4
L. Rondoni
gravitation, as well as on a variety of instruments developed thanks to our understanding of other physical laws. There must be some sense in which measurements
are indeed objective! This is at once a goal and a fact, as beautifully expressed by
Alexandre Koyré, while illustrating his view of Newton’s science.
2
To make sense of these ideas, in practice, let us observe that our measurement
tools show at once only a given facet of the phenomenon at hand. Imagine that we
are looking at the size of the orbitals of one atom of an aluminum bar. We don’t
see the bar, and we are not able to measure its lenght. We must zoom out and lose
resolution for that; almost paradoxically, too much accuracy makes impossible the
measurement of the lenght of the bar: on that scale the length of the bar has no
physical relevance. Indeed, was this not the case, wouldn’t we have liked to increase
further the measurement accuracy, reaching the internal structure of the nuclei of the
atoms? And then the internal structure of nucleons, and so on? As a matter of fact,
this project is physically missguided: higher measurement accuracy requires more
energy; but if the energy becomes too large, the object of interest may be destroyed,
and its properties turn meaningless; what is (physically) the length of the bar, when
it is vaporised?
Extreme resolutions may not be possible, not even in principle,
3 in fact they may
even be disturbing rahter than implying higher intelligibility.
Thus, besides the choice of observable quantities, tools and protocols, also the
resolution, the scale of observation, is fundamental and must be properly chosen by
the physicist. Once the details of what one wants to measure are set, different measurement methods lead to the same result within the relevant degree of “accuracy”.
For instance, one may use different kinds of thermometers to measure the thermodynamic temperature of a gravitational bar, including electronic devices that look
at microscopic vibrations and contact mercury thermometers. The measurement is
accurate when the results are the same up to a certain number of digits, keeping in
mind that many more digits would not correspond to the thermodynamic temperature,
but perhaps to some other physical property.
2 Citing Koyré, Ref. [2]: Thus it seems to me that I have the right to assume that when we are
speaking about Newton and Newtonianism we know more or less what we are speaking of. More or
less! Somehow this very expression used in connection with Newton strikes me as improper, because
it is possible that the deepest meaning and aim of Newtonianism, or rather, of the whole scientific
revolution of the seventeenth century, of which Newton is the heir and the highest expression, is just
to abolish the world of the “more or less,” the world of qualities and sense perception, the world
of appreciation of our daily life, and to replace it by the (Archimedean) universe of precision, of
exact measures, of strict determination. To which Koyré adds: this characterization is very nearly
equivalent to the mathematization (geometrization) of nature and therefore the mathematization
(geometrization) of science. And finally: This, in turn, implies the disappearance—or the violent
expulsion—from scientific thought of all considerations based on value, perfection, harmony, meaning, and aim, because these concepts, from now on merely subjective, cannot have a place in the
new ontology.
3 For instance, chaotic dynamics increase uncertainties at an exponential rate, therefore accurate predictions on even relatively simple phenomena would rapidly need an accuracy on initial conditions
requiring more energy than the object of interest can take.
L. Rondoni
gravitation, as well as on a variety of instruments developed thanks to our understanding of other physical laws. There must be some sense in which measurements
are indeed objective! This is at once a goal and a fact, as beautifully expressed by
Alexandre Koyré, while illustrating his view of Newton’s science.
2
To make sense of these ideas, in practice, let us observe that our measurement
tools show at once only a given facet of the phenomenon at hand. Imagine that we
are looking at the size of the orbitals of one atom of an aluminum bar. We don’t
see the bar, and we are not able to measure its lenght. We must zoom out and lose
resolution for that; almost paradoxically, too much accuracy makes impossible the
measurement of the lenght of the bar: on that scale the length of the bar has no
physical relevance. Indeed, was this not the case, wouldn’t we have liked to increase
further the measurement accuracy, reaching the internal structure of the nuclei of the
atoms? And then the internal structure of nucleons, and so on? As a matter of fact,
this project is physically missguided: higher measurement accuracy requires more
energy; but if the energy becomes too large, the object of interest may be destroyed,
and its properties turn meaningless; what is (physically) the length of the bar, when
it is vaporised?
Extreme resolutions may not be possible, not even in principle,
3 in fact they may
even be disturbing rahter than implying higher intelligibility.
Thus, besides the choice of observable quantities, tools and protocols, also the
resolution, the scale of observation, is fundamental and must be properly chosen by
the physicist. Once the details of what one wants to measure are set, different measurement methods lead to the same result within the relevant degree of “accuracy”.
For instance, one may use different kinds of thermometers to measure the thermodynamic temperature of a gravitational bar, including electronic devices that look
at microscopic vibrations and contact mercury thermometers. The measurement is
accurate when the results are the same up to a certain number of digits, keeping in
mind that many more digits would not correspond to the thermodynamic temperature,
but perhaps to some other physical property.
2 Citing Koyré, Ref. [2]: Thus it seems to me that I have the right to assume that when we are
speaking about Newton and Newtonianism we know more or less what we are speaking of. More or
less! Somehow this very expression used in connection with Newton strikes me as improper, because
it is possible that the deepest meaning and aim of Newtonianism, or rather, of the whole scientific
revolution of the seventeenth century, of which Newton is the heir and the highest expression, is just
to abolish the world of the “more or less,” the world of qualities and sense perception, the world
of appreciation of our daily life, and to replace it by the (Archimedean) universe of precision, of
exact measures, of strict determination. To which Koyré adds: this characterization is very nearly
equivalent to the mathematization (geometrization) of nature and therefore the mathematization
(geometrization) of science. And finally: This, in turn, implies the disappearance—or the violent
expulsion—from scientific thought of all considerations based on value, perfection, harmony, meaning, and aim, because these concepts, from now on merely subjective, cannot have a place in the
new ontology.
3 For instance, chaotic dynamics increase uncertainties at an exponential rate, therefore accurate predictions on even relatively simple phenomena would rapidly need an accuracy on initial conditions
requiring more energy than the object of interest can take.