Builds on the unfortunate situation described in the previous lines. You’re also high, and getting depressed and/or lethargic because of the drugs you’ve ingested.

Psilocybin mushrooms (“shrooms”) have well-known hallucinogenic properties and are often taken as recreational drugs.

In Chapter 5 of Carroll’s Alice, Alice nibbles a mushroom on the Caterpillar’s advice and has another bizarre experience as her head first falls to her feet (“moves low”), then rises high above her shoulders on a stretched-out neck:

‘And now which is which?’ she said to herself, and nibbled a little of the right-hand bit to try the effect: the next moment she felt a violent blow underneath her chin: it had struck her foot!

She was a good deal frightened by this very sudden change, but she felt that there was no time to be lost, as she was shrinking rapidly; so she set to work at once to eat some of the other bit. Her chin was pressed so closely against her foot, that there was hardly room to open her mouth; but she did it at last, and managed to swallow a morsel of the lefthand bit.

‘Come, my head’s free at last!’ said Alice in a tone of delight, which changed into alarm in another moment, when she found that her shoulders were nowhere to be found…

See Lewis Carroll’s Through the Looking-Glass, Chapter 2, in which the landscape of the looking-glass world is a chess game come to life:

‘I declare it’s marked out just like a large chessboard!’ Alice said at last. ‘There ought to be some men moving about somewhere—and so there are!’

In the book, pieces are frozen until they beg to be moved. Alice plays a Pawn who’s often bossed around by the senior pieces.

Allegorically, these lines probably refer to authority figures giving orders: policemen telling hippies or drug users to leave a place where they’ve been squatting; the state drafting citizens and sending them to the battlefield. (“White Rabbit” was written during the Vietnam War era.)

See Chapter 4 of Alice’s Adventures in Wonderland:

She stretched herself up on tiptoe, and peeped over the edge of the mushroom, and her eyes immediately met those of a large caterpillar, that was sitting on the top with its arms folded, quietly smoking a long hookah, and taking not the smallest notice of her or of anything else.

In Chapter 5, the Caterpillar gives Alice advice resembling the opening lines of “White Rabbit”:

‘One side will make you grow taller, and the other side will make you grow shorter.’
‘One side of WHAT? The other side of WHAT?’ thought Alice to herself.
‘Of the mushroom,’ said the Caterpillar, just as if she had asked it aloud; and in another moment it was out of sight.

Continuing the drug-culture allegory, it was common to be introduced to the scene by someone else, so you’d have to give a reference when buying or joining a party.

From Disney’s Alice in Wonderland, 1951

This phrase resembles “chasing the dragon,” a slang term for smoking opium.

JA relates this to Lewis Carroll’s Alice’s Adventures in Wonderland, in which Alice chases the White Rabbit down a hole into Wonderland–much as you’d plunge into a trippy world on hallucinogens.

If you’re looking for confirmation that illegal drugs work better (expand your mind more, provide more intense sensations) than “the ones that mother gives you,” go ask someone who’s gotten high on them.

See Chapters 1-2 of Lewis Carroll’s first Alice book, in which Alice eats a small cake (not a pill) and grows into a giant:

Just then her head struck against the roof of the hall: in fact she was now more than nine feet high, and she at once took up the little golden key and hurried off to the garden door.

Beatrice Sparks borrowed these lines for the title of Go Ask Alice, her 1971 memoir of teenage drug addiction.

So begin the references to Lewis Carroll’s Alice books. In the opening chapters of Alice’s Adventures in Wonderland, Alice drinks a potion that shrinks her:

‘What a curious feeling!’ said Alice; ‘I must be shutting up like a telescope.’

And so it was indeed: she was now only ten inches high…

She then eats a small cake and grows into a giant:

Just then her head struck against the roof of the hall: in fact she was now more than nine feet high…

(Notice there’s no mention of “pills”; these are the song’s invention, and make the drug connection more explicit.)

Similarly, drugs can act as a stimulant or a depressant, making you feel either much better or much worse–figuratively bigger and smaller. They can also distort your perceptions of size, shape, etc.

See the note on the “hookah-smoking caterpillar” below.