A Quote by Roger Penrose

If you come from mathematics, as I do, you realize that there are many problems, even classical problems, which cannot be solved by computation alone. — © Roger Penrose
If you come from mathematics, as I do, you realize that there are many problems, even classical problems, which cannot be solved by computation alone.
Problems cannot be solved by thinking within the framework in which the problems were created.
To my mind, the best SF addresses itself to problems of the here and now, or even to problems which have never been solved and never will be solved - I'm thinking of Philip K. Dick's work here, dealing with questions of reality, for example.
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.
Mathematics is much more than computation with pencil and a paper and getting answers to routine exercises. In fact, it can easily be argued that computation, such as doing long division, is not mathematics at all. Calculators can do the same thing and calculators can only calculate they cannot do mathematics.
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.
I tended to write poems about both social and spiritual problems, and some problems one doesn't really want to solve, and so the problems themselves are solved. You certainly don't want to solve problems in poems that haven't been solved in the world.
...I have wanted to believe people could make their dreams come truethat problems could be solved. However, this is a national illness. As Americans, we believe all problems can be solved, that all questions have answers.
We are more than our problems. Even if our problem is our own behavior, the problem is not who we are-it's what we did. It's okay to have problems. It's okay to talk about problems-at appropriate times, and with safe people. It's okay to solve problems. And we're okay, even when we have, or someone we love has a problem. We don't have to forfeit our personal power or our self-esteem. We have solved exactly the problems we've needed to solve to become who we are.
A wonderful thing happens when you give up on hope, which is that you realize you never needed it in the first place. You realize that giving up on hope doesn't kill you, nor did it make you less effective. In fact it made you more effective, because you ceased relying on someone or something else to solve your problems - you ceased hoping your problems somehow get solved, through the magical assistance of God, the Great Mother, the Sierra Club, valiant tree-sitters, brave salmon, or even the Earth itself - and you just began doing what's necessary to solve your problems yourself.
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.
The reason so many problems do not get solved in Washington is that solving those problems is not the No. 1 priority: Re-election is.
Our problems are not solved by physical force, by hatred, by warOur problems are solved by loving kindness by gentleness, by joy
The positive outlook that optimists project does not come from ignoring or denying problems. Optimists simply assume that problems are temporary and can be solved, so optimists naturally want more information about problems because then they can get to work and do something. Pessimists are more likely to believe that there is nothing they can do anyway, so what's the point of even thinking about it?
A Christian marriage is [not] one with no problems or even a marriage with fewer problems. (It may well mean more problems.) But it does mean a life in which two people are able to accept each other and love each other in the midst of problems and fears. It means a marriage in which selfish people can accept selfish people without constantly trying to change them -- and even accept themselves, because they realize personally that they have been accepted by Christ.
Problems cannot all be solved, for, as they are solved, new aspects are continually revealed: the historian opens the way, he does not close it.
There are no solved problems; there are only problems that are more or less solved.
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