I own a VIC-20 which I use with a TV set. I have seen ads for monitors with 40 or 80 columns. If I were to buy one of these monitors, would my VIC-20 display 40 or 80 columns? If so, would it change the screen memory?
Unfortunately, changing the display format of your computer isn't that simple. A video monitor or TV displays exactly what the computer tells it to display. The VIC generates a video signal for a picture consisting of 23 rows of characters with 22 characters per row, and 22 characters is what you see no matter whether you send that signal to a TV, a monochrome monitor, or a color monitor. The 40- or 80-column figure you mention is only the manufacturer's rating of the number of characters per row that the monitor is capable of displaying clearly—a measure of the resolution of the monitor.
A monitor that gives a good 80-column display should give an exceptionally crisp 22-column display when connected to a VIC. To actually get an 80-column display, you'd have to use one of the 80-column video adapter boards available for the VIC. The adapter would indeed change screen memory, and you'd probably be disappointed to learn that little of your favorite software would work with the 80-column adapter.