Memorizing the Irrational
March 14th is Pi (Approximation) Day, a glorious celebration of the mathematical constant π.
Why March 14 you ask? Because the Ancient Greek mathematician Archimedes first approximated π as 3.14. [Since π is an irrational number, some people argue we should celebrate Pi Day on July 22 or 22/7 if you live in Europe.]
I remember the first time I discovered π on my calculator, I spent the next hour memorizing the constant. To this day, I can still recall 3.141592654 (my calculator rounded the last digit, mind you) without breaking a sweat. After the billionth digit, however, things start to get a little hazy.
π is an irrational and transcendental number, meaning that its decimal form never repeats. Knowing the first 10 digits does not give you any insight into the next 10. The famous physicist Richard Feynman once joked that he had memorized π to a string of six sequential 9s [now known as Feynman point] just so could end his recitation with "nine nine nine nine nine nine and so on." Supercomputers are tested by how fast and far out they calculate π. In January 2010, a computer took 131 days to compute more than 2.7 trillion digits of π.
My early attempts to memorize π fall right into that memorization range revealed by Miller's famous psychological study "The Magical Number Seven, Plus or Minus Two: Some Limits on Our Capacity for Processing Information." On average, we have the cognitive capacity to memorize a chunk of about 5-9 digits. Think about how much easier it is to memorize a local 7 digit number than a long distance 10 digit number.
Yet these cognitive limitations have not stopped individuals from memorizing this irrational constant. As of October 2006, the world record for the number of digits memorized is 100,000.
Imagine that for a moment. 100,000 digits.
Which brings us to piphilology: the use of mnemonic devices to remember a span of digits in π.
One method involves the use of piems, or poems, in which the length of each word represents a single digit of π. Cadaeic Cadenza is perhaps the most famous example:
One / A Poem / A Raven / Midnights so dreary, tired and weary,
One = 3 letters = 3
A = 1 letter = 1
Poem = 4 letters = 4
etc.
The use of this mnemonic device allows a would be π memorization scholar to remember the first 3834 digits of π. Remember: before The Iliad and The Odyssey were put to paper, they were recited orally by memory. Creating a story or narrative helps facilitate the memorization process.
Unfortunately, if we are going for the π World Record, 3834 is not going to cut it.
A former World Record holder used a technique called the method of loci, which is a fancy and antiquated way of saying visual mnemonics. The method of loci involves using a unique and vivid image to commit a word or digit to long term memory. In the case of the world record holder, he envisioned himself walking down his neighborhood and each landmark he passed represented a string of digits. Abstract, but apparently it works.
You will probably never attempt to commit π to memory. But the next time March 14/July 22 rolls around or you find yourself measuring the circumference of a circle, take a good hard look at π. Although π in its representation as a letter of the Greek alphabet may look harmless, it is a mathematical concept of unfathomable magnitude.
100,000 memorized digits seems very impressive, but that is only 3.7037037 × 10-8 [entirely unrelated: I love that the HTML for superscript is the very bro "sup"] of the known digits of π.
It is like the furthest depths of the ocean: for all of our understanding, we simply do not know where either ends.
Why March 14 you ask? Because the Ancient Greek mathematician Archimedes first approximated π as 3.14. [Since π is an irrational number, some people argue we should celebrate Pi Day on July 22 or 22/7 if you live in Europe.]
I remember the first time I discovered π on my calculator, I spent the next hour memorizing the constant. To this day, I can still recall 3.141592654 (my calculator rounded the last digit, mind you) without breaking a sweat. After the billionth digit, however, things start to get a little hazy.
π is an irrational and transcendental number, meaning that its decimal form never repeats. Knowing the first 10 digits does not give you any insight into the next 10. The famous physicist Richard Feynman once joked that he had memorized π to a string of six sequential 9s [now known as Feynman point] just so could end his recitation with "nine nine nine nine nine nine and so on." Supercomputers are tested by how fast and far out they calculate π. In January 2010, a computer took 131 days to compute more than 2.7 trillion digits of π.
My early attempts to memorize π fall right into that memorization range revealed by Miller's famous psychological study "The Magical Number Seven, Plus or Minus Two: Some Limits on Our Capacity for Processing Information." On average, we have the cognitive capacity to memorize a chunk of about 5-9 digits. Think about how much easier it is to memorize a local 7 digit number than a long distance 10 digit number.
Yet these cognitive limitations have not stopped individuals from memorizing this irrational constant. As of October 2006, the world record for the number of digits memorized is 100,000.
Imagine that for a moment. 100,000 digits.
Which brings us to piphilology: the use of mnemonic devices to remember a span of digits in π.
One method involves the use of piems, or poems, in which the length of each word represents a single digit of π. Cadaeic Cadenza is perhaps the most famous example:
One / A Poem / A Raven / Midnights so dreary, tired and weary,
One = 3 letters = 3
A = 1 letter = 1
Poem = 4 letters = 4
etc.
The use of this mnemonic device allows a would be π memorization scholar to remember the first 3834 digits of π. Remember: before The Iliad and The Odyssey were put to paper, they were recited orally by memory. Creating a story or narrative helps facilitate the memorization process.
Unfortunately, if we are going for the π World Record, 3834 is not going to cut it.
A former World Record holder used a technique called the method of loci, which is a fancy and antiquated way of saying visual mnemonics. The method of loci involves using a unique and vivid image to commit a word or digit to long term memory. In the case of the world record holder, he envisioned himself walking down his neighborhood and each landmark he passed represented a string of digits. Abstract, but apparently it works.
You will probably never attempt to commit π to memory. But the next time March 14/July 22 rolls around or you find yourself measuring the circumference of a circle, take a good hard look at π. Although π in its representation as a letter of the Greek alphabet may look harmless, it is a mathematical concept of unfathomable magnitude.
100,000 memorized digits seems very impressive, but that is only 3.7037037 × 10-8 [entirely unrelated: I love that the HTML for superscript is the very bro "sup"] of the known digits of π.
It is like the furthest depths of the ocean: for all of our understanding, we simply do not know where either ends.
posted by d l wright at 4/09/2010 09:31:00 AM
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