“For a definition to be of any use, it must teach us to measure force; moreover that suffices; it is not at all necessary that it teach us what force is in itself, nor whether it is the cause or the effect of motion.”

— Henri Poincaré , book Science and Hypothesis

Source: Science and Hypothesis (1901), Ch. VI: The Classical Mechanics (1905) Tr. https://books.google.com/books?id=5nQSAAAAYAAJ George Bruce Halstead
Context: What is mass? According to Newton, it is the product of the volume by the density. According to Thomson and Tait, it would be better to say that density is the quotient of the mass by the volume. What is force? It, is replies Lagrange, that which moves or tends to move a body. It is, Kirchhoff will say, the product of the mass by the acceleration. But then, why not say the mass is the quotient of the force by the acceleration?
These difficulties are inextricable.
When we say force is the cause of motion, we talk metaphysics, and this definition, if one were content with it, would be absolutely sterile. For a definition to be of any use, it must teach us to measure force; moreover that suffices; it is not at all necessary that it teach us what force is in itself, nor whether it is the cause or the effect of motion.
We must therefore first define the equality of two forces. When shall we say two forces are equal? It is, we are told, when, applied to the same mass, they impress upon it the same acceleration, or when, opposed directly one to the other, they produce equilibrium. This definition is only a sham. A force applied to a body can not be uncoupled to hook it up to another body, as one uncouples a locomotive to attach it to another train. It is therefore impossible to know what acceleration such a force, applied to such a body, would impress upon such an other body, if it were applied to it. It is impossible to know how two forces which are not directly opposed would act, if they were directly opposed.
We are... obliged in the definition of the equality of the two forces to bring in the principle of the equality of action and reaction; on this account, this principle must no longer be regarded as an experimental law, but as a definition.<!--pp.73-74

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Henri Poincaré 49

French mathematician, physicist, engineer, and philosopher … 1854–1912

Stobaeus Ancient Greek anthologist

iv. 32a. 11
Quotes by and about Diogenes

“Any schoolboy could see that man as a force must be measured by motion, from a fixed point.”

Henry Adams (1838–1918) journalist, historian, academic, novelist

On the genesis of two of his historical and autobiographical works.
The Education of Henry Adams (1907)
Context: Any schoolboy could see that man as a force must be measured by motion, from a fixed point. Psychology helped here by suggesting a unit — the point of history when man held the highest idea of himself as a unit in a unified universe. Eight or ten years of study had led Adams to think he might use the century 1150-1250, expressed in Amiens Cathedral and the Works of Thomas Aquinas, as the unit from which he might measure motion down to his own time, without assuming anything as true or untrue, except relation. The movement might be studied at once in philosophy and mechanics. Setting himself to the task, he began a volume which he mentally knew as "Mont-Saint-Michel and Chartres: a Study of Thirteenth-Century Unity." From that point he proposed to fix a position for himself, which he could label: "The Education of Henry Adams: a Study of Twentieth-Century Multiplicity." With the help of these two points of relation, he hoped to project his lines forward and backward indefinitely, subject to correction from any one who should know better. Thereupon, he sailed for home.