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Welcome to adventurous math for the playground crowd! I am Moby Snoodles, and I love to hear from you at moby@moebiusnoodles.com

Book news

The book cover is almost ready! Do you like it? What would you change?

This week, we’ve been working on a glossary of main terms. We wanted each definition…

• Mathematically correct
• Accessible to math-anxious people
• Engaging for mathy people
• To have a clear example
• To have a clear counter-example

Function
Functions are machines that convert values to other values, or find correspondences between values. Function machines work by rules people make up. The starting values are called input. The converted or corresponding values are called output. The rule must find a single output for each input. Your stove is a function machine: it starts with the input of raw eggs, milk and spices, and makes the output of an omelet. The fantasy machine that starts with the same input and makes either omelets or live chickens is not a function.

Inverse Function
What a function does, the inverse will undo. Of course, some deeds cannot be undone. The function of “baby drops a cup of grapes on the floor” has an inverse, “parental unit crawls around, searching for grapes and putting them back into the cup”. On the other hand, the function of “drop a cup of orange juice on the floor” and the function “break an egg for an omelet” do not have inverses.

Cycle
Cycles are sequences of objects or series of operations that repeat. For example, “winter, spring, summer, autumn” is the cycle of seasons that repeats every year. There are cyclic stories and songs, like “99 bottles of beer.” Many household tasks are cyclic, such as washing dishes – “lather, rinse, repeat.” Cycles relate to recursion and iteration. Not all infinite sequences have cycles; for example, there are no cycles in the digits of Pi.

Sharing

You are welcome to share the contents of this newsletter online or in print. You can also remix and tweak anything here as you wish, as long as you share your creations on the same terms. Please credit MoebiusNoodles.com

More formally, we distribute all Moebius Noodles content under the Creative Commons Attribution-NonCommercial-ShareAlike license: CC BY-NC-SA

Talk to you again on December 15th!

Moby Snoodles, aka Dr. Maria Droujkova

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Welcome to adventurous math for the playground crowd! I am Moby Snoodles, and I love to hear from you at moby@moebiusnoodles.com

Next book news!

Every November, hundreds of thousand of people play a game called NaNoWriMo, or National Novel Writing Month. The rules are simple: you need to write a 50,000-word novel in 30 days. This year, while the first Moebius Noodles book is being prepared for production, Dr. Maria Droujkova is writing about me, Moby Snoodles! And of course, about other people of the ocean: Asym the dolphin,  Inte the turtle, Nautilus the nautilus and so on. You can see graphs of Maria’s progress at the site – about half-done as of this writing!

Humans who love math will recognize some of their favorite jokes, math art, or just beautiful definitions, problems and theorems. After all, calculus is as relevant on the ocean planet as it is on Earth. So far, about half of the stories are original and the other half existing calculus favorites, retold in ways accessible to young children. The idea is to read the book out loud to kids, or to use it for storytelling and roleplay.

For example, the story we are about to share is inspired by the article by Donald Byrd, called “Infinite Bottles of Beer: A cantorial approach to Cantorian arithmetic and other mathematical melodies“. A shorter version was published in Math Horizons.

Moby Snoodles and Brilliant Snails on the Wall

Moby Snoodles and Asym the dolphin were not moving very fast at all. That was because they were trying to swim backwards. Whales and dolphins could back up from something, of course. So Moby and Asym did the same thing many times in a row. They backed up, and then backed up again.
– I could do it forever and ever and ever! – said Asym the dolphin happily.
– Ummm, yes you could, – agreed Moby.
Asym liked things that went on and on and on. But Moby liked to move fast.

They were passing by the base of the Smooth Cliff. Moby noticed several snails who had climbed halfway up it. The sun was shining bright through the water. The shells were catching the sun, looking much brighter than usual. Moby wanted Asym to look. Maybe then they could stop swimming backwards.

– Look, five brilliant snails on the wall! – said Moby
– Five brilliant snails? – asked Asym absent-mindedly.

They stopped and looked for a while. The snails started to pull their soft parts inside their shells. Usually, snails pulled into shells very fast, when a sudden worry struck them. These snails were moving rather slowly.

– What if a snail should happen to fall? – asked Asym.
Moby thought Asym had a point. The Smooth Cliff was very smooth. When less and less of a snail’s foot was left to hold on, the snail was more and more likely to fall.
– If a snail should happen to fall, there will be four snails on the wall! – said Moby.
Asym laughed. The phrase did seem silly and funny somehow!

This was exactly what happened next. One of the snails lost the balance on the Smooth Cliff. The snail pulled all the soft parts into the brilliant shell. Then the snail slowly fell to the floor, spinning around and around. Whee! When the snail got closer, Moby recognized the patterns on the shell.
– Hello there, Tegra! – said Moby.
-*Good day to you. What are you up to?* – replied Tegra the snail. Tegra talked by touching Moby’s flipper. Asym watched Tegra’s tentacles move, so Asym could understand, too.
– We are learning to swim backwards! – said Asym.
– We are watching you on the wall! And when we talked about it, our words came out funny. – said Moby.
– *Tell me!* – asked Tegra.

So Moby collected all the words together. That is, all the words Moby could remember.

Five brilliant snails on the wall,
Five brilliant snails,
If a snail should happen to fall,
Four brilliant snails on the wall!
– *Ha-ha-ha!* – said Tegra.
Moby wondered how snails laughed when they were by themselves. Maybe they just thought, “Ha-ha-ha”?

Asym was still watching the snails on the wall. They kept pulling their soft parts into their shells slowly.
– That snail on the left looks unsteady! – said Asym.
– Yay! Our funny words work with four snails, too!

Four brilliant snails on the wall,
Four brilliant snails,
If a snail should happen to fall,
Three brilliant snails on the wall!

This is exactly what happened next. The snail on the left lost the balancel and fell slowly, spinning around and around. When the snail was on the floor, the soft parts came out again. The snail said *Hi* to Moby and Asym, and joined them in watching the wall. Moby wanted to share the funny words with the new snail. But now they had to be changed again! Would it work? Moby tried.

Three brilliant snails on the wall,
Three brilliant snails,
If a snail should happen to fall,
Two brilliant snails on the wall!

– Yay! The funny words keep working! – said Moby.
Another snail fell off and joined them. Moby told the new snail their funny words. Of course, Moby started from two snails this time.

– This won’t last forever, – said Asym the dolphin sadly. – What will you do when there is just one snail on the wall?
– *I know what us snails will do! We will all climb back halfway up the Smooth Cliff. Then we will play the game again.* – said Tegra the snail.

Moby tried to make up funny words to describe this. What made the words funny? Moby decided it was the sameness of their ends.

One brilliant snail on the wall,
One brilliant snail,
If that snail should happen to fall,
All the snails climb back up the wall!

Five brilliant snails on the wall,
Five brilliant snails,
If a snail should happen to fall,
Four brilliant snails on the wall!

Moby kept on talking and talking. The snails kept on playing and playing. Asym kept on thinking and thinking.
– This does last forever and ever and ever! – finally said Asym.
But nothing lasted forever. Just as Asym said this, three of the snails said they were tired, and left. Asym was a little worried. But Tegra and another snail kept playing.

Two brilliant snails on the wall,
Two brilliant snails,
If a snail should happen to fall,
One brilliant snail on the wall!

One brilliant snail on the wall,
One brilliant snail,
If that snail should happen to fall,
Both the snails climb back up the wall!

Two brilliant snails on the wall…

– What if another snail went home? – worried Asym.
– I think I can make it work just for Tegra! – replied Moby proudly.

Brilliant Tegra the snail on the wall,
Brilliant Tegra the snail,
If Tegra the snail should fall,
Tegra climbs back up up the wall!

Brilliant Tegra the snail on the wall…

– *I like the part where I am brilliant.* – said Tegra.
– You know what would be nice? If the snails went on forever and ever and ever, and never ran out! – said Asym the dolphin dreamily. – Can you make funny words about that?
– I will try! – replied Moby.

Infinite brilliant snails on the wall,
Infinite brilliant snails,
If a snail should happen to fall…
(Moby thought and thought. Asym and Tegra waited and waited.)
Infinite brilliant snails on the wall! – finally said Moby, and continued:

Infinite brilliant snails on the wall,
Infinite brilliant snails,
If a snail should happen to fall,
Infinite brilliant snails on the wall!

– You don’t have to change anything for infinite snails. – noticed Asym.
– *Just like the story when there is only me on the wall!* – added Tegra the snail.
– What is your favorite number, Tegra? – asked Moby.
– *Five!*
– Check this out!

Infinite brilliant snails on the wall,
Infinite brilliant snails,
If five snails should happen to fall,
Infinite brilliant snails on the wall!

Infinite brilliant snails on the wall…

– Well, my favorite number is infinity! – said Asym.
– I don’t think infinity is a number. – replied Moby. Asym looked a bit sad about that, so Moby added. – But I think it will work just the same as a number!
– *What do you mean, the same?* – asked Tegra the snail.

Infinite brilliant snails on the wall,
Infinite brilliant snails,
If infinite snails should happen to fall,
Infinite brilliant snails on the wall!

Infinite brilliant snails on the wall…

– Sounds about right. – said Asym the dolphin happily.
– *Wait, no! I think this one should go like my story!* – said Tegra the snail.
– What do you mean? – asked Asym.
– *I mean everybody falls, and then there are nobody on the wall, and then everybody climbs again.* – explained Tegra.

Infinite brilliant snails on the wall,
Infinite brilliant snails,
If infinite snails should happen to fall,
All the snails climb back up the wall!

– What do you think, Moby? – asked Asym.
Moby thought and thought. Asym waited and waited. Finally, Moby replied.
Infinite brilliant snails on the wall,
Infinite brilliant snails,
If infinite snails should happen to fall,
Three brilliant snails on the wall!

– *What?* Why? – asked Tegra and Asym at once.
– Because three is my favorite number! – explained Moby happily.

Sharing

You are welcome to share the contents of this newsletter online or in print. You can also remix and tweak anything here as you wish, as long as you share your creations on the same terms. Please credit MoebiusNoodles.com

More formally, we distribute all Moebius Noodles content under the Creative Commons Attribution-NonCommercial-ShareAlike license: CC BY-NC-SA

Talk to you again on November 30th!

Moby Snoodles, aka Dr. Maria Droujkova

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Welcome to adventurous math for the playground crowd! I am Moby Snoodles, and I love to hear from you at moby@moebiusnoodles.com

Book news

All the games for our book are ready, including illustrations. And we are working on the cover design. What else does our book need then? One thing we added in this development cycle is our special dictionary. We strive to be very correct mathematically. This means using a lot of beautiful math words, like fractal or exponentiation, which some readers may not know. Moreover, like every other big project, Moebius Noodles adds specific metaphors and meanings to terms. Thus even the readers who know the beautiful math words may find our definitions interesting.

For example, here are a few definitions that have to do with functions.

Function
Function is a machine that converts values to other values, or finds correspondences between values. Function machines work by rules people make up. The starting values are called input. The converted or corresponding values are called output. Your stove is a function machine: its input might be raw eggs, milk and spices, and its output – an omelet.

Transformation
When you change or combine rules, functions can be transformed. For example, you can turn your stove to the maximum setting and its timer to half an hour. Your input will stay the same – raw eggs, milk and spices; but your output will now be burned eggs and lots of smoke.

Inverse Function
What a function does, its inverse will undo. Of course, some deeds cannot be undone. A function of “baby drops a cup of grapes on the floor” has an inverse, “parental unit crawls around, searching for grapes and putting them back into the cup”. On the other hand, a function of “drop a cup of orange juice on the floor” or a function of “break an egg for the omelet” does not have an inverse.

Our blogs

Barbara of Numberland.net left us a note. Parents love their kids, so they create very lovely math projects for them – and then for the world! Numberland ideas, based on a University of Heidelberg research project parents and teachers have adopted, go with our chapter on intrinsic numbers.

Math is a wonderful, emotional, exciting and beautiful field and young children are more than open to dive into it. It is up to us to support them build their (individual) bridge from their inborn mathematical understanding to the abstract and formal language of math we developed. I very much like the approach of Moebius Noodles because it fits with the idea of a project I am involved in:
‘Let’s visit Numberland’ is a concept where we invite children to travel to a land where the numbers 1 to 10 live and where there is a lot to do, sing, find out… For example, we detect that Number 4 lives in a square garden, her house has four windows and she likes anything that is four times (…)

My daughter was three when she travelled to Numberland for the first time, and of course three was her favorite number. One day, at dinner table, she suddenly beamed: ‘We are sitting in a triangle!’ (Her, my son and me were sitting at the table) ‘And if Daddy was here we would sit in a quadrangle!’

Sharing

You are welcome to share the contents of this newsletter online or in print. You can also remix and tweak anything here as you wish, as long as you share your creations on the same terms. Please credit MoebiusNoodles.com

More formally, we distribute all Moebius Noodles content under the Creative Commons Attribution-NonCommercial-ShareAlike license: CC BY-NC-SA

Talk to you again on November 15th!

Moby Snoodles, aka Dr. Maria Droujkova