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.
This is the greatest untold story of the Roman Empire – that we were so scientifically advanced, so long ago. To think what might have been – where we might be today.
“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.”
If we can assume Aristotle came to his conclusion by observing bodies falling in oil and water (and that seems reasonable) why can’t we assume Philopon has dropped a few objects in air and saw what happens. He is inviting his readers to do the same, isn’t he?
It’s unclear. He doesn’t say he did this or saw anyone do this. He cites it the way any “common knowledge” is cited; and “common knowledge” is often enough hearsay or false.
Because he is responding to the literature, he may simply have gotten this idea from Hipparchus or Strato or others citing them. Since we can’t tell, we can’t claim to know, and consequently we can affirm nothing as to where or how Philopon got this idea.
By contrast, Aristotle describes learned facts that cannot have been known any other way than running the experiment. Unlike Philopon, Aristotle is not commenting on centuries of prior published empirical studies on falling objects. Even prior armchair theorists did not say the things Aristotle is, so he can’t have gotten it from them either. Again, unlike Philopon.
What impresses me about the ancient Greeks is how rational and empirical they were in a time dominated by superstitious and religious thinking. And yet 2500 years later the average person is the exact opposite. I understand that I’m comparing the elite thinkers from antiquity with regular people, but still… considering that we are 2500 years ahead, the contrast is still staggering.
Anyway, I have a question for you Richard about a probably historical event. I watched a documentary a while ago that claimed that Archimedes produced a piece of work on the same subject and perhaps on a similar level as Newton’s Pancyprian (I find that hard to believe given that Archimedes lived in antiquity), but unfortunately a Christian scribe scribbled over it, thus ruining our ability to access his full work. Is there any truth to this?
Well, your first qualifier is apposite: the difference between then and now is the percentage of people who are rational and empirical and not particularly superstitious and religious. That percentage has gone up, enormously. So you can’t really compare ancient elites (in fact, even a subset thereof; plenty were not so rational) with modern commoners. That disguises what has actually changed: more commoners now have access to and achieve elite intellectual capability (by ancient standards).
Nevertheless, that that percentage gain, though considerable, is nevertheless still alarmingly low is due to the fact that humans are apes. Our brains are naturally superstitious and irrational. Rational empiricism and effective critical thinking are artificial software patches we invented in the cultural package we try to install in each generation to override and “fix” their otherwise hopelessly broken biological brains.
And all the gains that has achieved signal that access to education (and its quality and type, and related investment resources, e.g. nutrition, safe home and community environments, etc.) is the determining factor. We have done relatively poorly at that even the last hundred years, much less two thousand. We should be investing many times more of our GNP to education at all levels (and direct that money more wisely). Ironically it is biological irrationality that keeps us from doing that (the vicious circle of irrational people irrationally hoarding wealth rather than investing it in the society they must endure and depend on, thus preventing us from efficiently getting rid of by aging-out-of-service those very same irrational people).
As to your question, I don’t know what you mean by Newton’s “Pancyprian” (there is no treatise by Newton of that name). I assume you meant to type Principia? That would be his treatise advancing the laws of motion and posing their application to planetary theory. It is notable for its development of a system of calculus (i.e. a means of calculating infinite sums), mathematization of the principle of inertia, the proposal and measurement of universal gravitation and its relation to mass and distance, and deriving Kepler’s laws of planetary motion therefrom (which Kepler had deduced empirically, not derived from theory), among a lot else.
This is a bunch of different things. It sounds like you saw something about calculus. Which is just one of those things. Because the Archimedes Codex was indeed a hymnal that was written over a scraped-off collection of otherwise lost scientific and mathematical treatises by Archimedes (an example of the catastrophic disinterest medieval Christians had in science, caused by their inherent anti-empiricism the seeds of which were laid in the ancient period as I document in The Scientist in the Early Roman Empire). And one of those treatises we recovered developed a proto-calculus more or less similar to Newton’s.
It’s important to understand the context of that. Before Archimedes developed that proto-calculus (which was otherwise completely lost; thus Newton had to reinvent the wheel as it were), the only way to “sum” infinite sequences was by the “method of exhaustion” (whereby you keep adding successively small fractions until you have as precise a figure as you need), which was more of a hack than a solution (since you could never actually ascertain the sum, just get as close to it as you wanted and had time for).
Archimedes came up with a means of actually solving the problem (principally in his treatise Method of Mechanical Theorems) by, essentially, using analysis of geometric curves to determine the actual sum of an infinite series. Which is the first step to developing a formal calculus. Archimedes had only just published it, probably before his death. He didn’t get to apply the method in any of his other scientific work. We don’t know if anyone continued where he left off (most ancient mathematics was lost in the Middle Ages, even in extant mentions).
So what Archimedes did is remarkable, impressive, and important. But it wasn’t really a fully developed calculus (though Newton could have built a calculus out of it had he known of it). And this is just a mathematical technique. Archimedes did not “discover” any of the scientific stuff in Newton’s Principia. Ancient scientists did muse about a lot of it (e.g. inertia and universal gravitation were live concepts debated at the time) but we don’t know that anyone developed empirically confirmable scientific laws out of them. The closest we could say is regarding the laws of planetary motion, though that would be Ptolemy centuries later, not Archimedes:
Ptolemy developed a law of planetary motion called “equal angles in equal times” which was very successful in predicting planetary motion. After Kepler over a thousand years later decided to rethink the solar system on a heliocentric basis, he transformed Ptolemy’s “equal angles in equal times” law into an “equal areas in equal times” law based on parabolas (not an alien notion to Ptolemy, e.g. his model for lunar motion—which is, after all, in reality geocentric—used combined motions to trace a parabolic orbit), which drew on another ancient mathematician, Apollonius of Perga (a friend and correspondent of Archimedes), who developed techniques for analyzing and quantifying parabolic sections (which planetary orbits actually are).
But even that, again, is not “the same thing” (equal angles in equal times is not exactly the same as equal areas in equal times, though the one did inspire the other), and wasn’t Archimedes.
After reading your reply it dawned on me that in the same comment that I was criticizing the irrationality of modern commoners, I made an irrational claim myself. How embarrassingly ironic. I was under the impression that back then people were a lot more religious than us. What if we compared today’s West with the ancient West? Would you still say that the percentage is roughly the same?
Also, would you say that having access to more data makes you more rational? I would argue that it doesn’t. Rationality means that you are basing your beliefs on evidence. If you don’t have access to the data that would support or refute a certain claim, and you don’t accept that the claim is true, then you are not being irrational. Right? Let’s say Socrates was asked the age of the Universe and he said that he didn’t know the answer, would he be less rational on this issue than a modern commoner who has looked at the evidence and accepted that the Universe is 13.8 billion years old? I think the two are not comparable. I believe Socrates would be rational or in the worst case non rational, but certainly not irrational compared to the modern commoner.
Regarding Archimedes, thank you for the information. You’re right, I meant to say Principia. So basically, Archimedes developed a proto-calculous and if it hadn’t been temporary lost due to Christian negligence, it would have saved Newton time in his development of calculous. What Archimedes did sounds so impressive. Would it be accurate to say that science began with the Greeks and Romans? I would like to learn more about ancient science. Thank you for the book recommendations. Apparently your book is out of stock.
I would like to ask one more question but if you are limited with time feel free to ignore it. In another documentary on the multiverse Michio Kaku said that an ancient group of philosophers (and musicians) called the Pythagoreans compared reality to a musical symphony and even suggested that there are other worlds out there. As you know this is how String Theory describes reality. So my question to you is, is there historical evidence that the Pythagoreans predicted the existence of the Multiverse? If the Pythagoreans did believe that there are other worlds out there, how would we know if they weren’t referring to galaxies?
No. As I said, the percentages have shifted notably toward secularism. Not only among the elite, but especially among the commons. Religiosity in the U.S. is at around 85% (Europe 75%) compared to what would surely have been over 99% in antiquity; because ancient rationalists tended to be religious still, in the same way as our Founding Fathers were in 1776. So there has been change, but as I said, it seems oddly slow a change given that it’s been two thousand years.
No. Only access to more tools of rationality makes you more rational. Irrational people can spin whatever they want out of any quantity of data.
Rationality is also not intelligence. Very intelligent people can even be more skilled at being irrational (which is why many high IQ people have totally bonkers conspiracy-theory worldviews). The smarter you are, the better able you are to rationalize any insanity against any evidence.
Information is not knowledge; knowledge is comprehension of the significance of information. Knowledge is not intelligence; intelligence is skill at problem solving (the ability to turn information into knowledge and “use” that knowledge to achieve an objective, which objective need not be in any way rational). Intelligence is not rationality; rationality requires understanding how the brain’s innate reasoning capabilities are flawed and what must be done to correct for them (meaning our brain’s ability to draw inferences in closer alignment to reality; which is more than merely problem solving or information processing). And rationality is not wisdom; one must reliably and consistently apply one’s rationality to all domains of one’s understanding to achieve wisdom (whereas most people only compartmentalize what subjects they apply even their skills of rationality to).
The example has nothing to do with measuring rationality. Admitting ignorance is only one component of a rational mindset, and is no more rational than concurring with the conclusions of sound evidential reasoning. Aristotle advanced reasons to believe the universe is infinitely old. His reasons were relatively sound, and in cosmological terms may be correct: most leading cosmological theories today entail past eternality prior to our local Big Bang event. But there is nothing irrational or nonrational in saying the evidence available to him suggests it is more likely than not the universe is past eternal. By contrast to a then-Jew or Christian insisting the earth is past finite and thus has a definite age “because the Bible says so.” They’d be potentially “correct” (insofar as we meant “universe” to mean only our local verse), but for no rational reason whatever; whereas Aristotle could be wrong, but for a perfectly rational reason.
Yes.
The questions of laws of motion and planetary theory are a wholly separate matter (that was also going on back then, also mostly lost, but had little to do with Archimedes; I tell that story more in Scientist).
Science as a formal, method-conscious enterprise, yes. “Science” in the looser sense of “whatever people figured out whenever about whatever” is older than even the human race (e.g. we have evidence folk-nature and craft knowledge begins with Homo habilis if not earlier, probably including astronomical and medical knowledge). It’s important to keep these distinct, if you want to make sure what it is you are explaining or asking about. I discuss what the difference is and why it matters in Scientist.
It will always be in stock. Whatever vendor you checked may be out for a moment, but they restock within 24 hours (often in mere hours). Delays are more common now due to the pandemic, but otherwise never significant in duration. Just check back. (Meanwhile, kindle and audible editions are always available, and instantaneously.)
No. Pythagoreans were largely irrationalists, and their only significant contribution to science was in launching harmonics as a formal science (but they made little progress in it; empiricists took up the mantle and advanced the science thereafter). Also much that is “claimed” about them is myth and legend, so I doubt it can be known what if anything they ever really said about “other” worlds.
We have a better read on what the atomists (who were very much anti-Pythagorean) said about this. And from very early on atomist cosmologies routinely argued that stars were distant suns with their own planets and civilizations and that there were probably infinitely many of these. They even proposed some of those worlds contain inhabitants—aliens—of advanced nature and that our impression of the gods arises from a kind of accidental “television” signal our brains pick up from those aliens and then mistake as depicting gods. This is closer to single-universe theory (one universe, with countless other worlds in the straigtforward sense). It has no similarity to string theory or multiverse theory.
I am not aware of any evidence of any ancient belief in multiverse theory. Ancient cosmologies are all universe theories, differing only on how big the universe is, what’s in it, and how it’s arranged. This includes even religious believers (the idea that heaven and hell exist in “other dimensions” and don’t have visible, reachable, physical locations in this universe did not exist in antiquity; that was invented far later).
Sorry, I misread what you said; I thought you said that religiosity percentages haven’t shifted since antiquity.
When I asked if the Greeks were the first scientists, I meant as a formal, method-conscious enterprise (was Aristotle the first scientist?). From my point of view, that’s what makes science, science. It’s defined by its reliance on methodology and a set of principles, such as testability, reproducibility and falsifiability; otherwise the term “science” would be too loose a term and pretty much any enterprise would be considered science, which is counterintuitive.
But thank you for sharing information on this interesting subject with us. This is definitely something I plan to learn more about in the near future.
Aristotle is perhaps the first full scientist; he founded the enterprise of system-wide formalization we now call “science.”
But there were proto-scientists before him, experts in various fields who began discussing methodology and using formal empirical methods to arrive at conclusions, in direct contravention of previous folk/myth methodologies. They were called the “Pre-Socratics,” possibly the first of which was Thales. I have an appendix on this group of “transitional fossils” as it were—half-scientists, half-speculators—in The Scientist in the Early Roman Empire. I otherwise start my history of ancient science with Aristotle and explain why there (Chapter 3).
We learned about the Pre-Socratics in school. Unfortunately I’ve forgotten almost everything. But who knows if what we learned is even true.
I hate that I’m ignorant about this subject. I found one of your YT videos on ancient science https://www.youtube.com/watch?v=Iq_E2R_hvTY&ab_channel=WonderfestScience. I’ll also get your book soon. Thanks!