It's been a long time since I've thought of Yoga Instructor & Flat Earth Promoter Eric Dubay. I see that he has a new flat earth movie out repeating many of the claims from his first, "200 Proofs..." movie. Of course most of those "proofs" aren't proofs, many are just unsubstantiated assertions, some are his failures-to-understand being presented as fact, and some are outright fabrications. Since he spends around 40 seconds per "proof" there's little to no time spent citing references or examining any claim.
I'd like to take a few minutes to look at one of the failures-to-understand that is claimed as a proof of earth's flatness. Dubay claims as his 15th "proof":
"15) If the Earth were truly a sphere 25,000 miles in circumference, airplane pilots would have to constantly correct their altitudes downwards so as to not fly straight off into “outer space;” a pilot wishing to simply maintain their altitude at a typical cruising speed of 500 mph, would have to constantly dip their nose downwards and descend 2,777 feet (over half a mile) every minute! Otherwise, without compensation, in one hour’s time the pilot would find themselves 31.5 miles higher than expected."
There are a lot of things wrong with this claim.
A) It relies on the earth being flat: The use of the word 'downward' is problematic. It has different definitions in a flat earth and a globe earth. On a globe earth, downward is a local phenomenon - towards the centre of the globe. A plane need not descend toward the centre of the globe to maintain its altitude. That's moronic.
On a flat earth, downward is an absolute - towards 'down.' For Dubay's argument to be understandable you must assume that the globe exists in a place that has an 'absolute down.' And that place with an absolute down is a flat earth. The only possible circumstance for Dubay's claim is if his airplane takes off from the "top" of a gravityless globe that is resting in the gravity field of a flat earth. One may surmise, that since pilots don't constantly correct downwards, our globe is not sitting on a flat earth.
B) It relies on bad math: Dubay uses the formula from his "Proof #9" as the foundation for the claims made in "Proof #15." As part of "Proof #9" Dubay introduces the idea that curvature of a globe earth must be 8 inches downward multiplied by the square of the mileage from the observer. This is the formula he uses to derive his claims of excessive altitude in "Proof 15". If you passed Grade 10 math you might remember that this is the formula for a parabola. If you didn't remember, you can be forgiven. You probably haven't needed to think about it since your last math test. But presenting it as part of this mathematical based 'proof' is not forgivable.
C) Dubay misunderstands/misrepresents what his bad math says: Dubay derives an average slope between 2 points on a parabolic curve, then presents an interpolation of that slope as if it has some 'real world' meaning. It doesn't.
Since no serious person has claimed that the earth is a parabola, and this slope only has meaning in relation to the 'absolute down' of a flat earth, it is a meaningless claim. It could easily be reworded as, "because the earth is flat the earth can't be a globe." And that's not a "Proof." (See the addendum for the math, if you like.)
D) It's disingenuous: Dubay uses a hodgepodge of 'flat earth physics' and imagery as the criteria to test globe earth claims. This, once again, starts with the assumption that the earth is flat and concludes with, "a globe earth doesn't make sense when the earth is flat."
If a person was honestly seeking truth the starting point might be something like: "These 2 models are incompatible. They can't both be true. They could both be false. Is there a way to test these models that doesn't depend on either model as a starting point?" The answer to the question is, "yes." But Mr. Dubay seems reluctant to explore that path choosing, instead, to always start from the assumption that the earth is flat.
Addendum
Extrapolate: extend (a graph, curve, or range of values) by inferring unknown values from trends in the known data.
Interpolate: In the mathematical field of numerical analysis, interpolation is a type of estimation, a method of constructing new data points within the range of a discrete set of known data points.
Dubay used his claim of being 31.5 miles too high 500 miles after departure then divided that by 60 to get an average value: "2,777 feet (over half a mile) every minute!" But because the slope of a parabola changes constantly the slope of a line between any 2 points can't be interpolated or extrapolated to give any useful information.
To make the math a little easier I'll speed up Mr. Dubay's plane from 500MPH to 600MPH. Now it's easy to see that 600mi/60min = 10mi/min and 10mi/60sec = 1/6mi/sec. Let's plug that back into the parabolic formula
y = 8in * (1/6)^2 = 8/36in = 2/9in
And there you have another solution to the parabolic world curve problem (if such a world existed); 2/9th inch every 1/6th mile or 2/9in every second at 600MPH. Now we plug those numbers back into the original story of a plane flying 500Mi.
500Mi = 3000 * 1/6Mi which corresponds to 3000 * 2/9th" =~ 56 feet
Or slightly less than 1 foot every minute! Imperceptible to a person on a plane without the use of instruments.
(At 500MPH the numbers change again to about 1/6" drop per second and therefore 47 ft over 500 miles, about 9" every minute! Nothing like Mr. Dubay's half mile claim.)
I can hear you saying, "But that was an extrapolation! Dubay interpolated. Surely that will give the same value as Dubay got." So let's try interpolating. If we use Dubay's formula for a flight of 1,000Mi. at 500MPH and 2 hours we get a "y" value (Dubay would say 'drop.') of 126Mi. which, interpolated to 1 hour, would be 63Mi. Or over 1 mile (5,555 Ft) every minute. That's twice what Dubay claimed it would be in his "proof." Such a route wouldn't take the plane around the curve of the world, it would take it through Dubay's parabolic planet!
So what does all of this mean? In the physical world it means nothing. It's just a demonstration that the bad math Dubay uses to bamboozle people produces crap results. The average value of a parabolic function is a meaningless number. A meaningless number used to support a baseless claim.
