After reading the pages in the beginning and the end of this thread I felt a need to comment on the topic.
ALL trading requires the use of historical data. ALL of our indicators are based on something that has happened in the past. ALL of our indicators are ultimately based on price.
There was some talk about only using the 'x' axis of the chart. I get a curvy line if I do that where the dots that make up the line are unrelated. Maybe someone can comment on the cone that professionals utilize.
To say someone trades without a chart is a misnomer to me in that if your application interrogates the history data for high and low points, averages, frequencies, etc., then you are basically reading a chart using mathematics rather than your eyes.
Taking the concept of trading without a chart literally, the only way this can be done is with an automatic system. I've spent the last several years writing such a system. It is completely on its own and does quite well. However, I do have to rely on charts when choosing symbols to trade and to review how well a stock is performing.