waaay off-topic (was: waay off-topic, previously way-off and Re: U2-darn few bugs...)

[David Auerbach auerbach@xxxxxxxx]

Sure, absolutely correct. The slide rule (Napier's bones) is based on
logarithmic scales and logarithms are ways of doing arithmetic with
exponents. I had this gorgeous double-length slide rule entering
high school in 1962. Then I took a class in high school that involved
first old-fashioned adding machines (you know, with shifting
carriages) that we wrote algorithms for. The slide rule got dusty
once we took on the IBM 1620. I still remember 2600020003 fondly. 
(Points to those who know.)



On Feb 25, at 1:33 AM, Carl Distefano wrote:

Reply to note from "Robert Holmgren"  Fri, 24
Feb 2006 14:55:12 -0500
What about negative roots? Do they make "sense"?

Well -- correct me if I'm wrong, David -- a root is a fractional
exponent, as in 2^(1/2) equals the square root of 2, so a negative
root must be the reciprocal of the fractional exponent, as in
2^(-1/2) equals 1 over the square root of 2, or 1/(2^(1/2)).

For me it all hangs together when I think of the slide rule (do kids
today even know what that is?), which works on the principle that to
multiply two numbers you add the exponents, and to divide them you
subtract. So, for example, to multiply 2^(1/2) times 2^(-1/2),
you'd add 1/2 plus -1/2, to get zero, and 2^0=1, and indeed if you
multiply those two numbers, which are reciprocals of each other, the
result is 1, and Bob's your uncle.

--
Carl Distefano
cld@xxxxxxxx