Lightning calculation and other "mathemagic" | Arthur Benjamin

TED
9 Jan 200815:15
EducationalLearning
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TLDRIn this engaging presentation, 'mathemagician' Art Benjamin dazzles the audience with his mental arithmetic prowess. He challenges volunteers to square numbers using calculators, while he squares them in his head, even with multi-digit numbers. Benjamin also demonstrates his ability to determine the day of the week for any given date and concludes with a complex five-digit number squaring, all while providing insights into his mental strategies and mnemonic devices, leaving the audience in awe of his 'mathemagics'.

Takeaways
  • 😀 Art Benjamin is a 'mathemagician' who combines math and magic to perform 'mathemagics'.
  • 🤔 He starts by asking the audience if anyone has a calculator and invites four volunteers on stage.
  • 🔢 Benjamin tests the calculators by having the volunteers multiply two two-digit numbers (22 and 47) to ensure they work correctly.
  • 🎓 He demonstrates how to square numbers on a calculator, explaining the process and mentioning the shortcut method.
  • 🏃‍♂️ In a challenge, Benjamin squares four two-digit numbers in his head faster than the volunteers can do on their calculators.
  • 📈 He then squares three-digit numbers in his head, again outperforming the volunteers, and even squares a four-digit number without assistance.
  • 🤔 Benjamin engages the audience in a guessing game where he correctly identifies the missing digit in a seven-digit number after hearing six of them.
  • 🗓️ He shows his ability to determine the day of the week someone was born by asking for their birth date and year, and then confirming with a calendar book.
  • 🧠 He attempts to square a five-digit number in his head, explaining his thought process and mnemonic devices used for calculations.
  • 📉 Benjamin acknowledges the possibility of making a mistake and asks the audience to let him know if he's close, but to confirm if he's correct.
  • 🎉 The presentation concludes with Benjamin successfully squaring a five-digit number in his head and receiving applause from the audience.
Q & A

  • What is the term 'mathemagician' as used by Art Benjamin?

    -A 'mathemagician' is a term coined by Art Benjamin to describe someone who combines the love of math and magic to perform 'mathemagics,' which involves mathematical tricks and demonstrations.

  • Why did Art Benjamin ask for volunteers with calculators on stage?

    -Art Benjamin asked for volunteers with calculators to verify the accuracy of the calculations during his performance and to participate in the demonstration of his mental math abilities.

  • What was the purpose of multiplying 22 by 47 at the beginning of the script?

    -The multiplication of 22 by 47 served as a test to ensure that the calculators brought on stage by the volunteers were functioning correctly, as the correct answer should be 1,034.

  • How did Art Benjamin demonstrate a shortcut for squaring numbers on a calculator?

    -Art Benjamin demonstrated the shortcut by showing how to square a number like five by pressing the number, then the 'times' key, and finally the 'equals' key on most calculators, or using an 'x squared' button on some calculators.

  • What is the significance of squaring four two-digit numbers in Art Benjamin's performance?

    -Squaring four two-digit numbers was a challenge set by Art Benjamin to compete with the volunteers' calculators, aiming to demonstrate his ability to perform mental calculations faster than calculators, even with the use of shortcuts.

  • What was the method Art Benjamin used to square numbers in his head?

    -Art Benjamin used a method of breaking down the problem into smaller parts, such as squaring individual components and then adding them together, which he referred to as 'mathemagics.'

  • How did Art Benjamin involve the audience in the process of squaring three-digit numbers?

    -Art Benjamin asked the audience members to call out three-digit numbers, which he then squared in his head and provided the result, engaging the audience in the interactive demonstration.

  • What was the challenge presented by Art Benjamin when he attempted to square a four-digit number?

    -The challenge was to square a four-digit number, which he created by having the audience call out individual digits, demonstrating his mental calculation skills on a larger scale.

  • How did Art Benjamin attempt to determine the missing digit in a seven-digit number?

    -Art Benjamin asked the volunteers to call out any six digits of their seven-digit number, and he attempted to determine the missing digit by using a combination of mental math and mnemonic devices.

  • What is the significance of the mnemonic device mentioned by Art Benjamin?

    -The mnemonic device is a phonetic code that Art Benjamin uses to convert numbers into words for easier memorization and later retrieval, aiding in his mental calculations.

  • How did Art Benjamin conclude his performance with a five-digit number squaring?

    -Art Benjamin concluded his performance by attempting to square a five-digit number in his head, thinking out loud to share his thought process, and using a combination of mental math and mnemonic devices to arrive at the answer.

Outlines
00:00
🎩 Introduction to Mathemagics

Art Benjamin introduces himself as a 'mathemagician,' a blend of mathematics and magic, and engages the audience by asking for volunteers with calculators. He tests the calculators with a multiplication problem and then demonstrates a shortcut for squaring numbers. He challenges himself to mentally square four two-digit numbers faster than the volunteers can with their calculators, racing against time and successfully providing the correct answers.

05:01
🔢 Advanced Mathemagics: Squaring Larger Numbers

Building on the initial demonstration, Art Benjamin squares three-digit numbers called out by the audience, providing the answers without the aid of a calculator. He then attempts to square a four-digit number, using a random method to select the number and successfully calculates it mentally. The audience is impressed by his ability to perform complex calculations swiftly, showcasing the capabilities of the human mind over technology.

10:04
📊 Interactive Math Challenge: Multiplying and Deciphering Numbers

Art Benjamin transitions to a more interactive segment, asking the audience to multiply a given number by a three-digit number of their choice without revealing it. He then correctly guesses the missing digit from a series of seven-digit numbers provided by the audience, demonstrating an impressive feat of mental calculation and memory. This segment highlights the interactive and engaging nature of his performance.

15:05
🗓️ Birth Day Calculations and Calendar Mystery

Art Benjamin diversifies his act by asking audience members for their birth dates and correctly identifying the day of the week they were born. He uses a book of calendars as a prop, but also demonstrates his ability to calculate the day of the week for any given date, even challenging himself with dates outside the 20th century. This segment adds a historical and personal touch to his mathemagics.

🧠 Concluding with a Mental Calculation of a Five-Digit Number

In the final segment, Art Benjamin attempts to square a five-digit number in his head, a task typically requiring a 10-digit calculator. He thinks out loud, revealing his thought process and mnemonic techniques, which include converting numbers into words for easier recall. Despite the complexity of the calculation, he successfully arrives at the correct answer, impressing the audience with his 'mathemagics' and concluding the performance on a high note.

Mindmap
Keywords
💡Mathemagician
A 'mathemagician' is a term coined by Art Benjamin to describe his unique blend of mathematics and magic. In the context of the video, he uses this title to introduce himself and his performance style, which involves performing mental calculations that are typically done with a calculator. This term is central to understanding the theme of the video, which is about showcasing the power of mental math and the performer's ability to perform complex calculations quickly.
💡Calculator
A calculator is an electronic device used to perform mathematical operations. In the video, Art Benjamin uses calculators as a benchmark for his mental math skills, challenging himself to perform calculations faster than the audience can with their calculators. This serves to demonstrate the impressive nature of his mental math abilities and is a recurring element throughout the video.
💡Square
In mathematics, 'squaring' a number means multiplying the number by itself. This concept is fundamental to the video as Art Benjamin demonstrates his ability to mentally square numbers, both two-digit and three-digit, faster than the audience can with their calculators. The script includes examples like '5 squared' which equals 25, and he later squares more complex numbers like '987 squared'.
💡Mnemonic device
A mnemonic device is a memory aid or technique used to help remember information. In the video, Art Benjamin mentions using a phonetic code, a type of mnemonic device, to convert numbers into words for easier mental storage and retrieval. This technique is crucial to his ability to perform complex mental calculations and is highlighted as a key part of his 'mathemagics'.
💡Two-digit number
A two-digit number is any number from 10 to 99. In the video, Art Benjamin starts by asking the audience to provide two-digit numbers, which he then uses to demonstrate his mental multiplication skills. The use of two-digit numbers sets the stage for the more complex calculations he performs later in the video.
💡Three-digit number
A three-digit number is any number from 100 to 999. The video progresses from two-digit to three-digit numbers as Art Benjamin challenges himself to square these numbers mentally. This escalation in complexity is part of the narrative that builds suspense and showcases his increasing mental math prowess.
💡Four-digit number
A four-digit number is any number from 1000 to 9999. Art Benjamin takes his mental math to the next level by attempting to square a four-digit number, which is a significant challenge even for calculators. This demonstrates the extreme capabilities of his mental math skills and is a highlight of the video.
💡Random guessing
Random guessing refers to the act of selecting an answer without any logical basis, purely by chance. In the video, Art Benjamin humorously mentions the odds of guessing correctly as one in 10,000, emphasizing the precision and skill involved in his mental calculations, rather than relying on mere chance.
💡Day of the week
Determining the day of the week for a given date is a complex task that involves understanding calendar systems and possibly using algorithms. In the video, Art Benjamin engages with the audience by asking for their birth dates and then correctly identifying the day of the week they were born. This demonstrates his ability to perform mental calculations that are typically more cumbersome.
💡Phonetic code
A phonetic code is a system used to represent the sounds of speech in writing. In the context of the video, Art Benjamin uses a phonetic code to convert numbers into words, aiding his mental calculations. This technique is part of his 'mathemagics' and is crucial for his ability to perform large mental calculations.
💡Ten-digit calculator
A ten-digit calculator is capable of handling numbers with up to ten digits. In the video, Art Benjamin challenges himself to square a five-digit number, which would result in a ten-digit number, using only his mental math skills. This showcases the upper limits of his abilities and the extent to which he can outperform even advanced calculators.
Highlights

Art Benjamin introduces himself as a 'mathemagician', combining math and magic.

Audience members are invited on stage with calculators to verify the performance.

A quick test of calculator functionality using the multiplication of two-digit numbers.

Demonstration of a shortcut for squaring numbers on calculators.

Benjamin squares four two-digit numbers mentally, faster than the volunteers with calculators.

Audience participation in calling out three-digit numbers to be squared.

Correct mental squaring of challenging three-digit numbers without a calculator.

Benjamin attempts to square a four-digit number mentally, showcasing impressive calculation skills.

Interaction with the audience to create a random four-digit number for squaring.

A humorous moment about the limits of calculator capacity.

A volunteer with a 10-digit calculator is identified for a more complex challenge.

Benjamin squares a five-digit number in his head, thinking out loud to share his process.

Explanation of the phonetic code mnemonic device used for mental calculations.

A light-hearted moment where Benjamin asks for confirmation without revealing mistakes.

Successful mental squaring of a five-digit number, impressing the audience.

Benjamin offers to determine the day of the week for audience members' birthdays.

Use of a historical book of calendars to verify the day of the week for a given date.

A closing challenge with a 10-digit calculator, squaring a number while explaining his method.

Benjamin concludes the presentation with a successful mental calculation and a humorous remark.

Transcripts

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