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.
I regard music therapy as a tool of great power in many neurological disorders -- Parkinson's and Alzheimer's -- because of its unique capacity to organize or reorganize cerebral function when it has been damaged.
[Science] is corrosive of religious belief, and it's a good thing too.
Mathematical science is in my opinion an indivisible whole, an organism whose vitality is conditioned upon the connection of its parts.
Climate Change is a national security issue. We found that climate instability will lead to instability in geopolitics and impact American military operations around the world. People are saying they want to be perfectly convinced about climate science projections. But speaking as a soldier, we never have 100 percent certainty. If you wait until you have 100 percent certainty, something bad is going to happen on the battlefield.
Science is what we have learned about how to keep from fooling ourselves.
In the last analysis the entire field of psychology may reduce to biological electrochemistry.
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