What is the difference between the arithmetic 3+5 = 5+3 and the algebraic a+b = b+c? One is a specific fact, another is a pattern valid in a multitude of situations. While arithmetic may hint at some regularities, algebra, as a language, gives expression to acknowledgement of patterns as such. How did people express general ideas before the advent of algebra in the 15th-17th centuries? A discussion of patterns and number systems with a Java applet showing Addition and Multiplication Tables in Various Bases. An interactive column for MAA Online that uses a Java applet to simulate a puzzle or mathematical problem, one not stated directly since the applet is intended to be such that the right answer to an as yet unstated problem should be easy to surmise. Also at http://www.cut-the-knot.com/ctk/between.html.