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The Egyptian hieratic script would be an example
of what Nick calls "data compression within a language".

It was devised as a kind of "court shorthand" to allow
the scribe to capture a written record of speech in
real time, just as our Pitman's shorthand was.

Typically, an hieratic "word" contains compression and
simplification.  The word is compressed into the first and
last character of the conventional hieroglyphic representation,
and the two characters are combined into a single cursive form.

This works because of an interesting feature of the
Egyptian script: whereas most of the written characters
by dynamic count are alphabetic, most of the characters
by static count are ideographs, and by convention the
first character of a word is an ideograph.  In most cases,
that ideograph alone tells you the word, or at any rate
the word class - for example anything to do with a
god would begin with the axe sign ntr, and anything
to do with water would begin with the wave sign nu.
So, same consonant, but two quite different initial

Simple recurrent formulae could be compressed
even further, into the initial character alone.  So,
for instance, "life", ankh, could be written with
three symbols - the ideographic crux ansata
followed by alphabetic "n" and "kh" - or be
abbreviated to the first symbol alone.  In hieratic,
then, "he lives" ankh-f, would be written as
a simplified ideograph fused with the masculine
ending "-f" (looks like a little snake with horns).

Hope that helps