The Bach-Peters Paradox

Pronouns refer to nouns. In the sentence Francis touched the beggar and cured him, we can “unpack” the pronoun him by replacing it with its referent, the beggar: Francis touched the beggar and cured the beggar.

But what if a sentence has two phrases that refer to each other? The pilot that shot at it hit the Mig that chased him. Now there’s an infinite regress:

The pilot that shot at the Mig that chased the pilot that shot at it hit the Mig that chased the pilot that shot at it.

It seems that no amount of unpacking can resolve these pronouns. Yet most readers can understand the sentence immediately. How are they able to do so?


  • The sum of the numbers on a roulette wheel is 666.
  • ANTITRINITARIANIST contains all 24 arrangements of the letters I, N, R, and T.
  • The Empire State Building has its own zip code.
  • 63945 = 63 × (-9 + 45)
  • “Isn’t it strange that we talk least about the things we think about most!” — Charles Lindbergh

Season’s Greetings

Comes Christmas merry? Hungry birds; no bright berries;
Rents high, not paid; long bills; empty barns, no peace and prosperity.

Read this backward and it becomes:

Prosperity and peace; no barns empty; bills long paid;
Not high rents; berries bright; no birds hungry; merry Christmas comes.

J.A. Lindon composed the following verse, in which the first line, the first word of each line, and the nth word of each nth line spell the same message:

A merry Christmas and a happy new year!
Merry, merry carols you’ll have sung us;
Christmas remains Christmas even when you are not here,
And though afar and lonely, you’re among us.
A bond is there, a bond at times near broken.
Happy be Christmas then, when happy, clear,
New heart-warm links are forged, new ties betoken
Year ripe with loving giving birth to year.

“The Siege of Belgrade”

An Austrian army, awfully arrayed,
Boldly by battery beseiged Belgrade;
Cossack commanders cannonading come,
Dealing destruction’s devastating doom;
Every endeavour engineers essay
For fame, for fortune, forming furious fray;
Gaunt gunners grapple, giving gashes good;
Heaves high his head heroic hardihood;
Ibraham, Islam, Ismail, imps in ill,
Jostle John, Jarovlitz, Joe, Jack, Jill,
Kick kindling Kutosoff, kings’ kinsmen kill;
Labor low levels loftiest, longest lines;
Men marched ‘mid moles, ‘mid mounds, ‘mid murd’rous mines.
Now nightfall’s near, now needful nature nods,
Opposed, opposing, overcoming odds.
Poor peasants, partly purchased, partly pressed,
Quite quaking, Quarter! quarter! quickly quest.
Reason returns, recalls redundant rage,
Saves sinking soldiers, softens seigniors sage.
Truce, Turkey, truce! Truce, treach’rous Tartar train!
Unwise, unjust, unmerciful Ukraine!
Vanish, vile vengeance! Vanish, victory vain!
Wisdom wails war — wails warring words. What were
Xerxes, Xantippe, Ximenes, Xavier?
Yet Yassey’s youth, ye yield your youthful yest,
Zealously, zanies, zealously, zeal’s zest.

— William T. Dobson, Literary Frivolities, Fancies, Follies and Frolics, 1880