All exact science is dominated by the idea of approximation.
Interpretation
The essence of scientific inquiry is to approach truth through approximations rather than claiming absolute certainty.
Bertrand Russell's quote emphasizes that the pursuit of scientific knowledge does not yield absolute truths but rather approximations of reality. This understanding encourages humility and open-mindedness in the scientific community, recognizing that as we refine our theories and models, we draw closer to understanding the complexities of the natural world, even if we never achieve complete certainty.
In practice
In a lecture on scientific methodology, one might reference this quote to illustrate the nature of scientific progress.
St. Paul introduced an entirely novel view of marriage, that it existed primarily to prevent the sin of fornication. It is just as if one were to maintain that the sole reason for baking bread is to prevent people from stealing cake.
Freedom comes only to those who no longer ask of life that it shall yield them any of those personal goods that are subject to the mutations of time.
Of these austerer virtues the love of truth is the chief, and in mathematics, more than elsewhere, the love of truth may find encouragement for waning faith. Every great study is not only an end in itself, but also a means of creating and sustaining a lofty habit of mind; and this purpose should be kept always in view throughout the teaching and learning of mathematics.
At all times, except when a monarch could enforce his will, war has been facilitated by the fact that vigorous males, confident of victory, enjoyed it, while their females admired them for their prowess.
Moreover, the attitude that one ought to believe such and such a proposition, independently of the question whether there is evidence in its favor, is an attitude which produces hostility to evidence and causes us to close our minds to every fact that does not suit our prejudices.
Extreme hopes are born from extreme misery.
The ascent of money has been essential to the ascent of man.
Evolution advances, not by a priori design, but by the selection of what works best out of whatever choices offer. We are the products of editing, rather than of authorship.
The fundamental reason why carbon dioxide in the atmosphere is critically important to biology is that there is so little of it. A field of corn growing in full sunlight in the middle of the day uses up all the carbon dioxide within a meter of the ground in about five minutes. If the air were not constantly stirred by convection currents and winds, the corn would stop growing.
When a scientist doesn't know the answer to a problem, he is ignorant. When he has a hunch as to what the result is, he is uncertain. And when he is pretty darn sure of what the result is going to be, he is in some doubt.
Name the greatest of all inventors. Accident.
The only useful function of a statistician is to make predictions, and thus to provide a basis for action.
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