Fixed Points | Summary and Q&A

TL;DR

An artist and engineer hid a ceramic tile with artworks on the Apollo 12 spacecraft bound for the moon, showcasing the potential existence of an art museum on the moon; this video explores the concept of fixed points in mathematics and science.

Key Insights

• 🧑‍🎨 Portion of artwork by famous artists, including Andy Warhol, were hidden on the Apollo 12 spacecraft and likely still exist on the moon.
• 😥 Brower's fixed point theorem explains the impossibility of fully mixing points within a bounded space continuously without cutting or gluing.
• 😥 Fixed points have applications in various areas, such as mathematics (calculating square roots, the concept of infinity) and science (Coulomb's theorem for temperature and pressure).
• #️⃣ The number four holds a special place in the English language, being the only number spelled with the same number of letters as its quantity.

Transcript

hey Vsauce Michael here there is an art museum on the moon supposedly we can't be sure until we go back and check but as the story goes in 1969 Fred wall Tower from Bell Laboratories and sculptor Forrest Myers convinced an engineer working on the Apollo 12 lunar lander to hide a itsy-bitsy roughly 2 by 1 centimeter ceramic tile within the gold blan... Read More

Questions & Answers

Q: How did an artist and engineer manage to hide artworks on the Apollo 12 spacecraft bound for the moon?

In 1969, artist Forrest Myers and engineer Fred Wallower convinced an engineer working on the Apollo 12 lunar lander to hide a ceramic tile with artworks within the spacecraft's gold blankets. The tile, with pieces by famous artists, including Andy Warhol, remained on the moon when the Apollo 12 team left.

Q: What is Brower's fixed point theorem, and how does it relate to mixing points within a bounded space?

Brower's fixed point theorem states that points within a bounded space cannot be completely mixed up without cutting or gluing. During continuous transformations, the points remain unchanged, leading to the impossibility of fully mixing the points while retaining their positions.

Q: How do fixed points play a role in calculating square roots?

The Babylonian method for calculating square roots utilizes fixed points. By repeatedly averaging guesses, the method converges to a more accurate approximation of the square root. The number of correct digits approximately doubles with each iteration, revealing the power of fixed points in mathematical calculations.

Q: What are Aleph numbers, and how do they relate to fixed points?

Aleph numbers describe the sizes of well-ordered infinities. Each Aleph number represents a larger infinity than the one before it. Interestingly, there is an Aleph fixed point, Aleph Aleph Aleph... This infinity is so vast in size that it is equal to the number of smaller infinities.

Summary & Key Takeaways

• In 1969, an artist and engineer successfully hid a ceramic tile with artworks on the Apollo 12 spacecraft that landed on the moon.

• Brower's fixed point theorem states that certain points remain unchanged after transformation, explaining why it is impossible to fully mix points within a bounded space continuously.

• Fixed points have various applications, such as understanding the properties of numbers, calculating square roots, and determining the number of infinities.