It may happen that small differences in the initial conditions produce very great ones in the final phenomena.
Interpretation
Small initial differences can lead to significant outcomes over time.
This quote by Henri PoincarΓ© highlights the concept of sensitivity to initial conditions, often associated with chaos theory. It suggests that even minimal variations in the starting point of a system can exponentially influence its trajectory and end result, emphasizing the importance of precision and care in scientific endeavors and in understanding complex systems.
In practice
In a discussion about climate change, one might use this quote to illustrate how small changes now can radically affect future weather patterns.
When the logician has resolved each demonstration into a host of elementary operations, all of them correct, he will not yet be in possession of the whole reality, that indefinable something that constitutes the unity ... Now pure logic cannot give us this view of the whole; it is to intuition that we must look for it.
It is a misfortune for a science to be born too late when the means of observation have become too perfect. That is what is happening at this moment with respect to physical chemistry; the founders are hampered in their general grasp by third and fourth decimal places.
A scientist worthy of his name, about all a mathematician, experiences in his work the same impression as an artist; his pleasure is as great and of the same nature.
. . . by natural selection our mind has adapted itself to the conditions of the external world. It has adopted the geometry most advantageous to the species or, in other words, the most convenient. Geometry is not true, it is advantageous.
The mathematical facts worthy of being studied are those which, by their analogy with other facts, are capable of leading us to the knowledge of a physical law. They reveal the kinship between other facts, long known, but wrongly believed to be strangers to one another.
What is a good definition? For the philosopher or the scientist, it is a definition which applies to all the objects to be defined, and applies only to them; it is that which satisfies the rules of logic. But in education it is not that; it is one that can be understood by the pupils.
The problem [with genetic research] is, we're just starting down this path, feeling our way in the dark. We have a small lantern in the form of a gene, but the lantern doesn't penetrate more than a couple of hundred feet. We don't know whether we're going to encounter chasms, rock walls or mountain ranges along the way. We don't even know how long the path is.
The process of discovery is very simple. An unwearied and systematic application of known laws to nature, causes the unknown to reveal themselves. Almost any mode of observation will be successful at last, for what is most wanted is method.
I would... establish the conviction that Chemistry, as an independent science, offers one of the most powerful means towards the attainment of a higher mental cultivation; that the study of Chemistry is profitable, not only inasmuch as it promotes the material interests of mankind, but also because it furnishes us with insight into those wonders of creation which immediately surround us, and with which our existence, life, and development, are most closely connected.
The human race has a yearning to explore. That's part of our biological and psychological makeup.
I'm enormously interested to see where neuroscience can take us in understanding these complexities of the human brain and how it works, but I do think there may be limits in terms of what science can tell us about what does good and evil mean anyway, and what are those concepts about?
The cyclic universe theory predicts no gravitational waves from the early universe.
Subscribe for the occasional hand-picked quote. No noise.