He did NOT believe what he saw, initially. He thought of multiple ways he could be wrong - perhaps this was the result of twinning. If it were, the pattern would go away if the diffraction came from a smaller part of the sample - it didn't. I think he also did electron microscopy. He knew it went against the basic tenets of crystallography, and he accepted what the data implied only after submitting it to every attempt at disproof he could come up with.
Then the scientific community did basically the same thing, on a larger scale. I believe Linus Pauling said of Schectman, "There are no quasi-crystals - only quasi-scientists." A key difference between scientists and mystics is that scientists as a community are professional skeptics. Yes, they can also be "dogmatic" about certain things, but those "dogmas" are not merely handed down by authorities as they are under the original meaning of the word but are hard-won principles that seem the best way to explain and organize the widest range of observations. And they can be overthrown.
Mystical experience is intrinsically personal and basically not subject to external scrutiny. Alleged truths derived from mystical experience may or may not be genuine truths, but the personal and subjective nature of that experience pretty much relegates such ideas to a very different realm from science. The success of science in assimilating new information in no way implies anything meaningful about the speculations of mystics possibly being correct.
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