futility of n-space

[Jon]

The restriction of n-space is reflected in the virtual impossibility of
finding roots to n-degree polynomials. If each coefficient is a component
to a vector of n dimensions, and each power of x is a component to a vector
of n dimensions, the two vectors are orthogonal since their dot product is
zero.

The liberty of n-space is that it opens up infinite possibilites. A
theorist can prove his brainchild in 4 dimensions if he can't do it in 3.
Just imagine. Associated with every point in (x1,x2,x3) is a point on the
x4 axis. That is, associated with every (x,y,z,t) is a point x4 hidden in
the system of points (x1,x2,x3,x4,t), not considering that furthermore t
(time) may be altered. The theorist becomes an artist producing
explanations at whim in equations that all come together perfectly.

Anything whatsoever can be "proven" using math of higher dimensions in E^n
where n>3.

This also delimits n-space math. On the one hand it is uselessly
constrictive and on the other uselessly diluted.

Consider a number of E^3 coordinate systems in synchrounous time with each
other separated by large distances. I think this is as best a model as can
be hoped for. One system is unbridled and actions in it mapped to form
reactions in the other systems. That way, associated with one system are
events in the other systems by cause and effect. When a tree is felled in
one system, a dam is caused to be broken in the other systems. This
meaningless association is diluted as well, but Master and Slave can swap
roles like a see-saw. This is in line with momentum that is channeled for
technological uses. No, there is no relationship. But can you find one?

The man's pulse was connected mechanically to regulate the speed of a
flywheel. After this went on for awhile, the technician altered the
flywheel and observed the man's pulse. He found out nothing. There are
some processes, however, that do swap Master/Slave relationships, like a
child's see-saw on a playground. What are they? These are good candidates
for multiple systems of E^3, particularly in distance relationships to
unknown cause and effect forces. The media may be EMR. The relatively
equipotential space-time around the planet may have anomalies, like
gradients or funnels. The ancient structures built in phylogeny are a
vortex. The path of least resistance is to delve and fall into them,
degenerating and destroying the foundations of everything that went in to
bringing the world up to the present.

Suppose one system was in the nucleus of a star and the other system in the
vortex of a Black Hole. Is there any cause and effect between the two?

No.

[Igor]

Jon wrote in message ...

Post by Jon
The restriction of n-space is reflected in the virtual impossibility of
finding roots to n-degree polynomials. If each coefficient is a component
to a vector of n dimensions, and each power of x is a component to a vector
of n dimensions, the two vectors are orthogonal since their dot product is
zero.

Could you put that in English? I don't speak gibberish.

Post by Jon
The liberty of n-space is that it opens up infinite possibilites. A
theorist can prove his brainchild in 4 dimensions if he can't do it in 3.
Just imagine. Associated with every point in (x1,x2,x3) is a point on the
x4 axis. That is, associated with every (x,y,z,t) is a point x4 hidden in
the system of points (x1,x2,x3,x4,t), not considering that furthermore t
(time) may be altered. The theorist becomes an artist producing
explanations at whim in equations that all come together perfectly.
Anything whatsoever can be "proven" using math of higher dimensions in E^n
where n>3.

That doesn't necessarily follow. Where's your proof?

[Frederick Williams]

Post by Igor
Jon wrote in message ...

Post by Jon
The restriction of n-space is reflected in the virtual impossibility of
finding roots to n-degree polynomials. If each coefficient is a component
to a vector of n dimensions, and each power of x is a component to a vector
of n dimensions, the two vectors are orthogonal since their dot product is
zero.

Could you put that in English? I don't speak gibberish.

I think it means

a + bx + cx^2 (e.g.)

is the dot product of vectors (a, b, c) and (1, x, x^2) in R^3, so

a + bx + cx^2 = 0

"says that" the two vectors are orthogonal.

[Sam Wormley]

Post by Frederick Williams

Post by Igor
Jon wrote in message ...

Post by Jon
The restriction of n-space is reflected in the virtual impossibility of
finding roots to n-degree polynomials. If each coefficient is a component
to a vector of n dimensions, and each power of x is a component to a vector
of n dimensions, the two vectors are orthogonal since their dot product is
zero.

Could you put that in English? I don't speak gibberish.

I think it means
a + bx + cx^2 (e.g.)
is the dot product of vectors (a, b, c) and (1, x, x^2) in R^3, so
a + bx + cx^2 = 0
"says that" the two vectors are orthogonal.

Two vectors j and k, in an inner product space V, are orthogonal if their
inner product (j,k) is zero.