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.
It stands to the everlasting credit of science that by acting on the human mind it has overcome man's insecurity before himself and before nature.
...as our friend Zach has often noted, in our days those who do the best for astronomy are not the salaried university professors, but so-called dillettanti, physicians, jurists, and so forth.Lamenting the fragmentary time left to a professor has remaining after fulfilling his teaching duties.
The unreasonable efficiency of mathematics in science is a gift we neither understand nor deserve.
And what I wanted to do was, I wanted to explore problems and areas where we didn't have answers. In fact, where we didn't even know the right questions to ask.
I suppose I can live with missing decimals, missing floors to tall buildings, and floors that are named instead of numbered. A more serious problem is the limited capacity of the human mind to grasp the relative magnitudes of large numbers. Counting at the rate of one number per second...to count to a trillion takes 32,000 years, which is as much time as has elapsed since people first drew on cave walls.
The difference between screwing around and science is writing it down.
Subscribe for the occasional hand-picked quote. No noise.