Fun With Science  /  Globe Deconstruction  /  Bottom-Up Observations  /  The Flat Surface Test

Something Did Disappear Over a Flat Surface

The arithmetic on his slide is right. A globe hides nothing at 540 feet. His own frames show what hid the raft — and it is not the atmosphere, and not the Earth.

On 18 August 2026, Levi Miller towed a white inflatable lounger 540 feet across a suburban pond and filmed it from a lens 0.375 inches above the water — Can an object completely disappear over a flat surface? first 3 attempts. The raft vanished, low end first. We measured the published video and his camera originals: geometry, fade, focus, water surface, the whole eleven minutes of the main run.

Observation concededNot evidence about the Earth
Where this lands

The claim. The book’s Claim #1, p. 2 (restated at p. 209): “Objects can disappear from the bottom up across a flat surface due to the limitations of angular resolution.” The video is its demonstration — a raft gone low end first at 540 feet, with nothing in the way.

His slide is right. Curvature hides nothing at 540 feet from any camera height he used — zero inches — and anyone answering this video by disputing the geometry has not checked it. Objects really can disappear over a dead-flat surface, and he went and showed it.

What hid the raft is not the book’s angular-resolution limit. By the book’s own 1/60th-of-a-degree criterion the raft should never have been lost: it clears that limit by 2.1× in height. What hid it was angular compression against a camera working five times below that limit. From a third of an inch up, every foot of water from fifty feet out to the far bank piles into about two arcminutes of visual angle (an arcminute is 1/60 of a degree; the full Moon spans about 30), and the camera’s finest renderable edge is 4.8 arcminutes — the pond watched with 20/100 vision. The raft never sinks behind anything: it loses every background it could be told apart from and dims below the noise floor, thin end before tall, the ordering a tapering target gives for free.

Compression does not swallow the raft. It removes any clean background to see the raft against.

Refraction is the one candidate the footage excludes. Bending strong enough to bury four inches at this range would end the pond in a band of false sky 127 feet from the lens. Eleven minutes of footage show the opposite signature: erect reflections running unbroken to the far bank.

None of it bears on the shape of the Earth. Whatever hid the raft is roughly 48× stronger than curvature could possibly be at that range, and it lives in the first inches above the water: in attempt two the camera descends at a fixed framing and the raft goes from plainly visible, to a dot, to gone. Curvature does neither. It should also reverse under magnification from the low position — the cheapest test in §5, and the one nobody has run. The pond cannot speak for a ship eight miles out, in either direction.

1 · What the video gets right

The calculation slide is correct, every line of it. Recomputed independently with R = 20,903,520 ft:

QuantityHis slideRecomputed
Horizon distance from 0.375 in1,143 ft1,143.01 ft
Sightline reaches water past targetover 600 ft603.0 ft
Threshold eye height, d²/2R at 540 ft0.0837 in0.08370 in
Ratio, 0.375 in to threshold~4.5×4.480×
Height hidden by curvature at 540 ft0 in0 in

It is conservative, too: fold in standard surveyor’s refraction (the refraction coefficient k, the fraction of the Earth’s curvature that ordinary air bends a sightline along, k ≈ 0.13–0.17 — the “seven-sixths Earth” rule) and the hiding threshold drops further, leaving his lens about 5.2× above it instead of 4.5×. “You forgot refraction” has it backwards.

He built a rig, checked his own arithmetic, published the raw files and invited criticism, and the arithmetic held up under it. The method visibly improves across his three attempts — fixed camera, towed target, thin strings, orientation corrections — and the fixes in §5 are the ones any experimentalist would reach for second time round.

But disappear covers three things. A target can fade, losing contrast until nothing is left to resolve; it can shorten, its thin end falling below what the lens can render; or it can be occluded from the bottom up, as a car is when a hot road bends the sightline into a false horizon. Only the last is what a curved surface would also produce; the other two happen to a target in plain view on a flat plane. Which took the raft is a question of evidence, and §2 measures it.

2 · What hid the raft

One observation repeats across all three attempts: the raft is plainly visible from a raised camera and gone from a lens under half an inch. That height-dependence retires two candidates at once — curvature, which hides zero from every height used, and the raft’s angular size, which does not change when a camera rises — and points at what the vantage does to the scene:

View from a lens a third of an inch above a pond: blurred water filling the lower third of the frame, a thin bright strip of mown grass along the far bank, a treeline above it, and two out-of-focus reed stems standing in the near foreground.
The whole pond, from a third of an inch up. The lower frame is near water out of focus; the far bank is a thin strip of grass under the treeline, and the raft at 540 feet is silhouetted against the bottom edge of that strip, not against water. Published video, 7:20, wide framing.
Where the pond lands in the picture, from two heights Two schematic camera views of the same pond. From six feet up, the water is a broad field filling the lower half of the picture, with distance markers at 50, 100, 200, 300 and 540 feet spread down the frame and the raft a distinct mark in open water, about seventy pixels below the far shore. From a third of an inch up, sky, treeline and a thin grass strip fill the picture and the entire water surface beyond fifty feet collapses to a line a few pixels tall, with the raft overlapping the base of the grass strip. A magnified strip below shows that slice at pixel scale: the raft is four pixels, the whole far pond about two, and a bracket shows the camera's smallest renderable edge, nine pixels, covering all of it. Where the pond lands in the picture Camera 6 ft up — the pond is a surface 540 ft 300 ft 200 ft 100 ft 50 ft far shore raft — its own mark, in open water, 38′ (≈ 70 px) below the far shore Same framing and angular scale in both panels. Gridline spacing is the real mapping: depression angle ∝ 1/distance. Camera 0.375 in up — the pond is a line raft — against the foot of the bank all water beyond 50 ft: 2′ ≈ 4 px near water, out of focus, fills the rest The boxed slice, at pixel scale — each band is drawn its true height in video pixels grass strip, far bank the raft — 4 px waterline + reflection fold + every foot of water from 50 ft to the far shore — 2 px near water, defocused 9 px the smallest edge this camera can draw The raft, the entire far pond, and the junction between them fit inside one edge width — all of them fighting to set the colour of the same few pixels.
The raft, the entire pond behind it, and the junction between them all fit inside one blur width. Four inches at 540 feet subtends 2.12 arcminutes. Every foot of water from fifty feet out to the far bank is squeezed into 1.95, all of it below eye level. Stacked, the whole scene — far water, waterline, reflection fold, the foot of the bank, and the raft on top — spans 4.07 arcminutes. The smallest edge this camera can draw is 4.8. The instrument cannot separate any of it from any of the rest — not because the raft is buried in the band (nine-tenths of its height projects clear above the entire pond, and anyone checking the frames will see it standing above the water) but because nothing clean stands behind it.

In units anyone can feel: the camera’s smallest renderable transition — nine pixels at 0.533 arcminutes each — is 4.8 arcminutes. An eye with 20/20 vision resolves about one. The video is watching the pond with roughly 20/100 vision, five times coarser than the person holding the phone. A 2.12′-tall, 37′-long, bright-white raft is a comfortable sliver to a human eye; to this camera its entire height fits inside half a blur width, and a pixel holds one colour, the average of everything that falls on it. Four inches of raft is outvoted by five hundred feet of scene sharing the same four pixels. It is the beach experience — the boat you cannot make out by eye, with the water visibly continuing past it, that binoculars bring straight back — built into the design: four hundred feet of “sea” squeezed into two arcminutes, watched with a fifth of the eye’s resolving power.

The fade says the same thing. The raft’s peak brightness against the background beside it:

t (s)415424433439445451460
Raft peak238225221181135140140
Local background109113113114111117118
Contrast12911210867242322

The background never moves; the raft dims where it stands, from full contrast to the noise floor in thirty seconds during which its distance changed three percent. That rules out a mirage line, which replaces what it hides with bright false sky: the background here never brightens.

The raft does not sink; it fades out where it stands — faint edges first, bright core last. One caveat is load-bearing: at four pixels under a nine-pixel blur, a genuine rising cut could not have been resolved either, so these frames cannot separate fade from cut on the raft itself. They do not need to: the two mechanisms that would draw a real cut, curvature and a mirage line, are excluded independently, and a tapering target under falling contrast reproduces the ordering with nothing hiding anything. The low end did go first. That is evidence of the shape of the raft, not of anything it was floating on.

What the three attempts add

Attempts one and two lose the raft over glass. Mirror-smooth water, no wind, no focus trouble — and the raft still dims out as an unresolved dot where bank, waterline and reflection meet, while a white bench a few feet up the same bank stays plainly visible in the same frames. Whatever removes it operates only at the waterline: compression on a calm day, needing nothing else.

The main run adds weather. For its first six minutes the pond is glass. Around t = 380 s ripple trains sweep in, the camera’s focus leaves the far field — the treeline goes from its usual 8-pixel edge to 20–22 — and the blurred near water climbs the frame across the raft’s image band. The raft’s contrast collapses inside that window, 415–450 s. Defocus accounts for roughly half the collapse; near-field chop, standing into a sightline that begins nine millimetres above the water, owns the rest.

Two frames of the far bank side by side. At t equals 300 seconds the water is mirror-smooth and the treeline's reflection runs unbroken down to the waterline, with a bright strip of grass visible below the trees. At t equals 445 seconds the near water is ruffled and blurred and has risen in the frame to cover the waterline.
Left, t = 300 s: glass. The treeline’s mirror image runs unbroken to the waterline — the signature a mirage-strength layer would destroy, present through every calm stretch. Right, t = 445 s: the wind event. Ruffled near water, defocused, risen to swallow the waterline and anything on it. From no crop.MOV, native-resolution crops.

That blur is differential — the treeline’s edges roughly double while a reed a few feet from the lens holds its 3–4 pixel edges in every frame, which fogging, encoder trouble and a shaking mount cannot do — and static: the softened treeline edge holds position between consecutive frames to about a tenth of a pixel in the median, under half a pixel in nine columns out of ten, against the 20–22 pixel blur it would have to account for. Air turbulent enough to double an edge width makes it dance. A lens refocused toward the near field, baited by the new ripple texture, does exactly this.

Three crops of the same near reed against the distant treeline. At 300 and 650 seconds the treeline shows leaf structure and the reed is slightly soft. At 430 seconds the reed renders crisply against a treeline that has lost its texture.
Reed edges hold, treeline doubles. Same reed, same treeline, three moments; in the middle frame the treeline has lost its texture while the reed stays at 3–4 px. Sparing the near field is the signature of focus, not weather. From no crop.MOV, native-resolution crops.

He anticipates the focus objection with a caption — the trees come back into focus and the raft is still not there — and he is right about that: four pixels against a nine-pixel floor predicts it stays invisible at full range. It cannot show why it went, because it went while the camera was soft and the near field was up.

The target itself. The lounger is a wedge — four inches at one end tapering toward nothing — towed on strings, and it yaws; his own method cards say he corrected its orientation mid-run. Thin ends carry less light, so under any uniform loss of contrast a wedge goes thin-end-first, and a yaw toward end-on cuts the visible streak severalfold. But a wedge losing its thin end gets shorter, not lower; bottom-up is the opposite ordering, height falling while length holds. At this range a low object shrinking a couple of arcminutes above the waterline reads as sinking — but the raft’s whole height is 2.1 arcminutes against a camera whose finest renderable edge is 4.8, less than half of one resolution element. There is no vertical extent to lose from the bottom; what can change is the length, and length is what the frames show changing.

The near shore. At the start of the run the raft is filmed through reeds inches from the lens, and an obstruction inches away needs almost no height: a half-inch crest fifteen feet out hides 4.9 inches at 540 feet. His calm-water check was filmed at the pond’s midpoint, where the lever arm is 2× instead of 36× and hiding all four inches takes a crest of about 2.2 inches — the one place along the sightline where surface state barely matters.

Extreme crop showing the white raft with its orange stripe, its outline interrupted by several dark vertical grass stems standing between it and the lens.
Not an inference. The raft — white hull, orange stripe — behind near-shore grass stems inches from the lens. A stem no taller than a finger covers a great deal of raft at 540 feet. From no crop.MOV, t = 20 s, enlarged.

3 · What it was not

4 · Why a pond cannot speak for the sea

Grant everything the video shows. To bury four inches of raft, something must hide four inches; curvature at 540 feet can hide at most 0.0837 inches, from a lens at zero height.

Whatever hid that raft was roughly 48× stronger than curvature could possibly be at that range. For curvature alone to do it, the raft would have to sit 4,876 feet away — nine times further than it was. He has not found a small curvature effect. He has found a large local one.

Local effects do not scale the way curvature does. Curvature’s hidden height grows with the square of distance beyond the horizon — 0.08 inches at this pond becomes forty feet at eight miles — while a near obstruction grows only linearly and the vantage effect dies when the observer stands up. What survives at sea ranges is the atmosphere, which accumulates along the path, and that connects this pond to the two classic low-camera anomalies:

The same grazing sightline, bending two ways Two side-by-side schematics comparing the Bedford Level and Rampion cases with this pond test. In both, a camera sits within inches of the water and looks along a nearly horizontal sightline to a distant target. On the left the near-surface air bends the ray downward so it follows the surface, and an object that curvature says should be hidden below the horizon stays visible. On the right the air above a warm surface bends the ray upward instead, so the sightline passes over a nearby object and it disappears even though curvature hides nothing at that range. The same thin layer produces both results, with opposite signs, and each has been presented as evidence against a spherical Earth. Bedford Level 1838 · Rampion near-surface layer camera, inches up ray bends down, hugging the surface base stays visible Something stays visible that curvature buries. Curvature at 8 mi / 11 mi: 23 ft / 53 ft should be hidden. Read as: “there is no curvature.” This pond, 2026 near-surface layer camera, inches up ray bends up, off the surface whole target hidden Something vanishes that curvature leaves alone. Curvature at 540 ft: 0.08 in — nothing at all. Read as: “hiding needs no curvature.” One thin layer, two signs, two opposite anomalies — and both have been presented as the same conclusion. Hidden heights assume a camera about 3 ft above the water.

One rule covers all of it: light bends toward denser air. Cool water under warm air bends rays down along the surface, and distant objects stay visible past where geometry buries them — the Bedford Level of 1838, and the Rampion turbines we answer on our own page. Warm surface under cool air bends rays upward, and low objects vanish early — the hot road, and the claim made for this pond.

What cannot be held at once is both anomalies as evidence against a globe. The Bedford reading requires the near-surface air to be optically quiet; the pond reading requires it to be violently active. Once the first inches of air are doing anything at all, the visibility of a low object stops being a measurement of the planet’s shape, in either direction. That is the yield of this experiment: sightlines grazing a surface belong to the surface layer and the instrument, not to geometry.

A hull-down ship is a different observation in kind. Its truncation is resolved: a sharp cut with a sharp superstructure above it, at a height that follows d²/2R, and zoom shows the cut more clearly without bringing the hull back. The pond fade is unresolved, smooth, and reversed by optics: where the camera height of his zoomed shots can be established, the zoom recovers the raft. That is the standard both sides’ low-over-water videos should be held to — a P900 superzoom pointed at a “missing” skyline is running exactly this test, and what it brings back was never hidden, only unresolved.

5 · The afternoon that settles it

Wallace resolved this experimental design in 1870: raise the sightline out of the surface layer, and give the geometry a graduated marker so it can be read rather than argued. The modern version is five items, four of them possible at the same pond in one afternoon.

And the free one, suggested by a commenter on the video: run it again on a frozen lake. Ice removes the ripples. It does not remove the reeds — dead stems stand all winter with the same lever arm — and it does not remove refraction: a cold surface under warmer air is the classic setting for a strong low-level inversion, which bends light down around the surface and can lift distant objects into view, the Arctic looming case, opposite to the effect being looked for. So the result forks: a winter run that recovers the raft refutes nothing here, and one that loses it confirms little. The probes from item 5 decide it — optional over water, decisive over ice.

What would change our mind — written before the fourth attempt

Committed on 23 August 2026, and sent to the author on 20 August, before any fourth attempt existed. The raft comes back under magnification from the low position: it was never hidden, only unresolved, and the compression account held. It stays gone under 5× magnification from a clear sightline, focus locked: something physical stands in the light path and compression is insufficient on its own — the qualifier matters, because magnification does nothing about a grass stem inches from the lens. It still vanishes from six feet, filmed simultaneously against a ground-level camera: every mechanism proposed here is dead, and what remains is a plain detection limit, a fact about cameras. A staff’s hiding line begins near 1,100 feet and grows as distance squared at a rate matching 1/R; we do not expect it inside 4,876 feet. A run on ice is read per the note above, and only the probes say which way.

What would not change our mind is the same run in 4K. A cleaner encode buys nothing; genuine 4K capture would roughly halve the camera’s floor — four pixels under a nine-pixel edge becomes about eight under ten. That is a factor of two where the claim needs tenfold, against focal length’s five-to-twenty and elevation’s everything, and it touches neither the geometry, the near field, nor the focus. The design, not the pixel count, is what the five items repair.

Method notes

Sources & further reading