Re: virus: maxims and ground rules and suppositions

Eric Boyd (6ceb3@qlink.queensu.ca)
Wed, 12 May 1999 23:50:39 -0400

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 --> infinity
and (here's the kicker...) diff(e^x, x) = e^x

1/sqrt(2) -- useful as a design coefficient (ideal damping ratio)

The Golden Ratio = [1+sqrt(5)]/2. Creates aesthetically pleasing rectangles. May be cultural or species dependent. It also turns up as part of the solution to a problem I talk about below... one of the many "small miracles" involved.

The Universal Gas Constant -- in metric (this number depends on unit definitions). Useless itself, but can be converted for use with specific gases via molecular weight, and *then* used in the Ideal Gas Law (itself only an approximation to reality)

Any "constants" which depend on units would be unrecgonizable to anybody without the context of our current system. (and our current system is mere historical/cultural accident, really)

<< 

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

On sequence which should definitely be included: The Primes:
1, 2, 3, 5, 7, 11, 13, 17, 19, 23, ...
(of course, they carry much more of a "frame of reference" then the others)

<<
So, if you agree with me that these digit sequences (numbers and progressions) are "useful truths" in that they denote certain "special" values tied into the fabric of the universe or the nature of numbers, and that they remain "useful truths" without a particular "frame of reference", then we need to look again at the postulated maxim.
>>

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"...