Children's Story Book to Introduce Set Theory, Order Theory

[mear...@gmail.com]

My wife and I are having out first child and I'd like to make sure it is properly inundated with science and math as the backdrop for its life. I've been recently learning about set theory and order theory myself, and had the idea to introduce some of the basic concepts subtly through a children's story book. I'm reaching out to the folks on this list for ideas on how to do this.

So far, I have a basic premise for a story about a man named George (after Georg Cantor) who travels through a strange land. The first three places he visits are towns which each represent a different type of binary relationship:
- Reflexiville, where the streets mostly go in circles and the town is populated by little rolling balls called the "Iams" who use strange greetings like "I am no taller than you" and "I have at least as many teeth as you."
- Symmetria, where all the streets are two way and the people have a tendency to express things in terms of equivalence ("the name of this town is equivalent to..."). The economy there works by barter (so that "I trade with you" is a symmetrical relationship), and George meets a couple who say they are married ("I to her, and she to me").
- Transitiville, where people speak indirectly, such as "You are a newcomer, newcomers are welcome" (therefore, you are welcome) and "I am related to you, he is not related to me" (therefore, he is not related to you).

That's about all I have so far, and I'm not sure how I feel about it (particularly Symmetria, where I think I'm conflating symmetry with equivalence too much). Some other concepts I'd like to include if they fit well are equivalence and partitioning; quasiordering, partial ordering, and total ordering; isomorphism (that might be a stretch, but it seems natural for some kind of physical metaphor); and the concept of subsets and inclusion. Set operations like intersection, union, and complement would also be very welcome. The only other idea I had so far was to personify Aleph-Null and/or Omega as the ruler of the kingdom or something.

If anyone has any ideas on how to illustrate, or even hint at, these concepts in a story for young children (I'm targeting anywhere from 3 to 7 years old), I'd love to hear them. I don't think I want actual explanations of concepts because I think that will be too dry and possibly too confusing for children. Anything that illustrates the ideas is good, as well as any other elements I can incorporate that /suggest/ the concept (for example, the roads that mostly go in circles in Reflexiville, suggesting reflexive paths in a directed graph). The idea here is not necessarily to teach these concepts to a young child, just to "plant" the ideas so that they will hopefully be more familiar when they encounter them later.

If I/We can successfully come up with a finished story, I will release it under a Creative Commons license and make an ebook available for free. Also, if you like the idea but hate the way I'm going with it, I have no problem with you taking the idea and running with it on your own. All I ask (as a favor) is to share either your ideas or the completed story with us (or at least let us know when/where it is available), so I can share it with my kid.

Lastly, if there are any other math or science books for young children that you like, I'd love to hear about them as well.

Thanks,
-Brian

[William Elliot]

On Tue, 23 Apr 2013, mear...@gmail.com wrote:

> My wife and I are having out first child and I'd like to make sure it is
> properly inundated with science and math as the backdrop for its life.
> I've been recently learning about set theory and order theory myself,
> and had the idea to introduce some of the basic concepts subtly through
> a children's story book. I'm reaching out to the folks on this list for
> ideas on how to do this.

> So far, I have a basic premise for a story about a man named George

> (after George Cantor) who travels through a strange land.

George the Cantor
Chanted strange incantations
of things so big and bigger yet
and numbers so long,
that twice a much was just as much.

> The first three places he visits are towns which each represent a
> different type of binary relationship:

Nary a difference binary and trinary but a nary so.

> - Reflexiville, where the streets mostly go in circles and the town is
> populated by little rolling balls called the "Iams" who use strange
> greetings like "I am no taller than you" and "I have at least as many
> teeth as you."

Reflexiville has not a mirror nor anything not boring.

> - Symmetria, where all the streets are two way and the people have a
> tendency to express things in terms of equivalence ("the name of this
> town is equivalent to..."). The economy there works by barter (so that
> "I trade with you" is a symmetrical relationship), and George meets a
> couple who say they are married ("I to her, and she to me").

Symmetria is a strange place where people spoke only in palindromes.
So madam, there's not much to say except how level.

> - Transitiville, where people speak indirectly, such as "You are a
> newcomer, newcomers are welcome" (therefore, you are welcome) and "I am
> related to you, he is not related to me" (therefore, he is not related
> to you).

Transitiville, not to be confused with Transvestitia,
needed a transit system but instead got a transitive
system: I tell you and you tell him is how I tell him.
Or I tell him and he tells you so I won't yell, but merely
tell you, I've never be in such boring boroughs.

> That's about all I have so far, and I'm not sure how I feel about it
> (particularly Symmetria, where I think I'm conflating symmetry with
> equivalence too much). Some other concepts I'd like to include if they
> fit well are equivalence and partitioning; quasiordering, partial
> ordering, and total ordering; isomorphism (that might be a stretch, but
> it seems natural for some kind of physical metaphor); and the concept of
> subsets and inclusion. Set operations like intersection, union, and
> complement would also be very welcome. The only other idea I had so far
> was to personify Aleph-Null and/or Omega as the ruler of the kingdom or
> something.

Give it up you're getting nowhere being too technical with no
immaginative flourish. Maybe in 9 months or with a toddler about,
something better will come of your notion. Be sure to have illustrations.

55 years ago, when I was in high school I remember coming upon
a couple of books about infinity in the Portland, Oregon library
in the vein of what you're attempting. In the mean time, read
the Cat in the Hat and lots of other stuff by Dr Suess. I recommend
you read them at been time to your young kid when he's old enough
to enjoy easy reading books with illustrations.

I don't need you to collaborate with nor am I interested in your project.
How man kids books have you read and are you pushing technical stuff too
early? Frankly I think it would be better for you to wait on this project
until you have lots of hands on experience understanding very young kids.

In the mean time, for your kid's health and well being, stop now eating
junk and yuck foods to have a well establed habit of healthy eating into
which you can raise your kid.

[Frank J. Lhota]

I wish you the best of luck with this project.

Martin Gardner once wrote a "Mathematical Games" column on infinite
cardinals. IIRC he tacitly assumed the Generalized Continuum Hypothesis,
but other than that, he wrote a fine introduction to the topic for the
amateur mathematician.

I would love to see an amateur / recreational introduction to ordinal
numbers. Once we succeed with this goal, we could look into creating a
version for children.

--
"All things extant in this world,
Gods of Heaven, gods of Earth,
Let everything be as it should be;
Thus shall it be!"
- Magical chant from "Magical Shopping Arcade Abenobashi"

"Drizzle, Drazzle, Drozzle, Drome,
Time for this one to come home!"
- Mr. Wizard from "Tooter Turtle"

[--CELKO--]

There are youtube animations of the Hilbert Hotel getting infinite busloads of guests that was fun. I can see a kid's book based on the room clerk, bellhop and chamber maid at the hotel handling the strange guests.

Look up the book of the late William Sleator; many of his kids/YA books have a math theme. https://www.google.com/search?q=william+sleator+books&oq=William+slea&aqs=chrome.2.69i57j0l5.7567j0j8&sourceid=chrome&espv=210&es_sm=93&ie=UTF-8

Google my name. I do SQL/relational database books and I have played with the idea of a kid's book on RDBMS with notched edge cards as a supplement.