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We have been examining the claims of a flat-earth advocate and found so far that all the evidence is consistent with a spherical earth with a radius of 3959 miles, and is inconsistent with a flat earth.  We will continue to analyze Jeff’s claims (in purple font) below, along with my response in black.

Jeff: If the earth is round, based on it’s [sic] dimensions, we should easily see curvature from ground level.  We should see buildings tilted due to curvature but yet there is no evidence of this.  For example, at 12 miles distance, the earth should show 96’ of downward curvature.  However, when we see pictures of cities from this distance, there is no evidence of curvature at all . . .none.

Lisle: How much does the earth’s surface curve over a distance of 12 miles?  Since the circumference of earth is around 24,875 miles which corresponds to 360 degrees, the curvature over twelve miles will be (12×360°/24,875) = 0.17° which is quite a small angle.  Furthermore, this angle is tilting away from the observer, not left or right.  It is not easy to measure an angle that is toward or away from your line of site, to say nothing of an angle that is only 0.17°.  So, no, the curvature of the earth is not easy to see directly over a distance of 12 miles in terms of tilt.  You would not be able to detect the tilt of a building that is only 0.17° and tilted directly away from your line of sight.

However, that building will appear slightly lower than it would otherwise, and indeed by about 96 feet.  Jeff is using an approximation that describes how much the ground curves away from a horizontal line with increasing distance.  Namely, the earth curves downward by about 8 inches per mile squared.  So at twelve miles, the ground will be (12x12x8”/(12”/1’)) = 96 feet below the surface of the spot on which you are standing.  Therefore, if your eyes are at ground level, you will not be able to see a building smaller than 96 feet that is 12 miles away, assuming no hills, valleys, or temperature gradients.  And this is indeed the case.  Remember that if your eyes are 6 feet above the ground, this adds an extra 3 miles.

We computed in a previous article that an object can be seen from distance r+s, where r= √(h2 + 2hR), s = √(H2 + 2HR), R is the radius of the earth, h is the height of the observer’s eyes above the surface of earth, and H is the height of the object above the surface of the earth.  This computation assumes that light travels in perfectly straight lines, which requires the air temperature to be consistent throughout the journey.  This result is consistent with observations.  On the other hand, on a flat earth, all objects should be visible and above the horizon at any distance.  This is not what we observe.

Jeff: Why can we see the entire skyline of Chicago from

Lisle: Jeff either didn’t finish this sentence, or it got clipped.  In any case, he is presumably referring to some location from which we apparently shouldn’t be able to see the Chicago skyline on a round earth.  Some flat-earth advocates have argued that we shouldn’t be able to see the Chicago skyline from the Michigan shoreline.  But where is the mathematical support for this claim?

The tallest building in Chicago, the Willis Tower, is 1451 feet from base to tip.  However, its base is 15 feet higher than the average elevation of Lake Michigan, for a total height of 1466 feet.  Thus, with eyes six feet above the surface of the lake, the (top of) Willis Tower could be seen from a distance of 50 miles.  Parts of the Michigan shoreline are closer than that, so of course the skyline will be visible.  Thus, from locations like New Buffalo (approximately 40-45 miles distant), the tops of the taller buildings are visible, but the lower portions are obscured by the water due to curvature.  See this image taken from New Buffalo.

Some locations like Warren Dunes, are 54 miles away from Chicago.  And so, you might at first think that no buildings in Chicago would be visible.  But these sand dunes are not level with the lake.  They rise between 50 to 180 feet above the typical water level.  This increases the viewing distance by 13 miles, putting the tops of the taller buildings within the range of visibility.  Observations confirm this, and also that the smaller buildings and ground are normally hidden.

However, on some occasions, more buildings are visible.  And sometimes the skyline can even appear upside-down as in the following image:

How do we account for this?  A flat earth does not explain why the smaller buildings and ground are normally obscured by the lake since they are actually above the lake, nor can it explain why the buildings sometimes appear upside-down.  But physics applied to the earth’s true shape can.  The instances where some of the smaller buildings become visible and/or appear upside down always coincide with a temperature inversion.  Normally, the air temperature drops slightly with increasing elevation.  But on some occasions, this situation is reversed, and the temperature increases with elevation for some distance above the ground.

Light travels slightly faster through (hot) rarified air than it does through (cold) dense air.  And when light passes through substances in which the speed of light changes, the light changes direction.  This is the principle of refraction.  In an isotropic medium, the bending of light as a function of its change in speed in different media is given by Snell’s Law: sin(θ1)/sin(θ2) = v1/v2 where θ1 is the angle of incidence, θ2 is the angle of refraction, v1 is the velocity of light in medium 1 and v2 is the velocity of light in medium 2.  In air, there is a gradual and continuous change in temperature and density, rather than at a sudden interface.  So, the refraction of light is gradual but continuous.

During a temperature inversion, the air very near the ground is colder than the air above it.  This causes light to refract downward – in the same direction the earth curves.  Therefore, on days with temperature inversions (and only on such days), you can see a bit farther than you otherwise could.  For an interesting demonstration and discussion of this phenomenon, see the following interview.  https://www.abc57.com/news/skyline-skepticism-the-lake-michigan-mirage. Note that normally, only the tops of the tallest buildings in Chicago can be seen from Warren Dunes, which would not be the case on a flat earth.

So how much farther can we see on a globe when there is a temperature inversion?  The full derivation of the math is lengthy, so I will give the result of one approximation.  First, the angle in radians by which light is bent is given by θ = (s/r)((v2/v1) – 1), where s is the distance the light travels, r is the distance from the bottom to the top of a layer of air, v1 is the speed of light at the bottom of the layer, and v2 is the speed of light at the top of the layer of air.  The speed of light in air can be approximated by v=c/(1+0.000293 PT0/(P0T)) where T is the temperature in Kelvins, T0 = 300 Kelvins, P is air pressure, P0 is air pressure at sea level, and c is the speed of light in vacuum.  Over a distance of s, a light beam that is initially horizontal will curve toward the earth, dropping by an amount h = s tan(θ/2).

Let’s plug in some numbers.  Let the temperature at ground level be 295 Kelvins (71.3° Fahrenheit), and standard air pressure at sea level.  Suppose we have a temperature inversion whereby the temperature increases by 0.1 Kelvin per meter in elevation.  Then how much will a horizontal light beam drop over a distance of s = 1 mile (1609.344 meters)?  The answer is about 5 inches.  Now, of course, the earth itself drops by approximately 8 inches per mile squared.  So, the earth drops only 3 inches per mile squared more than the light does in this situation, as if the earth were 8/3 larger in radius than it really is.  Under these conditions, how far from Chicago can the tallest buildings be seen from the ground?  The distance would be around 81 miles.

Notice that it doesn’t take a very strong inversion to nearly double the distance at which distant objects can be seen.  This is why I don’t generally recommend these types of experiments for non-scientists to detect the sphericity of earth.  They do work, but you must either work through the math to compute how much the light curves, or pick a day where the temperature gradient is very near zero.[1]  Temperature differences drastically affect the view of objects very near the horizon.  On the other hand, there are observations you can make to test the shape of the earth using celestial objects that are far from the horizon where atmospheric refraction is negligible.  We have an article that shows these experiments.

Jeff: When God stopped the sun and moon for Joshua, that’s what he exactly did.  God did exactly what he said he did.

Lisle: Correct.  He stopped them.  The question Jeff needs to ask is “stopped them relative to what?”  Motion is a change in position over time.  However, position requires a reference point.  What is the reference point we generally use?  More importantly, what is the reference point God uses when describing things in the Bible?

Jeff: Why didn’t he say he stopped the earth or the universe from spinning.

Lisle: It is the same reason why astronomers like myself talk about the time of sunset or sunrise, rather than the time “at which the earth rotates such that the horizon passes above or below the sun.”  It is convenient and appropriate to use the earth as a reference frame by which to describe the relative motion of the rest of the universe.  The rovers on Mars have observed sunrises and sunsets on Mars, and yet no one argues that Mars is stationary and the entire universe revolves around it.  I would hope that future readers of my books would understand this basic principle.  I certainly hope they would not argue, “Dr. Lisle clearly believed that the earth doesn’t rotate because he mentions ‘sunrise’ and ‘sunset’ in his books.”  That would severely misrepresent me.  I would hope instead that they would read my comments in context, recognizing that I often use the earth as a reference frame.  Let’s show God the same courtesy.

Jeff: Because you believe in the lie of a spherical earth, you must deny your rules of biblical interpretation and say this isn’t a literal account.

Lisle: No.  The passage is perfectly literal.  It is simply describing what people observed using the earth as a reference frame.  Joshua 10:13 states, “…and the sun stopped in the middle of the sky…” clearly specifying the reference frame: the sky of earth as seen from Joshua’s location.  This does not in any way disallow other reference frames, including Newtonian frames.  In other words, the fact that the sun and moon stopped relative to earth does not disprove the fact that the earth stopped relative to the sun and the moon.  In fact, the former requires the latter.  That is, if the sun and moon stopped relative to earth, then it follows logically that the earth’s rotation stopped relative to the sun and moon.  By the way, this issue has more to do with earth’s rotation than earth’s shape

Jeff: It also describes in that passage the exact locations over earth that each was stopped.  This is impossible if the sun was 93 million miles away.

Lisle: Why?  Perhaps Jeff is thinking of Joshua 10:12 where Joshua commands the sun to “stand still at Gibeon” and the moon “at the Valley of Aijalon.”  That is, Joshua is describing where the sun and moon appeared from his point of view.  Why would that be “impossible if the sun was 93 million miles away?”  I might describe the setting sun as “just above Pikes Peak,” but that doesn’t mean it is at the same distance as Pikes Peak – only in the same direction.

Jeff: Based on the video you sent me, I can also show you examples of flight routes that make so [sic] sense whatsoever on a globe earth but make perfect sense on a flat earth.

Lisle: No, Jeff cannot do this.  Flight paths are determined by a number of factors, including weather and political borders.  But apart from these issues, flight paths are generally geodesics – the shortest path between two points on a curved surface.  For a sphere, geodesics are arcs of a great circle (a circle whose center is the same as the center of the earth).  Flight paths, especially those in the southern hemisphere, are perfectly sensible on a globe, but make no sense whatsoever if the earth were flat as viewed in an azimuthal equidistant projection.

Jeff: I firmly believe that God has made earth the center of everything and he resides just above the dome of the earth.

Lisle: It would be better to firmly believe what the Bible actually teaches.  The notion that God made the earth the center of everything certainly does not come from the Bible.  Perhaps Jeff means that the earth is the center of the perimeter of the visible universe.  But he has no way of knowing that because we do not yet know exactly where the perimeter of the visible universe is, or if there even is such a thing.  And the Bible says nothing about this.  So, the belief is arbitrary and unwarranted.

Likewise, you will not find any place in Scripture that teaches that the earth is covered by some sort of transparent, solid dome.  This belief stems from the liberal critics who claim that the Bible is simply borrowing its cosmology from the Ancient Near Eastern mythologies.  Indeed, there were pagan religions that taught a flat, disk-shaped earth beneath a solid transparent dome.  Critics allege that the Bible was not written by inspiration of God, and thus its authors were merely borrowing from the cosmology of the day.  But you will not find any such evidence in Scripture.

Most problematic is the notion that God “resides just above the dome of the earth” as if God were a physical being that is found in one particular location in space.  Such a notion is heretical because God is an omnipresent spirit (Psalm 139:8; John 4:24) who fills heaven and earth (Jeremiah 23:24) and then some, for heaven and earth cannot contain God (1 Kings 8:27; 2 Chronicles 6:18).

Jeff: Not billions of light years away or in some other dimension.  The earth I believe in is such more magnificent than the one you believe because it proves without a doubt in intelligent design.

Lisle: The earth Jeff believes in is anti-biblical, non-functional, and nonexistent.  Recall, the Bible describes the earth as spherical in a number of ways.  The light from the sun that falls upon the earth covers half its surface at any one time, and the boundary between light and darkness (where sunrise and sunset occur) is a circle which is only possible on a spherical world.  This is revealed in Job 26:10.

Based on the biblically revealed shape of earth combined with the physics discovered by Newton, we can compute the times of sunrise and sunset for any location on earth, as well as the exact times of upcoming solar and lunar eclipses, and the motions of the other planets.  None of these work on a flat earth.  Indeed, there are no self-consistent flat earth models that can predict or explain any of these things.  It’s not a functional or rational hypothesis, which is why you will not find any flat-earth advocates that can compute flight paths for planes, or put satellites in orbit, or predict celestial events.

Jeff: The globe model was developed to prove there is no God and that we were created all by chance.

Lisle: !!?!?!  Where did Jeff get that idea?  Again, he provided absolutely no supporting evidence.  Do you know where the most ancient references to a round earth are found?  They are found in the Bible!  Job 26:10 refers to the earth’s terminator (the boundary between light and darkness – where sunrise or sunset occurs) as a circle!  The only shape that always has a circular terminator is a sphere.  Job was written around 2000 B.C.   As far as we know, at that time in history all the pagan nations believed in a flat earth.  Even by 800 B.C. it was a common pagan belief that the earth was a flat disk that floated in water.  But Job 26:7-10 taught that the earth is round and hangs upon nothing.  We now have pictures that show that the Bible was right all along.

Moreover, the Bible teaches a global flood in which all the mountains were covered.  This doesn’t make sense on a flat earth where the water would simply run off the perimeter.  Nor would a solid transparent dome work because this dome itself would constitute a mountain that was not covered by water.  The Bible teaches a global flood, and you cannot have a global flood without a globe.

In reality, Jeff has it backwards.  A flat earth was the common belief of virtually all pagan cultures before 600 B.C.  As far as we know, only believers in the Lord knew otherwise, as indicated in Job, Genesis, and Isaiah.  It was not until the 500s B.C. that the Greeks finally began to allow for the possibility that the Bible is right about the roundness of earth.

Jeff: I’m not hear [sic] to call anyone a liar, I just let the facts speak for themselves and there is no proof whatsoever of a curved earth without using CGI photos.

Lisle: False.  The photographs from the Apollo missions clearly show a round earth and CGI did not exist when these photos were taken.  In the late 60s and early 70s computers were very primitive compared to today.  Most of the people at NASA’s mission control were still using slide-rules.  Nobody was doing CGI in 1969 because the technology did not exist.  The famous Earthrise photo was taken with a Hasselblad 500 EL camera on 70 mm Kodak film.

During a lunar eclipse, the earth’s shadow falls on the moon.  And that shadow is always a circle, which is only possible if the earth is spherical.  If the earth were a flat disk, its shadow on the moon would be an ellipse, and occasionally a straight line, depending upon the relative orientation of the sun, earth, and moon.[2]  You can see a lunar eclipse with your own eyes and see that it is not a CGI image.

Moreover, I previously wrote an article about some experiments that you can do for yourself to test the shape of the earth.  These include measuring the angular altitude of the north star from two different latitudes on earth, watching a sunrise or sunset (especially over the ocean), watching the illumination of the mountains by sunlight during a sunrise or sunset, etc.  I would encourage Jeff and everyone else to do at least one of these and see the results for yourself.  Don’t just repeat internet claims.

Jeff: I hope you will research the facts from reputable flat earth sites and not the joke ones out there.

Lisle: There are no “reputable flat earth sites.”  There is not one flat-earth advocate who has correctly applied the scientific method, who has used both geometry and physics to make a testable quantitative prediction (including effects like temperature inversions) that was then verified by observation.  Nor will you find any such results published in any peer-reviewed literature whether Christian or secular.  You won’t find any flat-earth advocates computing flight paths for airlines, or predicting eclipses, or putting satellites into orbit, because these things only work on a spherical earth.

In fact, using the laws of physics applied to a round earth in a heliocentric solar system, I can predict the positions of the planets years in advance, or predict the precise path of the moon’s shadow during a total solar eclipse, such as the one coming up on April 8, 2024.  Can any flat earth advocate use physics and mathematics to make these kinds of predictions based on a flat earth?  Of course not.  And the reason is because physics and mathematics are not consistent with a flat earth because they reflect reality, not ancient anti-biblical mythologies.

Jeff: Do me a favor, as Dr. Lisle why is the south pole significantly colder than the north pole.   If we live on a globe earth, the poles should be the same temperature . . . they are not even close.  The average annual temp of the south pole is -40 degrees and the north pole is +4 degrees.  I can tell why this is on the flat earth model but it’s impossible on the globe earth model.

Lisle: First, there is no south pole on a flat earth.  There can be only one pole on a flat disk.  So, the question is only sensible if the earth is spherical.

The south pole is indeed colder than the north pole on average, and for the same reason that the top of Pikes Peak is colder than the base.  Under normal weather conditions, the temperature drops with increasing altitude.  This is because sunlight warms the surface of earth, the air is heated by contact with the ground, and transported upward by convection.  Thus, on a typical sunny day, the temperature drops about 5.4° F for every 1000 feet gain in altitude.  On a cloudy day, the temperature drops about 3.3° F per 1000 feet.

Earth’s north pole has no land, and is therefore at sea-level.  But the south pole is land.  Antarctica has an average elevation of 8200 feet, with the elevation at the south pole being 9285 feet.  So, on sunny days it should be (5.4° F x 9.285) = 50 degrees colder on average than the north pole, and on cloudy days it should be (3.3° F x 9.285) = 30 degrees colder on average.  Thus, the annual average should be somewhere between these two values, which of course it is.

Conclusions

During the time when the New Testament was being written, Christians had to deal with the false teachings of Gnosticism.  It is remarkably similar to the teaching of the flat-earth advocates today.  The Gnostics believed that they possessed secret knowledge, which made them far more enlightened than the orthodox Christians who allegedly misunderstood the Scriptures and had been fooled.   But in fact, their “secret knowledge” was actually false knowledge, and is almost certainly what Paul warned Timothy about in 1 Timothy 6:20-21.

It is our fallen human nature for every person to think that he or she is superior to others.  People want to believe that their superior intelligence has allowed them to see through the deception that has fooled everyone else.  Such pride is at the root of virtually all conspiracy theories.  And since all conspiracy theories presuppose a nefarious and organized campaign of misinformation, there is no way to falsify them because any evidence against the conspiracy theory is accepted as evidence for the conspiracy theory that was manufactured by the conspirators and is hence false.

For example, “Why do we have so much abundant evidence for a round earth?  Why does every picture of the earth show its spherical nature?”  The conspiracy theorist responds, “They are all fake – CGI!  It’s part of a massive campaign to fool us!”  It doesn’t matter that CGI didn’t exist at the time because the person will just conclude that NASA was hiding that technology too!  “What about pictures from other space programs such as Russia, China, Israel, or private companies like Space-X that all show a round earth?”  The conspiracy theorist responds, “They must be in on it too!”

And thus, no evidence will ever persuade a committed conspiracy theorist of his error.  His commitment to his belief is arbitrary, fundamentally unfalsifiable, and hence irrational.  The error is self-reinforcing, rather than self-correcting.  Hence, this way of thinking can never be corrected because that would require rational thought.  People who think that they are the only ones who have not been fooled, in reality have fooled themselves in the most absurd ways.  Only God can correct such thinking, which is why it is so important to teach students to think rationally from their youth, before they become trapped in circular, conspiratorial thinking.  As Mark Twain so aptly put it, “It’s easier to fool people than it is to convince them that they have been fooled.”

In fact, we should have a degree of skepticism when reading or hearing a new claim.  This includes what we are taught in school.  But we should have an even greater degree of skepticism regarding what we read or see on the internet.  There are absolutely no checks on most websites to ensure accuracy; anyone can claim anything without any consequences for posting false information.  Strangely, we now have “fact checkers” on YouTube and Facebook that will remove and censor true information!  The internet can be very useful, but only when applying discernment.  This is where flat-earth advocates fail to engage any critical thinking skills.  They should be the most skeptical of internet videos allegedly showing a flat earth, and yet they accept such claims without asking any questions.

There are many questions flat-earth advocates should be asking.  For example, “Why do we not see any pictures of a flat earth before CGI was invented?  A number of people have traveled to the south pole, but where is a picture of the edge of the flat earth?  If the earth is under a solid transparent dome, why are there no videos of rockets smashing into it?  Why are there no pictures of people leaning on it near the base?  What would be the motivation for attempting to deceive everyone about the shape of the earth?  Would you collaborate with millions of other people and spend trillions of dollars on faking evidence to convince people that the earth is, say, a cube?  Why?  What is to be gained?”  And most importantly, “why have you not tried any of the experiments that can distinguish between a round or flat earth?”

The flat-earth movement indicates a severe lack of discernment.  That people can be so easily fooled by internet videos is an indictment on our society.  But when Christians fall for such easily falsified claims, this becomes an impediment to sharing the Gospel.  How can Christians be taken seriously if they deny things that are directly observable, such as the roundness of earth, natural selection, or the existence of dinosaurs?  Those of us who want to honor the Lord with intellectual integrity need to gently correct those in opposition.[3]

[1] There is an online app that computes and simulates the view of an observer looking at a distant object on either (1) a round earth or on (2) a flat earth.  The app also computes the effects of atmospheric refraction.  Here is the link:  http://walter.bislins.ch/bloge/index.asp?page=Finding+the+curvature+of+the+Earth

[2] In the most common flat-earth view today, lunar eclipses should not happen at all because the sun and moon are always above the flat disk of the earth; hence earth cannot come between them.

[3] 2 Timothy 2:25