Math and the Mind

Sunday, September 16, 2007

What Is It

How does a bunch of grey matter in our skulls have the ability to solve mathematical problems? Are we the only species that can? Does catching a baseball require doing calculations? Join John, Ken, and their guest, noted cognitive scientist and NPR's "Math Guy" Keith Devlin, as they discuss the many ways our minds can do the math.

Listening Notes

Ken在程序开始时引用了伽利略的话,他曾经说过数学是上帝用来书写宇宙的语言。这个想法引起了肯的共鸣,当他想到蚂蚁、老鹰和蜜蜂的生活时,他似乎觉得动物必须是复杂的数学计算器。约翰非常肯定。如果宇宙建立在数学的基础上我们会看到符号,数字和方程的世界,但世界根本不是那样的。如果所有动物都天生擅长数学,那为什么数学这么难呢?

Guest Keith Devlin joins the program, and John asks Devlin if Galileo had it right. Devlin takes a third stance, he believes that math tells us more about the human mind than the world outside if it. Math is the science of patterns, patterns exist in the world and we use math to pick them out.

Thinking back to Ken’s idea that animals are mathematical calculators, John asks Devlin whether there is a line we could draw between doing mathematics and following mathematical principles. Devlin agrees with John, but says that it’s a fuzzy line. We could say an animal like a hawk is doing mathematics when it swoops down to catch its prey. On one hand is seems that the hawk must be using trigonometry to accomplish that task but on the other hand we human beings are just using mathematical principles to explain the hawk’s behavior.

Ken notes that Devlin seems to think our brains are built for math in the same way that our minds are built for language. Devlin agrees, and takes that idea a step further. He believes that our mathematic abilities are derivative of the fact we have a language capacity. All of us are wired for math and math comes naturally to all of us. Most of us experience some difficulty learning mathematics in school because written math is symbolic. Our brains are wired for math because they are wired for patterns, but it takes practice and skill to learn to manipulate mathematical symbols. The symbols are difficult, not the math itself.

  • Roving Philosophical Report(seek to 3:43) – Zoe Corneli speaks with Patrick Suppes, Director of the Institute for Mathematical Studies in the Social Sciences at Stanford University.
  • Sixty-Second Philosopher(seek to 41:27) – Ian Shoales visits the studio live to fill us in on the finer points of pledging to KALW.

Transcript