Exploding Dots

1.5 Wild Explorations

Here are some “big question” investigations you might want to explore, or just think about. All will become clear as the story unfolds in further chapters, but it could be fun to mull on these ideas now.

 

EXPLORATION 1:  WHAT ARE THESE MACHINES DOING?

Can you figure out what these machines are actually doing?

Why is the code for two hundred and seventy three in a \(1 \leftarrow 10\) machine, “\(273\)”? Are all the codes for numbers in a \(1 \leftarrow 10\) machine sure to be identical to how we normally write numbers?

If you can answer that question, can you then also make sense of all the codes for a \(1 \leftarrow 2\) machine? What does the code \(1101\) for the number thirteen mean?

Comment: EXPERIENCE TWO answers these questions.

 

 

EXPLORATION 2:  DOES THE ORDER IN WHICH ONE EXPLODES DOTS SEEM TO MATTER?

Put nineteen dots into the rightmost box of a \(1 \leftarrow 2\) machine and explode pairs of dots in a haphazard manner: explode a few pairs in the right most box, and then some in the second box, and then a few more in the rightmost box, and then some in the second box again, and so on. Do it again, this time changing the order in which you do explosions. And then again!

Does the same final code of \(10011\) appear each and every time?

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