Palindromes:semordnilaP

• A man, a plan, a canal: Panama
• Sums are not set as a test on Erasmus.
• Rise to vote, sir.
• Lager, sir, is regal.
• Cigar? Toss it in a can. It is so tragic.

What do all the above sayings have in common?

Bob,madam, 414, 1991, and the phrases on the Riverdeep.net home page are all examples of palindromes—a word, number, sentence, or verse that reads the same forward or backward. The name "palindrome" derives from the Greek palin + dromo, which means "running back again." Most sources claim that the first person to publicize palindromes was Sotades of Maronea,a Greek poet who lived in Egypt in the third century, B.C. In fact, palindromes are also called "sotadics."

The Greeks and the Romans frequently used palindromes as inscriptions. The following two-dimensional palindrome was found on a Roman wall in Pompeii, and roughly translates as "Arepo the sower holds the wheels with care." It can be read in four directions: upward, downward,backward, and forward. Like many palindromes, the form seems more interesting than the message:

Here are some interesting palindrome tidbits: 

• True palindromes are read letter for letter (or number for number) in either direction. Punctuation and spaces are ignored.

 
• The longest English single-word palindrome in common use is redivider.

• Two places in the U.S. with palindromes for names are Kanakanak (Alaska) and Wassamassaw (Road, near Summerville,South Carolina).

 
• Two titles that have been used for several albums are LiveEvil (Black Sabbath and Miles Davis), and its variant, Evil Live (Misfits). The Swedish group Abba had a hit called SOS.

 
• There was an actual bakery in Yreka, California: Yreka Bakery.

 
• Ripley's Believe It or Not featured the story of Leon Noel, born on Christmas Eve 1908 in Valparaiso. He died on Christmas day, '99. An Internet search shows that the palindromic name Leon Noel isn't so uncommon.

 
• The term palindrome is not itself a palindrome. According to the Merriam-Webster Dictionary, the word entered the English language in approximately 1629.

 
• Word palindromes are sentences that are read in either direction word by word: 
• First ladies rule the state, and state the rule,"Ladies First." 
• Fall leaves after leaves fall.

Sometimes you have to repeat the process several times to "reduce" the original number to a palindrome:

39 (not a palindrome)
39 + 93 = 132 (not a palindrome)
132 + 231 = 363 (yes a palindrome, in two steps)

Notice that we said a palindrome can be formed from almost any number. Some numbers require many steps to form a palindrome. The numbers 89 and 98, for example, take 24 steps to reduce the original number to a palindrome — and that palindrome is 13 digits long! The number 196 is the only number less than 10000 that has not yet been reduced to its palindrome. Math enthusiasts have tried using computers to reduce 196 to its palindrome. After thousands of steps and with the number reaching millions of digits, 196 has yet to reveal its palindrome.

In an article entitled "Palindromes and the Laws of 11," published in the Arithmetic Teacher, January 1985, Clarence Dockweiler observed that when using this process to create a palindrome,if the resulting palindrome has an even number of digits, it will be divisible by 11.

1326 + 6231 = 7557 (a palindrome)
7557 ÷ 11 = 687 (divisible by 11)

Palindrome Sees
Are palindromes just a fun word or number game? Maybe palindromes can show us that there are many ways of looking at things. In Barbara Kingsolver's best-selling novel The Poisonwood Bible(Harper Collins, 1998), the character Adah walks unsymmetrically with a limp. Yet intellectually, she loves symmetry and especially "palindromes, with their perfect, satisfying taste." She explains: 

When I finish reading a book from front to back, I read it back to front. It is a different book, back to front, and you can learn new things from it. It from things new learn can you and front to back book different a is it?

You can agree or not, as you like. This is another way to read it, although I am told a normal brain will not grasp it: Ti morf sgniht wen nrael can uoy dna tnorf ot kcab koob tnereffid a si ti.The normal, I understand, can see words my way only if they are adequately poetic: Poor Dan is in a droop. (p. 56)

In the 1989 book, Drawing on the Right Side of the Brain, Dr. Betty Edwards conveys her technique for teaching drawing skills based on the knowledge that the brain has two sides: a left brain that is the center of verbal and analytical thought, and a right brain that is nonverbal and intuitive for thinking in patterns and pictures. Her theory is that people can be taught to draw by training themselves to use the right, nonverbal side of the brain (R-mode, she terms it) while drawing. 

Edwards proposes a series of exercises in which the student turns the image to be copied upside down. "Familiar things do not look the same when they are upside down," she explains. Therefore, the verbal left side of the brain refuses to process the image, and the right side takes over. Edwards sums up the insights gained from the exercises:one can bring the shift from L-mode to R-mode under conscious control, and the shift to R-mode enables the student to see in the way a trained artist sees. 

Because palindromes are verbal, Edwards' drawing technique does not apply to them directly. However, her theory may shed light on the perceptual possibilities put forth by the character Adah. Can you explain how Edwards' theory might be applied to palindromes? 

• Can the "running back again" be applied not just to words and numbers, but also to physical sequences? Before considering the physical and philosophical implications of reversible events, see the activity Physics Explorer: Reversibility.

For a story written using palindromes, go to mywave, the student area of Riverdeep.


• Enjoy one of these books: 
• Sit on a Potato Pan, Otis!: More Palindromes, by Jon Agee. These palindromes and cartoons will keep you laughing. 
• Words at Play: Quips, Quirks & Oddities, by O.V. Michaelsen (himself author of the "A man, a plan, a canal: Panama" palindrome) and Richard Lederer 
• The Poisonwood Bible 
• The New Drawing on the Right Side of the Brain