# Let the Mirrors Do the Thinking

Glenn Clark and Shea Zellweger
Bridges: Mathematical Connections in Art, Music, and Science (1998)
Pages 113–120

## Abstract

Our story begins with a simple example. Suppose that someone asked you to keep a record of your thoughts, exactly, and in terms of the symbols given, when you are making an effort to multiply XVI times LXIV. Also suppose that, refusing to give up, you finally arrive at the right answer, which happens to be MXXIV. We are sure that you would have had a much easier time of it, to solve this problem, if you would have found that 16 times 64 equals 1024. This example not only looks at what we think and what we write. It also looks at the mental tools, the signs and symbols, that we are using when that thinking and that writing is taking place. How we got these mental tools is a long story, one that includes new developments today. What follows will run a replay of what happened when Europe took several centuries to go from MXXIV to 1024. This replay in not for numbers: it is for logic. Modern logic starts in the middle 1800s and with George Boole. This means that we have had only about 150 years to establish the symbols we now use for symbolic logic. These symbols leave a lot to be desired. We hope that we can draw you into taking a look at a lesson in lazy logic. If you follow us all the way, we hope to leave your with a new set of symbols, much better than any you have seen yet. Not only will it be easier for you to use them. Even mirrors will be able to use them.