The Advantage is that mathematics is a field in which one's blunders tend to show very clearly and can be corrected or erased with a stroke of the pencil. It is a field which has often been compared with chess, but differs from the latter in that it is only one's best moments that count and not one's worst. A single inattention may lose a chess game, whereas a single successful approach to a problem, among many which have been relegated to the wastebasket, will make a mathematician's reputation.
Interpretation
Mathematics allows for clear identification and correction of mistakes, unlike chess where a single error can lead to defeat.
In this quote, Norbert Wiener highlights the unique nature of mathematics as a discipline where errors can be easily corrected, signifying an important aspect of learning and improvement. Unlike chess, where one misstep can determine the outcome of a game, mathematics encourages a focus on successful solutions over failures, emphasizing the value of persistence and the clarity with which mistakes can be rectified in problem-solving.
In practice
During a mathematics class, the teacher emphasizes the importance of learning from mistakes.
In a very real sense, we are shipwrecked passengers on a doomed planet. Yet, even in a shipwreck, human decencies and human values do not necessarily vanish, and we must make the most of them. We shall go down, but let it be in a manner to which we may look forward as worthy of our dignity.
I have said that the modern man, and especially the modern American, however much 'know-how' he may have, has very little 'know-what'
Any labor which competes with slave labor must accept the economic conditions of slave labor.
We have modified our environment so radically that we must now modify ourselves to exist in this new environment.
We are but whirlpools in a river of ever-flowing water. We are not stuff that abides, but patterns that perpetuate themselves. _x000D_ A pattern is a message, and may be transmitted as a message.
Let us remember that the automatic machine is the precise economic equivalent of slave labor. Any labor which competes with slave labor must accept the economic consequences of slave labor.
Unfortunately, as a society, we do not teach our children that they need to tend carefully the garden of their minds. Without structure, censorship, or discipline, our thoughts run rampant on automatic. Because we have not learned how to more carefully manage what goes on inside our brains, we remain vulnerable to not only what other people think about us, but also to advertising and/or political manipulation.
But in the new (math) approach, the important thing is to understand what you're doing, rather than to get the right answer.
One good schoolmaster is worth a thousand priests.
I would never suggest to anyone that they drop school for chess. First of all even if you can make it in chess, your social skills need to be developed there.
Questions are the important thing, answers are less important. Learning to ask a good question is the heart of intelligence. Learning the answer-well, answers are for students. Questions are for thinkers.
Giving children the sense that you always ought to speak up for what's right, even if it costs you something, that's something you can do.
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