Wednesday, December 4th, 2013
Zero: The Biography of a Dangerous Idea
1) Why is zero such a dangerous idea?
Zero has properties different from other numbers. It means infinity and void simultaneously. The concept of zero is one that is very abstract, as if zero pertained to another world, a world of its own. Zero also has the power to connect and create, but also to destroy and render null. It has much substance, much meaning, much depth and complexity, yet at the same time embodies a void and emptiness. This mix of paradoxes, the circumlocution of the concepts of infinity and nothingness (also subjects to much debate and misunderstanding and confusion) at the same time creates a certain mysticism and uncertainty to zero, and makes it seem dangerous.
2) Was zero discovered or invented?
The concept of zero always existed (in some way). The designation of the concept as zero was invented.
3) What did reading about zero make you think about?
I had not realized how much zero can be subject to much questioning and wonders. I hadn't thought about zero under certain of the presented perspectives, especially the one about the multiplication. One of the most powerful properties that we use in math is the ZPP, or the Zero Product Property. It is true that thinking of a simple circular shape, known as zero, can render void an entire number, no matter how long and big, or how infinitely long and small. But then, in AP Calculus, I have been questioning similar topics over and over. We always end up talking about the concept of infinity and limits, and all. This also included zero, but we never really expanded the terms in depth. We mentioned these characteristics, but never named them concretely.
You know, following Pre-Calculus and AP Calculus and now ToK, I am increasingly drawn to the conclusion that maybe math may not all be about certainty only after all. The logic, the reasoning, behind math is certain, unquestionable. But the concepts themselves are open to much uncertainties and doubts.
Zero has properties different from other numbers. It means infinity and void simultaneously. The concept of zero is one that is very abstract, as if zero pertained to another world, a world of its own. Zero also has the power to connect and create, but also to destroy and render null. It has much substance, much meaning, much depth and complexity, yet at the same time embodies a void and emptiness. This mix of paradoxes, the circumlocution of the concepts of infinity and nothingness (also subjects to much debate and misunderstanding and confusion) at the same time creates a certain mysticism and uncertainty to zero, and makes it seem dangerous.
2) Was zero discovered or invented?
The concept of zero always existed (in some way). The designation of the concept as zero was invented.
3) What did reading about zero make you think about?
I had not realized how much zero can be subject to much questioning and wonders. I hadn't thought about zero under certain of the presented perspectives, especially the one about the multiplication. One of the most powerful properties that we use in math is the ZPP, or the Zero Product Property. It is true that thinking of a simple circular shape, known as zero, can render void an entire number, no matter how long and big, or how infinitely long and small. But then, in AP Calculus, I have been questioning similar topics over and over. We always end up talking about the concept of infinity and limits, and all. This also included zero, but we never really expanded the terms in depth. We mentioned these characteristics, but never named them concretely.
You know, following Pre-Calculus and AP Calculus and now ToK, I am increasingly drawn to the conclusion that maybe math may not all be about certainty only after all. The logic, the reasoning, behind math is certain, unquestionable. But the concepts themselves are open to much uncertainties and doubts.
"I am increasingly drawn to the conclusion that maybe math may not all be about certainty only after all. The logic, the reasoning, behind math is certain, unquestionable. But the concepts themselves are open to much uncertainties and doubts."
ReplyDeleteOh no! Is this a good thing or bad thing?