Introduction

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 now includes the presence of some new developments.

Our main idea comes from calling attention to a deep commonality that cuts across the parallel streams of development that in recent millennia have unfolded in the ways and byways of evolutionary notation. It took many centuries of collective search to devise a place-value notation for counting. Likewise to devise a sound-value notation for reading. Likewise to devise a note-value notation for singing. And so forth, for each neurologically specialized ability; in effect, a different specialized notation for each specialized ability. These observations, easily recognized in the history of evolutionary notation, strongly suggest that every kind of intelligence needs its own kind of notation.

In what follows, with emphasis on a fast-forward recapitulation, we 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 another specialized ability. It is for logic, when it is recast in terms of a shape-value notation. Modern logic starts in the middle of the 1800s and, as is well recognized, with the work of George Boole. This means that we have had only about 150 years to think up and to grow into the symbols we now use for symbolic logic.

These symbols, and they are only 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 you with a new set of signs, signs that are much better than any you have seen yet. Not only will it be much easier for you to use them. Even mirrors will be able to use them.

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