Alice and the Mad UnEqual To

I received some positive feedback about the Alice post and decided to continue the story a bit. When we last left Alice she had run away from At Least, At Most, and the Caterpillar. This excerpt starts with a conversation between Alice and my version of the Cheshire Cat (No One) regarding perspectives. Perspectives are sooooo important when trying to communicate with others, and I worry that differing perspectives get in the way when teachers and students talk to each other. The second part of this excerpt includes Alice's interaction with three characters: the Mad UnEqual To, Negate, and Twiddles (a term one of my undergraduate professors used for the tilde "~" that I adopted), though you really only learn the Mad UnEqual To's name here. These three characters are similar in the sense that they represent a sort of opposite of some other set (like if something is equal to 4, not equal to 4 are all numbers that are not 4, and a similar rationale could work for, say tea parties).

Alice soon became tired and had to sit down and rest for a bit.

“Are you having fun yet?” A voice above her asked. But when Alice looked up, no one was there. “I say, you look cross.”

When Alice looked up again, she saw a cat perched on a low hanging branch. “You were certainly not there a second ago,” charged Alice

“Of course I was, just because you did not see me, does not mean I was not here. You heard me speak, did you not?” asked the cat.

Alice could not deny that she heard him speak. “Who are you?” she asked.

“No One… of consequence; a mere observer of events good and bad. Tell me my dear, do you fancy less, or more?”

“I’m afraid I don’t understand the question,” said Alice.

“My question, more or less is: is less more, or is less less?”

Alice thought for a moment, “it’s a matter of perspective. I don’t think more is necessarily better, except in some instances. Why do you ask?”

“For no other reason,” replied the cat, “than to see your perspective.”

“Why would YOU want to know MY perspective?” inquired Alice.

“I feel that when conversing with someone else it is very important to determine from which direction they are viewing the discussion.”

“And what ‘direction’ are YOU viewing this conversation from, kitty-cat?”

“Residing above everyone else gives me the unique opportunity to have a superior vantage point than most. I see everything from above, giving me quite an angle on every conversation. I, of course, am viewing this conversation from every direction.” The cat twisted his head upside-down and smiled wickedly.

Alice was growing tired of this conversation with the cat, as he seemed to have nothing better to do but to waste time, and she wanted to get home. “Where do I go from here?”

“Well, it depends on where you want to go,” yawned the cat as he stretched out his claws and dug them into the tree bough, “to the left is the Mad UnEqual To, and the right will lead you home… or is it the other way around? I always forget whose perspective I am directing from.” With that the cat disappeared.

Alice desperately wanted to get home, so she went to the right, hoping the cat had given her directions from her perspective. At any rate, she was sure she did not want to run into the Mad UnEqual To, his name made him sound unpleasant. The trees of the forest gave way to an opening, but Alice was disappointed to find that it did not lead home.

Before her was a very long table strewn with dirty dishes. The table was so long that Alice could not see the end of it; it seemed to disappear into the distance. Three people, if you could call them people, sat abnormally close to one another at the near end of the table. Alice approached and sat down in an empty chair.

“Excuse me, I don’t mean to disturb your tea party, but –“

“You are very much most unwelcome, this is not a tea party!” Said the strange man in the shiny top hat. Which Alice took to be the Mad UnEqual To. Alice studied UnEqual To, her eyes must have been drawn to him because he was a bit odd looking. She noticed that he was a very tall gentleman looking type, with two parallel horizontal lines with a transversal line intersecting both (≠) that made up his mouth, and other than his every-direction googly eyes, he looked more normal than anyone else at the table.

“Well, what is it then?” Asked Alice as she looked around the table strewn with chipped teacups and kettles.

“It is NOT a tea party!” Replied UnEqual To very assertively. “It is an ‘a-tea’ party!”

The characters at the table burst out laughing.

“But what does that mean?” asked Alice.

“Have you not considered that not nearly no one declines, nay, rebuffs unproven, untested, and illogical logic? “ Said one of the others sitting at the table. The current speaker was a short, two-dimensional creature made up of geometrical shapes and had a tilde mustache (~) and tilde eyebrows.

Alice was confused and worked hard to figure out the question, “no,” she said with very little assurance, “or at least, not recently.”

“Well then, you can join us for tea!” said UnEqual To, “what is your name?” He indicated that she take the nearest cup and saucer.

“Alice,” replied Alice.

“A-liss? To not relieve from pain?” asked UnEqual To excitedly.

“No, just Alice… like the name.”

“Ah, well Just Alice, we have much to discuss!”

“Not ‘Just Alice’, my name is Alice.”

“Well, why didn’t you say so? Let’s give Alice a teacup!” The Mad UnEqual To handed her another teacup and saucer.

Alice pushed away the old teacup and politely accepted the new one and said, “I thought you weren’t having a tea party.”

“We weren’t! And we AREN’T! AND WE WON’T! It is not a tea party!”

“But what do you do at a not tea party?” asked Alice.

“You mean,” said UnEqual To, “’what do we do at a not a tea party?’ We drink tea and tell not-not jokes.”

The Mad UnEqual To handed Alice yet another teacup.

Everyone at the table roared with laughter, except Alice.

“Not-not” bellowed the third creature at the table, who began giggling uncontrollably and fell out of his chair.

“Enough not-not jokes,” said UnEqual To.

Alice arranged all the teacups that were near her so she had more room. “I would love to hear a ‘not-not’

joke,” said Alice. She was very curious as to what that might be.

“Not-not!” the creature repeated.

The three denizens of the table leaned in and waited for Alice to do something.

Alice looked around and realized she hadn’t a clue as to what she was supposed to say. The traditional

‘knock-knock’ jokes required an initial reply of ‘who’s there?’ as if to answer a door that had just been

knocked on. But how was one supposed to respond to ‘not-not’?

“Who’s not there?” Alice finally attempted.

“One not.”

“One not who?” Asked Alice.

The table burst into laughter. After the characters had gathered themselves they looked at Alice. They had clearly expected her to get the joke.

UnEqual To said, “get it? ‘one not who’… or, ‘one not two.’”

“Oh, I get it.” Alice now understood the joke but did not think it was particularly funny. She decided to change the subject. “So, you drink tea at a not a tea party?”

“Of course, we can have whatever we want, as long as it is not a tea party.” UnEqual To handed her yet another teacup and saucer.

Alice again rearranged her teacups. “What would make it a tea party?” challenged Alice.

“Not-not!” bellowed the two-dimensional character, who immediately burst into a fit of laughter.

The Mad UnEqual To glared at his companion until he quieted down and said, “that which fulfills the requirements that makes something a tea party! We can’t have a tea party, so we neglect some aspect of teatime.”

“Well, why can’t you have a tea party?” asked Alice.

UnEqual To’s face became very grave and he set down his teacup, “strict orders from the Queen. She decreed that none were to have a tea party.” UnEqual To perked back up and said, “so we decided to have a not a tea party, which can be anything but a tea party,” said UnEqual To.

“So, no one can have a tea party?”

“My dear, No One can’t have a tea party! None can, however.”

Alice started to understand that everyone here speaks literally and there were a plethora of unfortunately

named characters. Alice picked up on the little game, “who is None?”

“None will be found at the castle, he is husband to the Queen” said the third creature at the table. This

creature looked like a big ball of yin and yang, with what looked like a drop of sweat floating near his head.

“You mean he’s the King, don’t you?” asked Alice.

The same creature replied, “no, the Queen would never allow a King, you see, for she would need to

change the name of these lands to–“ but he was cut off by UnEqual To.

“WHAT TIME IS IT?” bellowed UnEqual To as he tore his pocket-watch from the innards of a very

full and very hot teakettle. His eyes bugged out and he jumped from his seat, “I must depart,” he

exclaimed. UnEqual To ran with great haste into the forest.

As UnEqual To left the clearing, the white rabbit came quickly bounding into the clearing from the other

side of the field. The rabbit came right up to Alice and demanded, “where have you been? I found you

just in time! But if things had been any different… well, she would have me de-headed for sure,” the rabbit sort of trailed off the last part into a mumble. “The Queen requests you join her for tea at the castle, be quick, and don’t be late! Twiddle-de-dee, I must be off. Mustn’t be late… or early for that matter, my, my, my, my, my,” the rabbit said more to himself than to Alice and he bounded off to the forest. UnEqual To emerged from the forest just as the rabbit left the clearing.

“That was a close one,” he said, “never have I been so close to not being early or late.”

“Remarkable,” said Alice, “how did you know the Equal To rabbit would bound through the woods at that moment?”

UnEqual To stood to his full height and clasped the flaps of his jacket nearest his chest and said, “because my dear, Equal To is always on time.”

Questions I might ask students about this story:

1. Why do you think UnEqual To had to leave the area when Equal To arrived?

2. What does this story have to do with mathematics?

3. How might neglecting “some aspect of teatime” allow these characters to have tea, but not a tea party?

There is more to this scene than I included here, but this felt like a good stopping point. The major focus in this excerpt is that the Equal To rabbit and the Mad UnEqual To cannot be in the same place at the same time. Also, it is not that they are constantly dodging each other, but that they occasionally run the risk of coming into contact (really, they are just close calls as, a value, x, and another value, not x, could come incredibly close without being the same).