Everyone rags on Aristotle for totally phoning in his theory of gravity. But in perspective, (a) Aristotle was a biologist, not a physicist, so his not being the best at physics should not be held to any more account than when a modern biologist goofs some esoteric physics, and (b) Aristotle was the first in human history to develop the sciences into formal, empirical systems. Yes, some empirical science predates him, but it wasn’t formally systematized; Aristotle created the doctrine of a formal science, and began categorizing the sciences, and he adjudicated what general methods they should employ (among competing programs at the time). In other words, like Freud to Psychology, Aristotle is to Ancient Science. We should not expect him to have gotten everything right, any more than Freud did. We should look, rather, to how he was corrected over time by his successors.

Which gets to today’s point:

• Medieval Christians threw away all subsequent science on gravity. So…what did we lose?

For example, working in the 4th century B.C., Aristotle’s biggest goof in biology—despite being his main field of expertise—was to claim that thought occurred in the heart and that the brain was just a cooling organ. Within a lifetime after his death he was empirically refuted by a subsequent Aristotelian: Herophilus of Alexandria. In the 3rd century B.C. Herophilus demonstrated that all motor and sensory function ties into and resides within the brain. He even began localizing brain functions (distinguishing which areas of the brain control vision, speech, hearing, and so on). Similarly Aristotle’s primitive theory of falling objects, based on “inherent tendencies” of the Light and the Heavy, was empirically refuted by Archimedes, who proved all material things (including air) could be heavy, and simply vary by density, such that objects (like balloons, clouds, or boats) will move “up” not because they possess “Lightness” but because their density is lower than the surrounding medium.

Correspondingly, we know of two crucial books that were published on experimental studies with falling objects specifically: first by the third chair of Aristotle’s school, Strato of Lampsacus, who published On Lightness and Heaviness (as well as On Motion) around the same time Herophilus was refuting Aristotle’s theory of the brain; second by Hipparchus of Nicea (yes, that Nicea), who spent most of his life as lead astronomer at Rhodes, who published On Objects Carried Down by their Weight in the 2nd century B.C. Rhodes was then the most advanced center for ballistic science (systematically applying its study to artillery design), and the recent invention of the torsion catapult had created a new empirical interest in studying the motion and fall of objects. Moreover, Hipparchus was writing under the influence of Strato’s work a century earlier. So we’d especially like to read what Hipparchus discovered. But alas, both works are completely lost (apart from scattered, often cryptic summaries or quotations in later authors).

First, Aristotle

It is commonly assumed Aristotle can’t have based his theory of gravity on experiments or observations, as had he dropped objects from a height he must surely have noted that they do not fall at a rate proportional to their mass as he avers. They always fall at pretty much exactly the same rate (not quite, really; but close enough to have ruled out his theory). But as I recently noted in Galileo’s Goofs, Carlo Rovelli points out that it’s highly unlikely Aristotle didn’t come to his conclusions about gravity from conducting experiments: dropping objects of different weights in different mediums, particularly those in which differences of motion are more readily observable, such as water and oil. This explains how Aristotle knew about acceleration and also terminal velocity. It is extremely unlikely he could have just “arm chaired” his way to both those conclusions. He must have observed them. But Aristotle’s work on gravity was cursory, and hardly constitutive of completed research. So he simply hadn’t done the experiment in air, nor made careful measurements yet to test his model by. We have evidence Strato and Hipparchus, however, had. Yet we don’t know the details of what they reported their results to be.

Indeed, Aristotle himself mentions other physicists already disagreeing with him about this. Including his important philosophical predecessor Democritus and subsequent adherents of his thinking, culminating in the thought and school of Epicurus in the next generation after Aristotle. Generally collectively referred to as the “atomists,” these thinkers continued to have successors well into the Roman period, and included Strato—the Aristotelian; in fact, no mere Aristotelian, but third successor to the leadership of Aristotle’s school at the Lyceum (after Theophrastus). And atomist thought was best captured in the famous Latin poem of Lucretius, which declares “through an undisturbed vacuum all bodies must travel at equal speeds even when impelled by unequal weights,” and it is only because of the resistance of a medium that heavier objects are sometimes perceived to fall faster, because they can push through air or water with more force (On the Nature of Things 2.225-254), a view closer to correct than Aristotle’s. Of course, no one could ever have experimentally observed how anything falls in a vacuum. Centuries later the Roman scientist Galen would complain that this debate between Aristotle and the atomists was idle until someone could actually run such an experiment (Scientist in the Early Roman Empire, p. 333).

The early Medieval Christian philosopher John Philopon would offhandedly declare in his commentary on Aristotle’s Physics that “if one lets fall simultaneously from the same height two bodies differing greatly in weight,” then “one will find the ratio of their times of motion does not correspond to the ratio of their weights” as Aristotle averred, but rather “that the difference in time is a very small one.” However, John never says he himself conducted such an experiment or what his source for this observation was. It could well have been Strato or Hipparchus, or someone relying on either. So what do we know about those guys?

Second, Strato

As I explain in The Scientist in the Early Roman Empire (where you’ll find my references and cited sources; index, “Strato”), the most renowned scientist in antiquity was the very Strato of Lampsacus. The generic material here comes from there, but I shall add to that by quoting Strato on gravity directly. Diogenes says Strato was “held in the highest regard” even in the Roman era, widely “nicknamed ‘The Natural Philosopher’ because he took the greatest care and consumed himself with natural theory more than any other,” studying a wide variety of subjects, including medicine, husbandry, meteorology, psychology, physiology, zoology, and mechanics, and publishing works on logic, ethics, and technology, among much else.

Lampsacus lay on the Eastern side of the Hellespont (now the northwest Turkish coast) and could claim both Anaxagoras and Epicurus as previous luminaries. So when Strato came to study Aristotelianism under Aristotle’s successor Theophrastus, he already came with a sympathy for atomist philosophies. He then served as royal tutor for several years in Alexandria, likely in close connection with the Museum there, absorbing the empiricism of its peers, and then took over Aristotle’s school in Athens. Medieval Christians preserved none of his many publications; but from countless descriptions and quotations, we can infer quite a lot about his views.

Strato is most noted for having combined Aristotelian and atomist philosophy and reinforcing it with a strong empirical and experimental scientific spirit. He thus became the father of an entire tradition in the history of ancient science that was nearly erased by the deliberate neglect of medieval Christian scribes and scholars, who preferred to save works that agreed with less atomistic (and thus less disturbingly atheistic) traditions. Indeed, Strato explicitly rejected providence, creationism, and intelligent design, and sought a system that would explain all phenomena in terms of natural weights, movements, and powers, which led him to reject even several Aristotelian dogmas, adopting in their place some of what we now know to be scientifically correct theories.

For example, in those two books On Lightness and Heaviness and On Motion Strato abandoned Aristotle’s doctrine of “natural places” in exchange for a more mechanical view of why some objects rise and others fall, which happened to be nearly correct: all objects are drawn to earth by a force but lighter objects are squeezed upwards by heavier ones (a concept later empirically proved by Archimedes, developing essentially the modern theories of buoyancy and specific density). Strato also abandoned Aristotle’s astrophysics, adopting instead in his own treatise On the Heavens the position of the competing atomists: that the same principles, elements, and physics operate in the heavens as on earth—even insisting the stars and planets are subject to the same pull towards earth as everything else, which is incorrect in its geocentricity, yet remained in antiquity the only answer for what causes the movements of the moon and planets that was close to being correct.

Strato based both his dynamics and his cosmology on a primitive theory of inertia (similar to what we find reported in, again, Lucretius, 2.62-166 and 2.184-332, and in Seneca, Natural Questions 7.14.3-5). This he also borrowed from the atomists, particularly the Epicureans, who held that everything falls at the same rate regardless of mass, and changes direction or speed only when struck, whether by a blow or a medium, and in proportions relating to its mass and the imparted force. Strato then combined this with the Aristotelian conclusion that falling bodies accelerate—which Strato proved empirically by observing falling stones and streams of water. Strato also thereby refuted the Aristotelian belief that objects gain “weight” as they fall, observing instead that (for example) stones make a greater impact the farther they fall solely because of their increased speed, not their increased mass.

It would appear that Strato also observed the fact that heavy drops of water do not fall faster than light ones, yet all fall faster the farther they have fallen, which would suggest a nearly modern view of gravity. But since we do not have a full or clear account of Strato’s physics we can say nothing certain on this point. Although it is most intriguing that the most famous friend and student of Strato was none other than Aristarchus of Samos, who became the first known scientist in history to propose a heliocentric theory of planetary motion. It is tempting to draw a number of inferences here, as Strato’s divergence from Aristotle in physics directly correlates with increasing the logic and explicability of heliocentrism generally.

As with his maverick physics of gravity and inertia, by merging Aristotelian with a more atomist physics Strato also developed a theory of void and air-pressure that, with some further developments, became central to engineering for the remainder of antiquity. Yet his pertinent treatise On Void is, again, lost. This same thinking also led Strato to anticipate many other developments in modern physics, such as his explanation of wind as caused by differences in air pressure produced by differences in air temperature, which he described in his treatise On Wind. Also lost. His theories of light and sound, presented in his (also lost) treatises On Sound and On Vision, expanded on atomist explanations, coming nearer the truth on both than anyone else in antiquity.

Strato was also the first philosopher, as H.B. Gottschalk says, “to use experiments systematically to establish” elements of his natural philosophy, and his methodology was nearly modern, for by every account we have, his “experiments are not isolated, but form a progressive series in which each is based on the result of the previous one.” In fact, “characteristic of Strato are the care taken to define the conditions in which the experiment takes place and to eliminate all possible alternative explanations of the result” as well as “the practice of pairing controlled experiments with observations of similar phenomena occurring under natural conditions.”

By emphasizing the methodological standard of physical experimentation even more than Aristotle had done, Strato set the gold standard for all subsequent physicists. He also contributed to a growing scientific interest in technology, writing On Mining Machinery and Examination of Inventions. Of course, again, not a single one of his books was preserved by medieval Christians. Yet his experimental methods were later picked up, used, and promoted by Hero of Alexandria, Menelaus, Galen, Ptolemy, and other scientists of the Roman era. Given that Strato was this meticulously empirical, relying on careful observation and experimentation for his many views, the loss of his treatises on gravity and motion may have been, indeed, a catastrophic loss to the whole world.

Most of what we know of what Strato said about the present subject comes from the rather backward-thinking of the medieval Simplicius, one of the last surviving pagan philosophers. Raised in an era of considerable intellectual decline, he largely rejects all past scientific advances to instead try and defend the original ideas of Aristotle. So we aren’t really talking about a scientist here, but more of an antiscientific thinker, producing “apologetics” in defense of his preferred dogmas, much as his Christian peers did. Nevertheless, he tells us some things we can use to try and reconstruct what Strato actually concluded and why. You can access this material in the collection of quotations of and references to Strato assembled by Desclos & Fortenbaugh or directly in the extant translations of Simplicius (the relevant volumes are his commentary on Aristotle’s On the Heavens Book 1 § 5-9 and on Aristotle’s Physics Book 5).

For example, Simplicius tells us that both “Strato and Epicurus say that all bodies are heavy and move downwards naturally, upwards unnaturally,” exactly contrary to Plato and Aristotle. Likewise, they explained differences in weights (by which we mean densities) by proposing that there is more void in less dense objects, spreading the weight out over a larger volume. Which is correct: even at an atomic level, what makes gold heavier than aluminum is that it packs more protons and neutrons together rather than spreading them apart, and what makes air lighter than water is that more void exists between the molecules composing it—until of course it is compressed to the point of itself becoming a liquid. Other medieval authors, like Stobaeus (and the proto-medieval Themistius), confirm to us that Strato explained upward movement in nature by reference to a primitive theory of buoyancy (a heavier medium pushes lighter objects upward, e.g. boats, balloons), which in the generation after him Archimedes would formally prove, developing what we now know to be the first correct mathematical law of physics regarding it.

After appealing to Strato’s empirical observation of falling water (whereby it can be seen that water falls faster the farther it falls, as the faster moving drops break away from the slower), Simplicius quotes Strato saying:

If someone lets go a stone, or something else possessing weight, holding it a finger’s breadth above the ground, it will certainly not make a visible impact on the ground, but if one lets it go holding it a hundred feet up or more, it will make a strong impact. And there is no other reason for that impact. For it does not have greater weight, nor is it impelled by a greater force; but it does move more quickly.

Simplicius then tries to use this evidence to argue for his own, anti-Stratonian explanation of natural movement; we are not told how Strato used this evidence, or what other evidence he combined it with. But we can infer from what is quoted that Strato is saying that velocity increases force, and that this alone explains why objects “hit harder” the farther they fall. This means Strato did not believe objects had an innate force within them (as then the force would never change so far as their mass did not) but that they were pulled (or pushed) downward by some external force. He would have explained this in his treatise; but we never hear that part.

Put all this information together and this is what we can infer:

• For Strato, matter simplicter all weighs the same, at all times; differences in the weights (the densities) of objects and materials is caused by matter being distributed more diffusely or more densely.
• Objects are pushed or pulled toward the center of the earth by a continuous external force, and this has two observable effects: those objects continue to speed up, and consequently, produce a greater impact when they eventually collide with anything.

There are hints that Strato was not granting other of Aristotle’s assumptions either. For example, by observing drops of water fall at the same but increasing rate regardless of size, and dropping stones of the same or different weights to observe their impacts, he would have noticed concentrating mass does not increase the rate of fall, except for any effect it would have on penetrating the resistance of a medium. But it’s also possible he came to other conclusions (as might be suggested in something we might have from Hero of Alexandria, which we’ll look at last).

Third, Hipparchus

I also cover Hipparchus’s story and achievements (so far as we know them) in The Scientist in the Early Roman Empire (index, “Hipparchus”). Just as Strato was in ancient times the most famous physicist, Hipparchus was antiquity’s most famous astronomer, the only one known to have been honored on ancient coins (even during the Roman Empire). He also is believed to have substantially advanced the mathematical fields of trigonometry and combinatorics, which would be entirely forgotten during the Middle Ages and had to be completely reinvented in the Enlightenment. And in astronomy he discovered axial precession, possibly observed and charted the first supernova, first accurately ranged the moon, and other feats. But in physics we know he also rejected Aristotle’s ideas about motion and followed Strato in adopting some form of impetus theory and sought to explain even gravity by reference to it. He similarly wrote works in experimental optics that likewise adopted Strato’s atomist theory of light (an early form of the modern particle theory of light), which confirms our observation of the popularity of infusing Aristotelianism with atomism.

We again learn from Simplicius that Hipparchus argued that falling objects accelerate due to their gradual overcoming of what we might today call the potential energy imported into the object keeping it aloft, which isn’t exactly correct, but it closer to correct than anything Aristotle imagined. This is how Simplicius summarizes (or perhaps quotes) Hipparchus:

In the case of [a clump of] earth thrown upwards, it is the throwing force which is the cause of its upward motion as long as it overcomes the power of the thing thrown, and it moves upwards faster in proportion to the extent to which it overcomes it. But when it diminishes, it first no longer moves upwards as quickly, and then moves downwards employing its own proper inclination even though some of the upward power still remains along with it; and the more it fades, the faster the descending object always moves downwards, fastest of all when that power finally gives out. … [Likewise] in the case of things dropped from above, for they too retain for a time the power of what held them back, which by counteracting [it] becomes the cause of the initial slower motion of the thing dropped.

Yet in the case of “weight,” Simplicius claims Hipparchus said “that things are heavier the further they are removed” (presumably meaning, from the center of the Earth?), but it seems more likely what Hipparchus actually said has become confused here. Simplicius is not actually reading Hipparchus, and in this case definitely not quoting him. Rather, he is summarizing in his own words another summary written by Alexander of Aphorodisias hundreds of years earlier (and hundreds of years after Hipparchus). And Alexander is intent on arguing that objects get heavier as they near the center, and poses this as arguing against Hipparchus, but it is unclear what exactly either would have meant.

As we just saw, when Simplicius gives us a statement much closer to a quote from Hipparchus (which he is again getting from Alexander), we see Hipparchus argued something quite different than this: that an object thrown up becomes “lighter” solely by virtue of a counteracting force, and thus grows “heavier” only in the sense that it gradually overcomes that counteracting force, not by virtue of its mere elevation. There is nothing about elevation affecting its downward force in the previous, clearer, and longer paraphrase of Hipparchus. Hipparchus said that when held aloft an object’s “weight” is the product of its downward force acting against the upward force continually needed to hold it there; not its elevation. Furthermore, if a heavier object would fall faster in this scheme, objects should decelerate as they fell; but Hipparchus clearly said the reverse. So in no way can Hipparchus have actually thought objects are “heavier” the higher up they are as Simplicius says—unless Hipparchus had concluded weight has no effect on rate of fall, which would be an even clearer embrace of a correct view of freefall. I think more likely Hipparchus had simply reiterated what Strato had concluded, and this simply got garbled in transmission: that the higher you lift a stone, the harder it will hit the ground. In other words, not weight increases with elevation, but force at impact. Which is equivalent to a heavier weight dropped from a lower distance. But since we don’t get to read Hipparchus, we can’t know for sure.

In any event, we can see Hipparchus is working with physical observations and coming to different conclusions than Aristotle about freefall and gravity and motion. And here we are only told about, essentially, two sentences in the entire treatise of Hipparchus on gravity and motion; and not even reliably at that. There clearly was a great deal more said and done in that work. And we have no idea what. So the loss of Hipparchus’s treatise appears to have been yet another catastrophic loss to the world. Indeed, especially as it may have contained much more.

Before the Roman era scientists had already been proposing a theory of universal gravitation, whereby all celestial bodies emanate attractive forces (thereby explaining the effect of the moon and sun on the tides), indeed that stars were distant suns orbited by their own planets that, like ours, remain in orbit because of their inertia of motion (by analogy to a slingstone remaining in orbit around its hurler until let go)—all more or less correct. We have reason to suspect Hipparchus or else Seleucus before him originated these ideas—Seleucus being the most famous student of none other than Aristarchus, and likewise a heliocentrist; indeed, Plutarch once cryptically said “Aristotle hypothesized heliocentrism, but Seleucus proved it,” yet we don’t know how, because, you guessed it, medieval Christians threw away everything Seleucus ever wrote. We cannot be certain Hipparchus proposed these same ideas, though his name, and that of Seleucus, are strongly associated with them in Plutarch’s dialogue Concerning the Face in the Moon (on which see Liba Taub’s study in Aetna and the Moon). In any event, these were commonly known theories by then, the late first century of our era. Aristotle’s physics of motion and gravity were thus beyond obsolete well before the rise of Christendom.

Fourth, Hero of Alexandria

Hero was a Roman physicist and engineer of the first century A.D. I won’t brief his resume here; I cover it in detail in Scientist (index, “Hero”). We know he was an atomist Aristotelian just like Strato, for example employing Strato’s science to prove essentially correct theories about air pressure and its relation to, and effect upon, a vacuum. But in none of his surviving works in Greek do we have a discussion of the physics of motion or gravity. It is only an Arabic translation of his treatise on Mechanics where we find two pertinent paragraphs, which appear to espouse some hybrid view confusing or merging the ideas of Aristotle and Strato. Unfortunately, we cannot be certain what the underlying Greek (if any) may have been. In fact, these paragraphs appear only in an appendix to that treatise which is organized like a Q&A. It is not uncommon for such things to be, in whole or in part, later additions to a work and not original. If so, these paragraphs could simply reflect the uninformed assumptions of medieval Arabic commentators, and not what Hero himself would have endorsed. We can’t know on present information. Likewise, even if the Arabic derives from Hero’s Greek, we can’t know how reliably the translation was rendered (it was effected by a 9th century Christian cleric, Kusta ibn Luka).

Nevertheless, for completeness, I will close with this, as until Simplicius gets to quoting Strato and Hipparchus in the early Middle Ages, all other discussions of this subject from antiquity are lost. In a series of questions about why different weights or tensions exert different forces, Hero never explicitly articulates Aristotle’s arguments or equations. But we find something that sounds partly like them, and partly more akin to the statements of Strato and Hipparchus. There are three “Question & Answer” paragraphs in particular we need to look at, as they appear in sequence and appear to reference each other (here using the English translation from the surviving Arabic provided me by Heydar Rashed, who answered my request for help with the surviving Arabic):

Why does the same weight cause a different inclination in balanced scales, so that when the load is low, it causes a greater inclination?

For example, if we had a balance with two pans, each of which contains three minas [a unit of weight], and we put another half mina into one of them, this pan will incline very much. But if there are ten minas in each pan, then we add half a mina to one pan, the inclination of the beam will be very slight.

Because in the first case it is shown that the load is moved by a great force. As the three minas are moved by an equal weight plus a sixth of it; the ten minas, however, are moved by the same weight plus a twentieth of it. Since half a mina is the twentieth of ten, but a sixth of three minas, and the load moved by a greater force is easier to move.

I include this as it relates to the following, because note, Hero (?) is here explaining that different weights push harder; not so much that they move faster. The text then immediately continues with:

Why do large loads fall to the ground in a shorter time than lighter ones?

Because, as it is shown by them, they can be moved more easily when the outwards moving force from outside is bigger, and the same happens when their own self-contained force is greater. The force and the attraction, however, are greater in natural movements with greater loads than with smaller loads.

Or in the translation of Cohen & Drabkin:

The reason is that, just as heavy bodies move more readily the larger is the external force by which they are set in motion, so they move more swiftly the larger the internal force within themselves. And in natural motion this internal force and downward tendency are greater in the case of heavier bodies than in the case of lighter.

Rashed includes a clause (“as it is shown by them”) that is absent from other translations, and he confirmed to me that phrase is there. He thinks it refers to the objects falling (that this is a reference to an unstated experimental observation). I think it more likely this suggests the author is referring back to the previous point about weight as a force acting on a scale. Similarly, Cohen & Drabkin alternate between the words “readily” and “swiftly,” while Rashed keeps to simply “easily.” These words do not all mean the same thing. So once again, it matters quite a lot what was actually in the original Greek. The Arabic consistently says “more easily,” not “more quickly.” Velocity is thus a consequence of a greater natural force, not a greater natural motion. This is more in line with Strato than Aristotle.

That all becomes the more important when we look at the very next question answered:

Why is it that the same weight when it is wide, falls slower to the ground than when it is round?

It is not, as some might believe, because the wide body due to its width meets more air, but the round one, since its parts are stuck to each other, meets only a little of air. But because the load, when dropped in a horizontal position, has many parts that each have a partial force, proportional to its width. So that when this load moves, each of its parts receives some part from the force according to its weight, but does not meet the same force as a whole.

This is a peculiar statement, and certainly incorrect (the actual reason is indeed the variance in air resistance, the very solution explicitly here rejected), but it does sort of relate to the question that follows it, which is about why an arrow is more forcefully projected when launched from the center of a bow’s string than its edges, which is correctly answered by appealing to the greater tension there produced. This would seem to suggest the same idea here: that spreading a weight out horizontally produces less downward force than stacking it. But in the real world, there is also a sense in which this is indeed true: when we assess impact force, the exerted “ground pressure.” If you drop a ten pound iron ball, it will make a much bigger dent in whatever you drop it on than if you vertically drop a ten pound plate: because the force is divided across more square inches of impact. Could this have been what Hero’s treatise originally meant?

This question is worth asking, because the first question, about speed of fall, appears to be answered solely in reference to force, not velocity. Likewise here. Has Kosta mistranslated the question? Was it not originally about time of fall but force of impact? Or was there something lost regarding the role of medium? The text does not say that heavier objects fall proportionally faster, only in some degree faster, which could be a reference to force cutting through a medium, e.g. water or air; a solution only denied for the second question. And if that question originally was about impact force, denying the role of air resistance would be correct. The reason a ball hits harder than a plate is not because of a difference in air resistance, but because the force is distributed over a wider area. It’s possible Hero (or whoever wrote this Q&A; it apparently closely resembles the thinking of Thabit ibn Qurra) is assuming that this empirical observation explains the other (the faster rate of fall). Which would be incorrect, but still also not the view of Aristotle, who would have insisted on the “air resistance” explanation, as in his system equal weights should not fall at different speeds—indeed, Aristotle is very particular about shape affecting speed of fall due to its effect on the resistance of the medium.

Or indeed, has something been left out of all this? What are the “loads” being spoken of here? In context, since the first question’s answer seems to reference the previous one (as it is shown “by them,” meaning the different weights just described), it seems to be talking about how fast the arm of a scale falls, not free fall. And in that context, the observation is correct: heavier loads do fall faster—indeed, almost as proportionately as Aristotle would think: add a light weight to a balanced scale and the arm will drop slowly, but add twice the weight and it will drop quickly. Indeed it is possible Aristotle was experimenting with balanced scales and not free fall; the error that results when conflating them is that on a scale there is an opposing force to contend with, which explains the retarded motion. Nevertheless, the answer we find in the Arabic would be correct: that difference in speed (in the fall of the arms of a scale) is a product of the greater force applied.

So there appears to be a confusion between force and velocity, and the context of what is falling and when, throughout this appended Q&A. Is that confusion a product of the Arabic translator? Of Hero’s brevity? Of this not originating with Hero at all? We can’t tell on present evidence. Hero’s Mechanics, to which this Q&A is appended, is almost entirely concerned with manipulating loads through one or another crane apparatus, which is relevantly equivalent to testing force and motion with a balance. If the “loads” we are talking about are weights held aloft by a crane and let go, then we have the counterweight slowing the fall, such that, indeed, heavier weights will be observed to fall faster (all else being equal), exactly as understood in the preceding question about the inclination of a scale. Likewise, one could have observed a crane dropping a broad load faster than a compact load of equal weight, and contrived a mistaken explanation for that observation from the correct observation of a difference of impact force, which, as we saw, Strato indeed argued was a consequence of a greater velocity. So if “greater impact = greater velocity” for any equivalent weight, one might erroneously infer compact masses fall faster (rather than accounting for the distributed effect of an impact).

In any event, as we cannot confidently attribute all this to Hero, nor do we have any competing views of falling objects from the Roman era, nor any more detailed discussions of related observations (such as we know were found in the lost works of Strato and Hipparchus), we can’t really ascertain what the various views were in the Roman period or on what they were based. Yet we know this was discussed and debated. Galen and Plutarch both reference open debates and discussions among disagreeing scientists over this very question; they just don’t relate any findings or details.

Conclusion

Aristotle is only the first to attempt a mathematical law of “gravitation” (meaning either of attraction or of any impulse toward the center of the earth), and only cursorily. And even when he did that, there were already competing views as to what the process was; some even already were closer to the truth (as we see with atomist theories of freefall, the role of force, and several ideas similar to inertia). And as with many other cursory assertions Aristotle made that were soon empirically refuted and replaced by scientific advances, we know after he started this debate it evolved considerably, with more empirical work done, and different conclusions reached, many even developing hybrid ideas adapting atomist to Aristotelian principles.

Yet we barely get to know how or what progress, exactly, was made in this area, or who embraced which findings. For we know competing scientific paradigms were abundant in antiquity, e.g. there were still heliocentrists, as well as dynamic geocentrists, under the Roman Empire that Ptolemy had to argue against. We likewise know ideas of “natural places” were still competing with “inert force” and “universal gravitation” theories of falling objects. But because of medieval Christian disinterest in preserving ancient science, particularly from scientists they didn’t ideologically agree with, we have been barred from knowing more.

Had Christendom not taken over the world and brought with it an antiscientific worldview that suppressed the curiosity, empiricism, and belief in progress that had animated the scientific world before their dominance, these competing views may have converged in a new consensus on the means to resolve them, within just another century or two—in other words, the Scientific Revolution might have occurred over a thousand years sooner. But that’s a longer story, which I explain and demonstrate in The Scientist in the Roman Empire. Today we have explored just one tiny piece of that story.