Brian Mullin - The Naples Experiment (Rectilinear) - Concave Earth gone wrong

Dear Brian Mullin,

Fact check: FAIL
Several errors caused Ulysses Grant Morrow's Naples Experiment (Rectilinear) to be flawed and conclude wrong results.

The Earth is not concave as Morrow concluded.

1. The results yielded positive and negative angle variations of the rectilinear line, but yet Ulysses Grant Morrow drew the final conclusion that the Earth is concave.

2. Measurements over a distance of 4-miles is insufficient to prove flatness or curvature. The measurements all fell within the standard deviation of error.

3. The rectilinear segments sagged and were not structurally flat over distance.

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Note: All text below is from the article written by Donald E. Simanek, Professor of Physics at Lock Haven University, Lock Haven, PA.
(https://www.lockhaven.edu/~dsimanek/hollow/morrow.htm)

Ulysses Grant Morrow, a newspaper editor, writer, poet, inventor, and geodesist, held views of cosmogony similar to Teed's, and Morrow joined the Koreshan Unity in Chicago.

The Koreshan Geodetic Survey of 1897.

Morrow refined the notion of solid rectangles with something more practical. He replaced each rectangle with a "rectilineator" of his own invention. It was a wooden structure 12 feet long, 4 feet wide, made of 19 year old seasoned mahogany. Steel bars provided cross-bracing between brass fittings at each corner. These brass parts were precisely made to allow each rectilineator section to be aligned precisely with its neighbors, then bolted together firmly. At least 4 sections were made, by the Pullman Railroad Car Company. Only section No. 2 survives.

Near Naples, Florida is a four mile north-south stretch of nearly straight beach—ideal for the experiment. At this time Florida was still a "frontier", sparsely settled with large areas of virtually untouched wilderness teeming with alligators, snakes and many biting insects. The summers were hot and humid. It is much the same today, except that it also has beach houses, condominiums, malls and tourists.



The rectilineator sections were each supported by two "standards"—vertical beams resting on "footpads" anchored on the beach. The first rectilineator section was carefully leveled, using a 12 foot long mercury level designed by Morrow, a standard calibrated spirit level, and a 4 foot plumb bob that could be placed at each end of a rectilineator section. The next section was aligned approximately with the first, then precisely positioned until the facing brass surfaces would just allow insertion of a celluloid card at each corner. When all was perfect, the sections were bolted together, and the process repeated. After all of the available 12 foot sections were in place, the first one was carefully removed, inverted top/bottom and relocated at the other end of the line, to compensate (average out) errors due to any slight initial error in parallelism of the cross beams.

Data were recorded each 1/8 mile. But every 12 feet the vertical distance between a reference mark on the rectilineator and the mean water level was noted. [Very likely the spirit levels and the plumb line were checked also, each time a 12 foot rectilinear section was put into place.] If the earth were convex, this distance should increase as the land line progressed southward. If the earth were flat, the distance should remain constant. If the earth were concave the vertical distance should decrease with the horizontal distance southward. Moreover, for a convex earth, the vertical distance should change slowly at first, then more rapidly as the line progressed southward.

The measurements of mean water level would seem to be a weak point of the experiment. The rectilineator line was on the beach. The water level needed to be determined in the water. This was done with caissons in the water. These damped out fluctuations due to waves sufficiently that a very accurate determination of a steady water level could be made. These were of course corrected for the continual tidal variations during the day and over many days. The water level at the caisson was "transferred" to the land line by telescopic sightings over the relatively short distance from beach to caisson. Over these distances, error due to light ray curvature was considered negligible, and these sightings were perpendicular to the 4 mile N/S land line. Besides, any such curvature error should be the same for every measurement, and would not affect the results. One caisson remained in place at the starting point, and changes in the water level there were continually monitored.

Morrow kept a notebook of data. Each measurement was checked by several persons and initialed by them. Morrow said he "directed and tested every Adjustment and Measurement of the entire Survey, and personally checked same in Record Books." These record books may have survived, and may reside in the un-catalogued archive materials at the Koreshan Unity Foundation Museum and Library, but have not been located at the time of this writing. We do have a very full account of procedures, and a table of data every 1/8 mile, in Part II of Teed's Cellular Cosmogony, written by Morrow. This includes data from the spirit level, the mercury level, horizon sighting, the plumb bob, and, of course, the elevation of the rectilinear line above mean water level.

A systematic error?

All of these suggest that the error is not in the water level measurements, nor in the actual shape of the water surface, nor in tidal variations (which were taken into account properly). If an error is present, it is in the actual rectilineator, or in the procedure of positioning and securing the rectilineator segments.

   

These five independent measures are consistent, within the expected measurement errors. They show the expected decrease of height, the expected shift of the plumb line southward, the expected movement of the spirit level bubble northward. These measures changed slowly during the first mile, and changed more rapidly the farther south the line extended. All these are consistent with the assumption of a convex earth.

Even more remarkable is the fact that the results were consistent with an earth circumference of 25,000 miles. Looking at the data with more modern techniques of data analysis than the Morrow team used, the data show that value to have an experimental uncertainty of a bit over 2%. It differs from the modern value by only about 2% also.

The fact that the average of the signed deviations is so small indicates that the individual values fluctuate about equally above and below the mean. This is an indication that the data is reasonably normal, and the distribution of random errors isn't skewed. While the individual values fluctuate about 10% from the mean, the average deviation of the mean is only about 2%, benefiting from the process of averaging 24 values. This "average deviation" measure is comparable, as a measure of "goodness of the result, to the standard deviation of the mean, a measure more commonly seen in research papers today.

So far, looking only at the data, this would seem to be a good experiment, with measurement uncertainties consistent with the instruments and methods used. But there's that nagging sign of the curvature: concave instead of convex. And that makes a huge difference. If the sign is negative, it effectively turns the whole universe inside-out.

Scientists, and especially students, know the frustration of trying to find the source of a "sign error" in a complicated mathematical derivation, or in the analysis of an experiment. This Naples experiment presents just such a challenge, complicated by the fact that now, over a century since it was carried out, it is a very "cold case".

The Koreshans fully expected the value of 25,000 miles, in agreement with that of conventional geodesy. Why? One conventional way to measure the curvature of a land surface is to use sighting instruments between points in a net of triangles. A large net of this sort can distinguish between a flat and a curved surface, and can measure the radius of a spherical surface. But it cannot determine the sign of curvature. The triangle net would have the same structure and angles on the outside surface of a sphere as it would on the inside surface of the same radius sphere. Thus Morrow could generally accept the results made by geodesists of many countries using these methods. But he simply disagreed on the sign of the curvature.

So, if we think the result is in error, what caused that error? If the error isn't a result of cumulative "random" error, it must be due to a systematic (consistently repeated) error of measurement or procedure.

This motivates us to look again at the rectilineator itself. Morrow assumed that it was a rigid body that simulated a perfect rectangle, and when adjusted to that condition, it remained in that condition throughout the experiment. A casual look at it gives the impression that it was designed for maintaining its geometry. Those steel cross braces look as if they were intended to provide rigidity and preserve that geometry.

Morrow says that the purpose of the steel rods was to allow initial adjustment of parallelism of the 4 foot cross beams at the ends of the rectilineator. In fact, adjustment of the rods will alter that condition by small amounts and allow one to achieve a high degree of parallelism initially. The rod tension acts against the tension in the mahogany structure. The rectilineator sections were flipped top/bottom each time they were reused, which might be expected to average out any slight and unnoticed lack of parallelism over the whole span of 1045 sections. This seems to be good experimental procedure.

The rectilineator isn't as rigid as it looks.

But there's no such thing as a perfectly rigid body. Bodies flex and warp under load, even under the load of their own weight. A horizontal beam suspended or supported at its center will bend so that the ends droop downward. This can be minimized by suspending or supporting the beam at two points, carefully located. Even then the beam bends somewhat, but in a way that doesn't affect the parallelism at each end. Knowing the materials and the dimensions of the parts, these points can be calculated precisely. Was that done? Morrow doesn't say.

The rectilineator sections were supported by standards (vertical support piers) at two points. Photographs and drawings show the standards in place, and they are consistently placed. And they are wrong. Calculation made from the photos, and from Morrow's drawings, shows that the points are both about 2.6 inches too close to the center of the rectilineator. This would allow the ends to sag downward.

   

The support points the Morrow team used would have been very close to the correct points if the four 45 degree wooden braces weren't present. Those braces make the ends heavier. One might wonder whether those braces were an afterthought, after the experimental design had been completed. But that can only be speculation without more information than we have in hand.

What about the initial carefully-established parallelism of the cross beams? Those steel cross rods do not connect to each other where they cross, and are secured to the wood center beam with 8 short wood screws no longer than 3/4 inch! Such a structure will be no more rigid than if the rods weren't there. In fact, if the main beam bends, the cross beams will move out of parallelism and the rods won't prevent that, because the rods will go slack.

   

 
These photos of a scale model rectilineator show that the cross rods do not contribute to rigidity. The end cross beams easily move out of alignment, and the more they depart from parallelism, the slacker the rods become.

This model is a better simulation of the Morrow rectilineator. In the first photo the horizontal beam is made rigid with a steel strip bolted to it. In the second photo nothing is changed except that the steel strip has been removed, and the thin plastic horizontal plate allowed to sag. The cross braces go slack again.

The initial adjustments for parallelism were apparently made with the rectilineator lying in a horizontal plane. So as soon as the rectilineator was positioned in a vertical plane, it lost its parallelism because of bending under the force due to gravity.


   


Even if the rectilineator had been designed properly, and as rigid as good engineering design would allow, the structure would still not be perfectly rigid. The error in the support point locations would still result in the ends sagging downward. But the fact that the rectilineator design allows unnecessary non-rigidity suggests that Morrow and his team did not consider rigidity an issue. Nowhere in the available accounts is this mentioned as a possible source of error to be dealt with. Nor did critics of the experiment suggest that possibility.

Inverting the rectilineator section top/bottom doesn't help either, for the structure will still sag in the same sense, with ends drooping. Could this be the systematic error that accounts for the results? With the materials used in the rectilineator, the sag can't be very large. But a sag of only 0.000003 degree in each section, multiplied by the 1045 sections in a four mile length, gives a cumulative error of 0.003 degree. That would be about the latitude difference between the endpoints of the survey. Such a small error was far too small to be measured or detected in just one, or even a string of a few, rectilineator sections.

This is a subtle source of systematic error. The preliminary tests of the rectilineator were done with only a few of those sections they had (four). The systematic error for these would be far beneath detection level during those tests. An individual section's cross arms might deviate from parallelism in one of two directions, or might, by sheer accident be nearly parallel for one orientation of the rectilinator. If it deviated in one direction, then when the section was inverted, the deviation would flip in the other direction and still be such as to cause the ends to bend downward. Even if by pure accident the first few rectilineator sections were aligned exactly parallel, the procedure of "recycling" sections and inverting them would ensure a systematic error from that point onward of about the same amount over the entire length of the survey.

The procedure of inverting the sections guaranteed that any initial systematic error would propagate to cause significant error in the results. If the cross arms had accidentally been initially perfectly parallel for all sections (a very unlikely situation) and the sections had not been inverted, then no systematic error due to bending would have been seen over the full length of the survey. If there were an initial error of leveling, and the sections had not been inverted, the systematic error could have given results showing either positive or negative curvature of the earth, with equal likelihood, and of size that could have ranged from zero to the value reported, or even more. The seemingly sensible systematic procedure of inverting sections when they were reused doomed this experiment to success, at least success as the Morrow team saw it.

Systematic error would automatically result in excellent agreement between the measuring instruments. They would all agree, all the way along the line. As the line progressed southward, the plumb bob on the end of the cross arm would deflect southward, the bubble on the spirit level would move northward, just as Morrow observed. All of these measures depend directly on the actual downward arc of the rectilineator land line. The horizon sightings would reflect this also. But all this time the experimenters thought the land line was straight, and the earth curving upward, when in fact the earth curved downward and the rectilineator land line curved downward even more.

Expectation bias?

But this seems too easy a solution. Surely it stretches credibility that the bending of the rectilineator would be just right to give a result of size within 2% of the expected value. By "expected" I mean the value of earth radius that the experimenters expected. And that may be the key word here. Expectation bias could have played an important role. {2}

Morrow notes that in the first 1/4 mile the changes in all data readings showed no clear evidence of curvature. This was no surprise, for the expected curvature was smaller than random instrumental errors. But by the end of the first mile the curvature was clearly shown, and it was in the expected direction. Morrow had previously calculated a table of numbers indicating what data should result for (1) a concave earth, and (2) a convex earth. When the numbers began showing curvature in the direction supporting the concave earth hypothesis, the entire team must have been encouraged and elated. Still, measured values weren't perfectly in agreement with expectations. Morrow wouldn't have been much concerned about that, attributing it to the expected random errors of individual measurements. This would work itself out as the rectilineator line became longer. Perhaps it did.


   

Now we can imagine the team continually checking heights above water level, plumb line and elevation, as the survey preceded southward. Each time a new 12 foot section of rectilineator was positioned, these were compared against the precalculated tables. Each measurement was made to the limits imposed by the instrument scales, and involved some judgment. Under these conditions there's a distinct possibility of unconscious bias to make each measurement agree more closely with expectations. It wouldn't take much "correction" each time. These measurements and adjustments were made every 12 feet for nearly 4 miles. That's nearly 1760 sets of measurements. In this way the experimenter's expectation bias can introduce a systematic error. Each measurement is biased just a bit in the direction of better, but not necessarily perfect, agreement with the precalculated values. [The published data tables show values only every 1/8 mile, over most of the 4 mile distance, a total of only 25 values.]

Nowadays we are more sensitive to the importance of avoiding the possibility of such errors. Experiments where such bias is possible are designed to be blind and double blind. In this case, the rectilineator positioning, manipulation, and measurements should have been done by people who had no idea what the expected outcome was. But even more important here, the design of the rectilineator and its initial adjustments should have been subject to independent and competent scrutiny. The persons making the measurements should never have had access to the previously calculated values expected for a concave earth, convex earth, or flat earth.

I have presented a plausible hypothesis explaining how a systematic error in the rectilineator design itself (allowing bending), a blunder in calculating the two support points, combined with a systematic error due to expectation bias, could easily account for the published results of the Naples Experiment. But because the case is so old, and the original sources we might like to examine are just not available, we may never be able to declare that all the "loose ends" of this experiment have been tied.

However, this analysis clearly establishes that the method of the experiment was flawed. Its assumption of perfectly rigid rectangles cannot be supported. It ignored the possible propagation of a very small determinate error, easily capable of accounting for the result the Morrow team observed.

Was this experiment doomed to failure?

But there's another interesting aspect to this. From what Teed has written, we see no indication that he ever worked out the full mathematics of the Cellular Cosmogony, but concentrated on qualitative descriptions. Morrow and Teed probably understood that their model of the universe required that the speed and direction of propagation of light both must change drastically with distance from its center. But there was little motivation to get mathematical about it. Morrow's writings don't indicate that he dealt with the mathematics of the entire model. Morrow's interest was focused only on the surface of the earth.

Even today we see small groups around the world who still advocate models evolved from Teed's Cellular Cosmogony. How does such a hollow earth idea survive today, in the era of space travel? The Koreshans didn't have to deal with explanations of anything from earth venturing far from their rock shell. They didn't have to sweat the mathematical details of variations of speed of light with distance from earth. The Koreshans could describe the Moon as an illusion caused by focalization of light. Today men have walked on the Moon, and the "illusion" idea doesn't survive, unless, like the modern flat-earthers, we assume that the entire space program is a giant conspiracy to deny the truth, faked on a Hollywood sound stage with clever special effects.

While most hollow earth promoters aren't capable of doing mathematics or physics, a few have at least looked at the mathematics. They make mathematical models of the universe based on a transformation of R to 1/R where R is the distance from the center of the earth (on the conventional view). In 1983 mathematician Mostafa Abdelkader published a paper in which he worked out the mathematical consequences of this. He concludes that there's no way to distinguish between this model and the conventional model—no way to tell if the universe is the way you learned it in school, or whether it is inside-out. He does conclude his paper by saying he favors the inside-out view. [6]

This is mathematically justified, and reminds us that mathematical models are our own invention to describe what we observe in nature, and sometimes several vastly different-appearing models can equally well do the job. But, accepting this, we must realize that this mathematical reconfiguring of the space metric works near the earth's surface also, so the Naples experiment would be doomed to failure even if everything had been done perfectly. Not just light paths are warped in this model, but so are angles. Physically "straight" rulers are warped also and we wouldn't know it. Even worse, you could have a 1/R² remapping, or any other consistent mathematical transformation, and you still couldn't distinguish one model from another by any clever experiment you might devise. [7]

Several websites promote variations of this idea. Two distinct versions are seen:

• The strict mathematical remapping of the geometry. These folks admit there's no experiment that one could devise to distinguish one model from another. None have taken on the formidable task of mathematically transforming physics, only the geometry. Therefore they tout their preferred model as being simpler and therefore better. Any such model may seem simpler if you do only the easy part of the transformations! The fact is that they are simply not capable of reworking the physics that would support their hypothesis.
• Others don't accept, or even understand, the indistinguishability of transformed models, and still cite long-discredited "evidences" for their model, such as the Naples Geodetic Survey, the Tamarack Mines Diverging Plumb Lines, radio trasmissions to any point on earth, etc. Some even hope to undertake their own experiments to determine the curvature of the earth, but are ill-equipped to design an experiment properly, or interpret its results.

Some of these folks seem to be motivated by religious beliefs, attempting to make the model consistent with their interpretations of their sacred literature. Some are motivated by a distrust and dislike of science. Many feel that science has become just too difficult for people to grasp, so there must be a simpler way to understand it. A few have even majored in a science at the university for a while, but dropped out because they found it distasteful. All are sustained by a monumental self-confidence in the "rightness" of their world-view. They comfortably accept the notion that scientists are part of a vast conspiracy to suppresss the truth, in order to maintain their own positions of power and prestige.

Like pseudoscientists of all varieties, they carefully select those aspects of experience they wish to incorporate into their model, ignoring the vast amount of other scientific phenomena that conventional science has already successfully dealt with. They cite old, discredited, or poorly documented, observations, experiments and theories that seem supportive of their views. They misinterpret and misrepresent sources to fit their beliefs. Often they wage a guerrilla war against "conventional science", and characterize scientists as imperceptive or even stupid for not acknowledging their cleverness and the truth of their alternative models. They imagine themselves a member of a select few, the elite, who can see things clearly, things that highly educated and experienced scientists are "too blind" to see.

Updates, July 2015.

I've been criticized for not mentioning that Morrow checked his data by extending the rectilineator line backward from the last position, back toward the starting point, and this recreated the curvature nearly exactly. This was reported only between mile markers 2 3/8 and 2 in the The Cellular Cosmogony. I naively assumed that it would be obvious to the reader that such an exercise would demonstrate nothing more than the fact that this "return survey" followed the same procedure as the forward survey. Apparently this was not so obvious to some.

Consider the forward survey's last rectilineator position. Now for the return survey, this section is left in place (already tilted downward toward the earth at the far end) and the other sections are then fastened in turn to it. If they sag consistently as in the forward measurements, the reconstructed backward measurements will duplicate the curved path of the forward measurements. The return survey only demonstrates that the measurementes were performed in the same manner both forward and backward, with the same procedures and (sagging) apparatus.
   

I've also been criticized for not emphasizing that a committee was always present to ensure that the measurements were correctly made, with no cheating or data fudging. However I did make clear that the results were mainly due to the non-rigidity of the rectilineator sections. One reader (an engineer) reminded me that the amount of sag of such a limp structure depends on the placement of the two vertical standards (supports) of each rectilineator section. Was Morrow aware of this, and did he calculate the proper placement of the supports that might ensure parallelism of the ends of each section? He doesn't address this issue at all. His procedure of inverting each section does not correct this possibility. My correspondent suggests that Morrow might have deliberately chosen the placement of the standards to ensure the desired result—concave water surface of the desired amount. This is, of course, speculation, but it would be an ingeniously clever way to deceive the observing committee, for all the tedious positioning of apparatus and the careful and precise measurements would then be honestly made, and only a very astute committee member would question the apparatus itself.

But I think the most fundamental criticism, from a physics student, has to do with something every physics and engineering student is supposed to learn and use in all laboratory experiments: analysis of uncertainties (error analysis). This mathematical procedure shows how uncertainties in the data propagate to determine the uncertainty of resuslts. This whole Naples experiment hinges on the assumption that the initial rectilinator position is exactly positioned relative to the water surface, as measured by the spirit level, mercury level and the plumb line. These measurements should be consistent, but they have limited precision. Any slight error in the placement of the initial 12 foot long section will propagate as other sections are successively attached and relocated. There's no way the final result, over four miles, could have the precision claimed. This strongly argues that something was fudged.

This also answers the question "Why has this experiment never been repeated by skeptics?" One reason is that they know that it is a poorly designed experiment even if performed honestly. It might be interesting as a student project to build one rectilineator section exactly as Morrow did, and then test its rigidity and the amount of sag as a function of the position of the two standards (supports), and also how it behaves when inverted.

But the whole business seems futile in the light of the Koreshan's fundamental notion that the geometry of the entire universe is warped in such a way that we have been deceived about it's "actual" construction. If that were so, the physical equipment used in the Naples experiment, the rectilinator, rulers, etc.) would also have been subject to this warping, and the experiment would prove nothing. In fact, there's no conceivable way we could establish a reference line guaranteed to be "straight", independent of this universal space warping.

I've also been asked about the justification for the title "Professor" that Morrow used. he had once been principal of The Corning School of Shorthand in Corning Iowa, and in 1888 published a book "Phonography" a textbook on his system of phonetic shorthand. He had no earned degree in anything, certainly not geodessy, but was apparently well read in techniques of surveying.

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Published on – April 4, 2017 

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