why proofreading is hard

Proofreading is hard, because there's a lot of processing going on between seeing and reading.

After reading the
the sentence, you are
now aware that the
the human brain
often does not
inform you that the
the word 'the' has
been repeated twice
every time.

We are pretty insensitive to letter shape (fortunately, given the plethora of fonts), so can quite readily overlook O-0 and I-l-1 problems, although these are worse in some fonts than in others.  An extreme example doing the rounds at the moment (although it's not new), based on maximal substitution of digits for letters, is:

‎7H15 M3554G3 53RV35 7O PR0V3 H0W 0UR M1ND5 C4N D0 4M4Z1NG 7H1NG5 1MPR3551V3 7H1NG5! 1N 7H3 B3G1NN1NG 17 WA5 H4RD BU7 N0W, 0N 7H15 LIN3 Y0UR M1ND 1S R34D1NG 17 4U70M471C4LLY W17H0U7 3V3N 7H1NK1NG 4B0U7 17

By it's not just doubled words and simple substitution that we can overlook.  The most extreme example I've seen is:

Aoccdrnig to a rscheearch at Cmabrigde Uinervtisy, it deosn't mttaer in waht oredr the ltteers in a wrod are, the olny iprmoatnt tihng is taht the frist and lsat ltteers be at the rghit pclae. The rset can be a toatl mses and you can sitll raed it wouthit porbelm. Tihs is bcuseae the huamn mnid deos not raed ervey lteter by istlef, but the wrod as a wlohe.

Spell checkers, though, are a boon for many of these problems.  So today's proofreaders can concentrate on higher-level issues

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Sources:

1. After reading the...
2. an early reference to 7H15 M3554G3
3. the research behind Aoccdrnig to a rscheearch