Me And My Shadow

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This diagram, from "Solar Geometry
On The Flat Earth," shows key points
in black and distances in red.

One evening, when the sky was clear, I went outside shortly after dinner and found a flat spot. Then I drove a stake into the ground, using a level to make sure it was vertical.

I measured the distance (H) from the top of the stake (T) to the ground (B), and recorded it in my notebook.

Then, at irregular intervals, I marked the end of the stake's shadow (P) and measured the length of the shadow (L). After each measurement, I recorded the time and the new value of L.

As the evening went on, the shadow grew longer and L grew larger. But I didn't pay much attention to the actual numbers. I just wrote them in my book.

After a while, the shadow got so long that I couldn't measure it properly, so I started using a shorter stake. I measured the new value of H and recorded it along with the time. Then I went back to measuring and recording L.

I stopped when the sun was so low in the sky that I couldn't see the shadow clearly. In this way I made about a dozen observations over a two-hour period.

~~~

Later, I typed my notes into a spreadsheet and ran a bit of math. Mostly I wanted to see how the ratio L/H changed over time. L/H is very interesting under the flat earth model, where the sun (S) is always 3000 miles (K) above the earth (M). It's interesting because if we multiply L/H by 3000, we get Q, the distance between M and P in miles.

When L/H = 1, Q is 3000. When L/H = 2, Q is 6000, and so on. So this is an easy way to figure out the distance to the place directly below the sun, and to the sun itself, under the flat earth model.

When I started measuring, L/H was slightly more than 3. So Q was more than 9000, and M, the spot on the earth directly below the sun, was more than 9000 miles away from me.

When I stopped, L/H was more than 14. According to the flat earth model, Q was more than 42000, which means that M was more than 42000 miles away from me.

This result poses a bit of a problem for the flat earth model, because I did my experiment in the summer, and I live the North of the equator.

~~~

Why is this a bit of a problem? The radius of the equator, the distance from the North Pole to the equator, is about 6250 miles. Therefore the diameter of the equator is about 12500 miles.

When it's spring or summer in the North, the sun is circling inside the equator, according to the flat earth model. That is to say, the sun is traveling in a circle whose diameter is less than 12500 miles.

As the sun circles in the sky, M traces a circle on the surface of the earth, and the diameter of that circle is also less than 12500 miles.

Remember what we mean by diameter: Given any point on a circle, if we drew a line through the center of the circle and extended it until it met the circle again, the length of that line would be a diameter.

The two points where the diameter intersected the circle would be as far apart as any two points could be, if they were both on the circle.

So the distance from any point on the circle to any point inside the circle must be less than the diameter.

And therefore Q must be less than 12500 -- all day, every day of spring or summer, for every observer North of the equator.

Since I am North of the equator, Q must be less than 12500 for me, too. Therefore, M, the spot on the earth's surface directly under the sun, must be less than 12500 miles away from me, according to the flat earth model.

But I used the same model to interpret the data I had collected, and it told me that when I stopped measuring, M was more than 42000 miles away. How can this be?

~~~

Well, I lied. This is not actually "a bit of a problem." M cannot possibly be less than 12500 miles away and more than 42000 miles away at the same time, so this -- for me -- is conclusive proof that the flat earth model is incorrect.

I can say with confidence that the flat earth model does not explain the evidence that I observed. I can even say the evidence undermines the model.

I have a handle on epistemology. I am on the path of evidence. I have seen strong evidence, evidence that I collected myself, and I trust its accuracy.

Therefore, I believe I am justified in rejecting the flat earth model. But this does not mean that you would be justified in doing the same.

I have described an easy way for you to do an experiment of your own. You can collect your own evidence. You can make up your own mind. If you can replicate my results, you too can reject the flat earth model with confidence.

If you live South of the equator, the numbers are different. The sun moves in larger circles during your summer. And you are farther away from the center of the solar circles. But no matter how far South you live, M could never be 42000 miles away from you, either. So if you can replicate my measurements, you too can confidently reject the flat earth model.

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Solar Geometry On The Flat Earth

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No matter when you look, the sun is directly above one and only place on earth, and in that place an object standing upright will cast no shadow.

Suppose we put a marker at that place, and we call that place M. Since the sun is always moving, M is always moving, too. But at any given time, M is the place directly below the sun.

In the diagram at right, S represents the sun, M marks the place directly below the sun, and the line through M and P represents the surface of the earth.

A vertical object in any place other than M will indeed cast a shadow, and this diagram (which is clearly not to scale) shows the geometry of that shadow. T represents the top of the object, B represents the bottom of the object, and P marks the end of the object's shadow.

And my questions for today are: Can we determine the distance from M to P? And if so, how can we do it?

The answer to the first question is, "Yes!" But the answer to the second question depends on the shape of the earth. With the Globe Earth model, it's fairly difficult. But with the Flat Earth model, it's easy.

It's easy because we can use the geometry of similar triangles. As the diagram shows, angle SPM is the same as angle TPB, and SMP and TBP are both right angles, 90 degrees each. Therefore, angle MSP and angle BTP are equivalent, and triangle SMP is similar to triangle TBP, which means the corresponding sides of these triangles are proportional.

We can simplify things a bit here by introducing a few abbreviations:

As shown in the diagram at right, we can let:

H = the height of the stake above the ground, or the distance BT.

L = the length of the stake's shadow, or the distance BP.

K = the height of the sun above the earth, or the distance SM.

Q = the distance from the mark under the sun to the end of the shadow, or MP.

Because the two triangles are similar, Q/K = L/H.

If we we multiply both sides of this equation by K, we can see that Q = K*L/H.

We can measure L. We can measure H. According to the Flat Earth model, K is constant. And we have a simple equation for Q in terms of L, H, and K.

Therefore we can easily find Q. And this is what I decided to do.

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Elliptical Thinking

Previous: "Guess The Number"

source: infactcollaborative.com

According to the flat earth model, the sun travels in circles, 3000 miles above the earth. And the circles vary in size over the course of a year, which accounts for the seasons. But it always takes exactly 24 hours for the sun to complete a circle, which accounts for day and night. And the center of the circle is always directly above the center of the earth, which we call the North Pole.

Since the earth is a plane and the sun is always the same distance above the earth, we can deduce that the sun moves in another plane, that the plane of the sun is parallel to the plane of the earth, and that the distance between these two planes is 3000 miles. Otherwise the sun would come closer to the earth, and/or move farther away, as it circled around.

As we know from experience, a circle observed from above or below doesn't appear perfectly round unless the observer is directly above or below the center of the circle.

From any other vantage point, the circle appears to be an ellipse. We can prove this is so, and see why, using projective geometry.

Projective geometry is the mathematics behind perspective graphics, which allows artists and computers to create realistic-looking 2-dimensional images of 3-dimensional objects.

Photographs look realistic if the lens preserves this geometry. Paintings and sketches look realistic if the artist can capture this geometry. And computers can generate realistic-looking moving graphics in real time because the arithmetic required by this geometry is very simple.

And that means: we can use this geometry to test the flat earth model.

We don't just know that the path of the sun will appear elliptical. We can determine precisely what that path will look like.

In other words, we can easily calculate the apparent position of the sun, as seen on any day of the year, at any time of the day, from anywhere on earth.

And this suggests a simple experiment. We could calculate where the sun would appear at a certain time, to an observer in a certain place.

Then we could put an observer in that place at that time, and have him measure and record where he sees the sun.

Or we could just go to that place at that time, look at the sky, and see for ourselves.

Either way, the experiment would involve the comparison of a prediction against an observation.

Of course, an experiment involving a single prediction and a single observation would not amount to a fair test. We would need a series of predictions, and a series of observations.

~~~

All these thoughts ran through my head, and I thought: Why not? What's the harm?

So I decided to build a mathematical model of the flat earth theory, generate some predictions, and test them.

This was my first hint that I was becoming delusional.

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Sunrise, Sunset

Previous: Who Changed the JFK Assassination?

source: Active Rain

The sun rises in the East and sets in the West. Or at least that's what everybody says.

And this is true. But it's not the whole truth.

The sun does appear to move in predictable daily patterns, but the whole truth is quite a bit more interesting.

We say the sun "rises" because it appears gradually over the horizon in the morning.

We see the morning sun in the eastern sky, but it doesn't rise at the same point on the horizon every day. The spot where the sun rises depends on where you live, and the time of year. And that point is not necessarily due East of you, although it might be, once or twice a year, depending on where you live.

The morning sun appears to climb higher and higher in the sky, away from the eastern horizon. Its path appears to take it on an arc directly over your head, or to the North or South of a point directly over your head, depending on where you live and the time of year.

In the Northern hemisphere, the sun climbs to higher and more southerly positions in the sky until mid-day, when it reaches its highest and most southerly position.

If the Southern hemisphere, the sun climbs to higher and more northerly positions in the sky until mid-day, when it reaches its highest and most northerly position.

The closer you are to the equator, the less the sun appears to move to the North or South, and the closer the sun appears to move directly over your head. Again, this depends on the time of year, and where you live.

In the afternoon, the sun begins to descend. It moves through lower and more westerly positions, until the evening, when it appears to "set," gradually disappearing under the western horizon.

The sun doesn't set at the same point on the horizon every evening. The spot where the sun sets depends on where you live, and the time of year. And that point is not necessarily due West of you, although it might be, once or twice a year, depending on where you live.

The sun is so bright that we can hardly ever look at it directly, so most of the sunlight that we see reaches our eyes indirectly. And we hardly ever notice it.

But we do notice indirect sunlight when the sun itself is obscured by clouds, or below the horizon. Indirect sunlight is very striking before sunrise or after sunset, for example.

The size and color of the sun also appear to change in predictable daily patterns.

During most of the day, the sun appears to be yellow, or almost white, and it is relatively small compared to its size at sunrise and sunset, when it appears larger and a bit darker, throwing fiery shades of orange and red across the sky.

Among all cosmological phenomena, the daily progression of the sun in the sky is by far the most important, not only to humans but to all life on earth; not only now but as far back in our history as you care to go.

It is also by far the most easily observed. We can all see it every day. We don't even need a telescope.

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The Flat Earth Model

Previous: Who Changed "Field of Dreams"?

source: Flat Earth Society

Contrary to what you have been told, the earth is flat.

It is not "a ball" or "a globe" or "an oblate spheroid".

It is a flat circle, like a big pie plate.

It is not spinning on its axis or orbiting around the sun.

It is still. It is motionless.The sun moves but the earth does not.

You may ask how I know this. I know this because I saw it on YouTube.

What we call the North Pole is at the center -- the middle of the pie. What we call Antarctica is a wall of ice surrounding the ocean -- the outer rim of the pie plate. What we know as the South Pole is a myth.

What we call the Northern Hemisphere fits in a relatively small circle in the middle of the pie. The perimeter of this circle is what we call the equator.

What we call the Southern Hemisphere is a larger ring around the smaller circle. The inside edge of this ring is the so-called equator; the outside edge is what we call Antarctica.

The imaginary lines that we call longitude radiate outward from the center of the pie to the outer edge. These lines meet only once: at the so-called North Pole.

They do not curve around and meet again, as shown on a globe. And even if they did, they couldn't meet at the South Pole. On the flat earth, there is no South Pole.

The imaginary lines that we call latitude run in concentric circles around the so-called North Pole. Circles smaller than the equator are called North latitude. Circles larger than the equator are called South latitude.

The sun is not, as you have been told, 93 million miles away. It is only about 3000 miles above the earth.

The sun moves in circles of varying sizes. The variations in size account for the seasons.

In the so-called Northern Hemisphere's spring and summer, the sun moves in circles smaller than the so-called equator. The sun's circle is smallest at the Summer Solstice, after which the circles begin to get larger.

In the so-called Northern Hemisphere's fall and winter, the sun moves in circles larger than the so-called equator. The sun's circle is largest at the Winter Solstice, after which the circles begin to get smaller.

The sun's circles never get small enough to melt all the ice at the so-called North Pole, or large enough to melt the ice that surrounds the ocean. This explains why there is a small frozen area in the middle and a large frozen area around the edge.

The sun completes one circle every 24 hours, accounting for day and night.

The light of the sun is not powerful enough to travel very far, so when the sun's movement takes it far away from you, you experience night. When the sun comes close enough so that its light can reach you again, you experience day. And so on.

This may strike you as utter nonsense, but many people believe it.

If you look around YouTube, you will find hundreds (or thousands) of hours of videos made by people who believe all this and much more.

They are now dedicated to spreading the word, freeing humanity from the shackles of its false belief that the earth is a spinning ball.

Or so they say.

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"Funnier Than Robin Williams"

Previous: Dr. Fetzer And The Flat Earth

source: robin-williams.net

As you probably know, if you use YouTube for a while, it starts to suggest videos that might interest you.

I think it must have a database that tracks which videos have been accessed and from where, and some code that drills through the database to find out where your interests lie, and tries to figure out how you can be induced to waste as much time as possible.

The database must be getting bigger all the time. And, unless I am mistaken, the code is gradually being refined as well. So YouTube keeps getting better at making suggestions.

I've never paid much attention to any of this, but I got thinking about it after I watched Dr. Fetzer's podcast about the flat earth, when YouTube started suggesting other flat earth videos.

I figured, "Richard Pryor and George Carlin are both gone, and I haven't seen anything this funny in a long time. So why not? What's the harm? Where am I going to find anything funnier?"

To be clear: the flat earth videos that I watched are not intended to be funny. The people who made them are all very serious. And that's what makes them hilarious. They're better than bad 'B' movies. There's an unlimited supply. And it's all free, right on my sidebar.

So I watched a handful of them, and I laughed. I told my sons about them, and we all laughed. One of the boys said, "That's funnier than Robin Williams!" and we laughed even harder.

Later I told my wife, who gave me a worried look. "I'm gonna have to keep an eye on you," she said.

"Don't worry," I replied. But her expression didn't change.

I said, "I've spent hours listening to John Marciano on American history, David Ray Griffin on 9/11, Doug Horne on the Assassination Records Review Board, and Michael Parenti on just about everything. I'm pretty well grounded in reality, but every now and then I need a break. And I can't find anything funnier." But her expression still didn't change.

"You don't have to worry!" I insisted. "It's all in fun!"

And it was all in fun, until YouTube started suggesting videos about The Mandela Effect.

"What is The Mandela Effect?" I wondered as I clicked on the sidebar.

That was one small step for a mouse, and a giant leap on the path to delusion. But I didn't realize this until later.

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Dr. Fetzer And The Flat Earth

Previous: Expedience And Delusion

source: What Happened On The
Flat Earth This Week?

It's fine to say that all points of view ought to heard; that in a "marketplace" of free ideas, the good ideas will rise and the poor ideas will fall, strictly on merit; that there is no harm in airing the occasional wacky idea. But, as with so many other grand principles, it's easier said than done, honored in the breach, the exception that proves the rule.

In the course of his research, Dr. Fetzer has met many intelligent researchers, and more than one of them have encouraged him to look into an old claim which is recently gaining new popularity, namely that the earth is not a spinning ball but a motionless plane.

And I have to give him credit for his reaction: Rather than dismissing the notion out of hand, as I would have done, Dr. Fetzer said, "Find me a guest who can present this point of view succinctly, and I'll give him half an hour on my show."

Then he did a show in which the first 30 minutes were dedicated to his guest's assertions about the shape of the earth, the movements of the sun, moon, and stars, the evidence supporting the "flat earth model," and some of the implications of this hidden "truth."

To my amazement, Dr. Fetzer didn't interrupt. He never said a word until the guest had finished. Then he presented a brief rebuttal, giving the names, dates, and descriptions of experiments which established the curvature of the earth, its rotation about its axis, and its orbit around the sun -- more or less what you might expect from a man who has spent most of his adult life teaching university-level courses on the history of science.

I can't say that Dr. Fetzer's rebuttal made any impact on his guest, nor that the guest's presentation made any impact on Dr. Fetzer. But that podcast had a profound impact on me, and it's no exaggeration to say I could not have become delusional without it.

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