Day 11, Play-by-Play

This video illustrates the patterns that student Trinity discovered on the Fraudini cards, and we begin to understand why those patterns appear. If you watch Vi's fingers as she counts up to 31, you'll see her thumb is behaving like a switch -- on, off, on, off -- depending on whether the number is even or odd (just like the "1" card for Fraudini); two (index finger) appears twice, then hides twice, etc. etc. -- just the "2" card. And so on.

• What do you notice? What catches your attention?
• Can you find any number patterns?
• Can you understand the writing system for numbers?
• What is this thing? What is its purpose?

1. Horizontal lines represent "1"
2. Vertical lines represent "5"
3. That if you sum up rows, you get a power of two!
4. That the rule is "add the two above, right and left, to get the next number.

We attempted to verify these rules, and managed to find that they are consistent; we couldn't contradict the rules -- although Becca noticed that there's a problem in the next to last row.

Upon closer examination, we discovered that there is an error in the table! Whoever wrote this, in 1200 AD or so, must have made a little mistake, and added a stroke. See if you can find it.

We'll talk more about symmetry as we get further into the course, but here's one place where it really shows up. Because we expect the table to be a mirror reflection of itself, left and right, we can spot errors -- where the symmetry breaks down.