The de facto “philosopher-kings”  of today have succeeded in damning Plato with faint praise. The publication explains:
Science has steadily moved beyond Plato’s conjectures, looking instead to the atom as the building block of the universe. Yet Plato seems to have been onto something, researchers have found. 
But to regard this finding as a perfection of Plato’s view is a tendentious reading of that brave philosopher.
A wise person once observed that average is not the same thing as normal, and in this she was tacitly expressing her consonance with Plato.  The reason that these two terms are different is that average describes an accidental relationship while normal indicates a paradigmatic one. The researchers above appear to believe that these two things are not worth differentiating. Indeed, the belief that average and normal represents a distinction without a difference seems to be a prevalent attitude of our time such that it is scarcely noticed and therefore almost never questioned. Dressed up as a scientific fact, today the tyranny of the statistical mean extends its reign of shadow throughout the domains of soft and hard sciences alike. Experts wield the same blind measuring scales to weigh systemic racism, the momentum of photons, the revolution of planets,  and the shape of rocks.
To show the limits of this approach, let us consider the following example: suppose that experts from the fields of maths and physics teamed up with potters and metalsmiths and glassblowers to determine the average shape of a cup. We know they will find it to be concave and with a ratio of height that exceeds its depth. We know this a priori without the need to consult the study’s results. The reason is that “cup” does not refer to an object but rather to a functional idea of which any cup, as an object participates, approximates, or instantiates. Turning this around: it is only in virtue of our ability to grasp this idea through intuition that we are able to recognise any cups as such in the first place which we may then proceed to perform pointless studies on. By the same token, it would be senseless to gather a representative sample of bicycles to discover by way of statistical average whether they all have two wheels. The reason it is senseless is because if a bicycle had a different number of wheels, would not be one. A bicycle with three wheels is not a bicycle but a tricycle, and a bicycle with one wheel is not a bicycle but a unicycle.
In a similar way, there is an important respect in which we cannot learn what a rock is by scouring the ends of the Earth and gathering together all of the rocks that we encounter in order to research them. Clearly this is a hyperbole both practically and rhetorically. But it is also deficient as a method for epistemological reasons. Attempting to come to the nature of rock by way of calculating statistical averages from a sample that is believed to be representative is deficient for the same epistemological reason as hypothetically gathering up every rock in existence. Namely, the researcher must already know what a rock is in order to recognise the instances of it with which he hopes to comprise his representative sample. Those objects that fall outside of the purview of this intuitive apprehension of what a rock is cannot enter into the calculation in the first place because they will not be perceived as rocks and therefore not selected for the study. Thus, the method of quantity presupposes the very thing it is enlisted to find out.
But surely some features of rocks can be determined in no other way than by examining many instances of them. The inductive, empirical approach to science famously popularised by Bacon of Verlum has ratified itself by “delivering the goods,” so to speak, by way of myriad forms of technological advances of which Lord Bacon could scarcely have dreamt. Indeed, the scientific method as it is conventionally understood is not without value. But that value is contingent—parasitic even—on the philosophical method that Plato practiced and which the mathematicians, geologists, and physicists responsible for the study quoted above demonstrate they are unaware. This may seem like an outlandish claim. But it is just the tacit paradigm or Vorstellungsart of contemporary science that blinds us to the logic of Plato’s view.
Perhaps an analogy will serve as a keyhole to peer into this logic. In 2006, Pluto was stripped of its title as a planet due to a discovery that it failed to meet a criterion of the accepted astronomical designation of the term. Specifically, it was observed that Pluto had not cleared the neighbourhood around its orbit. It may be imagined that an empirical observation of other bodies around Pluto was behind its reclassification as a “dwarf planet.” And this is correct so long as it is born in mind that the empirical determination supervened on a prior theoretical one. No empirical research, in principle, could have suggested a reclassification of Pluto if the concept and definition of “planet” had not been clearly delineated beforehand. The controversy around this reclassification suggests a discrepancy between the astronomical definition of planet and the intuitive one that people hold. Let it be noted that in any process of classification, many cases will be decided on the margin. Thus planets can be said to approximate or participate the theoretical ideal of “planet” and if they stray too far from this ideal, they will be called something else.
Another analogy may make this clearer. Galileo is famous for having upended the Aristotelian view of gravity, which held that the rate at which an object will fall is proportional to the mass of that object. Thus a hammer will fall at a faster rate than a feather. Galileo asserted, to the contrary, that acceleration due to gravity is a constant irrespective of mass, thereby presaging Newton’s famous formulation of his Laws of Motion a century later. Galileo is credited by contemporary scientists with having overturned the traditional view of gravity. In fact, astronaut David Scott verified Galileo’s theory of gravity on the Apollo 15 mission to the Moon in 1971 after holding a hammer in one hand and a feather in the other, releasing them at the same time, and observing their simultaneous landing. And yet, anyone who tried to reproduce this experiment at home would be disappointed unless he was an Aristotelian who also does not mind craters in his floor. The reason being, of course, that the hammer will arrive at the floor almost instantaneously while the feather will arrive there gently after floating, thus seeming to corroborate Aristotle’s expectation, and that of most everyone else as well.
It is crucial to understand how this connects to Plato’s rocks. Galileo’s view of gravity is a theoretical postulate that assumes “ideal conditions.” This is to say that it treats gravity in abstraction from any concrete scenario in which it is liable to be encountered in life. This is why Davis Scott had to go to the Moon to verify Galileo’s theory. Anyone who attempts this on Earth will discover that the factor of differential wind resistance exerts far more influence on the outcome of the experiment than the theoretical uniformity of gravitational acceleration. And yet, empirical observations which might seem to contest Galileo’s view in fact do nothing of the sort. Instead they are everywhere regarded as exceptions that prove the rule. Falling objects are perceived to approximate a theoretical ideal from which they manifestly depart. That they achieve a closer approximation to this ideal on the Moon than on the Earth serves to call into question whom these scientists mean to serve. “Everybody’s got to serve somebody,” as Dylan observed.
Plato approached the categories of natural elements in a manner that was consistent with the way scientists approach laws of nature. “Rock” is an idea or ideal to which any particular rock will be found to approximate. An element of the contemporary definition of “planet” is that it have cleared the neighbourhood around its orbit. An element of the Galilean definition of “gravity” is that it generates uniform acceleration of bodies in a vacuum. For Plato and other traditional philosophers, an element of the definition of “rock,” or more properly, the element of Earth, is that its archetypal form was a cube. Other elements partook of different signature forms. Fire, for instance, approximated the archetypal form of the tetrahedron. In the case of any individual quantum of “rock,” or again, more properly, “Earth,” it is possible to pose the question: to what degree does this specimen approximate its archetype? Naturally, if it is liquid, it is very far from the archetype of Earth, just like a celestial body that gives its own light is not a planet at all but a sun. Similarly, the further its form, in its whole and in its parts, strays from the cube, the further that particular instance of “Earth” is from its ideal, or definition, or logos.
 Plato famously outlined an ideal state in Republic that was ruled by a caste of disinterested “philosopher-kings.”
 Anecdotally ascribed to Ida Rolf (1896-1979).
 This is not the first time that modern experts have anointed the precepts of traditional cosmology with the seal of scientific fact. In March of last year, for instance, the discovery that Mercury is, on average, the next to nearest celestial body to the Earth after the Moon upended the long-held belief that the Copernican revolution had revealed the error of the traditional ordering of planets. A heliocentric model of planetary revolution leaves no doubt that Venus is next in sequence to the Moon after the Earth while Mercury is three planets removed and adjacent to the Sun. But the Copernican model is just that: a model. Like any model, it reveals some features of its object while blinding us to others, and like any model it is only as good as its inputs.