A Quote by Daniel Levitin
Across a range of inferences involving not just language but mathematics, logic problems, and spatial reasoning, sleep has been shown to enhance the formation and understanding of abstract relations, so much so that people often wake having solved a problem that was unsolvable the night before.
Related Quotes
Mathematics is a language plus reasoning. It's like a language plus logic. Mathematics is a tool for reasoning.
Inferences of Science and Common Sense differ from those of deductive logic and mathematics in a very important respect, namely, when the premises are true and the reasoning correct, the conclusion is only probable.
Metaphorically speaking, of course, if I put a problem behind my pillow and fall asleep, very often because my brain went to sleep with that idea or the problem alive, very often in the middle of the night I wake up, and I wake up with a solution or with a direction of solution.
Mathematics and logic have been proved to be one; a fact from which it seems to follow that mathematics may successfully deal with non-quantitative problems in a much broader sense than was suspected to be possible.
For most problems found in mathematics textbooks, mathematical reasoning is quite useful. But how often do people find textbook problems in real life? At work or in daily life, factors other than strict reasoning are often more important. Sometimes intuition and instinct provide better guides; sometimes computer simulations are more convenient or more reliable; sometimes rules of thumb or back-of-the-envelope estimates are all that is needed.
Mathematics is not just a language. Mathematics is a language plus reasoning.
If explicit metadata is a real problem, it raises problems that just can't be solved. It's not that we're not good at it; it's the problems cannot be solved because we're not going to agree about these deep questions of how we organize.
In every enterprise ... the mind is always reasoning, and, even when we seem to act without a motive, an instinctive logic still directs the mind. Only we are not aware of it, because we begin by reasoning before we know or say that we are reasoning, just as we begin by speaking before we observe that we are speaking, and just as we begin by seeing and hearing before we know what we see or what we hear.
It’s a way of life to be always texting and when you looks at these texts it really is thoughts in formation. I do studies where I just sit for hours and hours at red lights watching people unable to tolerate being alone. Its as though being along has become a problem that needs to be solved and then technology presents itself as a solution to this problem…Being alone is not a problem that needs to be solved. The capacity for solitude is a very important human skill.
When you start a company, it's more an art than a science because it's totally unknown. Instead of solving high-profile problems, try to solve something that's deeply personal to you. Ideally, if you're an ordinary person and you've just solved your problem, you might have solved the problem for millions of people.
Deep in the human nature, there is an almost irresistible tendency to concentrate physical and mental energy on attempts at solving problems that seem to be unsolvable. Indeed, for some kinds of active people, only the seemingly unsolvable problems can arouse their interest.
Washington doesn't have just a spending problem, or just an entitlement problem, or just a taxing problem. We have a leadership problem. Fix that, and the first three problems are solved.
Night terrors are very different from nightmares. A lot of people will think they're the same, but they're really not. Night terrors - you want to look at the time of night when you're having the problem. Night Terrors happen in deep sleep. Nightmares tend to happen in a lighter REM sleep.
Some of our problems can no more be solved correctly by majority opinion than can a problem in arithmetic and there are few problems that cannot be solved according to what is just and right without resort to popular opinion.
We can... treat only the geometrical aspects of mathematics and shall be satisfied in having shown that there is no problem of the truth of geometrical axioms and that no special geometrical visualization exists in mathematics.
It is impossible to overstate the imporance of problems in mathematics. It is by means of problems that mathematics develops and actually lifts itself by its own bootstraps... Every new discovery in mathematics, results from an attempt to solve some problem.
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