...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.
Can the mind see the truth of its own incapacity to know the unknown? Surely if I see very clearly that my mind cannot know the unknown, there is absolute quietness.
GNP measures neither our courage, our wisdom neither our compassion. It measures everything except what makes life worthwhile
We need criminals to identify ourselves with, to secretly envy and to stoutly punish. They do for us the forbidden, illegal things we wish to do.
The heights of popularity and patriotism are still the beaten road to power and tyranny.
A myth is, of course, not a fairy story. It is the presentation of facts belonging to one category in the idioms appropriate to another. To explode a myth is accordingly not to deny the facts but to re-allocate them.
Islam is itself destiny and will not suffer destiny.
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