[HN Gopher] Galileo Bad, Archimedes Good
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Galileo Bad, Archimedes Good
Author : hoerensagen
Score : 19 points
Date : 2025-09-28 10:21 UTC (3 days ago)
(HTM) web link (intellectualmathematics.com)
(TXT) w3m dump (intellectualmathematics.com)
| graemep wrote:
| I was going to say this is BS, and that Gaileo's big achievement
| was not undermined by this argument.
|
| I then found that what I was going to argue was his big
| achievement was not as original as I had thought:
| https://en.wikipedia.org/wiki/Galileo's_Leaning_Tower_of_Pis...
|
| On the other hand he still seems to have made a significant
| contribution to laws of motion in his writing, but I am not sure.
| tsimionescu wrote:
| It's also interesting to note that the thought experiment is
| actually plain wrong, unless you consider general relativity a
| given.
|
| Galileo's argument is that the theory where heavier objects
| fall faster is inconsistent a priori, because affixing a small
| stone to a larger stone would cause the composed object to fall
| faster than the smaller stone was falling when it was free.
| However, there is no logical contradiction here: what could
| happen is that the combined object would have an acceleration
| that is the (weighted) average of the acceleration of the
| components - slower than the lighter object but faster then the
| heavier object.
|
| In fact, this is exactly what happens in an electric field: if
| you have two objects with the same mass but different negative
| charge moving towards a large positive charge, they will
| accelerate at different rates (the one with the bigger negative
| charge will "fall" faster). If you then tie the two objects
| together, you'll get a combined object that has more mass and
| more charge; the total electric force will increase, but its
| larger total mass will mean that it accelerates less.
| Alternatively, you can explain it as the less charged object
| dragging the heavier object down, such that the combined object
| moves at an average of their speeds.
|
| The fact that this doesn't happen with gravity is a very
| special property of gravity, that only experiments can prove. A
| priori, gravitational mass/charge could have been entirely
| unrelated to intertial mass, just like electrical charge. Only
| much later, with Einstein's general relativity, did we get an
| explanation of gravity that makes this more than a coincidence
| - and it turns out that gravity is not a force at all, at least
| not one that acts on objects.
| mrguyorama wrote:
| Galileo may not have done the exact "drop balls off the tower"
| experiment but he did formally study gravity by rolling balls
| down a ramp and timing it, and that experiment would have shown
| that heavier things don't fall faster than lighter things
| (until you get to things being large enough that the gravity
| force between them is meaningfully increased, but they wouldn't
| have been able to do that).
|
| It still took like a thousand years for this to be
| _experimentally_ demonstrated.
|
| The important part of this "thought experiment" in the history
| of science is that it is part of the shift to empiricism that
| really drove science. It was important to go from "Well they
| were smart and they said, so it must be true" to "I don't care
| how smart you are, what you say doesn't match the data"
|
| This is important, because "smart" people like Archimedes said
| a lot of stuff that was never true, but was taken as true for a
| millennia, often because it "sounded" right or obvious. More
| importantly, Archimedes could have done the exact same
| experiments that Galileo (and others) used to demonstrate he
| was not correct. There was no technological advancement
| required. He didn't, because the philosophy at the time was to
| "just think really hard about it" and "reason from first
| principles" and you would obviously get the right answer if
| only you are smart enough. Who needs data? You're smart and you
| thought hard about it, so you cannot be wrong!
|
| People should recognize how important that is to remember in
| the current world.
| MadxX79 wrote:
| Isn't a mathematician arguing that Galileo was a bad scientist
| because he wasn't as good at deriving the area under some
| function as Archimedes, a bit like a fish arguing that Galileo
| was a bad scientist because he couldn't swim as fast as a tuna?
| constantcrying wrote:
| Archimedes really is an underappreciated figure. His ideas,
| specifically about calculating the area of shapes, already
| preempted the idea of the integral almost two millennials before
| Leibnitz and Newton.
|
| When reading about ancient Greek mathematics it always is
| striking how little it resembles the mathematics taught in
| schools and how much it resembles the mathematics taught in
| University.
| vharuck wrote:
| IIRC, the ancient Greek mathematics we learn about today was
| the university-equivalent mathematics of that era. Common
| people did not use geometric abstractions to figure out math
| problems. Before Fibonacci brought algebra to Europe, everyday
| calculations were done on an abacus. If no abacus was nearby,
| people emulated one by placing stones in lines on the ground.
|
| Pre-university schools, even today, focus on teaching practical
| math. Most people can get by just fine without skills in
| abstract math, theorizing, and proofs (though those skill would
| make a lot of people much better at whatever they do).
| constantcrying wrote:
| My point was that we should consider how advanced the Greeks
| were with their understanding of mathematics, especially
| their desires for proofs. And we should contrast that with
| how mathematics is taught today.
|
| It's obvious that "practical math" has always been the most
| important and first skill to teach. But that ends at basic
| trigonometry.
|
| Students are learning how to do integration in highschool
| (not exactly a relevant skill), long before they are
| confronted with the idea of proof in mathematics.
| momojo wrote:
| I know this is polemical article is in good fun but chatGPT gives
| me the impression Descarte should not be counted with the others:
|
| https://chatgpt.com/share/68dd758f-2bc0-8008-955d-a7dbd89399...
|
| " Given:
|
| - The blog offers no primary evidence for Descartes's having a
| proof.
|
| - Scholarly histories, based on critical assessment of surviving
| letters, treat the solution of the area problem as due to
| Roberval (and independently Torricelli) rather than to Descartes.
|
| - The more carefully vetted sources place Descartes in the
| position of reacting to, or endorsing, Roberval's result but not
| of originating it.
|
| Therefore, the weight of evidence supports that the historical
| consensus is correct -- Descartes did not solve the area under a
| cycloid; the blog's claim is likely an overstatement or
| misinterpretation."
| ioasuncvinvaer wrote:
| I never understand peoples' desire to copy paste their slop
| into a comment.
| horizion2025 wrote:
| What's up with the Galileo hate? Even if he couldn't derive the
| area of a cycloid, doesn't give justification to condemn a whole
| scientific career (Galileo is the most overrated figure in the
| history of science?!). Shouldn't Galileo be measured what he did
| solve rather than what he didn't... failing one problem is hardly
| proof of general incompetence. Besides, he's not really known as
| a mathematician but more for his works in physics, and he
| certainly isn't considered one of the great mathematicians of his
| time.
|
| Just a few things we owe Galileo in physics:
|
| * The principle of relativity. You might think that was Einstein,
| but the first theory of relativity was by Galileo in his 1632
| "Dialogue Concerning the Two Chief World Systems" (before Newton
| was even born!). Galileo introduced this idea with a brilliant
| thought experiment: He asked the reader to imagine being in a
| windowless cabin on a smoothly sailing ship. He argued that no
| experiment you could perform inside the cabin (dropping a ball,
| watching flies, etc.) could tell you whether the ship was at rest
| or moving at a constant velocity. All the laws of mechanics would
| behave identically. This is the cornerstone of classical
| mechanics. In the context of special relativity, Einstein
| "merely" added 'the speed of light is c' to the list of laws of
| nature that hold in all inertial frames. But the general way of
| viewing laws of nature relative as being invariant to motion was
| Galileo's (the principle of inertia), and essentially the
| starting point for Newtonian mechanics. It doesn't seem like the
| work of someone only able to fiddle around with scales.
|
| * The Law of Falling Bodies: The discovery that the distance an
| object falls is proportional to the square of the time. The first
| truly modern mathematical law of physics.
|
| * Detailed telescopic observations: Moons of Jupiter, Phases of
| Venus, Mountains on the Moon & Sunspots, etc.
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