There was an awful rainbow once in heaven:
We know her woof, her texture; she is given
In the dull catalogue of common things.
        —John Keats, Lamia  

I am guessing—though it is only a guess—that Keats himself did not know the woof and texture of the rainbow.  Not the way that Newton understood rainbows.  Perhaps not even at all.  Maybe Keats just read, somewhere, that Newton had explained the rainbow as "light reflected from raindrops"—

—which was actually known in the 13th century.  Newton only added a refinement by showing that the light was decomposed into colored parts, rather than transformed in color.  But that put rainbows back in the news headlines.  And so Keats, with Charles Lamb and William Wordsworth and Benjamin Haydon, drank "Confusion to the memory of Newton" because "he destroyed the poetry of the rainbow by reducing it to a prism." That's one reason to suspect Keats didn't understand the subject too deeply.

I am guessing, though it is only a guess, that Keats could not have sketched out on paper why rainbows only appear when the Sun is behind your head, or why the rainbow is an arc of a circle.

If so, Keats had a Fake Explanation.  In this case, a fake reduction.  He'd been told that the rainbow had been reduced, but it had not actually been reduced in his model of the world.

This is another of those distinctions that anti-reductionists fail to get—the difference between professing the flat fact that something is reducible, and seeing it.

In this, the anti-reductionists are not too greatly to be blamed, for it is part of a general problem.

I've written before on seeming knowledge that is not knowledge, and beliefs that are not about their supposed objects but only recordings to recite back in the classroom, and words that operate as stop signs for curiosity rather than answers, and technobabble which only conveys membership in the literary genre of "science"...

There is a very great distinction between being able to see where the rainbow comes from, and playing around with prisms to confirm it, and maybe making a rainbow yourself by spraying water droplets—

—versus some dour-faced philosopher just telling you, "No, there's nothing special about the rainbow.  Didn't you hear? Scientists have explained it away.  Just something to do with raindrops or whatever.  Nothing to be excited about."

I think this distinction probably accounts for a hell of a lot of the deadly existential emptiness that supposedly accompanies scientific reductionism.

You have to interpret the anti-reductionists' experience of "reductionism", not in terms of their actually seeing how rainbows work, not in terms of their having the critical "Aha!", but in terms of their being told that the password is "Science".  The effect is just to move rainbows to a different literary genre—a literary genre they have been taught to regard as boring.

For them, the effect of hearing "Science has explained rainbows!" is to hang up a sign over rainbows saying, "This phenomenon has been labeled BORING by order of the Council of Sophisticated Literary Critics.  Move along."

And that's all the sign says: only that, and nothing more.

So the literary critics have their gnomes yanked out by force; not dissolved in insight, but removed by flat order of authority.  They are given no beauty to replace the hauntless air, no genuine understanding that could be interesting in its own right.  Just a label saying, "Ha!  You thought rainbows were pretty?  You poor, unsophisticated fool.  This is part of the literary genre of science, of dry and solemn incomprehensible words."

That's how anti-reductionists experience "reductionism".

Well, can't blame Keats, poor lad probably wasn't raised right.

But he dared to drink "Confusion to the memory of Newton"? 

I propose "To the memory of Keats's confusion" as a toast for rationalists.  Cheers.