I protest against the use of infinite magnitude ..., which is never permissible in mathematics.
Carl Friedrich GaussRead
We must admit with humility that, while number is purely a product of our minds, space has a reality outside our minds, so that we cannot completely prescribe its properties a priori.
Interpretation
This quote emphasizes the distinction between human-created concepts and the objective reality of space.
Gauss highlights the idea that while numbers and mathematical concepts are inventions of the human mind, space itself is an objective reality that exists independently of our perceptions. This suggests that our understanding of the universe is limited by our mental frameworks, and we must remain humble in recognizing that we cannot fully define or control the properties of space solely through our intellect.
In practice
In a lecture about the philosophy of mathematics, this quote could illustrate the limits of human understanding.
I protest against the use of infinite magnitude ..., which is never permissible in mathematics.
Mathematics is the queen of sciences and number theory is the queen of mathematics. She often condescends to render service to astronomy and other natural sciences, but in all relations she is entitled to the first rank.
To praise it would amount to praising myself. For the entire content of the work... coincides almost exactly with my own meditations which have occupied my mind for the past thirty or thirty-five years.
The problem of distinguishing prime numbers from composite numbers and of resolving the latter into their prime factors is known to be one of the most important and useful in arithmetic.
Life stands before me like an eternal spring with new and brilliant clothes.
When I have clarified and exhausted a subject, then I turn away from it, in order to go into darkness again.
Esteem must be founded on some sort of preference. Bestow it on everybody and it ceases to have any meaning at all.
The book, as it stands, seems to me to be one of the most frightful muddles I have ever read, with scarcely a sound proposition in it beginning with page 45 [Hayek provided historical background up to page 45; after that came his theoretical model], and yet it remains a book of some interest, which is likely to leave its mark on the mind of the reader. It is an extraordinary example of how, starting with a mistake, a remorseless logician can end up in bedlam.
Our conscious motivations, ideas, and beliefs are a blend of false information, biases, irrational passions, rationalizations, prejudices, in which morsels of truth swim around and give the reassurance albeit false, that the whole mixture is real and true. The thinking processes attempt to organize this whole cesspool of illusions according to the laws of plausibility. This level of consciousness is supposed to reflect reality; it is the map we use for organizing our life.
The ultimate value of life depends upon awareness and the power of contemplation rather than upon mere survival.
'Death with dignity' is our society's expression of the universal yearning to achieve a graceful triumph over the stark and often repugnant finality of life's last sputterings. But the fact is, death is not a confrontation. It is simply an event in the sequence of nature's ongoing rhythms.
Everything is true,' he said. 'Everything anybody has ever thought.' 'Will you be all right?' 'I'll be all right,' he said, and thought, And I'm going to die. Both those are true, too.
Subscribe for the occasional hand-picked quote. No noise.