Can our thoughts, meditation, and prayers change the world? Of course, for starters, they can change the way we speak and act, thereby indirectly changing the world. Beyond that, some speculate that our minds may be able to change the world more directly.
Despite the clamor of Bible literalists, there is not objective evidence that a worldwide flood occurred a few thousand years ago, as suggested by some popular interpretations of the Noah story. On the other hand, perhaps megafloods that occurred a few million years ago impressed our early ancestors sufficiently to result in ritual narratives that persisted in varying oral forms up to the time that they were adapted into the various written accounts we now find in ancient texts, both in the Bible and elsewhere.
"In the beginning was the Word, and the Word was with God, and the Word was God." This passage of text from the Gospel of John calls to mind the power of language and reason. The Greek word from which "Word" was translated is "logos", which is the root of "logic" and meant something like reasoned explanation. Some early Greeks considered logos to be the governing principle of the universe. The Gospel of John probably associates this Greek idea with the Christian God as a missionary appeal to persons with a neoplatonist perspective, which may be considered the science of those times.
While listening to speakers at church today, I considered my internal reactions to the various ideas and feelings expressed. At times I was inspired, at times indifferent, and on occasion annoyed. Consideration led me mostly to familiar explanations, ranging from degree of shared perspective to volume of persons near me, but at least one new explanation also came to mind.
A well-meaning anonymous fellow Mormon once chastised me, encouraging more focus on the powers of prayer and priesthood and less focus on the powers of technology. He argued that it will be the traditional religious mechanisms that will save us. I responded with a question: why does the Church use technology to share it's message? He didn't answer. The question stands.
No surprise to learn that neuroscientists at Duke University have found evidence that popular music can be predicted based on harmonics characteristic of human speech. Of course, the link between anatomy and esthetics goes far deeper than this.