What are these codes? What are we doing representing numbers this way? Are these codes for place-value in some base?
One can do arithmetic in this weird system! For example, ordinary arithmetic says that \(6+7=13\) and the codes in this machine say the same thing too! Question: Does it make sense that the final digits of these codes cycle \(1,2,0,1,2,0,1,2,0,\ldots\)? Question: Does it make sense that only the digits \(0\), \(1\), and \(2\) appear in these codes? In fact, here are the \(2 \leftarrow 3\) codes for the first fifteen numbers.
#One half times base one plus base 2 code#
We see the code \(2101\) appear for the number ten in this \(2 \leftarrow 3\) machine. This machine seems to do interesting things.įor example, placing ten dots into the machine This machine replaces three dots in one box with two dots one place to their left.Īh! Now we’re on to something. What do you think of a \(2 \leftarrow 3\)machine? Both fire “off to infinity” with the placement of a single dot and there is little control to be had over the situation. What do you think of the utility of a \(2 \leftarrow 1\) machine?Īfter pondering these machines for a moment you might agree there is not much one can say about them. What do you think of a \(2 \leftarrow 1\) machine?
What happens if you put in a single dot? Is a \(1 \leftarrow 1\) machine interesting? Helpful? What do you think of a \(1 \leftarrow 1\) machine?
Here is a video from Goldfish & Robin and friends “Where Young Minds Collide” demonstrating the weird 2 <– 3 machine.