When I was in Cambridge reading mathematics, I went to Amsterdam for the International Mathematics Congress. There I saw M.C. Escher's fascinating work. That inspired me to try my hand at drawing such impossibilities.
Roger PenroseRead
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.
Interpretation
What this quote means
Mathematics involves problems that go beyond mere computation and require deeper understanding.
In this quote, Roger Penrose emphasizes the limitation of computational methods in solving certain mathematical problems. He suggests that while computation is a valuable tool, it is not always sufficient; many classical mathematical challenges require insight, creativity, and a profound grasp of the underlying principles rather than just algorithmic processing.
Themes
MathematicsComputationProblemsUnderstandingInsight
In practice
Example use cases
A professor might use this quote to illustrate the limitations of algorithmic approaches in advanced mathematics courses.
More from Roger Penrose
All quotes βSome people take the view that the universe is simply there, and it runs along - it's a bit as though it just sort of computes, and we happen by accident to find ourselves in this thing. I don't think that's a very fruitful or helpful way of looking at the universe.
Roger PenroseRead
Consciousness ... is the phenomenon whereby the universe's very existence is made known.
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Some years ago, I wrote a book called the Emperorβs New Mind and that book was describing a point of view I had about consciousness and why it was not something that comes about from complicated calculations.
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I believe there is something going on in a conscious being, which includes many animals, as well as ourselves, that is not a computational activity. And to be conscious at all is not a quality that a computer as such will ever possess - no matter how complicated, no matter how well it plays chess or any of these things.
Roger PenroseRead
Some people take the view that we happen by accident. I think that there is something much deeper, of which we have very little inkling at the moment.
Roger PenroseRead
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