There is something unique about Alice and her mesmerizing adventures in Wonderland – something special that catches our eyes. Otherwise, how do you explain the countless adaptations, puzzles, and works, inspired by Lewis Carroll’s books: “Alice’s Adventures in Wonderland”, and “Through the Looking-Glass, and What Alice Found There”. It must be something fundamental in human nature, and it’s probably has something to do with fantasy, imagination, the written word, and math.
We too wrote a few articles about Alice: Alice in Mathland, and Alice Through the Math-Glass, based on each Alice’s book, respectively. What came as a surprise to us, is what we didn’t find in these books: Palindromes. So today, so close to Lewis Carroll’s birthday, January 27 (1832), we will do a small gift as an appreciation to Carroll’s creation, and talk about palindromes.
A palindrome is a word, number, phrase, or other sequences of characters that reads the same backward as forward, such as refer or level. It includes numbers like 12022021 (hey! It’s also a date: 12/02/2021, which is either February 12, 2021, or December 2, 2021 – depending on your date format. A great date(s) for palindromic celebrations!)
In sentences punctuation, capitalization, and spaces are usually ignored, as in the following famous palindromes: “Madam, I’m Adam” (1861), “A man, a plan, a canal – Panama” (1948), “Won’t lovers revolt now?” and “So many dynamos!”. Although, sometimes spaces are included, which makes it more challenging: “Step on no pets”, “Able was I ere I saw Elba” (alluding to the first exile of Napoleon to Elba) and the very nice example by a Stack Exchange user: “Is it crazy how saying sentences backwards creates backwards sentences saying how crazy it is?” Note that the last sentence is a word-by-word palindrome, where the words are read as-is without reversing the letters.
By the way, names can also be palindromes: Bob, Anna, Hannah, Eve, and Elle.
Palindromes are quite ancient. It seems like there is something appealing to the human mind when you can read a sentence both forward and backward. For example, a palindrome was found as a graffito at Herculaneum, a city buried by ash in 79 CE. This palindrome, called the Sator Square, consists of a sentence written in Latin: “Sator Arepo Tenet Opera Rotas” (“The sower Arepo holds with effort the wheels”). It is remarkable for the fact that it can be arranged into a word square that reads in four different ways: horizontally or vertically from either top left to bottom right or bottom right to top left. As such, they can be referred to as palindromic.
If the name “Sator” reminds you of something, it’s probably of the recent Christopher Nolan’s movie Tenet. The whole movie is sort of a palindrome by itself, and we will say no more to not ruin your fun watching it, except that you can pay attention that Nolan used every word from the “Sator Square” in his move, including the movie’s name.
Byzantine Greeks often used the palindrome ΝΙΨΟΝ ΑΝΟΜΗΜΑΤΑ ΜΗ ΜΟΝΑΝ ΟΨΙΝ upon baptismal holy water fonts, like outside the church of Hagia Sophia in Constantinople. It is attributed to Gregory of Nazianzus (329- 390), which means “Wash the sins, not only the face”.
Now you see why it was such a surprise the absence of palindromes in Carroll’s works, who dedicated his literary creations to wordplay, brainteasers, and verbal logic. It’s especially missing in the “Through the Looking-Glass” which is all about symmetry. Nevertheless, Carroll did contribute to the palindrome-related genre: He created or at least was the first reference to the underlying concept of the Semordnilap.
Semordnilap is a special type of anagram (a word or phrase formed by rearranging the letters of a different word or phrase, typically using all the original letters exactly once.) It is a word that, when spelt backwards, gives you another word. For instance, if you reverse the letters in the word “strap”, you get “parts”. This means that “strap” is a semordnilap. Other examples in English are “desserts”/”stressed”, “Evian”/”naive”, and “no”/”on”.
As you may notice, “Semordnilap” is “palindromes” spelled backwards. Presumably, this is Lewis Carroll’s version of the old complaint that the word “palindrome” is not a palindrome.
To fix the unbelievable situation of absence of palindromes in Alice’s adventures, Sam Loyd (January 30, 1841 – April 10, 1911. Note that his birthday is also right around the corner!), an American chess player, chess composer, puzzle author, and recreational mathematician, created the following puzzle in 1897:
CONTINUING A former reference to Alice’s trip through wonderland. We call attention to her remarkable experiences with the Cheshire cat which had such a way of vanishing away into thin air, so that nothing but its irresistible smile remained. Of course every one remembers the dilemma of the king’s executioner, who, being commanded to cut off the head from a cat which had no body, was as sorely puzzled as was the Irishman who was told to decapitate the head of an elephant from the trunk. When Alice first saw her feline friend she desired to find out what species of animal it was, and as they always ask questions in wonderland by writing, she wrote out her query. But as they generally read things backward, or up and down in wonderland, she wrote it as shown in the puzzle. This permits readers to commence and end where they please, just as they should in wonderland; but, as Lewis Carroll forgot to give the answer to his conundrum of why a desk was like a crow, he also forgot the main question in this riddle, which is simply to tell how many ways there are to read the question: “Was it a cat I saw?”
You can find the source here, and there is a web-site, that is fully dedicated to this riddle, here: wasitac.
How many ways did you find? And, can you think of your own palindromes?
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