INTRODUCTION TO REASONING
WEEK 11: More Early Modern Scientific Reasoning
Good morning :D
Good morning! :)
I hope you all had a good Thanksgiving vacation.
Yes! How about you?
It was good to be with family.
I can attest
OK, today we look again at the early modern scientists and their methods of reasoning.
Two weeks ago, we looked at some early modern scientists, including Copernicus, Galileo and Newton, who together developed a new theory of motion. We saw that their theory of motion succeeded in doing away with one kind of complexity (different kinds of motion for rocks, earth, planets, and stars), but introduced a new kind of complexity (the earth’s motion turned out to be quite complex).
Do you have any questions about that?
I think it was pretty well covered.
OK, remember that they started with phenomena that had already been explained, but came up with a new explanation, and new concepts with which to explain.
Today we are going to look at some more early modern scientists, and I hope to induce you to reason along with them. Learning by doing: that’s how we explore how scientific reasoning works.
So let’s imagine you are Galileo (it is the early 1600s).
One day you are looking at a cistern, which is a big pit in which rainwater has been collected for use during the dry season. There is a pump in the cistern the main part of which is a vertical pipe. The bottom of the pipe extends down into the water. There is a piston that goes up and down inside the pipe above the water level.
Have you got a mental picture of this?
Take a moment to imagine the blue Italian skies and the pine trees swaying in the warm breeze.
Let's see... yes.
When the piston is pulled up, a one-way valve at the bottom of the pipe opens and allows water to enter the pipe. The water follows the piston up inside the pipe well above the level of the water in the cistern. This is step one.
Can you picture this?
Cool, we've been studying about all of this stuff in science recently. :-)
When the piston is pushed down again, the one-way valve at the bottom of the pipe closes, so the water can’t get out the bottom of the pipe. Another one-way valve in the piston itself opens. This allows the water in the pipe to flow through the piston, and it ends up in the part of the pipe above the piston. This is step two.
Can you picture this?
When the piston is raised again, the water above the piston is expelled through an outlet several feet above the surface of the water in the cistern, and new water is drawn into the bottom of the pipe. This is step three.
Can you picture how this pump works?
I recall a similar device on Lopez
OK Galileo, you think you already know what is going on. You know that “nature abhors a vacuum.” Therefore, as the piston goes up, nature tries to prevent a vacuum from forming in the pipe below the piston; the water is sucked up inside the pipe to keep any vacuum from forming. This kind of pump is said to lift the water “by attraction” because something seems to be pulling the water up into the pipe. The vacuum seems to attract the water.
Let’s stop for a second and ask a question. What kind of explanation are we giving when we say that “nature abhors a vacuum”? Is it a scientific explanation or not?
It is a fact without scientific explanation.
Its sounds more like a phenomena
It's asking "what is this?" not "why is this doing that?"
Not very scientific giving nature feelings
But cloaked in it is something we don't observe in nature, so I guess we are the ones that would abhor it ;)
Right. When we say "nature abhors a vacuum," are we attributing desires/interests to nature, and thus asking a "why" question, rather than a "what" or "how" question?
It is a "what" question.
A placeholder theory XD
Hmm, Lucy, I want to explore with you why you think "because nature abhors a vacuum" is answering a "what" question.
On second thought, maybe it's a "why" question. :-) "What is happening here?" "Water is being sucked up into a vacuum." "Why?" "Because water abhors a vacuum."
That's the way I saw it.
But there is much to what Edmund says as well. A scientist could treat "nature abhors a vacuum" as just a placeholder for a theory or explanation that we don't yet have.
Just as "matter exerts gravitational attraction" reflects a phenomenon we can measure, but can't clearly explain.
OK, file that idea away for the moment.
I guess I was thinking that a "why" question would be a more scientific one, like "why does water abhor a vacuum."
Now an interesting thing happens. As you watch, the pump works away and the water level in the cistern falls. But there comes a point where the pump stops working. The piston goes up and down but no water comes out. You call to a workman and you suggest he fix the broken pump.
He replies as follows:
“No, good Master Galileo, the defect is not in the pump. The water has fallen too low to be raised by the pump. In fact, it is not possible to lift water even a hair’s breadth above 18 cubits [about 34 feet] using any pump that works through attraction, no matter whether the pump is large or small.”
Hmm, what are we to make of this? Let me start by telling you the workman’s suggestion:
Seems oddly specific
“Good Master Galileo, I think it is like this. You know that a rope, or rod of wood or iron, if sufficiently long, will break of its own weight if held by its upper end. Well, isn’t this same thing happening in the pump? The attraction of the vacuum pulls the upper end of the column of water. At 18 cubits, the weight of the water is so great that the column of water breaks, like a rope that breaks on account of its excessive weight.”
What do you think of this explanation? Does water appear to act like a rope or a rod of iron?
What makes you say so?
Because the water's being pulled up
OK, so you and the workman are on the same page.
What does he mean by the water breaks?
That when you try to lift water higher than 18 cubits in the pump, it doesn't work. The water refuses to go up that high.
"Water refuses" is another placeholder perhaps.
Do you understand what I mean by placeholder?
So water is too heavy once it gets to 18 cubits to allow the piston to come back up?
That seems like a satisfactory answer, I suppose.
Lucy: The piston goes up, but beyond 18 cubits the water won't follow it any more.
Imagine that you, Galileo, now try some experiments to determine how different sizes of pumps (that is, pumps with different diameters) behave. What you find is that, sure enough, as the workman said, it doesn’t matter whether the pump is one foot in diameter or two feet in diameter: you can’t get the water to rise (below the piston) farther than 18 cubits.
Above the piston is a different matter. Once you get water above the piston, you can push it up farther. But 18 cubits appears to be limit of "attraction" below the piston.
As Edmund notes, the distance appears oddly specific, but there it is. An interesting phenomenon.
Let’s try to follow Galileo’s thought process.
Here’s an idea: let’s consider the relative weight of the water in the two pumps. The formula for the volume of a cylinder is pi times the radius squared times the length. So if two pipes are the same length but one has double the radius of the other, the volumes should differ by the square of the radius. Right?
So when two pumps of different diameters raise water to the exact same level (18 cubits), one of them is holding up a lot more water than the other. Why should one pump hold up so much more water than the other before the column of water breaks?
Volume of the tube? Viscosity?
You wouldn't think that the viscosity of the water would be different; it comes from the same cistern.
Here is where the workman's theory breaks down, I think, right?
Do you have any alternative explanation of what is happening with the pump?
it's not able to generate the vacuum needed?
something to do with pressure maybe?
Pressure of what?
Gravity is clearly involved. The water (in the cistern) is happy to sink to the lowest level it can. Our pump is fighting that tendency.
the pressure of gravity is greater than the vacuum created by the pump, so there must be a leak in the pump system or something
work is force times distance, so the distance to draw the water takes more force than you can generate
So we have been asking "what is sucking the water up?" Maybe that question is the wrong one. Can we ask a less specific question, one that doesn't presuppose a certain kind of answer (i.e. X is sucking the water up).
When asking scientific questions, it's important not to limit your possible answers in advance. Asking about "sucking" assumes that the pump is going to be explained by sucking. But maybe it won't be.
Would they compare the force to another?
What makes the water rise?
A good general question.
Or why does the water rise?
So now we can ask, is sucking the only force that can make water rise?
gravity pushing down on the water also
OK, we have liberated our minds by generalizing our question. Good scientific move.
Maybe something is pushing down on the water and making it go up the pipe of the pump.
An interesting idea but, I would suggest, a puzzling one. Have you ever tried to press down on water? What happens?
It yields, but there's also a tension
Could you push down on the surface of the water in the cistern and make it go up the pipe?
And why not?
Well, yes, actually.
If the top of the water has ice on it, then yes
If you seal everything off so that the water MUST go up the pipe (or not go anywhere).
water density must be a factor too
So if you try to push down the water with your hands, it just slips through your fingers (as Princess Leia used to say).
You could push down with a stiff board or a stiff piece of ice and, if the water had nowhere else to go, it might get squeezed up the pipe.
But our cistern has no stiff board on top of it.
Okay, I had a thought about why water stops rising... so maybe the water's weight eventually equals that of the air pressure, and so everything balances out.
So the air is pressing down on the surface of the water in the cistern?
Is that what you have in mind?
Or the pressure of the vacuum?
I don't know which.
So if the air is pressing down on the water and none is “leaking through the air’s fingers” as it were, we have to imagine the air pressing equally on every little bit of the water, right?
Sounds good again
Now I can imagine pressing down on water with a large flat stiff object, like a board (in fact, that’s what we do when we row a boat). But air is not a large stiff object, is it?
So let’s file away the “pressing down” idea for a minute (we’ll get back to it).
Let’s now imagine you are another assistant of Galileo’s, named Torricelli. You are interested in the pump phenomenon, but find it cumbersome to work with columns of water 18 cubits high. Can we find some heavier liquid that might work on a smaller scale?
Milk? Or oil?
Heavier liquid? Like oil or something?
Oil actually floats on water, so it's lighter.
We all had the same wrong idea!
What’s the heaviest liquid we know about?
(at room temperature)
Is mercury heavy? :-/
Any idea about whether mercury would be available to 17th century Italians and, if so, why?
Uh, I don't know how one gets mercury.
It certainly has a Latin sounding name.
Yes, because they use it to cure fur
Which is why the mad hatter is mad?
Mercury is also used in refining gold, so there were people around who could manufacture it for you.
Let’s think of a smaller scale model that can help Torricelli analyze the pump situation. Take a glass tube, closed at one end, and about three feet long. Fill it with mercury. Then hold your finger over the end and invert the tube into a dish filled with mercury, taking care that the open end is under the level of the mercury in the dish when you remove your finger. What happens?
It stays pretty much the same
Does all the mercury pour out of the tube?
Correct. It stays up in the tube, just as the water did in the pump, but there is now an apparently empty space above the top of the mercury (which we can see through the glass).
The pressure of the mercury in the dish pushing UP keep the mercury inside the tube?
By the way, be careful about trying this at home because mercury is poisonous not only when ingested but to some extent to the touch as well.
Though I played with mercury as a child and it didn't seem to have any ill effj jw dn fia;l dso#!
In my science studies, we learned about a lot of scientists in that time that died from such experiments, especially with florine. :-)
And Madame Curie died of radiation poisoning.
You played with mercury? Did they sell that as a toy?
Just as the water refuses to rise more than 18 cubits, the mercury won’t rise more than about a cubit and a quarter (about 30 inches).
You could buy mercury in a little tube at the drug store, as I recall.
So we have the tube with a column of 30 inches of mercury and an apparently empty space above.
What is in that space?
Have we made a vacuum?
How could we test to find out whether we have made a vacuum?
Or whether there is air in there.
Put a match in it
or a flame
Well, there is 30 inches of mercury to get through.
How would you get a flame in there, Lucy?
Torricelli tried this: in the dish containing mercury, he filled water in several inches above the mercury (water floats on mercury because it is less dense). Then he slowly lifted the tube until the bottom of the tube was above the mercury but still in the water. What do you think happened?
The mercury fell through.
Because the pressure of the water was not great enough to hold up the mercury.
the mercury flowed out and the water plugged it up
Right, the mercury fell down and the water rushed in to fill the tube completely. In other words, the water floated on the mercury right up to the top of the tube.
What can we conclude from this? Notice that as the water rushed in to fill the top of the tube, nothing appeared to bubble out.
There was a vacuum.
There was nothing there, so then it must be a vacuum, because nature abhors a vacuum ;)
If there had been air or something like that in the empty end of the tube, the water could not have filled it completely.
OK, so has Torricelli shown that nature abhors a vacuum? Remember that "abhors" means "hates".
He's proven the opposite, hasn't he? That nature creates vacuums.
Far from it
Or at least the
Yes, because it discriminates against it
Or at least that Torricelli creates vacuums.
If you look around your room, you will probably see something that used to be manufactured using a Torricelli vacuum. Can you guess what it is?
Lightbulbs have vacuums inside (otherwise the filiments would burn out). Early lightbulbs were made using Torricelli's process for creating vacuums.
In fact, Torricelli showed he could create a vacuum whenever he liked.
Do light bulbs need a vacuum so that the friction of the filiments vibrating won't burn them up?
So let’s ask this: what have we learned about why the mercury (or water) rises in the tube in the presence of a vacuum? Is it the attraction of the vacuum or something else?
the equalization of pressure, right?
Lucy: light bulbs need a vacuum because otherwise heating the filiments to the point where they glow would cause them to burn in the presence of oxygen.
Oh, I see.
So back to Torricelli. Torricelli concludes that the cause of the phenomenon (water and mercury rising in tubes) is not the attraction of the vacuum but some force from outside. That force arises from the weight of the surrounding air. (I told you we’d get back to this.)
It is not the attraction of the vacuum, but the pressure of the substance underneath it.
Which is in turn being pushed up into the tube because of air pressure?
Or the pressure of the air above the water (or mercury). The air causes the water (or mercury) to have internal pressure.
So the air presses on the surface of the fluid, that pressure is imparted to all parts of the fluid, and the part of the fluid in the dish causes the fluid in the tube to rise.
Or so Torricelli thought.
He said, we live (as it were) at the bottom of an ocean of air.
So now we have two theories to choose from: the vacuum attraction theory and the air pressure theory.
Let’s try an experiment to test whether the vacuum really attracts the mercury or not. If some vacuum attracts the mercury, wouldn’t you suppose that more vacuum might attract the mercury more? If so, can you think of a way to test this with two mercury tubes, one of which has a larger vacuum than the other?
Measure the amount sucked up in a set amount of time?
Well, once you set up the mercury tube the mercury just sits there at about 30 inches.
How do you make vacuums of different strengths?
Well, at least we can make them of different sizes?
vacuums of different sizes? you mean in bigger test tubes?
fat tube, skinny tube filled with mercury in same tray and see if they go down equal distance
It has already been proved that test tubes of varying sizes don't affect the height of the liquid.
Or just a stronger suction source
Different diameters don't produce different results (same as the pump experiment).
the fatter tube would have a bigger vacuum because there's more vacuum volume displacement?
What about the height of the tube? If you made it taller, then supposedly you'd have more vacuum.
In our 3-foot long glass tube, we end up with about 30 inches of mercury and about 6 inches of vacuum. How could we make the vacuum bigger?
ah better idea
We make one tube longer than the other (or put a large bulb in the end of one tube), fill both with mercury, put our fingers over the ends, and immerse the open ends in dishes of mercury. What happens?
you get mercury poisoning ;)
But I still don't think it's going to make a difference because the amount of vacuum would be the same in a taller or fatter tube.
We are wearing rubber gloves.
It doesn't matter which one you use.
The mercury ends up at the same level no matter what the closed top of the tube looks like and how big it is. This suggests, but perhaps does not prove, that what is going on is pressure from without rather than attraction from within because the pressure from without is the same while the vacuums within are different.
Let’s think about the pressure from without. Can you feel any air pressure?
yes and it hurts
You can if you swing your arms around you, or up and down. You can feel pressure of air against your arms.
I'm sitting in my chair and not floating
That might be gravity rather than air pressure.
No, I can feel the resistance of air.
But maybe that's not the same thing as air pressure.
And swinging your arms around in a room full of cobwebs might create a feeling of resistance, but we don't think the cobwebs are pressing on us.
Hmm, maybe we are just used to it. When you swim around in the pool, do you feel water pressure?
Yes, if you go deep enough. My ears start to hurt.
The pressure comes from the weight of the water. Does air have weight?
How can we tell?
Air does have weight, and you can feel it. When we go up in airplanes, we can feel the lack of air pressure in our ears.
go to a mountain
Aha, not an experiment available to Torricelli, but right.
The airplane, I mean.
Let’s suppose that the air has pressure even if we don’t feel it. The air pushes down on the dish of mercury, driving the mercury up the tube.
Again, remember that you couldn’t push down on the mercury. It would slip through your fingers. So we must imagine that the air has no “fingers,” as it were. The air must press equally at all points on the mercury surface. If it were otherwise, the mercury would splash around.
This is kind of hard to imagine, isn’t it? That the air always presses exactly the same amount at all points on the mercury surface?
Now imagine you are a French scientist named Pascal. You wonder one day whether there is a way to test whether the explanation of the Torricelli mercury tube is outside air pressure.
Can you think how to put together a Torricelli mercury tube that is not surrounded by air (space travel not being an option for Pascal)?
They had machines that could create a vacuum. Scientists would put objects inside and see what happened. The candle experiment in oxygen was done in one of these machines.
conduct the experiment under water?
well, the water itself has pressure
Lucy has it right.
You'd have to surround it with a vacuum.
but you said not surrounded by air
We put the tube and dish, with the mercury standing about 30 inches high, into a larger vessel. Then we pump the air out of the larger vessel. So now there is no air pushing down on the dish of mercury. What happens?
Hmm, no mercury goes up the tube?
And the mercury that was in the tube falls into the dish.
Right, the mercury falls out of the tube into the dish. Does this prove that what was holding the mercury up in the tube was outside air pressure?
I think so.
But consider this: we have now created a vacuum outside the dish. So isn’t it possible that this larger vacuum has attracted the mercury more than the vacuum in the top of the tube?
But what did Torricelli’s experiments show about whether a larger vacuum exerts more attraction?
No, because we already completed an experiment that proved that a larger vacuum does not affect the liquid.
So our results so far strongly suggest that Torricelli was right: it is the pressure of the outside air that causes the mercury to remain up in the tube, not the attraction of the vacuum within.
Let’s think of another way to test whether the mercury rising in the tube is because of the attraction of the inner vacuum or the pressure of the outside air.
Suppose it’s true that the air is pressing down. What do you think causes the air to press down?
Which gives the air weight.
Because air has mass, and gravity gives it weight.
So here at the surface of the earth the pressure comes from the weight of all the air piled up above?
Yes, and other gases yet above that.
Does the air extend infinitely high above the earth’s surface?
No, it stops at about space
No, it stops at the outside perimeter of our atmosphere.
So what would the air pressure be like at the top of a mountain, with less air above us?
The pressure would be less on a mountain than in a valley.
less air pressure
Now remember the vacuum attraction theory. Can you think of any reason why the vacuum would be less attractive at the top of a mountain as opposed to the bottom?
I experienced this when I went to Denver Colorado from Arkansas.
A vacuum is a vacuum, anywhere, so it wouldn't have less attraction.
Or on an airplane. Less air resistance?
OK. So can you think of a way to test the vacuum vs. air pressure theory by using a Torricelli mercury tube and a mountain?
go on top of a mountain and do the same experiment
Right. You carry a tube up a mountain where the outer air pressure (in theory) is less.
How do you make sure that some temporary atmospheric phenomenon (some kind of low air pressure caused by weather) isn’t affecting the tube you are carrying up the mountain?
Taking a control experiment below the mountain, then test it on the mountain to determine resistance?
Try his experiment up on a mountain, and if the air pressure is lower, then theoretically, the liquid should be lower in the tube.
Stupid lag :/
Right. You should have two tubes, one that stays at the bottom of the mountain and one that goes up the mountain.
If the mercury is held up in the tube by the attraction of the vacuum, what should you observe when you carry the tube up the mountain?
You should notice that the mercury is lower in the tube.
If the mercury is held up by the attraction of the vacuum?
No, if it's air pressure that affects the height of the liquid.
Isn't it colder on top of a mountain so wouldn't temperature be a factor also?
Good thinking. Mercury travels slower when it's cold.
Good point. The medium of mercury might be affected
Yes, good point. We can experiment to determine whether temperature affects the mercury level.
Temperature could change the viscosity of the liquid
And what do you observe in fact?
Okay, so if it's a vacuum that affects the liquid, then on a mountain, the liquid should reach the same height as always.
And if it's air pressure, the liquid should be lower in the tube than normal.
that is, what do you observe when you take the tube up the mountain?
Probably lowered resistance, so it's slightly higher?
Why would it be higher?
Or would the vacuum be equal?
If there's less resistance pushing down on the mercury from outside, then wouldn't it be lower? And the vacuum would be equal.
The vacuums would be equal, but the outside air pressure different.
You do in fact observe that the mercury is lower in the tube on the top of the mountain.
And from this is it reasonable to conclude that the mercury is held up in the tube by outside air pressure?
Really? So the "30 inch rule" is not always so in all locations?
And therefore is held up less at the top of the mountain where the air pressure is less?
Yes, I think we've closed our case!
Yeah it's called a thermometer
Right, the 30 inch rule (or 18 cubit rule for water) works only around sea level.
Aren't thermometers filled with mercury?
It's called a barometer.
I'm above sea level, but I'm sure it would be about that here.
But good point about thermometers: they indicate that the mercury is affected by temperature.
Congratulations! You have followed the thought process of some important early modern scientists.
We're geniuses! *g*
Here’s a follow-up. We have explained the Torricelli mercury tube in terms of air pressure, and we have to imagine that the air is pressing equally on all parts of the mercury surface.
At the same time, we need to imagine that the pressure exerted on the surface of the mercury is transmitted to all parts of the mercury, holding the mercury up in the tube.
This is called “Pascal’s Principle”: the pressure in a fluid (like mercury) is exerted equally through all parts of the fluid (which means in all directions and at all points).
OK, that’s about it for today.
Today we followed the thought process starting with Galileo and proceeding through Torricelli and Pascal. We began with observations of a suction pump, proceeded to build a model using mercury, and then came up with some experiments to try to determine whether the behavior of the pump and the mercury should be explained by the attraction of the vacuum or the pressure of the outside air. We concluded that air pressure was a better explanation.
We’ll look next time at another famous scientist, Darwin.
See you next week.
You too, and thanks professor :)
Fantastic! Thanks for a really fun and interesting discussion today! Have a good week, everyone--bye!
Thanks for class!
Thanks for class!
Have a great weekend!
Good day everybody!