Hi,
TheHermit <carlw@hermit.net> writes:
<<
1.41421... 3.14159... 6.626...x10^-41 2.71828... 0.70711... 1.618... 8.3145107...
Ohhh! A challenge... let's see:
1.41421...
sqrt(2) -- commonly used in 45/45/90 triangles (this number was the
centre of a massive controversy with Pythagoras and his group, since
it couldn't even be represented by their number system... let alone
allowed to exist!)
3.14159...
Pi -- ratio of circumference to diameter in a circle
6.626...x10^-41
Plank's constant ??? I thought that was at 10^-34 ??? The smallest
unit of energy. Depends on unit definitions.
2.71828...
e -- useful in calculus; equals
lim (1+x)^(1/x) = lim (1+ 1/x)^x x -->0 x --> infinityand (here's the kicker...) diff(e^x, x) = e^x
1/sqrt(2) -- useful as a design coefficient (ideal damping ratio)
<<
1,2,3,4,5,6,7... 1,1,2,3,5,8,13... 1,2,4,8,16,32,64... 1,4,9,16,25,36,49,64...
Counting (Arithmetic Sequence with a=1 d=1)
The Fibonacci Sequence[1]
Exponential Growth (Geometic Sequence with a=1 r=2)
(also the place values in base two (*very* familiar)) The Perfect Squares
TheHermit: Every single one of those numbers and sequences has a context; or "frame of reference" (some even have a culturally defined context, rather than a naturally defined one) -- and most are utterly useless unless you happen to be doing something special. One does not escape "frames of reference" merely by making that frame reality -- becuase we still have to choose how to describe that reality, if only the trivial choice of base and representation system (see _Number: The Language of Science_ to learn that our number system itself is a vast collection of implicit knowledge (read: a frame of reference), or prove it to yourself by thinking what a first century Roman would see in the above -- nothing but scribbles on a page).
ERiC
[1] Much talked about -- it seems these numbers, amoung many other things, specify the differing groups into which flowers can be sorted -- via the number of petals they possess. (it also explains the apparent rareness of four leaf clovers...) My math professor says that an excellent intelligence test is asking for the general (nth) term of this sequence -- one will not stumble upon it by chance. It is just the type of thing an intelligent group of aliens might require of a species before "first contact"...