The phrase “thoughts and prayers” has received a lot of well-deserved mocking lately. After each mass shooting, it seems our political representatives really mean “thoughts and payers,” and their only god is the National Rifle Association.

But what do most people — the vast majority of faithful, heartbroken people — mean when they say they’re offering “thoughts and prayers”? Do they perceive a meaningful distinction between those two functions: thought and prayer?

The Pew Research Center keeps track of how many Americans pray and how often (more than half of us pray every day). But what exactly is prayer for Americans? Is it merely an expression of sympathy for the victims and their loved ones? Do we expect some kind of divine response? That is, is prayer efficacious? — all prayers, or just some kinds of prayers, or just some kinds of prayers from some kinds of people?

Is prayer a species of reverent begging? A holy wishing? A desperate request thrown out into the void? Do we believe that if implored with sufficient fervency, an all-loving, all-powerful God will intervene in human history and stop this carnage, divert the path of a bullet, temper a madman’s rage?

The distinctions we make for different kinds of prayers are curious.

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Sally Quinn, a former writer for The Washington Post and the widow of executive editor Ben Bradlee, recently published a book called “Finding Magic: A Spiritual Memoir.” Putting the words “magic” and “spiritual” next to each other — separated by just a flimsy colon — makes some believers squirm. Good folks want to imagine that magic and spirituality live in entirely different neighborhoods.

Even more problematic is Quinn’s tale of casting hexes on people — people who later died. There have been jokes about this, of course. In the 17th century, she might have been hanged — though not burned. We Americans never burned our witches. That barbaric practice was for uncivilized Europeans.

But what really rubs us the wrong way about Quinn’s claim?

Is it that people were killed? (Surely, no one believes that.) Is it that Quinn was appealing to dark forces instead of heavenly ones? (That seems like the objection of a much earlier era.) Or is it that she dares to posit that her “thoughts and prayers” could actually have a tangible effect in the real world? Most of us, after all, like our thoughts and prayers as benign as a Hallmark greeting card. We get a little uncomfortable if anybody starts mixing our material and immaterial realms. Oh, we might pray for a sick loved one, but most of us would agree with that conflicted believer Emily Dickinson:

“Faith” is a fine invention

For Gentlemen who see!

But Microscopes are prudent

In an Emergency!

In other words, argue that your thoughts and prayers might actually do something specific, and you’re a loon.

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One person who took such loons seriously was the late British historian Richard Cavendish. This year marks the 50th anniversary of “The Black Arts,” his foundational study of “witchcraft, demonology, astrology, and other mystical practices throughout the ages.” The book has been republished with a fresh introduction by Mitch Horowitz, a scholar of New Thought.

No less a figure than I.B. Singer once praised the remarkable breadth and sensitivity of Cavendish’s survey. And Singer went on to defend the relevance of his subject. “We are all black magicians in our dreams, in our fantasies, perversion, and phobias,” Singer wrote in his 1967 review. “Consciously or subconsciously, we call upon the forces of good to assist us. We try to appease the powers of evil with magical methods that often are secret even to ourselves.”

Who’s to draw a line between certain kinds of acceptable thoughts and prayers, legitimate spiritual forces and forbidden occult ones? These questions are easy for the strict atheist or the rigidly devout, but most of us aren’t blessed with such soothing certainty.

In his introduction, Horowitz writes: “We are not very different from the classical magician when we strive, morally and materially, to carry forth our plans in the world — to ensure the betterment of ourselves and our loved ones; to heal sickness; to create, sustain, and, above all, to generate things that bear are markings, ideals, and likeness. All of this is the expenditure of power, the striving to physically establish our inner drives and images.”

“The Black Arts” makes for a weird read today. Despite consorting with creepy spells and bizarre practices, it’s written for a lay audience, with a disarmingly level tone. Cavendish offers agnostic descriptions of everything from blood baths to burned effigies — basically the background trappings of every episode of “Buffy the Vampire Slayer.”

Though not strictly a work of history or anthropology, the book stirs in both those approaches. This may be a witch’s brew, but it’s served cold and organized by subject, e.g. “The Stone and the Elixir,” “Astrology,” “Names and Numbers.” That structure can cause fits of historical whiplash as Cavendish flies from one time period to another, one country to another, sometimes on the same page. (Whiplash, by the way, can be cured by applying crushed mandrake root in the light of a full moon.)

No, Cavendish never makes jokes like that. That’s just me and my nervous laughter around this subject. I don’t believe in magic or numerology or hexes. No comparison can be drawn between that silly stuff and my faith. I’m a thoroughly modern person who understands Western science and the reliability of independently confirmed physical evidence. I just also happen to believe that my desires — purified in the crucible of prayer — are sometimes answered.

How do I reconcile all that?

God knows.

Ron Charles is the editor of Book World.