- May 11, 2002I was not offended. My comments were directed at the verbiage

and not at the author--certainly not at the poster.

I'm afraid that I cannot agree that nonsense if thought provoking--

entertaining, maybe. No vague talk about "infinity", "energy" or

"the fourth dimension" could be half as interesting as the real thing.

Take "infinity". Many people would be surprised to learn that it

is a number (a cardinal number, to be precise). In fact, it is

many numbers, for there are different kinds of infinity.

The "smallest" one is countably infinite, symbolized by aleph-null.

Things that are countably infinite can be put into a one-to-one

correspondence with the natural numbers 0,1,2... (Any two

sets that can be put into a 1-to-1 correspondence have the same

cardinal number.)

Georg Cantor proved in that the rational numbers (numbers that can

be expressed as fractions) are countably infinite. He did this

in a very clever way. He made a table of all rational numbers

1 2 3 ...

1 1/1 1/2 1/3 ...

2 2/1 2/2 2/3 ...

3 3/1 3/2 3/3 ...

... ... ... ...

It's easy to see that any N/M must occur exactly once in this

table, so it includes every rational number. Starting at the

upper left hand corner, Cantor counted off each item moving

diagonally though the table in a zig-zag path. In this way,

he enumerated the rational numbers (put them into a 1-to-1

correspondence with the natural numbers), demonstrating that

they are countably infinite.

(People have been very sophisticated about infinite for a very

long time. The proof that there are a countably infinite

number of prime numbers was given by Euclid around 300 B.C.

In 2002, shouldn't we try to be at least as sophisticated about

these things as Euclid was in 300 B.C.?)

On the other hand, the set of real numbers is also infinite, but

it can be proved that you cannot enumerate it. In effect, there

are more real numbers than natural numbers (or rational numbers),

though both are infinite. This order of infinity (the cardinal

number of the continuum) is symbolized by the German letter 'c'.

Working intuitively (without axioms) in set theory, Cantor

eventually ran into a paradox. Consider the set of all sets,

S, having the cardinal number N. Clearly N is the largest

possible cardinal number. Now consider the set of all subsets

of S, having cardinal number M. By a standard theorem M > N.

(Cantor's Paradox 1899). This and a more famous paradoxes found

by Bertrand Russell in 1901 eventually changed how people do

mathematics.

There are more orders of infinity, and more surprising results,

but that's enough to show that the real, precise notion from

mathematics is more interesting and fruitful than vague, wooley talk.

The same can be said about the concept of "energy" in physics.

Spirtualists, mediums and New Age gurus talk a lot about "energy"

and "good vibrations". Have they ever said anything as interesting

as the law of conservation of mass-energy (and E=MC^2)? Have they

ever produced anything as powerful as a nuclear explosion? Can

they explain the energy source of the sun? Nope.

I am totally in favor of exploring "occult" subjects. But it must

be done without degenerating into nonsense or indulging in

pseudo-science. Words like "infinity" and "energy" mean something

just as precise (more precise, actually) as "doorknob" or "interest

rate". No spiritualist ever saws "I am getting in touch with the

psychic doorknobs and interest rates from the Astral Plane." "Psychic

energy" sounds just as ludicrous to someone who understands energy as

"psychic doorknob" does to everyone.

Mark

>

> i am rather distressed that i should have posted anything that would

> provoke such a violent reaction.

>

> i actually have no interest at all in defending the writer who i

> quoted, who may indeed be full of hot air as you suggest. the

> observations just seemed to me to stimulate thought (as they clearly

> did in your case).

>

> my impression of the areas of study that we are involved in is that

> they may begin by seeming something very strange or absurd and yet

> may end up communicating profound understandings of ourselves and the

> world around us.

>

> however, even if the writer's comments are way off base, as you say

> they are, they can still bear fruit. as sherlock holmes said to

> watson in sir arthur conan doyle's novel "the hound of the

> baskervilles":

>

> "I am afraid, my dear Watson, that most of your conclusions were

> erroneous. When I said that you stimulated me I meant, to be frank,

> that in noting your fallacies I was occasionally guided towards the

> truth."

>

> thank you for your useful observations and accept my apologies for

> having offended you.

>

> best, romeman

>

> --- In sacredlandscapelist@y..., "Mark G. Ryan" <mgryan@c...> wrote:

> > super_romeman@y... wrote on Fri, 10 May 2002 10:29:49 -0000:

> > >

> > > "In the fourth dimension the infinite number of solids in the

> > > Universe are in relationship with each other through time and

> > > energy. ... The Fourth Dimension is portrayed geometrically by

> >

> > Time? Energy? WTH!! This is completely vague and says nothing.

> >

> > Time and energy actually mean something in physics. They are not

> > just impressive-sounding words.

> >

> > > fractals and by the Hypercube. The Hypercube is the symbol used

> in

> >

> > Not a symbol. It is a geometrical solid: a mathematical object

> > just as understandable as the cube.

> >

> > > mathematics to try and represent the fourth dimension in two

> > > dimensions (a drawing on a piece of paper - a plane). From the

> center

> >

> > Incorrect. The hypercube is the trace in 3-dim. of a 4-dim. cube.

> >

> > It is no more "infinite" or "symbolic" than the square, which

> happens

> > to be the trace in 2-dim of a 3-dim cube.

> >

> > > of the Hypercube through its 8 diagonals the Hypercube is related

> to

> > > everything in the Universe. The infinity in the Fourth Dimension

> lies

> > > in the infinity of relations."

> >

> > "Infinity" actually means something in mathematics. It is possible

> to

> > talk about it with complete precision. It is not just a fancy word

> > used to impress people and a peg on which to hang New Age nonesense.

> >

> > >

> > > http://www.fractalwisdom.com/FractalWisdom/fourth.html

> > >

> >

> > I'm very impressed by most of what is posted to this list and

> generally

> > just lurk, but this was such a puff of hot air that I had to

> comment.

> >

> > Mark - << Previous post in topic