# Why did it take so long to realize acceleration is independent of mass?

Why did it take 2000 years to challenge the Aristotelian notion that objects fall at different rates dependent on their mass? If you use something like a feather for one of the masses, you will see a difference, but how is it that no one tried what Galileo did?

Thanks,
Rob

Acceleration is not independent of mass, they are inversely related:

F=mA

Acceleration due to gravity however cancels out the effect of mass as both the force and the mass are equally related.

But your question may have something to do with air resistance but also may have to do with the weight of objects and the observed extra effort needed to move them.

Mass and acceleration look like independent terms to me. You can plug in any two values you want to into that equation.

Nobody even had a clear, mathematically definable concept of acceleration before Galileo.

Even then, nobody had a clear concept of mass, not until Newton.

Aristotle did ot hold that acceleration depended on mass, he held that speed (which he did not differentiate from velocity) of fall depends on weight and on the density of the medium.

It does, of course depend on the density of the medium, and, indirectly, on weight (though really on the relation between mass and surface area). A feather falls more slowly thorough air than a pebble, and the difference is even more pronounced if they fall through water. It took Galileo to realize that these observable facts were best ignored in favor of an unobservable idealization concerned with what might happen in a vacuum.

It took 2000 years because science is hard, although hindsight is easy.

It is a fairly good rule of thumb in the history of science that the more obvious a conceptual innovation looks in hindsight, the more profound it was, and the harder to attain in historical reality.

Incidentally, I am not sure what you think Galileo “tried”. The reconceptualization of fall, and of motion in general, that he achieved, did not depend on a single simple experiment (certainly not dropping objects off the tower of Pisa, which never happened). Galileo came to his new understanding over many months or even years of deep thought and of painstaking experimentation with rolling balls down inclined planes, and measuring their speed over various intervals with a water clock. He actually eventually proved his point about the independence of weight and speed of fall (under the idealization of fall in a vacuum) not with an actual experiment, but with a highly ingenious thought experiment about how different sized weights tied together would behave. (An Aristotelian account of such a system leads to self-contradictory predictions).

In fact, would it not be correct to say that “science” was not really what we think of as “science” until about the time of Galileo? It wasn’t until about the 17th century that the scientific method that we all know and love was routinely applied to advance knowledge.

They had better things to do than roll things down inclines to discover something no one had any use for.

For the same force (F), the greater the mass the smaller the acceleration.

It’s nowadays fashionable to denounce the ignorance of the people in the past, who were held by dogmatic faith in Aristotelian physics from denouncing its obvious shortcomings, but actually, Aristotelian physics survived as long as it did mainly because it was a good theory, valid in the everyday surroundings we find us in, and an approximation to Newtonian physics in a similar way to how the latter approximates Einsteinian physics, while diverging from it if extended beyond its domain of applicability. Rovelli has recently made the argument to this effect in a very convincing way (though I’m not enough of an expert on the matter to say how much of Rovelli’s Aristotelian physics is just his interpretation).

Part of the answer may be that they had no pressing need to know that. It’s not really practical knowledge in a primitive society that exist on a world with a atmosphere that distorts any practical application anyway.

Except it does have one possible primitive use, and that is non-scientific, the bar wager. I do find it likely that some people knew how to make a few, well not bucks, but perhaps sheckles off of this.

Frankly, this is to obfuscate the reality of the situation rather than to clarify it. There is no new, well-defined thing called “the scientific method” that suddenly gets invented in the 17th century (or any other time), and there is no sharp, clear line to be drawn (historically, conceptually, or otherwise) between ‘philosophy’ and ‘science’. In fact, the actual practitioners did not start calling what they were doing “science” rather than “philosophy” until well into the 19th century. The newly invented distinction was then projected back into history to place the transition from philosophy to science in the 17th century, but the actual conceptual innovators of the 17th century recognized no such distinction (and if they had, their innovations would very likely have been stymied).

I am not saying there is no difference, but it is not a sharp, well defined one, more a matter of degree (probably varying along several independent dimensions). Furthermore, merely pointing to the difference does not explain anything, but, rather, tends to conceals the actual problematic issues.

In general, even in more recent times, the greater the ‘scientist’ - that is, the more conceptually innovative there work was - the more more the actual methods they used, when examined closely, tend look as much or more like our stereotypical idea of ‘philosophy’ rather than our stereotypical idea of ‘science’. This certainly applies to people like Einstein and the founders of quantum mechanics (and probably will apply to the people currently working in areas like string theory and quantum gravity, should they turn out to be right) quite as much as it applies to the people like Galileo, Descartes, Kepler, and Newton who collectively brought ‘modern science’ into being in the 17th century. If any of these people, or even many lesser scientific innovators, had truly relied on the caricature ‘scientific method’ of “think of a hypothesis then test it experimentally”, science as we we know it would not exist.

Perhaps instead of saying “science is hard, although hindsight is easy,” I should have said “advancing our understanding of the universe is hard, although hindsight is easy,” but that would be to buy into the notion that there is some marvelous new “method” suddenly invented in the 17th century that, all at once, transformed what had been philosophy into science. It is much less misleading, I think, to use the modern term “science” to mean (as it does now) the enterprise of trying to understand how the universe works, and to recognize that there were people usefully engaged in this enterprise before the 17th century, just as there have been since. Certainly we see a huge increase in the rate of scientific progress from the 17th century onwards, but that is not because people started doing something fundamentally different in kind, but more because it is about then that the exponential(ish) curve of increasing knowledge turns from being near horizontal to near vertical, simply because the more you know the more you can apply that knowledge to the enterprise of discovering more. (Also, of course, an improved economy and the development of a less rigid and hierarchical society in that era meant that many more people had the opportunity to contribute to the advancement of knowledge.)

¬¬¬¬¬¬¬¬¬¬¬¬¬¬
Also, what Half Man Half Wit said (although I don’t know anything about Rovelli’s work).

I put so many conditionals in my post that I can’t fathom why you would have thought I was saying there was some distinct line when “science” suddenly burst into being. All I was saying is that sometime around the 17th century there was a formulation of scientific inquiry (what they would call natural philosophy) that became widespread (although clearly not universal) in Europe.

As noted in the wikipedia article on the Renaisance:

Yes, well, it does not surprise me that the sort of people who write and edit Wikipedia articles are also the sort of people who like to reify “The Scientific Method”. This is just he sort of thing that makes it important to read Wikipedia critically, and never treat it as an authority, especially on matters of interpretation (as opposed to a useful and reasonably reliable source of factual information, which it is).

As for your post, that I was replying to, I am not seeing all these conditionals that you refer to. You do, it is true, put it in the form of a question: Would it not be correct …?" Well, my answer to your question, which I justified at length, is no, it would not be correct (or, more accurately, to put things the way you suggest is considerably more misleading than it is illuminating, and hides the historical reality rather than helping to reveal it). I stand by my post. Why do you feel the need to defend yours, if you intended it so tentatively?

Of course our understanding of the natural world changed, fairly radically, over the course of the 17th century, and the dominant methods used for the investigation of nature also changed, though somewhat less radically (it is more a shift of emphasis rather than type - it is simply not true that nobody did experiments, or used mathematics to help them understand the world, before this era). However, those changes did not come about because something new called “science” or “the scientific method” was discovered, or caught on, over that period, or because something old called “philosophy” was abandoned by anyone. (The methods in fact used used by the leading figures of the scientific revolution were, in fact, very diverse. Copernicus, Galileo, Kepler, Descartes, Huygens, Bacon, Boyle, Hooke, Newton, etc., all pursued their researches in very different ways.)

Why don’t you do this on everything

The answer to all questions of the form “why did it take so long to realize [thing now taught in the first weeks of high-school science classes]?” is, first, that (as njtt noted) it’s more obvious in retrospect, and second, it wasn’t until the last five or six centuries that anyone in the West thought that observation was a useful way to learn things.

Correction: It wasn’t until the last five or six centuries that the people who thought observation was useful were influential. I’d wager that there have always been people trying to systematically learn through observation; they just couldn’t get most other folks to pay attention to what they found.

This is nonsense. People have always thought that observation is a useful way to learn things, and people have always paid attention to what has been learned through it. If you think that the revolution in astronomy and physics that happened in the 16th and 17th centuries happened simply because people started observing things that they had not bothered to notice before, you could not be more mistaken. The scientific revolution came about not because of new observations, but because of new, highly sophisticated, developments of theory. (This subsequently led to new observations or new realizations of the significance of certain observations. Without suitable theoretical guidance, however, observations are of little value. Without theory, you do not know what things, out of the overwhelming plethora of stuff that can be experienced in the world, are worth paying attention to, nor do you know what to make of any random observations you may have gathered.) Observation without theory is blind.

Copernicus did not simply notice that the Earth was going round the Sun rather than vice-versa. Indeed, he was scarcely an observational scientist at all. Rather, he found that (according to some standards) the mathematics of the detailed prediction of the movements of the planet across the sky was more elegant if you assumed that the Earth was moving rather than the Sun. This theoretical advance then enabled Kepler the realize the significance of the unprecedentedly large and accurate mass of astronomical measurements that had been collected by Tycho Brahe, originally mainly for purposes of astrology, for casting horoscopes for the King of Denmark. These were new observations, certainly (although they were gathered not because people suddenly started caring about observations where they hadn’t before, but because Tycho Brahe was OCD enough to want to make them, and the King of Denmark was loopy and superstitious enough to be willing to pay for it), but they would not have mattered if Kepler had not already been committed to Copernican heliocentrism, and hadn’t realized that this data was the tool he needed to prove it true. Likewise, Galileo would not have known what the dots and smudges and blurs of light that he saw through his telescope meant, if he had not had the Copernican theoretical framework in which to interpret them. Other people of the time, looked at the moon, stars and planets through telescopes, and failed to see what Galileo saw, because they were trying to fit what they saw into a different, older, theoretical framework.

Likewise, Galileo’s key realization about falling bodies came not (primarily) from observation, but from the realization that what really mattered for the fundamentals of mechanics was not how things move through a medium, like air or water, but how they would move in the (for him) unobservable, idealized case of moving through a vacuum. If you observe things falling through the air, let alone through some denser medium like water (and why not? It is still an observation. Why shouldn’t it be the right one to make and pay attention to?), you find that heavier things really do fall faster than lighter ones, just as Aristotle said. (OK, it is really the ratio of mass to surface area that matters, but to a first approximation weight works, and it is only when you have some theory suggesting otherwise that you know that a first approximation, in certain instances, might be misleading.)

People have always observed the world around them. Primitive hunter-gatherers observe plenty, even though their best explanation of some natural event maybe that spirits of the forest did it. It is only as theory advances that we start to get a grip on which things are worth observing carefully, and perhaps even measuring, and on what those observations might mean. Emptying your mind of preconceptions and opening your mind does not give you science, it gives you an empty mind filled up with meaningless clutter.

Many people did indeed think that way, which is what I said. But not everyone, and some of those who didn’t value observation, like Plato and Aristotle, were given undue reverence through much of history.