Do you think it's possible, then, that the things that aren't verifiable like the other dimensions or universes, or a God/higher intelligence/consciousness have been deliberately designed for us not to be able to analyse? If the universe shows sense of creative and intelligent design, then perhaps the designer made certain things off-limits?

The 1998 film Pi depicts a mathematician who starts seeing patterns (as well as synchronicities) in the cosmos, and evidence of very fine-tuned mathematics. Synchronicity itself is a mystery that science will probably never really be able to grasp.