Ger suggested teaching Archimedes decimal notation. Well, if you speak decimal notation—our home culture’s standard representation of numbers—into the chronophone, then the chronophone outputs the standard representation of numbers used in Syracuse. To get a culturally nonobvious output, you need a culturally nonobvious input. Place notation is revolutionary because it makes it easier for ordinary people, not just trained accountants, to manipulate large numbers. Maybe an equivalent new idea in our own era would be Python, which makes it easier for novices to program computers—or a mathematician trying to standardize on category theory instead of set theory as a foundation for mathematics.
I think that the rules for the chronophone are either inconsistent, or incorrectly applied. There is not a fine enough distinction between our “cognitive policies”, and our “meta-cognitive policies”.
That is, if you were to explain Python into the chronophone, you are executing two different cognitive policies at two different levels of reduction:
Explain a non-obvious kind of math in our culture which makes it easy for ordinary people to do things previously reserved for professionals. Or the meta-policy of
Say something into the chronophone which will result in decimal notation (something standard in our culture) coming out of the chronophone
Now, presumably, if Archimedes says something into the chronophone to himself, it comes out unchanged. Therefore, the rules predict that what will come out the chronophone will be (depending on which level of meta-cognitive-policy you choose):
A non-obvious kind of math in Archimedes’s culture which makes it easy for ordinary people to do things previously reserved for professionals. E.g. decimal notation.
Something that Archimedes could say into the chronophone which will result in a standard representation of math in his culture coming out of the chronophone.
You see the problem here. If level 2 is the “correct” way of looking at it, (which seems more fundamental to me), then whatever you say, it has a root goal of getting Archimedes to understand something obvious in your culture. Even if you say something unobvious.
(I suppose you could say something “doubly-unobvious” to get it to say something merely unobvious in both his culture and ours, but it’s unobvious to me what that would look like. What useful ideas are unobvious both to our culture and Archimedes, and more, are the same level of unobviousness, that you could iterate the unobviousness and get useful output? If that’s too unclear, I can try to clarify it.)
– (From the follow up article)
I think that the rules for the chronophone are either inconsistent, or incorrectly applied. There is not a fine enough distinction between our “cognitive policies”, and our “meta-cognitive policies”.
That is, if you were to explain Python into the chronophone, you are executing two different cognitive policies at two different levels of reduction:
Explain a non-obvious kind of math in our culture which makes it easy for ordinary people to do things previously reserved for professionals. Or the meta-policy of
Say something into the chronophone which will result in decimal notation (something standard in our culture) coming out of the chronophone
Now, presumably, if Archimedes says something into the chronophone to himself, it comes out unchanged. Therefore, the rules predict that what will come out the chronophone will be (depending on which level of meta-cognitive-policy you choose):
A non-obvious kind of math in Archimedes’s culture which makes it easy for ordinary people to do things previously reserved for professionals. E.g. decimal notation.
Something that Archimedes could say into the chronophone which will result in a standard representation of math in his culture coming out of the chronophone.
You see the problem here. If level 2 is the “correct” way of looking at it, (which seems more fundamental to me), then whatever you say, it has a root goal of getting Archimedes to understand something obvious in your culture. Even if you say something unobvious.
(I suppose you could say something “doubly-unobvious” to get it to say something merely unobvious in both his culture and ours, but it’s unobvious to me what that would look like. What useful ideas are unobvious both to our culture and Archimedes, and more, are the same level of unobviousness, that you could iterate the unobviousness and get useful output? If that’s too unclear, I can try to clarify it.)