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> Galileo famously (and likely apocryphally) demonstrated the principal by dropping lead balls of different weights off the Leaning Tower of Pisa and observing

> Galileo famously (and likely apocryphally) demonstrated the principal by dropping lead balls of different weights off the Leaning Tower of Pisa and observing them hit the ground at the same time. This never made sense to me as something you'd need to test, once the question had been considered. Imagine 1000 cannonballs all connected to each other with threads. The result is a single object with 1000x the mass of a cannonball. Would you expect it to fall faster?

contact_fusion 8y ago
It may seem obvious to our modern eyes, but the notion that objects of different mass fall at the same rate is not at all obvious outside of the framework of physics that Galileo helped build. Without proper notions of force, gravity, mass, density, and the form of the laws of gravity, surely you realize that the answer to your hypothetical is not trivial. This was kind of the whole point of Principia.
- phyzome 8y ago
  I agree that it's well-established at this point. What I'm poking at is the question of "what is an object?" since that's also fundamental to the question of "do heavier objects fall faster?" And it's a question that Newton could easily have asked, as far as I can tell.
  - contact_fusion 8y ago
    But a more complete notion of "object" isn't what solved the problem. Much of what constituted physics prior to the advances by Galileo and Newton (and many others) was essentially what was developed by Aristotle. Within the Aristotelian framework, which is what most educated people knew at the time, the concept of a distinct "object" is perfectly well defined. My point is that the natural philosophers at the time were quite capable of asking the question, "do heavier objects fall faster?" without being led astray by an incomplete notion of "object." In other words, the problem is conceptual, not semantic. The Aristotelian - again, the dominant framework back then - was instead led astray by the notion that all objects had a "natural" tendency to move towards the center of the Earth, and that this tendency was stronger for heavier objects. This worldview had a very long history, and a fair amount of evidence (such as it was) to back it up. In this context, what matters is not the distinct objects but instead what properties influence their dynamics. It should be clear then why it was necessary to demonstrate the empirical truth. Many plausible theories had emerged, including the prevailing Aristotelian one, which accounted for the differences in, say, a lead weight falling versus a feather. Or, to get back to your original example, the Aristotelian would have answered, probably confidently, that yes, your chain of cannonballs would fall faster than separate ones. Your (correct Newtonian) intuition is that the mere act of chaining them together should not alter them, given that the threads would not exert forces in free fall, and therefore mere mass should not alter the falling rate. But, those notions depend entirely on the Newtonian framework. "Force" and "free fall" are the undefined concepts, not "object." A key insight was needed, namely that you could separate out different causes in the motion; in this case, gravity and air resistance. (Though, of course, "cause" is itself a thorny concept...) Galileo's experiments demonstrated the point elegantly. More formally, this resulted in the development of the notions of inertial reference frames and linearity, which underpin much of classical physics. I hope you don't think I'm belaboring the point. Newton's revolution was so total, so complete, that it changed everything about how we think about physical problems. Centuries of difficult philosophical and scientific work has been condensed down into a semester of freshman physics. To us, the problem is trivial, and it is easy to think that such experiments are so trivial as to be useless. To Galileo, this would not have been the case. A single thought experiment would not have been enough back then, even though it suffices now.
    - phyzome 8y ago
      I suppose what you're basically saying here is that I'm so steeped in Newtonian thinking, culturally, that I'm more or less incapable of understanding the Aristotelian viewpoint. Which, fair.
fvdessen 8y ago
Well yes, especially if they fall vertically as the bottom cannonballs would pull the top ones and that would make them fall a lot faster.
- phyzome 8y ago
  Oh, I wasn't imagining them in a vertical string. Imagine a horizontal line of them, instead.
SketchySeaBeast 8y ago
We shouldn't write off the difficulty of the problem, just because it feels self-evident now. It's much easier to come up with a thought experiment once you have the answer. It's completely intuitive that "0" is a thing, I mean, you can just go "whats 2-2?" but it wasn't always the case. It's very hard to get into a frame of mind that includes only those items the contemporary discoverer would have known.
- dboreham 8y ago
  I'm pretty sure that "0" as in "2-2" has been known since before we became the current species. What was new and interesting was the use of "0" as a place holder to allow decimal number representation.
newen 8y ago
Well...imagine dropping a cannonball and a feather from the top of a tower. Obviously the cannonball is going to hit the ground first. You can then extrapolate this result to heavier objects and conclude that heavier objects fall faster. To explain the behaviour of a small cannonball and a large cannonball, both of which fall to the ground almost at the same time: you see, as the weight of an object increases, an object starts to behave more and more like an extremely heavy object. Thus the difference in dropping time for a heavy object and a heavier object gets immeasurably smaller as the objects increase in mass. You can come up with all sorts of theories to explain phenomena. It's pretty hard to deduce the underlying rule from observation. But it's pretty easy to explain the phenomenon once you know the underlying rule.
ithkuil 8y ago
Indeed, Galileo approached at this problem with the very same thought experiment you're describing (even cited as an example of what a thought experiment is, right in the Overview section).
- phyzome 8y ago
  Ah, that's good to hear!

contact_fusion 8y ago

It may seem obvious to our modern eyes, but the notion that objects of different mass fall at the same rate is not at all obvious outside of the framework of physics that Galileo helped build. Without proper notions of force, gravity, mass, density, and the form of the laws of gravity, surely you realize that the answer to your hypothetical is not trivial. This was kind of the whole point of Principia.

phyzome 8y ago
I agree that it's well-established at this point. What I'm poking at is the question of "what is an object?" since that's also fundamental to the question of "do heavier objects fall faster?" And it's a question that Newton could easily have asked, as far as I can tell.
- contact_fusion 8y ago
  But a more complete notion of "object" isn't what solved the problem. Much of what constituted physics prior to the advances by Galileo and Newton (and many others) was essentially what was developed by Aristotle. Within the Aristotelian framework, which is what most educated people knew at the time, the concept of a distinct "object" is perfectly well defined. My point is that the natural philosophers at the time were quite capable of asking the question, "do heavier objects fall faster?" without being led astray by an incomplete notion of "object." In other words, the problem is conceptual, not semantic. The Aristotelian - again, the dominant framework back then - was instead led astray by the notion that all objects had a "natural" tendency to move towards the center of the Earth, and that this tendency was stronger for heavier objects. This worldview had a very long history, and a fair amount of evidence (such as it was) to back it up. In this context, what matters is not the distinct objects but instead what properties influence their dynamics. It should be clear then why it was necessary to demonstrate the empirical truth. Many plausible theories had emerged, including the prevailing Aristotelian one, which accounted for the differences in, say, a lead weight falling versus a feather. Or, to get back to your original example, the Aristotelian would have answered, probably confidently, that yes, your chain of cannonballs would fall faster than separate ones. Your (correct Newtonian) intuition is that the mere act of chaining them together should not alter them, given that the threads would not exert forces in free fall, and therefore mere mass should not alter the falling rate. But, those notions depend entirely on the Newtonian framework. "Force" and "free fall" are the undefined concepts, not "object." A key insight was needed, namely that you could separate out different causes in the motion; in this case, gravity and air resistance. (Though, of course, "cause" is itself a thorny concept...) Galileo's experiments demonstrated the point elegantly. More formally, this resulted in the development of the notions of inertial reference frames and linearity, which underpin much of classical physics. I hope you don't think I'm belaboring the point. Newton's revolution was so total, so complete, that it changed everything about how we think about physical problems. Centuries of difficult philosophical and scientific work has been condensed down into a semester of freshman physics. To us, the problem is trivial, and it is easy to think that such experiments are so trivial as to be useless. To Galileo, this would not have been the case. A single thought experiment would not have been enough back then, even though it suffices now.
  - phyzome 8y ago
    I suppose what you're basically saying here is that I'm so steeped in Newtonian thinking, culturally, that I'm more or less incapable of understanding the Aristotelian viewpoint. Which, fair.

fvdessen 8y ago

Well yes, especially if they fall vertically as the bottom cannonballs would pull the top ones and that would make them fall a lot faster.

phyzome 8y ago
Oh, I wasn't imagining them in a vertical string. Imagine a horizontal line of them, instead.

SketchySeaBeast 8y ago

We shouldn't write off the difficulty of the problem, just because it feels self-evident now. It's much easier to come up with a thought experiment once you have the answer. It's completely intuitive that "0" is a thing, I mean, you can just go "whats 2-2?" but it wasn't always the case. It's very hard to get into a frame of mind that includes only those items the contemporary discoverer would have known.

dboreham 8y ago
I'm pretty sure that "0" as in "2-2" has been known since before we became the current species. What was new and interesting was the use of "0" as a place holder to allow decimal number representation.

newen 8y ago

Well...imagine dropping a cannonball and a feather from the top of a tower. Obviously the cannonball is going to hit the ground first. You can then extrapolate this result to heavier objects and conclude that heavier objects fall faster. To explain the behaviour of a small cannonball and a large cannonball, both of which fall to the ground almost at the same time: you see, as the weight of an object increases, an object starts to behave more and more like an extremely heavy object. Thus the difference in dropping time for a heavy object and a heavier object gets immeasurably smaller as the objects increase in mass. You can come up with all sorts of theories to explain phenomena. It's pretty hard to deduce the underlying rule from observation. But it's pretty easy to explain the phenomenon once you know the underlying rule.

ithkuil 8y ago

Indeed, Galileo approached at this problem with the very same thought experiment you're describing (even cited as an example of what a thought experiment is, right in the Overview section).

phyzome 8y ago
Ah, that's good to hear!