PROOF POSITIVE OF THE SHAPE OF THE EARTH

USE YOUR BRAINPOWER!

It is disappointing when I encounter people who don’t want to put much, if any, effort into thinking about anything outside their habitual comfort zone. It seems that most people would rather watch Television than read a non-fiction book, even if the book contains world-changing ideas and there is evidence that too much TV can cause brain atrophy. This may sound like a complaint, and I don’t want to be a complainer, I just want to spur people on to think just a little bit outside the box. Is it too much to ask people to try to understand a new paradigm, or why the old one doesn’t work? Is it too much to ask someone to think beyond one or two logical steps? Too often I’ve heard: “Oh, that makes my head hurt! I’m not a genius you know!

But you may be smarter than you think. Why not try to use more of the brain power you have? Psychologists tell us that most people never use more than 10 to 20 percent of their brain power, so you could be anywhere from five to nine times smarter than you think you are, in fact, you may be smarter than your IQ test indicates. IQ experts used to think that everyone is born with a fixed Intelligence Quotient that will stay constant throughout your life, except for a possible decrease in case of injury and the eventual inevitable decline in old age. We now know, that that is not true. The experts are now saying that you can increase your IQ by perhaps as much as 10 to 15% by putting your brain to work learning a new language or exercising it by solving puzzles of different types. So, if you have an IQ score of 120 on a standard IQ test, by working hard, you might increase it to 132 to 138, which is enough to get you into MENSA! And if you have an IQ of 138 to start with, with hard work, you might raise it to 152, enough to get into ISPE. The average IQ of PhD recipients is about 130, and IQ experts have estimated Einstein’s IQ at about 160. Would you like to be smarter than the average PhD? Or smarter than Einstein?

It doesn’t take a genius to figure out that people who ascribe to some of the most outlandish false theories and/or conspiracy theories, are either pulling your leg, are not very bright, or are just too lazy mentally to follow the logic that clearly disproves them. The flat-earth hypothesis is a prime example of a false theory that you can disprove yourself in a few minutes, if you want to. The idea that the Earth is flat except for irregularities like mountains and valleys, of course, was common in most primitive cultures, because to the casual eye, it looks that way. In modern times, a number of relatively uneducated writers and preachers have argued that the Earth is flat. The Flat-Earth Society traces its roots back to an English writer named Samuel Rowbotham, who argued for a flat Earth based on the results of some experiments that failed to find any curvature of the water surface over the length of a drainage ditch in England. He published a book titled “The inconsistency of Modern Astronomy and its Opposition to the Scripture.” The ‘proof’ put forth by Rowbotham and others who supported the flat earth theory, was ‘proved’ back then by statements like:

“There are rivers that flow for hundreds of miles towards the level of the sea without falling more than a few feet — notably, the Nile, which, in a thousand miles, falls but a foot. A level expanse of this extent is quite incompatible with the idea of the Earth's convexity. It is, therefore, a reasonable proof that Earth is not a globe.”

Anyone with a rudimentary acquaintance with logic, will realize that this is not a proof at all, but simply a feasibility argument. The concept behind this reasoning is that, if the Earth is round like a ball, and water seeks the lowest possible uniformly flat level, then a convex curvature would require that the water run uphill to the half-way point in its route to the sea, and downhill the rest of the way, and everyone knows that water always runs downhill. If the Earth is relatively flat overall, there would be no ‘hump’ of curvature to cause a problem. But this is not proof of a flat Earth, because the problem is also resolved if the Earth is actually spherical, and gravity, which causes water and everything else to seek the lowest possible level, pulls everything toward the center of the sphere. And Sir Isaac Newton, and others, showed that the gravitational pull of any spherical object, whether a cannon ball or the moon is always toward the center. So there are two possible ways to explain why the Nile flows tranquilly to the Mediterrean, making the statement no more than a feasibility argument.

The flat-earth nuts (I call them nuts advisedly, or maybe even lovingly, because I know that some of them are just enjoying poking fun at the scientific establishment, which I also enjoy) even have websites and a You-tube video that boasts 20 proofs that the Earth is flat! But every one of the 20 ‘proofs’ are bogus because they either ignore some well-known and easily provable fact, or they are based on unproved and unprovable assumptions. So I could publish sound counter arguments refuting each and every one of the so-called proofs. But I don’t need to waste my time doing that, because there is an easy demonstration anyone can do that proves unequivocally that the surface of the Earth curves between Denver and New York City by an amount consistent with a sphere having a circumference of approximately 24,900 miles. And this is a proof that anyone can perform. I’ve published it twice, but I’ll copy it here again for the readers’ convenience:  

All you need to do is have someone in New York City and someone in Denver call you on the same day, exactly when the sun comes over the horizon at their respective locations. (Notice that this eliminates any confusion that might arise from time zone differences because you are noting the times of the calls on your clock.) If the Earth’s surface is flat, the calls will come virtually simultaneously, because there are no mountains between Denver and New York high enough to block the line of sight. If the Earth’s surface is curved, the call from Denver will come in later than the call from New York, because the sun will be hidden behind the curvature of the Earth until it reaches the height necessary for it to be seen in Denver. If the Earth is spherical, with a circumference of about 24,900 miles, the calls will be about 2 hours apart. This is easily calculated, but completely unnecessary for the demonstration.  

If you get two friends to do this, you will find that the time between the two calls will actually be about 2 hours, give or take a few minutes depending on exactly where your friends are located in the Denver and New York areas. I can say this with great confidence because I effectively done the experiment myself. I have spent time in both Denver and New York City, and have friends in both areas, and we find that it is always necessary to allow that same amount of time difference if you are in one area and want to connect by telephone or skype at a specific time with someone in the other area. If the Earth were flat, the sun would be seen to rise at the same time in Denver and New York, but would reach the zenith (straight overhead) about 2 hours apart in in the two locations, Denver 2 hours behind New York. So the diurnal time difference would vary during the day, from zero to 2 hours, making synchronizing watches for a given time to schedule a phone call between the two locations very difficult. Obviously this is not the case; the time difference between similar solar inclinations in relation to the horizon in the two locations is always the same. Conclusion: the surface of the Earth between Denver and New York is effectively the surface of a sphere. Now that wasn’t hard was it?

Now, concerning government and NASA conspiracies; there is no doubt that they often lie to us. But it’s not to keep us from knowing that the Earth is flat! It’s just that the Flat-Earthers, in order to support their hypothesis, have to go to great lengths to explain the many things that have to be accounted for to maintain the illusion that the surface of the Earth is flat, and explaining away NASA photos showing the Earth’s curvature is just one of them. The Earth is definitely and provably an oblate spheroid spinning in space. Anyone who denies it is either delusional, not capable of following simple logic, or enjoying seeing how many people they can fool with confusing, half-baked arguments.

THE FLAT EARTH HYPOTHESIS: SEEING IS BELIEVING!,

THE FLAT EARTH HYPOTHESIS: SEEING IS BELIEVING!

Thanks to a Facebook friend, I am going to take this opportunity to make what I think are some very important points about seeing, believing, and the scientific paradigm of the mainstream establishment. People all too often don’t question the prevailing scientific paradigm, because, after all, it brought us television, computers, smart phones, etc., etc., …and mainstream scientists have spent virtually their entire adult lives studying science, so surely, they must know what they’re doing, right? Wrong! They are just as fallible as anyone, and because of academic specialization, they tend to have tunnel vision and are often not very open minded.

This Facebook friend deserves credit for bringing up the flat-earth hypothesis is spite of the ridicule he’s sure to get from people who think they know the Earth is round.  He deserves even more credit for having an inquiring mind, and not just accepting what the scientific establishment says, but wanting to see the truth for himself. It is very easy to just laugh at him and say, surely no one in this day and age really believes that the Earth is flat!  That’s been disproved ages ago! The Earth is just one of the planets orbiting the Sun. Hasn’t he seen Star Trek, or Star Wars?  Of course Star Trek, Star Wars, and other science fiction movies that show the Earth like a ball suspended in space, were not actually shot from outer space, those images are just special effects. And NASA could certainly produce such films and pass them off as real if they actually have not gone to the Moon, or sent an unmanned probe to Mars.

There may or may not be a massive conspiracy and cover-up going on; maybe we’ll get to that later, but first, let’s consider my FB friend’s position: He has taken the position that seeing is believing and has stated that the Earth looks flat from 100,000 feet up. Furthermore, he contends that the fact that no curvature can be seen in the horizon from that altitude proves that the Earth is actually flat because, he believes that if the surface of the Earth were curved as scientists say it is, you would be able see that curvature from 100,000 feet. But, is that true? The Flat-Earth people apparently believe it is, and it sounds right. But, if we’re going to reason this out, we can’t just accept it as true because it sounds right, we need to think of it as a hypothesis and actually prove it either true or false.

Seeing is Believing

The belief that, if the surface of the Earth is curved, then we should be able to see that curvature from 100,000 feet up is based on the idea that light always travels in a straight line, at a constant speed. It turns out that this is not always true. It is usually true in everyday circumstances, like looking across the room or down the street, but looking at the horizon which is a great distance from you, from 100,000 feet (18.9 miles) up, is different. There are several physical phenomena that cause light to slow down and follow a curved path and significantly affect what we see when looking at the horizon from 100,000 feet up. These phenomena are either too minor to be noticed over short distances, or non-existent in our normal environment. The most relevant one in this case is refraction.

Refraction is what makes a straight straw in a glass of water look bent. It happens because light moves more slowly in a dense medium. In our case, the atmosphere of the Earth is like the water in the glass, except the atmosphere is most dense at the surface of the Earth and thins out to nothing at about 327,360 feet. So, light coming to the eye of an observer at 100,000 feet from the horizon is curved as it passes through the atmosphere, making the horizon look even farther away than it really is. This makes the horizon look flat until you get high enough that, looking straight down, the Earth will look round regardless of which model is correct.

Why is this so? Imagine you are standing on a huge ball, a few miles in diameter. Depending on the actual size of the ball relative to your height, if you are tall enough, you will be able to see the curve of the ball. Now, suppose you are instead, standing at the center of a flat, circular disc shape, like the Flat-Earth model shown on the various Flat Earth Societies’ websites, with it horizontal diameter the same as the diameter of the ball. Because the surface of the disc is flat, you will have to be taller to see the curve of the edge of the disc than you had to be to see the curvature of the ball, but if you are tall enough, or you stand on something to gain enough altitude, you will see the curved edge, just like you did on the ball.

The fact that at a certain height above the surface, the Earth will look round regardless of which model is correct, means that to use this approach to prove which model is actually correct we will have to calculate the heights at which we can see the curved edge for both models and then go to those heights to see which one is real. But, different from standing on the ball or disc, to accurately determine those heights above the surface of the Earth, we will also have to calculate the proper adjustment for the curvature effect from the light passing through the Earth’s atmosphere for each observation, since the density of the atmosphere varies with height. As I mentioned above, the atmosphere thins out to nothing at about 327,360 feet. This has been determined two ways: both mathematically by calculating the effect of gravity on the gasses of the atmosphere, and by direct sampling with measuring devices called sondes, attached to balloons. Calculating the respective heights for observing the edge of the disc or the curvature of the sphere, and flying high enough to check them out would be a fun experiment and would give us an absolute proof positive answer. But before we try to get funds to do it, there are other less labor-intensive ways to approach the problem of determining which model is correct.

Perhaps the easiest one is the sunrise experiment I proposed in an earlier FB post. It doesn’t require funding or high-flying observations, just cooperation from a couple of friends or acquaintances. Just have someone in New York City and someone in Denver call you on the same day at dawn at their respective locations. If the Earth’s surface is flat, the calls will be virtually simultaneous because there are no mountains high enough between Denver and New York to block the line of sight. If the Earth surface is curved, the call from Denver will come in after the call from New York, because the sun will be hidden behind the curvature of the Earth until it reaches the height necessary for it to be seen in Denver. If the Earth is nearly spherical, the calls will be about 2 hours apart.

If you try this, you will find that the time between the calls will actually be about 2 hours, give or take a few minutes depending on exactly where your friends are located in the Denver and New York areas. I can say this with confidence because I have been in both Denver and New York City a number of times, and I have friends in both areas. It is always necessary to allow that same amount of time difference if you are in one area and want to connect by telephone or skype at a specific time with someone in the other area. If the Earth were flat, the sun would be seen to rise at the same time in Denver and New York, but would reach the zenith (straight overhead) about 2 hours apart in in the two locations, Denver 2 hours behind New York. So the diurnal time difference would vary during the day, making synchronizing watches for a given time to schedule a phone call between the two locations very difficult. Obviously this is not the case. Conclusion: the surface of the Earth is effectively the surface of a sphere.

THE FLAT EARTH HYPOTHESIS REVISITED… AGAIN!

AS THE EARTH TURNS 

I have a Face Book friend who posted that he has decided that the Flat Earth theory is correct. I could say everyone is entitled to believe whatever they choose. But that would be the lazy man’s answer. Here is my answer to him:

I will defend your right to listen to arguments and decide for yourself. However, I’ve gone to the link you posted and watched the videos and listened to the arguments and, in my opinion, they are all based on ignoring a lot of facts and believing that for some reason, there is a global conspiracy to make people believe the earth is an oblate spheroid. But I will refrain from saying what most scientists might say about the videos. A blunt astrophysicist will tell you that all of the 200 arguments are completely bogus and call them “pseudoscience”, and call those who peddle them stupid, or at the very best, delusional and misguided. Yes, some NASA photos are re-touched, but not for the reasons implied by the video maker, i.e. to hide the supposed ‘fact’ that the earth is flat.

As an aside, I think the name ‘pseudoscience’ is misused by many people claiming to be scientists. Scientists do not know everything. Science is always incomplete. See my post on the incompleteness theorems proved by Gӧdel. So calling an idea ‘pseudoscience’ just because it doesn’t fit the current model is a sure sign that the name-caller doesn’t really understand science. On the other hand, some ideas are easily disproved. Those can legitimately be called pseudoscience. The flat-earth theory is one of those.

My friend asserted that there is no evidence of a curved horizon even at 100,000 feet altitude. 100,000 feet sounds like a long way up, but it's only seven one-hundredths of one percent of the circumference of the earth. The curvature of the horizon is very small, virtually indiscernible at that distance above the earth. 100,000 feet is less than 20 miles. Compare that with the distance from New York to San Francisco. It is about seven-tenths of one percent of that distance. At 100,000 feet you can't see both SF and NY at the same time because of the curvature of the earth, even though the horizon appears flat.

I’ve flown polar routes personally, and I can tell you that direct observations absolutely refute the flat earth theory. I could point out the fallacies in most of the 200 arguments, but my time is valuable so I’ll just prove to you in a direct manner that the earth is approximately spherical:

1. Standing on our eastern shoreline at sunrise, the sun appears to come up out of the Atlantic Ocean, but we know England, Ireland and Europe are on the other side. If the earth were flat, how do you explain this?

2. Sunrise tomorrow, April 13, 2016, in New York City is at 6:20 AM. Sunrise tomorrow in Denver Colorado is exactly 2 hours and 5 minutes later. The elevation of New York City is only a few feet above sea level. Denver is about one mile (5,280 feet) above sea level. That’s why it is known as the ‘mile-high city’. The highest mountain between Denver and New York is the highest point in the Allegheny Mountains, Spruce Knob at 4,863 feet above sea level. If the earth is flat, on a clear day, people in Denver would be able to see the sun come up east of New York City, as the New Yorkers see it, not 2 hours later. Even accounting for haze, someone on Lookout Mountain, just west of Denver at 7,377 feet above sea level would see the sunrise over the Atlantic at the same time it is seen in New York.

You can check this out for yourself: Ask someone in New York, and someone in Denver to call you when the sun comes up tomorrow morning. If you are in Oklahoma, you’ll get the call from your friend in New York about 40 minutes before you see the sun, and you’ll get the call from Denver about 35 minutes after you see the sun rise. Based on the difference in sunrise times, and the distance in miles between New York and Denver, you can calculate the curvature of the surface of the earth, and from that its circumference, proving that the surface of the earth is curved, and refuting the flat earth theory for yourself.

ERATOSTHENES REVISITED AND IS TDVP NEW SCIENCE, OR A NEW RELIGION?

IS TDVP NEW SCIENCE, OR A NEW RELIGION?

We have stated that transcendental physics, and in the broader sense, the paradigm shift TDVP integrates science and spirituality. Does this make TDVP both a science and a religion? I am flattered to have been compared with Einstein more than once, and with religious reformers like Martin Luther. It has actually been suggested that my mission in life is to start a new scientific religious movement. If bringing science out of the dead end of materialism is a religious movement, then I’m guilty as charged, and happy to be an agent of positive change. But I’m a mathematician and physicist by academic training, and Dr. Neppe is a medical doctor and neuroscientist.

Dr. Vernon Neppe and I have proved that gimmel, a third form of reality that is neither matter nor energy, is absolutely necessary for there to be any stable atomic structure, i.e., any physical universe, at all. We have proved that the third form had to exist before any stable particle could emerge from the big bang or any other origin event. In addition, we have proved that it is this third form that conveys logical structure with purpose and meaning to existence. Our proofs are not just verbal arguments with the inevitable semantic problems that come with verbal representations, we have proved that gimmel exists with rigorous mathematics.

IS MATHEMATICS A RELIGION?

Most people think of mathematical proof as very much the opposite of belief, and belief, or faith, as the foundation of all religion. But someone said recently that: “Mathematics is not a science at all, it’s a logical religion!”  Here is his reasoning: Religion is based on belief in things that can be neither proved nor disproved. Gӧdel’s incompleteness theorem, which I have discussed more than once in these blog posts, proved that there are legitimate mathematical statements that cannot be proved or disproved, including the axioms of arithmetic. Therefore, mathematics, just like religion, is based on belief in things that cannot be proved or disproved, and that makes it a religion!

But, you may object that science, and mathematics -the language of science, are based on solid facts, not assumptions. If you believe that, then I’m afraid you are wrong! Both science and mathematics are only logically consistent within the axiomatic system upon which they are built. The dictionary definition of an axiom is: “a self-evident truth that needs no proof, or a universally accepted principle.” However, that which is self-evident to one person may not be self-evident to another; and are universally accepted principles always true? No. For example, it was once universally accepted by millions that the Earth was stationary and the moon, sun and stars all revolved around it. Since science and mathematics are only logically consistent within the axiomatic system upon which they are built, they cannot be said to contain absolute truth. Eratosthenes’ proof is a good example.

WAS ERATOSTHENES EXPERIMENT REALLY PROOF THAT THE EARTH IS ROUND? 

As noted in the previous post about the Flat Earth hypothesis, Eratosthenes may have gotten the idea that the Earth was round from books in the Great Royal Library of Alexandria where he worked, probably from the works of Pythagoras, who lived about 200 years before Eratosthenes. Pythagoras believed, among other things, that the Earth was a sphere. He also believed in reincarnation and said he remembered at least four of his past lives.

Eratosthenes started with the axiom that the Earth was round. If he had started with the axiom that the Earth was flat, the exact same measurements of the pole and shadow would have proved that the sun was less than 4,000 feet above Syene Egypt, not far off of the Flat Earth Society’s claim! So the statement that we find in text books and on Wikipedia that Eratosthenes proved the Earth was round 1700 years before Columbus is incorrect. Eratosthenes’ famous experiment simply demonstrated that the physical evidence of the shadows of identical poles 500 miles apart in Egypt was consistent with the assumption that the Earth was round. As it turns out, he was correct. There is plenty of evidence that the Earth is an oblate spheroid, slightly flattened at the poles because of the fact that it is spinning at about 1000 mph at the equator. The point here is that the same empirical evidence can support two vastly different realities.

IS SCIENCE OR RELIGION ULTIMATELY PROVABLE?

So we have to ask, is there any real difference between science and religion with regard to absolute truth? Each new discovery, like our discovery of gimmel, the third form of reality, just pushes what we know farther toward the assumption of an absolute reality.

THE SCI-LEGION OR REL-IENCE OF TDVP 

Perhaps TDVP is both science and religion. Perhaps the scriptures of TDVP are number theory texts, George Spencer Brown’s Laws of Form, the Calculus of Distinctions in Transcendental Physics, and Neppe and Close’s Reality Begins with Consciousness. www.BrainVoyage.com

SHADES OF THE FLAT EARTH SOCIETY

IS YOUR WORLD FLAT OR FAT?

Most who frequent this blog are probably wondering why I would spend any time on this subject. Doesn’t everyone know that the Earth is an oblate spheroid spinning in space and revolving around the sun? No, apparently everyone does not know this. The main reason that I decided to discuss the Flat Earth Hypothesis here is because I like to encourage people to think for themselves, to use the intelligence God (or the Universe, depending upon the semantics you like to use to refer to Reality) has given them. And, yes, I said the ‘Flat Earth Hypothesis’. It actually is a scientific hypothesis because in can be proved or disproved by observation, measurement and mathematical logic. It actually meets the criteria for a legitimate scientific hypothesis. So let’s start with a little historical background.

The flat Earth hypotheses originated in modern times with the English writer Samuel Rowbotham (1816–1884). Rowbotham published a 16-page pamphlet, Zetetic Astronomy, which he later expanded into a 430-page book, Earth Not a Globe, in which he described the Earth as a round, flat disc with the North Pole as its center. He claimed that the disc was bounded by a wall of ice, known as Antarctica, with the Sun and Moon only 3,000 miles above the Earth and the stars 3,100 miles above Earth.  He also declared that the "Bible, alongside our senses, supported the idea that the Earth was flat and immovable and this essential truth should not be set aside for a system based solely on human conjecture”. Rowbotham created a Zetetic Society in England and New York, publishing over a thousand copies of Zetetic Astronomy.

After Rowbotham's death, one of his followers, Lady Elizabeth Blount, established a Universal Zetetic Society. The society published a magazine, The Earth Not a Globe Review, and remained active until around 1910. A flat Earth journal, Earth: a Monthly Magazine of Sense and Science, was published between 1901and1904, edited by Lady Blount.

The first organization to use the title ‘Flat Earth society’ was the International Flat Earth Research Society (IFERS), founded by Englishman Samuel Shenton in 1956. Shenton died in 1971, and from 1972 until 2001, The IFERS was headed by Charles Johnson, an American. The belief lacked representation after Johnson’s death in 2001, until the name was reclaimed in 2004 by Daniel Shenton, an American from Virginia now reportedly living in Hong Kong.
Members of the Flat Earth Society argue that all photographic evidence of a spherical Earth is faked by NASA and the world’s governments for monetary reasons. Could the photos be faked? Sure. Hollywood’s computer-generated realities can make anything we can imagine look real.  

TESTING THE HYPOTHESIS
Is the Earth really flat? Let’s look at the evidence:
Samuel Rowbotham waded into the Old Bedford River in the summer of 1838 and held a telescope just eight inches above the water level to watch a boat with a five-foot mast row slowly away from him. He knew that if surface of the Earth is curved, the water surface would be curved according to the accepted circumference of a spherical earth, and the boat should slowly descend as it moved away from him on the curved surface, until even the top of the mast should be below his line of sight.

Rowbotham reported that the entire vessel remained constantly in his view for the full six miles, all the way to Welney Bridge, which would indicate a flat Earth. He repeated this experiment several times, but his claims that the Earth is flat were ignored by the scientists of the day, until, in 1870, one of his supporters, John Hampden offered a wager that he could prove to anyone, by repeating Rowbotham's experiment, that the earth was flat. A famous naturalist and professional surveyor, Alfred Russell Wallace, accepted the wager. Wallace, with surveyor's training and knowledge of basic optics knew that Rowbotham may have made a mistake by setting his telescope too close to the water’s surface allowing the boat to be visible because of atmospheric refraction in the humid air just above the river’s surface.

Wallace avoided this by setting his line of sight 13 feet above the water, to avoid the effects of atmospheric refraction. The boat was then seen to be slowly descending below the line of sight as it moved away, because of the curvature of the surface of the Earth. The referees for the wager who held the money involved, declared Wallace the winner and awarded him Hampden’s money, and Hampden promptly sued, claiming that Wallace had cheated. Several versions of the experiment were subsequently carried out by various people, including Lady Blount with various results. Both sides accused the other side of cheating, Hampden wound up in jail for threatening to kill Wallace, and the controversy raged on for years. The public loved the controversy and as a result, Lady Blount and her followers sold a lot of magazines, and the Flat Earth Society was born.

Why did Rowbotham devise his experiment in the first place? Galileo’s sun-centered solar system had been validated by astronomers like Johannes Kepler, and Kepler’s three laws of planetary motion were already known 200 years before Rowbotham’s experiment, and in addition, Newton’s, laws generalizing and confirming planetary physics had been published about 100 years before the Bedford River Level experiments. All of this rigorous physics and astronomy required a spherical or nearly spherical Earth. It appears that Rowbotham was motivated by religious belief.

In tracing the historical origin of the Flat Earth Society, we’ve uncovered evidence that the understanding that the Earth was shaped like a ball like the other planets preceded the Flat Earth hypothesis by hundreds of years, but was there any simple direct proof? The answer is: Yes, there was, and it was even much, much earlier; at least 2,245 years ago!

According to a papyrus scroll from 230 B.C. :

Greek Librarian, Eratosthenes, Calculates the Diameter of the Earth!

Alexandria, Egypt: The Honorable Chief Librarian of the Ancient Library, Eratosthenes, peered into a well here at noon and came up with the diameter and circumference of the Earth! He did it with measurements made during the summer solstice in Alexandria and Syene.

Did Eratosthenes come up with it himself, or did the idea that the Earth is a spherical planet go back even farther? Eratosthenes had access to the largest known depository of knowledge in the world at that time. Could it be that he found the information in a book that was already centuries old at that time? We may never know, but somehow he figured out that he could calculate the Earth's circumference. His method is simple, requiring no advanced equipment or mathematics.

 So we can prove the Earth is a sphere using a simple formula that's over 2,200 years old!

He calculated the circumference of the Earth using the following method: It was general knowledge that on the summer solstice, the longest day of the year, at midday, the sun above Syene, Egypt, would be directly overhead. The day of the solstice could be determined by looking into a well, because the sun illuminated the bottom of a vertical well only during the solstice. So on the summer solstice, he measured the shadow cast by a vertical pole in Alexandria and saw that at noon the sun missed being directly overhead by about 7.2° angle.

   

The following figure shows how Eratosthenes's earth measurement worked.

Eratosthenes divided 360° by 7.2° and got 50, which told him that the distance between Alexandria and Syene (500 miles) was 1/50 of the total distance around the Earth. So he multiplied 500 by 50 and concluded that the Earth's circumference was about 25,000 miles. The distance around the Earth at the equator has been accurately measured as 24,901 miles.

You can use Eratosthenes’ method to measure the circumference of the Earth yourself, if you want. You will need to measure, as accurately as you can, the length of the shadows cast by two straight poles that are a few hundred miles north and south of each other at the same time on the same day. You can measure at one location and have a friend measure at the other, or you can travel and make all of the measurements yourself. If you make the measurements at the same time of day on consecutive days, the difference of the angle on consecutive days will be less than the margin of error in the measurements.

Make the measurements at local noon.  You can do this by looking in the local paper for the time of sunrise and sunset - local noon is half way between these times.

Be sure that the pole is vertical.  Record both the length of the pole and the length of the shadow.

You can measure the angle either by making a drawing to scale of the poles and shadows and measuring the angle with a protractor, or by using trigonometry. Once you have the angle, you can easily calculate the Earth’s circumference as follows:

The angle of separation of the two points on the Earth is to 360° as the distance between them is to the circumference of the Earth.

(Angle of Separation)/360° = (Distance Between Points)/(Earth’s Circumference)

 Then by simple transposition,

Earth’s Circumference[EC1]  = (Distance between Points x 360°)/(Angle of Separation)

If you do this carefully and measure as accurately as you can, your calculation of the Earth’s circumference will be very close to the number Eratosthenes obtained.

SEEING IS BELIEVING

Is there any other easy proof that the Earth is spherical? Here are some personal observations:

There are some very flat places on the Earth. Like Kansas. Driving across Kansas and sailing across the ocean have something in common. In both cases, you can only see something on the ocean, or on the plains about 21 miles away. Why is this? Is it because our eyes can only see that far? No, because on a cloudless night, we can see all the way to the moon! Is it because of atmospheric density? No, because we can see the Rocky Mountains as much as 100 miles away, because of their height. We don’t see the town that is only 25 or 30 miles away because it is hidden from straight line sight by the curvature of the Earth.

A few years ago, on a Lufthansa flight, I flew from San Francisco California to Frankfurt Germany over the polar route. I left San Francisco about 9:00 PM. It was a clear night and I could see the moon reflected in lakes and streams even from 30,000 plus feet, about six miles high. We went over several states, part of Canada and Nova Scotia, Greenland and Iceland, down over Scotland, and into the heart of Europe. Somewhere after Iceland, the sun came up in the northeast, moved along the horizon for a few hours, and dipped down below the horizon again in the northwest. I cannot explain what I saw if the Earth is a flat disc as hypothesized by the Flat Earth Society. If the Earth is an oblate spheroid, I can explain it.

Also, the Earth can’t be a disc with the North Pole in the center and Antarctica as a wall of ice around the southern edge of the disc, because if this were true, sailing or flying around the ice wall would be an extremely long trip, a distance much greater than the distance around the equator, if the Earth is flat. But the continent of Antarctica has been circumnavigated 10 times since 1772, and best estimate of the distance around the continent, is a mere 8,000 miles, much less than the trip around the equator, not the nearly 40,000 miles it should be if the Earth were flat.

It is also important to note that the distance around the equator is, within the margin of error, the exact same as the circumference of a spherical Earth calculated by Eratosthenes!

The similar opposing wind patterns over the north and south hemispheres, unexplained by a flat disc Earth, also fit very well with a spinning spheroid Earth.

I have noticed that many people will believe whatever they want regardless of the facts. Think about politicians, for example. I also know that some people like to take the other side of any idea, however obvious, and argue as if the contrary position is the truth. It is no wonder that there are intelligent people out there who still don’t believe the theory of relativity, when something as obviously goofy as the Flat Earth hypothesis can still gain supporters.

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 [EC1]