...nature seems very conversant with the rules of pure mathematics, as our own mathematicians have formulated them in their studies, out of their own inner consciousness and without drawing to any appreciable extent on their experience of the outer world.
Interpretation
Nature embodies mathematical principles that mathematicians recognize through introspection rather than external observation.
In this quote, James Jeans suggests that the inherent structures and rules of mathematics can be found in nature itself. He points out that mathematicians often uncover these principles not through direct observation or experience of the physical world, but rather through an intuitive understanding that emerges from their inner thoughts and consciousness. This highlights a deep connection between abstract mathematical concepts and the natural world, implying that mathematics is a fundamental part of the universe's fabric.
In practice
In a lecture about the relationship between math and nature, this quote can illustrate how deeply connected the two are.
The stream of knowledge is heading towards a non-mechanical reality; the universe begins to look more like a great thought than like a machine. Mind no longer appears to be an accidental intruder into the realm of matter...we ought rather hail it as the creator and governor of the realm of matter.
Put three grains of sand inside a vast cathedral, and the cathedral will be more closely packed with sand than space is with stars.
The universe begins to look more like a great thought than a great machine.
...to many it is not knowledge but the quest for knowledge that gives greater interest to thought-to travel hopefully is better than to arrive.
I think I would have been a totally different kind of writer if I'd gone to England. I might have developed a cynicism about my origins, a belittling of them, or an excessive nostalgia for them.
Not only does democracy make every man forget his ancestors, but also clouds their view of their descendants and isolates them from their contemporaries. Each man is for ever thrown back on himself alone, and there is danger that he may be shut up in the solitude of his own heart.
If we desire a society without discrimination, then we must not discriminate against anyone in the process of building this society. If we desire a society that is democratic, then democracy must become a means as well as an end.
Lamentations comfort only by lacerating the heart still more. Such grief does not desire consolation. It feeds on the sense of its hopelessness. Lamentations spring only from the constant craving to re-open the wound.
Everything is explained now. We live in an age when you say casually to somebody 'What's the story on that?' and they can run to the computer and tell you within five seconds. That's fine, but sometimes Iβd just as soon continue wondering. We have a deficit of wonder right now.
A miracle is a violation of the laws of nature; and as a firm and unalterable experience has established these laws, the proof against a miracle, from the very nature of the fact, is as entire as any argument from experience can possibly be imagined.
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