The concept of numbers exist in peoples minds before they expressed
writing. For example a farmer plowing a field 3,000 BC years ago may have completed
only 1/2 the field. She didn't record that on a piece of paper but instead registered it
in her head. Likewise if in the morning half a sack of wheat was in her kitchen and
when she returned 2 hours later 1/4 a sack remains she knows that some has been stolen.
A symbol to record the amounts 1/2 or 1/4 probably didn't exist. If
symbols existed they were
usually pictorial. For example a diagram of a sack with a line cutting it in half could be
used to indicate a sack that is half full.
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