# Addendum on analogies

[From Bill Powers (2003.04.27.2113 MDT)]

It occurred to me that the view of analogies as relationships unnecessarily
confines us to one level of perception. I think we get analogies any time a
single higher-order perception can be perceived in significantly different
sets of lower-order perceptions. We say that two sets of lower perceptions
are analogous if we get from them the same higher-order perception.

Thus we cn have a scream which pierces the ears in a way analogous to the
piercing thrust of an epee. There can be a logical arrangement of tools on
a pegboard, analogous to the logic of their use. A person can follow a diet
"religiously," meaning in a way analogous to the way a devotee follows the
precepts of his sect.

This would imply that two statements that are paraphrases of each other are
also analogous in terms of their common meaning.

Best,

Bill P.

From Bill Powers (2003.04.28.0931 MDT)]

In the series 1,2,4, obviously these numbers are not squares of integers
since 2 is not the square of an integer. The rule is x =
2-to-the-(x-1)th-power.

For those who wonder what sort of rule could generate 1,2,4,8,208245 etc
all you need is to find the roots of an Nth order equation, where N is the
number of the next element of the series. This is the same principle that
says you can fit a curve exactly to any finite set of data points if the
highest power of the variable is equal to the number of points. A finite
set of data points says nothing about the behavior of the fitted curve
between the points.

Best,

Bill