“Of course, when the effective causes are too obscure, but the final causes are more readily ascertained, the problem is commonly solved by the indirect method”

introduction to De Curvis Elasticis, Additamentum I to his Methodus Inveniendi Lineas Curvas Maximi Minimive Proprietate Gaudentes 1744; translated on pg10-11, "Leonhard Euler's Elastic Curves" https://www.dropbox.com/s/o09w82abgtftpfr/1933-oldfather.pdf, Oldfather et al 1933
Context: All the greatest mathematicians have long since recognized that the method presented in this book is not only extremely useful in analysis, but that it also contributes greatly to the solution of physical problems. For since the fabric of the universe is most perfect, and is the work of a most wise Creator, nothing whatsoever takes place in the universe in which some relation of maximum and minimum does not appear. Wherefore there is absolutely no doubt that every effect in the universe can be explained as satisfactorily from final causes, by the aid of the method of maxima and minima, as it can from the effective causes themselves. Now there exist on every hand such notable instances of this fact, that, in order to prove its truth, we have no need at all of a number of examples; nay rather one's task should be this, namely, in any field of Natural Science whatsoever to study that quantity which takes on a maximum or a minimum value, an occupation that seems to belong to philosophy rather than to mathematics. Since, therefore, two methods of studying effects in Nature lie open to us, one by means of effective causes, which is commonly called the direct method, the other by means of final causes, the mathematician uses each with equal success. Of course, when the effective causes are too obscure, but the final causes are more readily ascertained, the problem is commonly solved by the indirect method; on the contrary, however, the direct method is employed whenever it is possible to determine the effect from the effective causes. But one ought to make a special effort to see that both ways of approach to the solution of the problem be laid open; for thus not only is one solution greatly strengthened by the other, but, more than that, from the agreement between the two solutions we secure the very highest satisfaction.

Adopted from Wikiquote. Last update May 19, 2024. History

Help us to complete the source, original and additional information

Do you have more details about the quote "Of course, when the effective causes are too obscure, but the final causes are more readily ascertained, the problem is…" by Leonhard Euler?
Leonhard Euler photo
Leonhard Euler 11
Swiss mathematician 1707–1783

Related quotes

Augustin-Jean Fresnel photo

“If nature has offered to produce the maximum effect with minimum causes, it is in all of its laws that it had to solve this major problem.”

Augustin-Jean Fresnel (1788–1827) French engineer and physicist

in
Context: If one was sometimes led astray by trying to simplify the elements of a science, it is because one has established systems before putting together a fairly large number of facts. Some assumption, which would be very simple when one considers only a class of phenomena, requires many other assumptions if one wants to leave the narrow circle in which we had initially withdrawn. If nature has offered to produce the maximum effect with minimum causes, it is in all of its laws that it had to solve this major problem. It is without doubt difficult to discover the foundations of this wonderful economy, i. e. the simplest causes of phenomena considered from such a wide point of view. But if this general principle of the philosophy of physics does not lead immediately to the knowledge of truth, it can direct the efforts of the human spirit, by leading it away from theories which relate the phenomena to too many different causes, and by adopting preferably those based on the smallest number of assumptions, which show to be more fruitful in consequences.

Martin Luther King, Jr. photo

“The best way to solve any problem is to remove the cause.”

Martin Luther King, Jr. (1929–1968) American clergyman, activist, and leader in the American Civil Rights Movement

1960s, The Rising Tide of Racial Consciousnes (1960)

George Santayana photo

“Miracles are propitious accidents, the natural causes of which are too complicated to be readily understood.”

George Santayana (1863–1952) 20th-century Spanish-American philosopher associated with Pragmatism

Introduction to The Ethics of Spinoza (1910)

Maya Angelou photo

“Hate, it has caused a lot of problems in the world, but has not solved one yet.”

Maya Angelou (1928–2014) American author and poet

Nearly identical quote attributed to a 1995 TV show, Touched by an Angel https://www.imdb.com/title/tt0732136/quotes: Tess: No, hate has caused a lot of problems in this world, but it's never solved one yet.
Misattributed

David Wheeler (computer scientist) photo

“Any problem in computer science can be solved with another level of indirection.”

David Wheeler (computer scientist) (1927–2004) British computer scientist

Attributed to David Wheeler by Butler Lampson in his Turing Lecture https://web.archive.org/web/20070221210039/http://research.microsoft.com/Lampson/Slides/TuringLecture.doc (17 February 1993)
Lampson uses the phrase without attribution in Authentication in distributed systems: theory and practice https://doi.org/10.1145/138873.138874 (November 1992)

Frederic Dan Huntington photo

“Christendom, as an effect, must be accounted for. It is too large for a mortal cause.”

Frederic Dan Huntington (1819–1904) American bishop

Source: Dictionary of Burning Words of Brilliant Writers (1895), P. 135.

Friedrich Hayek photo
W. Somerset Maugham photo
Jean-Baptiste Say photo

“Whence it is evident that the remedy must be adapted to the particular cause of the mischief; consequently, the cause must be ascertained, before the remedy is devised.”

Jean-Baptiste Say (1767–1832) French economist and businessman

Source: A Treatise On Political Economy (Fourth Edition) (1832), Book II, On Distribution, Chapter VII, p. 336

Related topics