Inconsistent Spelling-to-Pronunciation Rules Inhibit Educ...

Since the bulk of human knowledge is recorded in books, one of the first steps in the education of the child is to teach him to read. Told that each separate letter, or group of letters, printed in his primer or reader represents a spoken word, the child, being gifted with reason, expects to find an invariable re- lationship between the sound of any given word and the letters composing it. He soon discovers, to his dis- may, that no such invariable relationship exists. Unreason in Sp...

 Infinity Times Zero is Not Zero

The problem is that the laws of addition and multiplication you are using hold for natural numbers, but infinity is not a natural number, so these laws do not apply. If they did, you could use a similar argument that multiplying anything by infinity, no matter how small, gives infinity, thus ∞×0=∞. More sophisticated arguments can also be made, like ∞×0=limx→∞(x×1/x)=1. Clearly all these different values for ∞×0 mean that ∞ cannot be treated like other numbers. In order to ...

 The Point of Argument

The point of a good argument isn’t for one person to simply win over the other. It’s ideally for both to come away with cognitive gains. Even if the goal of an argument is to reach a decision, the goal isn’t to win, the goal is to define the parameters for a good decision and then make the best possible decision with that in mind. I’ve come to believe that when two reasonably smart people disagree on a subject, at the core, it is often because one of the following: One or both of the ...