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.
Space, the final frontier. These are the voyages of the starship Enterprise. Its five-year mission: to explore strange new worlds, to seek out new life and new civilizations, to boldly go where no man has gone before.
Science is a way of getting knowledge. It's a method. It's a method that really relies on making mistakes. We propose ideas, they are usually wrong, and we test them against the data. Scientists do this in a formal way. It's a way that everyone can go through life; that's how we should be teaching science from a very young age.
Simplification of modes of proof is not merely an indication of advance in our knowledge of a subject, but is also the surest guarantee of readiness for farther progress.
It is an error to imagine that evolution signifies a constant tendency to increased perfection. That process undoubtedly involves a constant remodeling of the organism in adaptation to new conditions; but it depends on the nature of those conditions whether the direction of the modifications effected shall be upward or downward.
Unless a price can be put on carbon emissions that is high enough to force power companies and manufacturers to reduce their fossil-fuel use, there seems to be little chance of avoiding hugely damaging temperature increases
A lot of scientists hate writing. Most scientists love being in the lab and doing the work and when the work is done, they are finished.
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