That Tesla quote unfortunately applies to a bunch of modern cosmologists and physicists, who theorize about multiverses and string theory without any connection to experimentation and observation. I don't consider such stuff real science. In my daily life as a biochemist I am confronted with experimental reality every day, which is sometimes an uplifitng but often a humbling experience, putting hypotheses to shame, as attractive as they may have seemed. I don't see why some so-called scientists should be exempt from confrontation with observed reality. After all, not just hypothesis, but constant testing of hypothesis, is what science is all about.
Tesla was a genius and a great inventor, no one has doubts on it, mostly known for his great work on electromagnetism and electromechanical devices. But, unfortunately his views on modern physics were completely outdated and his beliefs on theoretical physics were completely wrong - the quote being referred was really a very unhappy comment against the great discoveries of modern physics. Fortunately he was completely wrong - he was a firm believer in the old theories of the ether, did not believe in electrons and was against Einstein's theory of relativity.
Just to say I can not see how people can congratulate with Tesla myopic views on modern and theoretical physics, that were proved to be completely wrong, and even extrapolate based on such internet quotes.
And yes, probably the structure referred in the quote had a relation with reality - it was the reality.
Interested people can see it all at the Nikola Tesla entry in Wikipedia: https://en.wikipedia.org/wiki/Nikola_Tesla#On_experimental_and_theoretical_physics
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