scientists find the paper clip trick astonishing.
  • The speaker spent just over an hour exploring the paper clip trick.
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