Taxonomy-based games (Colleen's Thinking Blocks, Richard Elwes polyhedra, etc.)

[Maria Droujkova]

It would be nice to develop some generic game mechanics around systems where combinations of parameters produce a "zoo" of entities. In particular, when parameters are "freedoms" for entities. It will make sense in a minute, hopefully.

For example, consider quadrilaterals. If you make all sides and all angles equal, you get squares. Relax angle requirement, get rhombuses. Relax side requirement, get rectangles, etc.

Or consider Colleen's Thinking Blocks http://www.mathplayground.com/thinkingblocks.html
You can view number types (natural, whole, fractions) as having more and more freedom.

At Richard's presentation, he talked about a zoo of polyhedra, with a very nice way of turning five types of freedoms (e.g. convex polygons, interchangeable faces) on and off. You can see the slides here: http://mathfuture.wikispaces.com/RichardElwes

Sooo, maybe we can have a talk about this type of systems and their game mechanics some time in June or July, too? There got to be similarities there. And "freedom" (or gaining more or less of it) is a nice setup for roleplay. I started to sketch a game called "Squares go everywhere" about creatures that can morph their bodies and are allowed into different territories based on that (.swf attached).


Cheers,
Maria Droujkova

Make math your own, to make your own math.

 

[Colleen King]

Maria,

I really appreciate the imagery of objects having more or less freedom and how that influences actions/options. While I see it very clearly with shapes, and I can imagine it applied to transformations and number operations, I'm less sure how it applies to number types. Can you say more about that?

I see a lot of potential for your Squares game. Very nice. Did you do the graphics yourself? I like your style.

I missed Richard's live event but will make sure I listen to the recording. Count me in for the discussion.

Colleen

 

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"Let's build a better math game."

[Maria Droujkova]

As numbers get more enlightened (during the human Enlightenment, coincidentally... hehe) they become more free and can do cooler things. At first, the can only attach themselves to sets of objects, add and multiply.

When they reach the next dan, they also learn to subtract. So, whole numbers.

Then they become free to do division and become Rationals (I wish more of the humans would become rationalists... ahem)

Then they discover some cooler geometry and become Reals.

Basically, this is the story of number system extensions through operations and functions. We can go all the way to quaternions and beyond - there are such cool number types these days, like superreals or p-adic numbers.

The pictures are by Victoria Kolchenko - she works for Natural Math. She made art for the front page, multiplication poster and so on. I like her style a lot, too.