Hidden Math in Alice in Wonderland

Thanks to KiwiCo for sponsoring this video. Hello, I'm Toby and welcome to this video where I'm going to take a little look at the famous story Alice in Wonderland written by Lewis Carroll. It is a very creative story, a little absurd and sometimes strange, but behind some of these writings there is supposedly also a bit of

math

ematics

hidden

. You see, Lewis Carroll is actually the pseudonym of 19th century

math

ematician Charles Dodgson and he initially devised the story for 10-year-old Alice Liddell, daughter of the dean of his university, and told the story to her and her sisters on a trip in ship. in 1864.

The fact that Carroll is much more famous as a writer than as a mathematician perhaps speaks to the fact that his mathematical work was comparatively insignificant. He wrote several books on mathematics, including an elementary treatise on determinants.   His work focused on the fields of geometry, linear and matrix algebra, and mathematical logic, so let's take a look at some of the mathematics that made its way into history. After falling down the rabbit hole, Alice is a little distraught. She says, "I'll try if I know all the things I used to know. Let me see: 4 times 5 is 12, and 4 times 6 is 13, and 4 times 7 is Oh my God!

I'll never make it to 20." At that rate!" According to Martin Gardner, who has written an annotated version of Alice in Wonderland, the simplest explanation here is that Alice adds one every time she does a multiplication by four and if you continue in this way you will get four times 12, being equal up to 19 and children especially only know how to multiply up to 12, so they won't be able to go any further and won't be able to get to 20. This is a meaningless form of multiplication, but it prepares us for the nonsense of coming. Later in the story we meet the Cheshire Cat "'All right,' said the cat; and this time he disappeared very slowly, beginning with the end of the queue and ending with the smile, which remained for some time after the rest. 'Well, I've often seen a cat without a smile,' thought Alice, 'but a smile without a cat is the strangest thing I've ever seen in my life.'" This smile could refer to something abstract or pure mathematics.

That it doesn't necessarily have a cat to go with it, which would be the real-life applications or even the obvious uses of what mathematical researchers are working on, they're doing it just for the pleasure of mathematics itself and they're living in the. abstract world of equations. Over in Wonderland, Alice is talking to Gryphon and Mock Turtle, she asked them about the lessons: "And how many hours a day did you do lessons?" said Alice, in a hurry to change the subject. 'Ten hours the first day,' said the Mock Turtle: 'nine the next, and so on.' 'What a curious plan!' Alice exclaimed. "That's why they're called lessons, because they teach day by day." This was a fairly new idea for Alice and she thought about it for a bit before making her next comment: "So the 11th must have been it." holiday." 'Of course it was,' said the false turtle, 'and how did you manage on the 12th?'   Alice continued enthusiastically: 'Enough of the lessons.'" This could be a fun way to introduce the idea of ​​negative numbers, something that also baffled early mathematicians.   In this case, what would happen on the 12th?

Would the students start teaching the teacher? We then go to the famous tea party scene, there is the Mad Hatter, a hare and a mouse and Alice is also informed of a fourth character, the weather, who is absent from the party due to a fight with the hatter. As a result, the three at the tea party are always stuck at tea time and are always going around and around the table.  "The Hare takes out a clock and Alice comments: 'What a funny clock! It says the day of the month and it doesn't say what time it is.' 'Why should I?' -murmured the hatter. -Does your watch tell you what year it is? "Of course not," Alice replied very easily, "but that's because it stays the same year for a long time."  'Which is exactly what happens with mine,' said the hatter." Later he says that "'It's always six o'clock.' 'Is that the reason why so many things are served for tea here?' Alice asked, "Yes, that's all," said the hatter, "it's always tea time and we don't have time to wash things in between."  "So you keep moving, I guess," Alicia said. "Exactly," said the hatter. "Now, it may be nothing more than the idea of ​​three characters stuck going around and around and not making much sense without time.

It shares some similarities with the idea of ​​quaternions, something that was introduced not long before the story was written. The quaternions consist of three spatial dimensions i, j and k that are imaginary and a fourth dimension that is real and that is perhaps in the tea party the three characters are the imaginary and timeless units. they don't really make sense. One property of quaternions is that when you multiply them they are not commutative, which means that the order really matters. Normal multiplication, like 3 times 4, is the same as 4 times 3 is commutative. quaternions i times j is not the same as j times i and there is a scene at the tea party where this comes up in the language: 'You mean you think you can find the answer?' said the March Hare. said Alice.  "Then you should say what you want to say," continued the March Hare.  "Yes," Alice replied hurriedly, "at least, at least I mean what I say, that's the same thing, you know?"  "They are not even the same thing," said the hatter, "you might as well say that I see what I eat is the same as what I eat." "You could also say," she added in the March Hare, "that liking what I get is the same as getting what I like." So if the characters at the tea party are used to a form of non-commutative multiplication, then perhaps that is why they are so dissatisfied with Alice claiming that word order doesn't matter.

Something that happens a lot to Alice during the story is that she often changes size and she has to eat or drink something to return to the proper proportions. A caterpillar even tells Alice to keep her temper and Alice interprets this to mean not to get angry, however, with our mathematical eyes in place, we could see that Carroll is making a pun and that there is a more mathematical definition of temper. which would have been more familiar to Victorians at the time and has to do with scale and proportions. We see examples of widening and stretching that affect Alice's body differently.

We tend to use the word enlargement even if we are making something smaller, in which case we would simply use a scaling factor between 0 and 1 and the mathematical use of the word enlargement could make sentences like "you will get shorter" a little smaller. a little more sense. The stretches would act on one point, so if Alice stretched around her waist, each point would be twice as far from the center as it used to be, which could explain why her neck grows so much and, in this case, Alice has lost her mathematical temperament. .   The caterpillar could be telling Alice to keep her body in proportion regardless of her size.

Carroll loved Euclidean geometry and wrote some books based on Euclid's elements, and in Euclidean geometry it doesn't matter what the magnitude of the shapes is, the only thing that matters is the relationship between the sides or the proportions. I have seen many other interpretations of the Alice in Wonderland story, people claim to have found comments on social and political issues or references to Victorian literature. Given the author's background, it makes sense that there would be a bit of math involved as well, but perhaps the nature of the story simply lends itself to these interpretations. Anyway, I hope you enjoyed taking a look down the rabbit hole and let me know if you find any other mathematical references.

If you like playing with math or finding creative ways to share science, check out this video's sponsor, KiwiCo. They create these cool hands-on toys and projects designed to expose people to science, technology, engineering, art, and math concepts.   They sent me a couple of their monthly boxes, I have the 'DIY Stereo Headphones' and the 'Electroluminescent Sculptures'. I found that the projects contain a good amount of creativity and problem solving, especially for people encountering these ideas for the first time. Each box comes with all the materials needed for that project, instructions, and an educational magazine. They target different age groups, so you might enjoy the projects yourself or know some kids you want to share the joy of creating with and who knows what they might end up doing with those skills.

I made a flamingo, something Alice later uses to play croquet.   You can get 50% off your first month on any box by visiting kiwico.com/tibees, which will be linked in the description below. Many thanks to KiwiCo and, as always, thanks to my Patreon followers for helping me make these videos. Special shout out to Patreon's Cat of the Day, Xena, Warrior Princess.