Mathematics is an obscure field, an abstruse science, complicated and exact; yet so many have attained perfection in it that we might conclude almost anyone who seriously applied himself would achieve a measure of success.
From a certain temperature on, the molecules 'condense' without attractive forces; that is, they accumulate at zero velocity. The theory is pretty, but is there some truth in it.
The human understanding is of its own nature prone to suppose the existence of more order and regularity in the world than it finds. And though there be many things in nature which are singular and unmatched, yet it devises for them parallels and conjugates and relatives which do not exist. Hence the fiction that all celestial bodies move in perfect circles, spirals and dragons being (except in name) utterly rejected.
It is clear that there is some difference between ends: some ends are energeia [energy], while others are products which are additional to the energeia.
If someone separated the art of counting and measuring and weighing from all the other arts, what was left of each (of the others) would be, so to speak, insignificant.
The intellect has little to do on the road to discovery. There comes a leap in consciousness, call it Intuition or what you will, the solution comes to you and you don't know how or why.
The logic now in use serves rather to fix and give stability to the errors which have their foundation in commonly received notions than to help the search for truth. So it does more harm than good.
As agonizing a disease as cancer is, I do not think it can be said that our civilization is threatened by it. ... But a very plausible case can be made that our civilization is fundamentally threatened by the lack of adequate fertility control. Exponential increases of population will dominate any arithmetic increases, even those brought about by heroic technological initiatives, in the availability of food and resources, as Malthus long ago realized.
Take an arrow, and hold it in flame for the space of ten pulses, and when it cometh forth you shall find those parts of the arrow which were on the outsides of the flame more burned, blacked, and turned almost to coal, whereas the midst of the flame will be as if the fire had scarce touched it. This is an instance of great consequence for the discovery of the nature of flame; and sheweth manifestly, that flame burneth more violently towards the sides than in the midst.
Man carries the world in his head, the whole astronomy and chemistry suspended in a thought. Because the history of nature is charactered in his brain, therefore he is the prophet and discoverer of her secrets. Every known fact in natural science was divined by the presentiment of somebody, before it was actually verified.
We have lost the art of living, and in the most important science of all, the science of daily life, the science of behavior, we are complete ignoramuses. We have psychology instead.
...neither is it possible to discover the more remote and deeper parts of any science, if you stand but upon the level of the same science, and ascend not to a higher science.
For it is the same whether you take it that the Earth is in motion or the Sky. For, in both the cases, it does not affect the Astronomical Science. It is just for the Physicist to see if it is possible to refute it.