[robinofloxley]

A couple of weeks ago I saw this post from Tom:

Aristotle's most famous proof for the rotundity of the Earth is the Lunar Eclipse. He said that only a round Earth could cause a round shadow. Since the shadow is round, the earth must also be round. However, he was incorrect, and apparently did not experiment much with that idea. Due to the shape of the Moon, a flat sided shadow can also cause a round shadow to appear:

The image is taken from https://wiki.tfes.org/Lunar_Eclipse_due_to_Electromagnetic_Acceleration

I was surprised that such an apparently simple experiment could so utterly demolish Aristotle's argument, so decided to have a go at repeating it myself. I couldn't find a very suitable spot at home, so decided to model it instead. Here's what I came up with:



However, in modelling this, I discovered something quite interesting. If you take a close look at all the shadows (not just the moving shadow), you'll notice that whilst the observer is more or less directly in front of the alcove, the light source (a torch) is coming from somewhere off to the left and above. That's the only explanation for these shadows. And since "the Earth" (a rectangular folder in this experiment) is blocking the light source, then it too must be off to the left and above. I worked out that looking back from the moon, the angular separation between the Earth and the observer needs to be approximately 22 degrees.

In RE terms, that means the observer is located in space approximately 90 thousand miles from the Earth.

So not very realistic then.

I then moved my observation point to where the folder is to simulate an Earth bound observer. This is what I see now.



So not such a devastating demolition of Aristotle at all, just a very misleading image in the Wiki.

[Tom Bishop]

Thanks, that's interesting. So you verify that if the shadow is coming from a slightly different angle than the observer, the curvature would occur. If the shadow were exactly  coming from the observer's location, the curvature would not occur.

Is there any reason to assume that the shadow is coming directly from the observer other than because that's what RE says?

Your model with a curving shadow seems to disprove Aristotle's claim that only a round object can cause a round shadow. We see a round shadow. It seems appropriate to say that Aristotle was wrong, and that a flat-sided shadow can project as round on a round moon.

[JSS]

Your model with a curving shadow seems to disprove Aristotle's claim that only a round object can cause a round shadow. We see a round shadow. It seems appropriate to say that Aristotle was wrong, and that a flat-sided shadow can project as round on a round moon.

You are slightly misquoting Aristotle's argument by leaving out a word. Here is the quote:

“the earth is spherical…in eclipses the outline is always curved: and, since it is the interposition of the earth that makes the eclipse, the form of this line will be caused by the form of the earth’s surface, which is therefore spherical.”

He wasn't saying it's impossible for a flat surface to project a curved shadow.

He is saying that only a sphere would ALWAYS project a round shadow.  If the Earth were flat or some other shape, you would sometimes see a line, or a thin oval down the middle. His argument is that you never see anything but a curved shape, and the only shape that presents a curved surface from all directions is a sphere.

So showing a flat object casting a round shadow doesn't disprove his argument, as that wasn't what he was claiming.

[BRrollin]

So you verify that if the shadow is coming from a slightly different angle than the observer, the curvature would occur. If the shadow were exactly  coming from the observer's location, the curvature would not occur.

Is there any reason to assume that the shadow is coming directly from the observer other than because that's what RE says? Under the EA explanation for the Lunar Eclipse I could see the Moon being exactly full, in the vertical rays of the Sun, with the angle of the incoming shadow offset from exactly vertical.

Your model with a curving shadow seems to disprove Aristotle's claim that only a round object can cause a round shadow. We see a round shadow. It seems appropriate to say that Aristotle was wrong, and that a flat-sided shadow can project as round on a round moon.

Was that Aristotle’s claim though? He said:

As it is, the shapes which the moon itself each month shows are of every kind straight, gibbous, and concave but in eclipses the outline is always curved: and, since it is the interposition of the earth that makes the eclipse, the form of this line will be caused by the form of the earth's surface, which is therefore spherical.

So from my reading of it, it sounds like to me that he didn’t claim that only curved shapes produce curved shadows. It sounds like to me that he claimed the surface of the Earth must be curved under the assumption that the shadow comes from the same angle as the observer: “since it is the interposition of the earth that makes the eclipse.”

So if the shadow on the moon comes not from the earth where we are but some other object, it seems like that object can be flat, according to the demonstration, yet not contradict Aristotle’s claim, since it departs from his assumption.

[somerled]

Doubt whether Aristotle stated anything that is attributed him. Only fragments of his work survive - parts of about 30 manuscripts. Most of what we are told we know of his works comes from medieval manuscript transmission - Corpus Aristotelicum - and from Bekkers interpretations of these interpretations.

 A bit like the Eratosthenes crap , none of whose work survived, whose main source is a book published by a Greek astronomer who we know nothing about but may have lived anytime from 200bc to 2 or300ad if I remember correctly. .

Funny how all the globey bits of lost manuscripts survive.

[robinofloxley]

Thanks, that's interesting. So you verify that if the shadow is coming from a slightly different angle than the observer, the curvature would occur. If the shadow were exactly  coming from the observer's location, the curvature would not occur.

I'd baulk at the idea of 22 degrees being called slightly in this context. I didn't position the observer very precisely in the model (in the 3rd image), just approximately in line with the folder representing the Earth, so there may still be some curvature, but as you can see, it's not discernible. The main point I'm making is that the original image is misleading because the observer is a very long way away from where they could be in reality. In reality, I think they could only be around +/- 1 degrees or so from the centre line joining the light source and the centre of the moon (because I believe the Earths diameter as seen from the moon is around 2 degrees - so half that).

Is there any reason to assume that the shadow is coming directly from the observer other than because that's what RE says?

Well it's more that the intent of the image is to undermine the RE model, so I think in this case, it's fair to accept the parameters of an RE model (for the sake of argument) in order to then attack it.

Your model with a curving shadow seems to disprove Aristotle's claim that only a round object can cause a round shadow. We see a round shadow. It seems appropriate to say that Aristotle was wrong, and that a flat-sided shadow can project as round on a round moon.

I imagine Aristotle took it for granted that his readers would understand that he intended that the observer would be located somewhere on the Earth, not tens of thousands of miles away. Yes this experiment shows that if you observe from a location way out in space, you would see something very different and much more obvious to that observed by someone on Earth.

[robinofloxley]

Doubt whether Aristotle stated anything that is attributed him. Only fragments of his work survive - parts of about 30 manuscripts. Most of what we are told we know of his works comes from medieval manuscript transmission - Corpus Aristotelicum - and from Bekkers interpretations of these interpretations.

 A bit like the Eratosthenes crap , none of whose work survived, whose main source is a book published by a Greek astronomer who we know nothing about but may have lived anytime from 200bc to 2 or300ad if I remember correctly. .

Funny how all the globey bits of lost manuscripts survive.

Yes, but it's the argument which really matters, not who made it. It's convenient to attribute the argument to someone because then you have a label to use and in this case, it's Aristotle. That these ideas have survived at all in any form is a minor miracle. It's much the same with Shakespeare, there are many arguments about who exactly he was and which if any of his plays were actually written by him. And he's much more recent than Aristotle.

[AATW]

Your model with a curving shadow seems to disprove Aristotle's claim that only a round object can cause a round shadow. We see a round shadow. It seems appropriate to say that Aristotle was wrong, and that a flat-sided shadow can project as round on a round moon.

JSS has done a good job of dealing with this, the headline being that Aristotle's claim isn't what you say it is.
But while it is indeed interesting that a straight surface can cast a curved shadow, how does that help FE?
In FE a lunar eclipse is either caused by EA in some way or by a speculated "shadow moon" object.
I'm not aware of a FE model where the earth could be casting a shadow onto the moon to cause an eclipse as in RE because in your model the moon and sun are both above the plane of the earth so clearly the earth can't be getting in between the sun and moon to cast a shadow onto the moon.

[Tom Bishop]

I then moved my observation point to where the folder is to simulate an Earth bound observer. This is what I see now.

According to this the shapes of objects should reflect its actual shape throughout the duration of the eclipse. If the source is a straight edge, it should appear as straight throughout its duration. If the source were a sphere it should likewise appear in that shape throughout its duration.

Why is it, then, that the shape of the shadow changes during the duration of the lunar eclipse?



The arc of this shadow is not consistent. The edge of the shadow on the first image of the Moon from left to right is more curved than the third image.

Another eclipse:



Again, we see that the shadow warps in shape over its duration.

It looks more like the image you posted of a straight-edged shadow being warped onto a sphere:

Your model with a curving shadow seems to disprove Aristotle's claim that only a round object can cause a round shadow. We see a round shadow. It seems appropriate to say that Aristotle was wrong, and that a flat-sided shadow can project as round on a round moon.

You are slightly misquoting Aristotle's argument by leaving out a word. Here is the quote:

“the earth is spherical…in eclipses the outline is always curved: and, since it is the interposition of the earth that makes the eclipse, the form of this line will be caused by the form of the earth’s surface, which is therefore spherical.”

He wasn't saying it's impossible for a flat surface to project a curved shadow.

He is saying that only a sphere would ALWAYS project a round shadow.  If the Earth were flat or some other shape, you would sometimes see a line, or a thin oval down the middle. His argument is that you never see anything but a curved shape, and the only shape that presents a curved surface from all directions is a sphere.

So showing a flat object casting a round shadow doesn't disprove his argument, as that wasn't what he was claiming.

Aristotile is wrong about the implication of a shape being "always" the same too. The shape of the shadow changes over its duration.

"Always" could also mean that the conditions repeat themselves. Aristotile does hardly anything more than speculate that curved objects make curved shadows.

[GreatATuin]

Why is it, then, that the shape of the shadow changes during the duration of the lunar eclipse?



The arc of this shadow is not consistent. The edge of the shadow on the first image of the Moon from left to right is more curved than the third image.

Another eclipse:



Again, we see that the shadow warps in shape over its duration.

It looks more like the image you posted of a straight-edged shadow being warped onto a sphere:

The arc of this shadow is not consistent. The edge of the shadow on the right is more curved than it is on the left.

See a pattern?

[JSS]

Your model with a curving shadow seems to disprove Aristotle's claim that only a round object can cause a round shadow. We see a round shadow. It seems appropriate to say that Aristotle was wrong, and that a flat-sided shadow can project as round on a round moon.

You are slightly misquoting Aristotle's argument by leaving out a word. Here is the quote:

“the earth is spherical…in eclipses the outline is always curved: and, since it is the interposition of the earth that makes the eclipse, the form of this line will be caused by the form of the earth’s surface, which is therefore spherical.”

He wasn't saying it's impossible for a flat surface to project a curved shadow.

He is saying that only a sphere would ALWAYS project a round shadow.  If the Earth were flat or some other shape, you would sometimes see a line, or a thin oval down the middle. His argument is that you never see anything but a curved shape, and the only shape that presents a curved surface from all directions is a sphere.

So showing a flat object casting a round shadow doesn't disprove his argument, as that wasn't what he was claiming.

Aristotile is wrong about the implication of a shape being "always" the same too. The shape of the shadow changes over its duration.

"Always" could also mean that the conditions repeat themselves. Aristotile does hardly anything more than speculate that curved objects make curved shadows.

You are misreading his quote again.

He said "the outline is always curved" not that it is "always the same" as you misquoted.

He is not speculating that "curved objects make curved shadows". 

"Curved" and "sphere" are not the same thing. You can't replace words in a quote and then argue against it.

[Tom Bishop]

You are misreading his quote again.

He said "the outline is always curved" not that it is "always the same" as you misquoted.

He is not speculating that "curved objects make curved shadows". 

"Curved" and "sphere" are not the same thing. You can't replace words in a quote and then argue against it.

Aristotile is clearly implying that the shape of the shadow on the moon reflects the shape of the projecting source. He is wrong about that. It's not "always" the same curve. At some parts it's also a "flattened curve," or perhaps part of a larger circle. It's different. It tends to flatten out. Aristotile did not really do any experiments on his statements.

The OP experimented and found that, from a certain RE position near the shadow edge, that the shapes of objects should reflect their true shapes on the Moon. Since the shadow warps in shape, we can see which explanation fits better.

[JSS]

You are misreading his quote again.

He said "the outline is always curved" not that it is "always the same" as you misquoted.

He is not speculating that "curved objects make curved shadows". 

"Curved" and "sphere" are not the same thing. You can't replace words in a quote and then argue against it.

Aristotile is clearly implying that the shape of the shadow on the moon reflects the shape of the projecting source. He is wrong about that. It's not "always" the same curve. At some parts it's also a "flattened curve," or perhaps part of a larger circle. It's different. It tends to flatten out. Aristotile did not really do any experiments on his statements.

The OP experimented and found that, from a certain RE position near the shadow edge, that the shapes of objects should reflect their true shapes on the Moon. Since the shadow warps in shape, we can see which explanation fits better.

I'm afraid you're making the same mistake again.

Aristotile said: the outline is always curved

Tom said:  It's not "always" the same curve

You continue using the word "same" but he never made that claim.

Nobody is saying a flat shape can't make a curved shadow on a round object. The argument is only a sphere always makes a curve from any angle. That's just geometry.

Of course the shape of the curve is going to change as it's projected over different parts of a sphere. The only way it would always be the same is if the MOON was flat.

[Tom Bishop]

I'm afraid you're making the same mistake again.

Aristotile said: the outline is always curved

Tom said:  It's not "always" the same curve

You continue using the word "same" but he never made that claim.

Nobody is saying a flat shape can't make a curved shadow on a round object. The argument is only a sphere always makes a curve from any angle. That's just geometry.

Aristotile fails to document any experiments that he made with flat edges and round moons. You can't claim that he did these experiments. Aristotle has a well-known reputation for performing NO experiments for his science.

Aristotile says that since the shadow is always curved, the Moon is curved. However, the shape of the shadow is not always the same curve. It flattens out. Since the shadow changes shape, this puts his statements regarding the shadows being the true shape of the objects into question.

Of course the shape of the curve is going to change as it's projected over different parts of a sphere. The only way it would always be the same is if the MOON was flat.

Read the OP again. At a certain position near the light source, like in RE, straight line shadows maintain a straight line. Shapes maintain their shape on the Moon and do not warp.

Since in the real eclipse the shape of the shadow on the Moon does warp, this falsifies the explanation given.

You can't have it both ways.

[JSS]

Aristotile fails to document any experiments that he made with flat edges and round moons. You can't claim that he did these experiments. Aristotle has a well-known reputation for performing NO experiments for his science.

When did I ever claim he did experiments? What experiments does one conduct on the moon, which is 250,000 miles away. I'm curious what experiments using round moons you would suggest to prove the shadow is or isn't caused by a sphere.

One of the physical experiments I recall, was landing on it. But that was not possible back in his day.

[AATW]

Aristotile says that since the shadow is always curved, the Moon is curved. However, the shape of the shadow is not always the same curve. It flattens out. Since the shadow changes shape, this puts his statements regarding the shadows being the true shape of the objects into question.

I suspect the shape of the shadow on the moon is explained by the fact that a spherical object (the earth) is casting a shadow onto another spherical object (the moon).
I don't think it's intuitive what that would look like, it needs a bit of modelling, but what of it?
Do you think that Aristotle being wrong about something (if he was) nearly two and a half thousand years ago is a point for FE?
In FE it's not the earth which is casting the shadow on to the moon in the event of a lunar eclipse anyway.
I'm not sure what you're actually getting at here.

[Tom Bishop]

Do you think that Aristotle being wrong about something (if he was) nearly two and a half thousand years ago is a point for FE?

Considering that modern scholars and scientists continue to cite Aristotile as evidence for the earth's spericity, yes.

Recently, several scholars highly praised Aristotle’s empirical arguments. Stephen Hawking admired Aristotle for delivering “two good arguments for believing that the earth was a round sphere rather than a flat plane.”⁹ [Professor of Philosophy] Daniel Graham stated, “Aristotle defends and indeed proves the sphericity of the earth in the De Caelo with adequate scientific arguments.”¹⁰ [Theoretical Physicist] Carlo Rovelli, in a paper on Aristotle’s physics, wrote about Aristotle’s most famous argument, which used the shape of the shadow on the moon during a lunar eclipse to prove the earth’s sphericity: “This proves empirically, and very solidly indeed, that the earth has a shape that is (approximately) spherical.”¹¹ ”

When did I ever claim he did experiments?

You didn't and couldn't. It is well known that Aristotile did not perform experiments. He just said things:

" In the past scientists did not use the scientific method we use today. For example, Aristotle was a great thinker in ancient Greece. He carefully observed and tried to check things for himself. But he also wrote things down that had not been proven by the kind of careful experiments scientists complete today. Sometimes Aristotle was wrong. But his work was so respected in Europe that 1,000 years later few people doubted what he had written. Until the 1500's university students were not supposed to question what Aristotle and other ancient thinkers had written. They were just supposed to memorize it. Experimenting and checking things were simply not done. ” —Suzane Glass, Analyze This!: Understanding the Scientific Method

No experimentation. Just human 'logic' and 'intuition'.

What experiments does one conduct on the moon

I'm pretty sure candles and shadows and spheres existed in Ancient Greece. The OP shows experiments which may imply that that a round shadow doesn't necessarily mean that it's from a round shape.

[robinofloxley]

Read the OP again. At a certain position near the light source, like in RE, straight line shadows maintain a straight line. Shapes maintain their shape on the Moon and do not warp.

Since in the real eclipse the shape of the shadow on the Moon does warp, this falsifies the explanation given.

You can't have it both ways.

The experiments (both the original and my own) are not especially true to life. For example, in reality, the observer is going to be stationary on the earth, whereas in these experiments, the observer is stationary and the earth (the folder) moves back and forth in front of a stationary light source. Furthermore, I don't think anyone has ever suggested a rectangular folder is a sensible model for the earth.

Probably a more realistic model would be to replace the folder with a stationary sphere of a sensible size, locate the observer on the sphere and move the light source to create a moving shadow. Something easier to do in a model than with real objects in a real room. My models are simply intended to mimic a real experiment as documented in the Wiki.

Aristotle's basic point surely is that only a sphere can be rotated about any arbitrary axis and still cast a shadow of exactly the same shape. Certainly any flat surface, whether circular or some other shape, when put in front of a light source and projected, will create a variety of shadow shapes as it is rotated about various axes.

How these shadows then interact with a spherical object (the moon) is interesting, difficult to visualise, but perfectly possible to model.

However my original point is simply that the image in the Wiki is misleading and unrealistic due to the placement of the light source, the folder (representing the earth), the observer and the moon globe. Because it is misleading, I don't believe (on its own) it is good enough evidence to dismiss Aristotle's ideas.