The complex number is in the form a+bi.
a being the real part.
The hypothesis is that all non trivial numbers will lie on the line 1/2+bi. The modern version is all non trivial zeros will be with a real part 1/2+bi=0.
The zeta function is like any other function such that each different input will put out a output.
Were they use the term height is such that the zeta function can be drawn in a graph form that it 3d.
This means using z, y, z axis to do so.
the trivial and non trivial zeros are of course on the plane formed by the x,y lines.
Now look at the input form used to get this.
The reals for the line with a+0i. The imaginary part intersects this at 0 in a perpendicular form, or 0+bi.
This is a right angle of course.
Now realize all trivial zeros are at every negative even integer (real).
So far all known non trivial zeros are on the line of 1/2=bi, or a perpendicular line to the reals.
See a pattern??
Input is perpendicular and output may be the same in the form of 1/2+bi to the real line.
Well as stated the trivial zeros are at every negative even integer starting at negative 2. Let's see if the pattern hold to the original input point. -2+2=0. Yet of course the value of the zeta function at zero is not 0. It is -1/2. Well by subtracting this from zero you get of course 1/2.
Interesting?
As for the know values of the non trivial zeros and the patterns of the zeta function, it shown a phase relation between the real and imaginary parts of a graph. Both parts can be draws in the wave form. Also the polar form can be used to see this relation.
To see what I am saying on this point view
http://en.wikipedia.org/wiki/Riemann_hypothesis
and
http://en.wikipedia.org/wiki/File:RiemannCriticalLine.svg
Also the page at
http://www.math.ucsb.edu/~stopple/zeta.html
scroll down the page to
Riemann Hypothesis Movie
Of course if some one can prove that instead of the critical strip, it is a critical line, if it can be, then a proof would be found.
Hope this all helps.