Checking length of string in an admin area field onblur with jQuery

There are a number of issues with your code but most importantly you need to call val on the text input. Here is how your make_year_created_equal_4_chars function might look:

function make_year_created_equal_4_chars() {
?>
<script type="text/javascript">
    // This is a shorthand for "jQuery(document).ready()"
    jQuery(function($) { 
        $('#acf-field-artwork_created').blur(function() {
            // Please notice the declaration of 'selected_length'.
            // It is important to declare it with 'var' so that
            // you don't end up with it in the global scope.
            var selected_length = $(this).val().length;

            if (selected_length != 4) {
                alert( 'A 4 digit year must be entered in the Artwork Created field' );
            }
        });
    });
</script>
<?php
}