Bode plot vs. 3D visualization of magnitude of a transfer function

Acknowledgement:
(1) http://www.seas.upenn.edu/~ese216/handouts/Chpt14_3DPlotTransferFunction.pdf
(2) A Filter Primer, Maxim Integrated; https://www.maximintegrated.com/en/app-notes/index.mvp/id/733
(3) http://electronics.stackexchange.com/questions/159446/poles-and-bode-plots
We say that, in a Bode plot, there is a drop in gain of 20 dB per decade whenever a pole is encountered. But aren't poles defined as the values of 's' which make the transfer function infinity? So why doesn't the gain go up at this point instead of going down?
Lets solve the mystery.....
This code generates the following plots to clarify the confusion:
(1) Top-Left : Bode magnitude plot of the transfer function
(2) Top-Right : 3D surface plot of the magnitude of the transfer function
(3) Bottom-Left: The same surface plot with the magnitude axis limited to a small value so that smaller variations are visible.
(4) Bottom-Right : The surface plot along with its projection along the 'Sigma=0' axis
The projection of the surface plot along the "Sigma = 0" axis, appearing as red color line with yellow markers in the bottom-right plot, is our BODE MAGNITUDE PLOT !!!!