A few reasons for suspecting that this sort of iterative process is in play:
It would fit with the relationship to “That Alien Message” where the idea is that each frame (here, each number) is the “next” state of affairs as something evolves according to simple rules.
There are many cases in which it sure looks as if one number is derived from its predecessor. (Or maybe from its successor.)
It’s an obvious thing to do, if you want to set a challenge like this.
Note that I am not necessarily conjecturing that each number is a function of its predecessor. There might be other internal state that we don’t get to see.
Do you see how such an iteration can produce the long-distance correlations I mention in a message below, between floats at positions that differ by a factor of 2/e? It seems that this would require some explicit dependence on the index.
Its not exactly 2/e. Here is a plot of the “error” of those points. The x axis is the larger point. The y axis is the smaller point minus 2/e times the larger.
So its within about 1% of 2/e, suggesting it might be a real thing, or might just be a coincidence.
A few reasons for suspecting that this sort of iterative process is in play:
It would fit with the relationship to “That Alien Message” where the idea is that each frame (here, each number) is the “next” state of affairs as something evolves according to simple rules.
There are many cases in which it sure looks as if one number is derived from its predecessor. (Or maybe from its successor.)
It’s an obvious thing to do, if you want to set a challenge like this.
Note that I am not necessarily conjecturing that each number is a function of its predecessor. There might be other internal state that we don’t get to see.
Do you see how such an iteration can produce the long-distance correlations I mention in a message below, between floats at positions that differ by a factor of 2/e? It seems that this would require some explicit dependence on the index.
Its not exactly 2/e. Here is a plot of the “error” of those points. The x axis is the larger point. The y axis is the smaller point minus 2/e times the larger.
So its within about 1% of 2/e, suggesting it might be a real thing, or might just be a coincidence.