When Alice just falls down the rabbit hole and drinks from the bottle that shrinks her. She wonders if she'll just keep getting smaller or go out entirely. This seems like a reference to limits in calculus.

I analyzed Alice in a linguistics seminar at university, and its language games can really teach you a lot about semantics and pragmatics. Learning something about the math behind the story made it even more fascinating to me - thank you!

The original Winnie-the-Pooh book is like this too. Its author A. A. Milne had a degree in mathematics and snuck in some stuff that certainly appears mathematical to me.

Guys, don’t let her great videos distract you from the fact that Mr.Krabs sold spongebob’s Soul for a few cents

Thumbnail meme game is still strong, Toby.

Actually the multiplication she is doing in the hall is even more astonishing! Instead of base 10, use base 18 in answer 1 and add 3 to the base every time she does a new multiplication. Then you'll see that what she's saying is very true indeed. So: 4 * 5 = 12 correct when you use base 18 4 * 6 = 13 correct if you use base 21 4 * 7 = 14 correct if you use base 24 (...) 4 * 12 = 19 correct if you use base 39 And the funny part comes when she stops there, because in base 42 the right answer to 4 * 13 would be 1a. - "She shall never get to 20 at that rate" Besides from that, the number 42 is known to be Lewis Carroll's favorite number and can be seen several times in the book.

"How long is infinity?" asked Alice. "Sometimes just one second" replied the Queen maybe from Through the Looking Glass

your voice is so relaxing

I love how she's an asmrist without even trying

Just imagine publishing multiple books on mathematics only to be described as "un-noteworthy" in that area! :O

The master was an old Turtle - we used to call him Tortoise -" "Why did you call him Tortoise, if he wasn't one?" Alice asked. "We called him Tortoise because he taught us," said the Mock Turtle angrily: "really you are very dull!”

I would love to see a video on explaining some of the most abstract concepts of pure mathematics, you're great at breaking down complex ideas, explaining them, and then reformulating them in a way that doesn't seem so hard to understand.

This was a delight in so many levels. The scientist, the artist and the child in me are all so happy. And my anxious self feels calmer with your voice.

As a philologist I can say that one of the best interpretations that the book has is related to the search for her own identity: Alice is a little girl who suddenly enters the world of Wonderland, where each character is unique and she has to adapt and grow looking for her own individual identity to survive in this world. The first book deals with this search for individual identity that did not exist in Victorian society and less so for women, while in the second, Alice puts this new identity to the test (grows and matures so to speak). The card games of the the first book and the chess of the second is also related to this idea. In addition, the first book talks about language and its ability to control the reality that surrounds us: language is power as the king shows. And I could go on but it would be very long. Good video.

My discrete maths class used the "i mean what I say" part from Alice in wonderland to describe logic.

There's a great article you can find online entitled "When Peter Met Alice," explaining the meeting, as adults, of the namesakes of Alice in Wonderland and Peter Pan. They were never really happy with an author making them famous as children by basing famous fiction works on them. Even worse was Christopher Robin whose father used his real name (and his real childhood stuffed aninals that still get displayed at museums) for the characters in Winnie the Poo and it haunted him for much of his life.

This is one of my favorite books! This is the best math channel on the whole KZfaq.

I loved "Alice in Wonderland" and "Through the Looking-Glass" so much when I was a child that, growing impatient having to wait for an adult, I was inspired to take matters into my own hands, and, apparently through sheer force of will, acquired the ability to read. I still enjoy re-reading them every few years. I think a lot of people conceive of "Alice in Wonderland" in terms of the Walt Disney feature, which is probably among the least egregious adaptations that have been made for screen and stage and I have no criticism of the artists and animators who contributed to that project. Still, such adaptations have always fallen short of the mark for me, and now I realize it's not snobbery. The reason they seem to lack something is just that "Alice" owes so much of its delightful absurdist humor to Carroll's system of formal logic, whose implications, while highly visual on the page, are sufficiently abstract there don't seem to be many obvious choices for the screenwriter seeking to represent the story on film or video. There is a book-length adaptation, though, which I highly recommend: The 1999 edition of "The Annotated Alice" includes extensive and exhaustive footnotes by Martin Gardner*, with alternate versions of the Tenniel illustrations, etc. By the way, I've been really enjoying your videos. Thank you for producing thoughtful and engaging content. Cheers! 💙 * Edit: That's what I get for firing off a comment before watching the video. Lol. I see you're aware of Gardner. Love it!

You mind is brimming with hundreds of ideas, and all presented in a very entertaining and lively fashion. Thank you, Toby, for your wonderful videos.

I’m pretty sure I could listen to her talk all day and never get tired of it.

I like your interpretation of Alice in Wonderland. My chemistry professor would reference Alice in Wonderland when referring to quantum mechanical models in organic chemical reactions. This added interest to the topic.

“Would the students start to teach the teacher?” ❣️Tobie consider writing your own delightful books.

"I hope you've enjoyed a little look down the rabbit hole" Yes. I get it.

I'm currently coloring the Alice's Adventures in Wonderland coloring book illustrated by Charles Santore. 😊 I just caught a bit of a contradiction in the story. Alice says she's _seen many a cat with a grin, but not a grin without a cat..._ But in the another part of the story she says, _I didn't know that Cheshire cats always grinned; in fact, I didn't know that cats could grin._

I feel like every good story has layers to it, and can be read from different angles.

I always knew this stuff was included within the story but nobody ever pointed out the specifics! Love your channel

I legit got scared because of the thumbnail! I was like; wtf happened to Toby,and who is this witch!

Another mathematical connection is that Tenniel's drawings of the Mad Hatter look exactly like Bertrand Russell, who was not born until 1872, after the book was published.

Tibees! It had been a while since I watched your videos. I was in University for Computer Science but I did not do well in traditional education. I realized that while I was interested in CS and Math it was not my true calling. I am much too distracted complete subjects in such a linear fashion, and my passion was ultimately compromised from schooling. I work a regular job now, and live a normal life. However, these types of videos make me happy, and I myself am much happier with computer science and some math staying closer to the hobby side of things. I love the videos!

I have a 3 yr old niece. I am going to have my mom play this for her the next time she is visiting her. I will get her an Alice in Wonderland book like what you have on here. Marvelous video! :)

I "like" your videos before I even see them. I know they're going to be good.

Fun! Did you notice his hat?! “In this style 10/6” which is “irrational” when solved 1.66666666666666666! I love your videos! Thank you sooooo much!

Just commenting to say: that thumbnail is phenomenal!

I also enjoyed Carroll’s short mathematical dialogue “What the Tortoise said to Achilles”

The electro-luminescent sculptures look great for any age. edit: I just tried to find the sculptures on their site, and nothing came up.

Super glad to hear from you!!!! Great topic you have picked!!! Btw, thank you for your time and contribution in informing us !

2:55 Ah, so at the end of time, they will have had 55 hours and 5 minutes of lessons.

Art teachers should collaborate with Mathematics teachers on common hands-on projects/ assignments. Not only would it lessen apprehension of complex concepts by students but it would titillate and stimulate their intellectual curiosity.

6:05 I always thought of this as illustrating the distinction between 'if' and 'iff'. Charles Dodgson was a noted logician. Thanks for another wonderful video!

But when Alice returned to reality, she laughed and said: Yes, Infinity is an illusion Numbers have no end just a myth

This has to be one of my favorite of your videos. I love Alice in Wonderland and math. Thank you!

I am not a mathematician but a composer of music..same difference when you try to delve into the nitty gritty of it all..This lady is very cool..Did not know Lewis liked the math..but so did Debussy..his use of the "Golden section" in "La Mer"..might be worth a look..

I've read about the tea party thing when I was studying quaternions and it's became my favourite part of the story since then.

Great insight, the Mad Hatter scene in Alice in wonderland was written in reference to quaternions which were later incorporated in Heisenbergs matrix mechanics! In the mathematics of 'non-cummutative' geometry, it matters the order in which you do something, for example, take a square photograph of someones face and place it face down. By doing 90 degree rotations clockwise or counterclockwise, you'll find that the face points in a different direction. The same principle is at the heart of many mysteries in quantum mechanics. Heisenberg came up with an uncertainty principle that says we can never know the position and momentum of a particle. The mathematical reason for this uncertainty is that it matters in which order you measure the position and the momentum. Heisenberg invented "matrix mechanics" when he was trying to understand how atoms jump from one state to another, emitting and absorbing radiation. In modern language, Heisenberg took a groupoid with n objects, each one isomorphic to each other in a unique way. He called the objects "states" of a quantum system, and he called the morphisms "transitions". Then, he formed its category algebra. The result is the algebra of n × n matrices!

Carol also had an artistic interest in photography.

In Through The Looking Glass, there is a curious conversation between Alice and the Knight: The name of the song is called 'Haddocks' Eyes.'" "Oh, that's the name of the song, is it?" Alice said, trying to feel interested. "No, you don't understand," the Knight said, looking a little vexed. "That's what the name is called. The name really is 'The Aged Aged Man.'" "Then I ought to have said 'That's what the song is called'?" Alice corrected herself. "No, you oughtn't: that's quite another thing! The song is called 'Ways and Means': but that's only what it's called, you know!" "Well, what is the song, then?" said Alice, who was by this time completely bewildered. "I was coming to that," the Knight said. "The song really is 'A-sitting On A Gate': and the tune's my own invention." Though there are certainly linguistic and philosophical explanations of what’s going on, I always felt it was akin to pointers in computer programming. A variable can have a name and another variable with a different name can point to the variable. Multiple variables can have the same value, and multiple pointers can point to the same variable. Anyway, there’s a distinction between the value, the name of the variable that holds the value, and the names of other pointer variables that reference the location where the value is stored.

I love the annotated version of Alice in Wonderland and Through the Looking Glass. It's been in my library my entire life. I highly encourage people to track down a copy. There is so much more to the stories than first meets the eye.

The book is one piece of culture that transcends its author. Funny take, Tibees, thank you for this.

Through the looking glass is an essay on compactified time creating a temporal boundary layer. Matter on one side and its perfect inversion , antimatter, on the other.

Random book for kids Tibees: there are maths inside of it

Well, THAT was new to me. I bought a copy from UK's Penguin books where almost a quarter of the volume was about the author's obsession with (grammatical) proper language and a lot of references to a book that time used by those women emploied to educate children of upper classes - reffered to in Mary Poppins too. And a lengthy explanation of a (hidden) chess-game involved when Alice has to cross some ground. It seemed to me that translating the book into any other language would be rather difficult. So thanx for this addition!

Just as I do with Bob Ross, I watch your videos for the soothing quality of your voice as much as the interesting content. Thank you!

Lovely presentation, the text is very witty and your video makes me want to read the original version of Alice in Wonderland!

I am missing these math videos !!! Today,you tube gave me suggestion to watch this video..Worth it !!

In Cardcaptor Sakura, Sakura is often compared to Alice, especially in the newer season. At the start of the original show, Sakura says that she is bad at math, but during this sequel she remarks that she is getting better at it. I wonder if it was done on purpose.

These videos are always so interesting

My therapist: Long Toby isn't real, she can't hurt you Long Toby:

Your way and style of reading makes it exciting and interesting!

I love the unique creativity to use always use towards your approach to mathematics!

Your videos are so creative and fun. You’re a natural educator.

My 10th grade geometry teacher used phrases from AIW all the time. In my case, it kept me interested enough that it paid off in spades when l went into wood working as a profession later.

I think. you are right. He used a lot of mathematical logic and some mathematical objects in the Alice in Wonderland. I liked recently this video on youtube made with Alice in Wonderland film 2010 and some good Russian music: "Алиса и Террант/Безумный Шляпник" (Alice and the Terrant / Mad Hatter). I think, it is really nice and you may like the idea too.

A delightful foray down the rabbit hole, fascinating.

The complete works is such a great tool to have, and I am grateful for my oddball maths teacher for introducing me. It was useful to have to show to my child to help them think their way around a problem, to not see mathematics as just numbers but to understand how to appreciate a problem whatever it may be and to be equipped to create new tools and perspectives to deal with these problems. To say it short, I told them, "I wish your school would teach you logic a little better, so your answers weren't limited to what's on a list."

There was a indie band called the mock turtles. It was Steve coogans brothers band and had a hit with the song "can you dig it" ... God i really have to get out more, and/or get other intreasts

it's been a useful way of spending time. best wishes for you from tamil nadu, India

Oh God I was scared by the thumbnail when it suddenly appeared when I clicked this video when it popped up in my notifications!

The stretches/growing/shrinking are references to linear transformations in linear algebra

If only I had a Maths teacher like Tibees.

I had never seen a video like this before nor have I ever thought about this- very intriguing! This makes all the difference to how I view Alice in Wonderland, I appreciate the story (and maths!) even more thanks to you!

Hi Toby , I’ve been watching a lot of ur videos Im nerdy as well and I’ve been having trouble because I have no friends In my school , I gotta say that ur videos are super cool And I feel like ur my only friend I know it’s a weird thing to say But tank you ! Also I didn’t know this book was written by a mathematician and all the math behind it It’s super cool !

I just want an hour if you talking about math and other stuff. Your voice is soothing

You may enjoy the short story by Padgett, ‘Mimzy Were The Borogroves’ later repackaged as The Last Mimzy movie… which took the Hollywood happy-happy ending, but I rather like the mystery/ennui of the original.

The Cheshire Cat is actually a fourth dimensional being

I love the way the math and science accounts

Wow, in this pandemic... Tobe is very cool and calm... Not sure good thing or bad thing

That was very interesting. You are so good at storytelling. I could listen to your voice for hours. :)

A little concerning that insanity is considered great literature. And I always suspected that you were the cheshire cat :)

PHD in Mathematics 😱😱 OMG

I can't think of a more beautiful voice to distinguish and illuminate such a classic. Thanks Toby! :-)

Does anyone know if the "glass half empty/glass half full test of disposition comes from Carroll? The earliest reference I can find is in a Maths school book: The Mathematics Teacher, Volume 20 (1927): "Do you know Algebra?" Said the Rabbit. "Yes, I liked it in High School," said Alice. "What is one of the axioms of Algebra?" "Equal multiples of equals are equal," said Alice, selecting the first she remembered. "Indeed!" said the Rabbit. "You will admit that a bottle half-full is a bottle half-empty." "Yes," said Alice, wondering what was coming now. "Well, multiply both sides by two, and a bottle full is a bottle empty," said the Rabbit. "Well, it is that way in the United States anyhow," said Alice, a little impudently.

We also need more Bob Ross presentation - they're soothing and calming sessions for the distressed.

Congratulations on making a KiwiCo project flamingo.

Very cool. You know just yesterday I've read, apparently there exists microstates which can only be distinguished by factoring in imaginary numbers, fascinating. From the article: "Alexander Streltsov from the Centre for Quantum Optical Technologies (QOT) at the University of Warsaw with the participation of scientists from the University of Science and Technology of China (USTC) in Hefei and the University of Calgary, found quantum states of entangled photons that cannot be distinguished without resorting to complex numbers."

I've been looking for this video to exist since I found out he was a mathematician

i never ever thought that math could be so awesome

Well! This is one of the more interesting videos I've watched in a couple of years, and these have been a couple of very interesting years.

About the multiplication Alice references, a 2022 journal by Firdous Ahmad Mala says "4 × 5 = 1 × 18 + 2 so it can be written as 12 in base 18 arithmetic; 4 × 6 = 1 × 21 + 3 so it can be written as 13 in base 21 arithmetic; 4 × 7 = 1 × 24 + 4 so it can be written as 14 in base 24 arithmetic; 4 × 8 = 1 × 27 + 5 so it can be written as 15 in base 27 arithmetic [and so on].... However, 4 × 13 = 1 × 42 + 10 cannot be written as 20 in base 42 arithmetic" so interesting!!!

Oh my goodness, I listen to alice and wonderland every night when I sleep, and I graduated from undergrad math last year :o

This is actually the reason I bought the Annotated Alice, but so far there have been no math explanations. I'm to the point where she gets to the Caterpillar.

THERAPIST: "Long Toby doesn't exist, she can't hurt you!" LONG TOBY:

9:05 With that smile of yours, I honestly expected you to fade away leaving your "grin" behind. I think you missed the chance to do that, unless you have another Alice in Wonderland story to tell us.

This is like inventing the past. Like a detective novel about how Euler lose is sight trying to guess a way to be a mathematician without the lateral thinking...did you ever use Jacobi's method to solve a hard geometry problem?

Dodgson made significant contributions to "social choice theory", commonly described as theory about committees and elections. Other mathematicians, Condorcet and Borda, had set out conditions when voting rules lead to paradoxes. Check out "Arrow's Impossibility Theorem" for an insight into this area. Dodgson's contribution is routinely cited in the literature.

Girl, you should totally start a story telling channel.

I have seen a grin without a cat lots of times. When you see a person grinning, there isn't always a cat involved.

getting this info with such a constant smile brings joy to my ears

Somewhere physics and calculus have to be involved. To determine how much to eat or drink to obtain the appropriate height Alice needed.

Dear Toby, your videos always enlighten my soul!

Lewis Carrol is an anagram for Charles Ludwig. Reverse it, translate it into Latin, and back to English.