cover of episode Zeroworld

Zeroworld

2023/12/29
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Karim Ani
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Lulu Miller
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Steve Strogatz
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Lulu Miller:探讨了数学中禁止被零除的规则,以及违反该规则可能导致的逻辑混乱和数学体系的崩溃。她以机械计算器为例,说明了被零除会导致无限循环的结果。 Karim Ani:从数学可逆性的角度解释了为什么不能被零除,并阐述了他对被零除这一禁令的个人思考,认为它指向了数学框架之外的某种现实,这种现实可能类似于宗教或神秘体验中描述的“合一”状态。他认为,数学本身的局限性也体现了它的伟大之处,因为它承认自身的不完整性。 Steve Strogatz:从数学史的角度,他指出打破数学规则往往能带来新的数学发现和发展,例如虚数的引入。他认为数学家拥有创造的自由,只要他们的方法是逻辑一致的。他同时指出,寻求统一性是科学进步的重要驱动力,但同样重要的是要认识到多样性的存在。他提出了一个“零世界”的模型,在这个模型中,所有数字都等于零,以此来回应Karim Ani的思考。 Lulu Miller: This episode explores the mathematical rule against dividing by zero and the potential logical inconsistencies and collapse of the mathematical system that could result from breaking this rule. She uses the example of a mechanical calculator to illustrate how dividing by zero leads to an infinite loop. Karim Ani: Explains from the perspective of mathematical reversibility why it is not possible to divide by zero, and elaborates on his personal thoughts on this prohibition, believing that it points to a reality outside the mathematical framework, a reality that may be similar to the "unity" state described in religious or mystical experiences. He believes that the limitations of mathematics themselves also show its greatness, because it acknowledges its incompleteness. Steve Strogatz: From a historical perspective of mathematics, he points out that breaking mathematical rules often leads to new mathematical discoveries and developments, such as the introduction of imaginary numbers. He believes that mathematicians have the freedom to create, as long as their methods are logically consistent. He also points out that the pursuit of unity is an important driving force for scientific progress, but it is equally important to recognize the existence of diversity. He proposes a model of a "zero world" in which all numbers are equal to zero, in response to Karim Ani's thoughts.

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Karim Ani dedicated his life to math. He studied it in school, got a degree in math education, even founded Citizen Math) to teach it to kids in a whole new way. But, this whole time, his whole life, almost, he had this question nagging at him.

The question came in the form of a rule in math, NEVER divide by zero. But, why not?

Cornell mathematician, and friend of the show, Steve Strogatz, chimes in with the historical context, citing examples of previous provocateurs looking to break the rules of math. And he offers Karim a warning,

“In math we have creative freedom, we can do anything we want, as long as it’s logical.”Listen along as Karim’s thought exercise becomes an existential quest, taking us with him, as he delves deeper, and deeper, into Zeroworld.

EPISODE CREDITS: Reported by - Lulu MillerProduced by - Matthew Kieltywith help from - Ekedi Fausther-Keeys, Alyssa Jeong PerryOriginal music and sound design contributed by - Matthew Kieltywith mixing help from - Arianne WackFact-checking by - Diane Kellyand Edited by - Pat Walters

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