Claim: Panama Canal plan proves a flat earth

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This meme shows a planning drawing of the Panama Canal, and implies that since the mean sea level on both sides of the canal is the same, the earth must be flat:

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A higher resolution image of the plan is:
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Is the fallacy here just that "mean sea level" is being misinterpreted? I'm trying but struggling to formulate a concise description of why this drawing does not imply a flat earth.
 
The combined width of all three divisions is ~50 miles. If this plan was drawn to scale, the left level would be angled up 0.36⁰, the center would be horizontal, and the right would be angled down 0.36⁰. The angles are so small because Earth is really big, and 50 miles is just a small fraction of its circumference. I'm sure it'd be a pain to draw, and it would not convey any useful information (you probably wouldn't even notice it with the naked eye). So the surveyor draws the level straight, even though it's not.

In reality, the sea level is defined as a level of equilibrium pressure, and it's spherical (Archimedes knew this!). Because of the tides, and climate changes etc., the oceans don't really conform to it, it's just something that surveyors use, calling it a "datum". But obviously, because all oceans are connected, the actual sea levels everywhere don't vary much from this datum.
 
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tl;dr if you build a canal to a level (historically, mean sea level; today, WGS 84), that canal is going to be curved, because the level is curved. This is true even if the construction drawing shows the level as straight for simplicity.

P.S.: You can see some beautiful pictures of curved level lines at https://www.metabunk.org/threads/beautiful-photographs-that-show-the-earths-curvature.11456/ .

P.P.S.: If you'd like to find out what engineers do when they need to build a long tube that is straight (not level), look up the precision alignment of the LIGO 4km arms. LIGO stands for Laser Interferometer Gravitational-wave Observatory.
 
What “level” really means is conformance with a gravitational equipotential surface. For a spherical gravitational field that surface is spherical. since this drawing is measured relative to this surface it will look “flat”. The curvature is baked into the mean sea level line.

Keep in mind that flat earthers discount even the most basic physics — forces — when discussing their subject so there will just be no convincing them ever.
 
It's remarkable how deep their denial will go. For example: They deny that there is such a thing as Inertia (!)

FE'ers will claim that if you jump straight up off your moving skateboard you will land on the ground because you will fall straight down while the skateboard continues moving forward out from underneath you.

- This is easy to disprove by getting on a skateboard and trying it. But they don't.

- They don't question why the skateboard would keep moving. (cough*inertia)
 
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It's interesting to contemplate an idea developed by Aristotle - or perhaps a more widely held contemporary idea that he agreed with and was reporting.

In this model, terrestrial matter has an innate linear motion. That motion is toward the center of the Earth. Matter on the surface of the Earth is still trying to move toward the Center; it is just impeded by other matter. It's being held back. Like a man holding back a goat by pushing against its head.

The innate linear motion of matter can be translated into a lateral motion when there is a clear path to an area that is closer to the Center. A landslide is an example. You can see that on the grand scale this would lead to a spherical Earth. On the local scale, Earth will have a rough surface. On the local scale, there are areas that are closer or farther away from the Center. And that is a part of the lamentable imperfection of the Earthly realm.

Water flowing down hill is an example of the innate linear motion of matter being translated into a lateral motion. Water is taking the only path it can toward the center of the Earth. If a lake has no outlet, the innate linear motion of water toward the center of the Earth will hold it there. If you open a canal that leads to an area that is closer to the center of the Earth, the innate linear motion of water toward the Center will be translated to a lateral motion toward that area that is closer to the Center.

The innate linear motion of water toward the center of the Earth will not be translated to a lateral motion toward a distant part of the Earth's surface just because it is "around" the circumference of a sphere. That's not the nature of the geometry. It is only the distance to the center of the Earth that has a geometric importance. It's the radius not the circumference.

One can see an analogy to the modern concept of sea level.
 
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It's remarkable how deep their denial will go. For example: Inertia.

FE'ers will claim that if you jump straight up off your moving skateboard you will land on the ground because you will fall straight down while the skateboard continues moving forward out from underneath you.
There's a common physics demonstration called "ballistics cart" that disproves the claim; you can find numerous videos of that on the web. Basically, a moving cart shoots a ball straight up that lands back down exactly on the moving cart.

Source: https://m.youtube.com/watch?v=nAifrGXkE2k
 
It's interesting to contemplate an idea developed by Aristotle - or perhaps a more widely held contemporary idea that he agreed with and was reporting.
Do you have a source for this?
And how do tides fit with that?

Aristotle's "innate force" is similar to FE's mantra "water seeks its level". But that's wrong; it is instead true that water follows any force, innate or not. If water wanted to go down always, soap bubbles would not be possible. Water kept in a bucket swung on a line, held by centrifugal force (actually inertia) would not be possible. Lawn sprinklers would not work. And of course we have video of blobs of water in freefall aboard the ISS.
 
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