Suddenly an oft-heard story comes alive. It begins to glow, throb, throw off implications like solar flares, take center stage, where before it had been one of many, and no more than its bare literal self.
So I felt reading Numbers: The Universal Language by Denis Guedj in a little glossy highly illustrated book I picked up at MIT. The epiphany? The number system we use is a conceptual and practical creation: of course, but how that fact struck me. Whatever the internal logic of the system we have invented, it came about through human ingenuity. Indeed, the adoption by the West of the Arabic numerical system in the late Middle Ages democratized arithmetic and opened up the world of practical calculation and mathematical exploration that is still, today, a work in progress.
I thought: put a simple system of working with numbers in the hands of the general public and who knows what can happen. When the abacists were replaced by the algorists, the mysteries of the universe and the power of its operations were open to anybody who could use a pencil and paper, upper class or low.
All of a sudden the system my wife struggles to teach her tutees took on the aspect of a great historical achievement. In a flash, I saw history as a process of incessant conversion of the 'not yet' into a new capability, a new presence, a new expansion of the future. So many obvious things seemed marvelous creations or discoveries: why had they not dazzled me before?
Walking the hallway today, I found book snatched away for perusal by a fellow teacher. In the conversation, I found myself sharing with others one or two simple (obvious) points that had hit me for the first time, such as: the fact that the system we use (not the only possible or historical one) correlates the length of numbers with their size, so relative scale can be assessed at a glance. Of course. It's right there, but...
I could see you, colleagues, becoming intrigued--and why not? I went to my first class of the day feeling elevated. The day progressed; my energy level dropped; the brilliance became somewhat banal. Still, continued reading keeps stirring up the coals. Affairs needn't have been ordered the way they were, but once done, a republic of reason was established in accounting houses and classrooms.
What next? What ungainly and thought balking systems are we now struggling with that with a few flashes of genius can turn into something simple and powerful enough for quick boys or girls to use to make what has never been conceived, much less invented? It's worth waiting to see.
So I felt reading Numbers: The Universal Language by Denis Guedj in a little glossy highly illustrated book I picked up at MIT. The epiphany? The number system we use is a conceptual and practical creation: of course, but how that fact struck me. Whatever the internal logic of the system we have invented, it came about through human ingenuity. Indeed, the adoption by the West of the Arabic numerical system in the late Middle Ages democratized arithmetic and opened up the world of practical calculation and mathematical exploration that is still, today, a work in progress.
I thought: put a simple system of working with numbers in the hands of the general public and who knows what can happen. When the abacists were replaced by the algorists, the mysteries of the universe and the power of its operations were open to anybody who could use a pencil and paper, upper class or low.
All of a sudden the system my wife struggles to teach her tutees took on the aspect of a great historical achievement. In a flash, I saw history as a process of incessant conversion of the 'not yet' into a new capability, a new presence, a new expansion of the future. So many obvious things seemed marvelous creations or discoveries: why had they not dazzled me before?
Walking the hallway today, I found book snatched away for perusal by a fellow teacher. In the conversation, I found myself sharing with others one or two simple (obvious) points that had hit me for the first time, such as: the fact that the system we use (not the only possible or historical one) correlates the length of numbers with their size, so relative scale can be assessed at a glance. Of course. It's right there, but...
I could see you, colleagues, becoming intrigued--and why not? I went to my first class of the day feeling elevated. The day progressed; my energy level dropped; the brilliance became somewhat banal. Still, continued reading keeps stirring up the coals. Affairs needn't have been ordered the way they were, but once done, a republic of reason was established in accounting houses and classrooms.
What next? What ungainly and thought balking systems are we now struggling with that with a few flashes of genius can turn into something simple and powerful enough for quick boys or girls to use to make what has never been conceived, much less invented? It's worth waiting to see.
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