This blog is for nonprofit, educational purposes - media is incorporated for educational purposes as outlined in § 107 of the U.S. Copyright Act.

Monday, January 9, 2017

Flat Earth Follies: We should see the stars!

Flat Earth Claim

We should see the stars in NASA photos of Moon or Earth!

The Facts

This is yet another case of Moon Landing Hoaxers and Flat Earthers making false statements about things which they know nothing about.  Ask them how they determined that and you'll get something between a blank stare and a bunch of hand waving.

Truth is, they have NO idea - it's just a stupid meme they pass around.

Here is an image I took of the moon through a very nice set of binoculars I own...

Figure 1. The moon via binoculars & iPhone. 

The moon is probably actually a little overexposed here since it is losing detail in the brightest areas.  But even with that, absolutely NO STARS ARE VISIBLE at this exposure level.

Why can our eye see both but the camera can't?  First of all, a full moon will make it incredibly difficult for you to see all but the brightest stars around it.  If we put you to the test you would fail to see much of anything next to a full moon.  But a deeper answer is that your eye is actually pretty good.

A healthy human eye can see over a range of about 20 stops under scotopic vision conditions (low-light - but only about 10 stops in bright light), which means the brightest parts of the scene you see can be about 1,000,000 times brighter than the dimmest parts (that is, roughly, 2^20).  That is all 'stop' means, in this context 1 stop means the brightness has doubled.  Double that 20 times and you get just a little over 1 million times brighter.  Your eye achieves this in part because the pigments in your retina that sense the light do not have a linear response.

When a camera records 14-bit RAW format it means you could have 2^14 (or 14 stops) of range, but in practice the camera sensor may limit you further than this even though it is recording 14-bits of data it doesn't mean all 14 bits are perfectly recorded and accurate.  But there are some cameras which get pretty close to true 14 stop recording such as the Sony PMWF55, which will also cost you about $35,000 list.  I've little doubt that in the coming years we can push that to 16 bits or even 20 bits eventually (some of which already exist in limited forms).  But dynamic range also comes at a cost in terms of noise and other image quality factors.  When you care about low-light sensitivity you need a large sensor area, that means you usually sacrifice pixels for quality.  There are many other trade-offs that must be made when sending a camera into space for a specific mission.  Whoever is paying for the mission sets those parameters, for example they may need infrared sensitivity which means you aren't going to find a 4K sensor with 14 stop dynamic range in infrared.  You might only get an 8 bit sensor in this case, and it might only be 1024x1024 pixels.

So here is the problem...

The moon from Earth has an apparent brightness magnitude of about -12.5 and even the brightest star, Sirius A, has an apparent magnitude of only -1.5 (and most of the stars are much dimmer than Sirius A).  The Magnitude scale is similar to 'stops' except that 5 magnitude = 100 times brighter.  So that means that the moon is about 25118 times brighter than the brightest star or 14.6 stops.  That's just outside of the range of the best Earth-bound technology sensors -- and it usually takes a few generations before bleeding edge technology can be space hardened to use in the planning stages for a mission and then another decade before the mission is ready to fly.  So even a mission going to space today would be using 10-20 year, space-hardened technology.

So, because of the brightness range of our sensors (dynamic range) and the great disparity between the brightness of the Moon (or Earth) and the stars, it is incredibly unlikely to see stars in an image where a fully lit Moon or Earth are properly exposed.

If some Flat Earther needs to see the stars and the moon in the same shot then I recommend they fund such a mission on their own using a Sounding Rocket and see how well that works out for them.

When you DO find images of the Moon with stars in them you can almost be certain that it is a composite image of different exposures which has later been remixed.  There is a very popular technique for this called HDR Photography (High-Dynamic Range) which does exactly that, you take 2 or more images at different exposures and the software will mix those images together to give you details in the shadows and highlights that would be missing from a single image.

Conversely, there are TONS of images of stars where the Earth or Moon are way overexposed.

There are also images from ISS showing stars and a dimmer side of Earth such as ISS044-E-45215:

Image Credit: NASA ISS044-E-45215


The claim is completely false if not entirely disingenuous in many cases and there are plenty of images of stars from space - even some showing a dimly lit Earth.

Friday, December 9, 2016

Flat Earth Follies: The Sun Gets Smaller As It Sets

Flat Earth Claim

The Sun Gets Smaller As It Sets

The Facts

No, all you have done is allowed your camera sensor to be overwhelmed and as the Sun (or Moon) gets closer to the horizon it is going through much more atmosphere which filters out more and more of the light, so the exposure becomes closer to correct and the bright object appears closer to actual size.

I took the following two pictures with my iPhone at the same time, when the moon was well in the sky.

Moon closer to proper exposure:

Moon overexposed, taken about the same time - just wrong exposure.

The moon didn't get bigger in the few seconds between the images.

Here is a random pic I took of the moon on my iPhone on a completely different day, properly exposed & through binoculars.  Hi Moon.

And here is a streetlamp magically getting closer and closer and closer - according to Flat Earthers.

So no, when properly exposed the Sun doesn't change size - thousands of people have verified this. You are cherry-picking your data and ignoring the obvious and well-known explanation. By making such a blatantly false statements you make yourself look disingenuous.

Sunset Timelapse - By Odd Høydalsvik, Bergen, Norway

Thursday, December 8, 2016

No More Excuses - Flat Earth Fails

What is the distance from the North Pole to the Equator?

~ 6214.93 miles.

What is the circumference around the Equator?
For Flat Earth assume we mean the ground track path of the Sun at the Equinox.

~ 24,901 miles.

Whoops, Flat Earth just failed the most basic of geometric tests.

On a North Pole centered Flat Earth the distance of 6214.93 miles would be a radius and would give a circle of circumference of ~ 39050 miles for the Equator (or path of the sun at the Equinox).  This is BASIC geometry - 2π × 6214.93

That is NO WHERE NEAR the actual value.  You can compare hundreds of sources of information about both distances - thousands of flights, shipping routes, people driving.  We know for a FACT it's nowhere even close to 39050 miles.


Spherical Triangles Explained

What is the sum of the angles on a spherical triangle?

Here is a simple version that ignores the technical details:

Tiny triangle on huge ball, triangle sum will be close to 180° but never exactly 180°
Along the equator, cuts ball exactly in half, is exactly 540° (3x180)
Go all the way around and you get (3x360)-180 is just under 900°
And the ball radius matters to figuring out the actual angles but doesn't change the minimum or maximum possible values.

Here are the technical details along with a (hopefully easy) to understand rationale:

The first point I would like to make is that we first have to define what we're going to count as the angles.  On a simple plane we're ALWAYS talking about the INTERIOR angles of the triangle but a sphere doesn't technically have a natural INTERIOR / EXTERIOR - so you have to define what you want to measure.  Usually people just take the smaller of two and know there is an inverse as well but you can calculate both sum of angles just as easily.  So we will do that.

First of all the SIZE of the sphere is irrelevant to the minimum and maximum values.  Just as the center of a circle has 360° around it regardless of the size each point on the sphere has only 360° immediately around it.  However, the size of sphere does affect the actual angular values for a triangle of some size so you DO NEED that information.  It's not totally irrelevant any more than the length of the sides are irrelevant -- it just doesn't change the minimum or maximum values.


Imagine drawing a 1" x 1" x 1" triangle on one of those rubber balls you get from the vending machine - let's say it's a 4" circumference ball.  It would go all way from the North Pole, down to the Equator, all the way 1/4 around the Equator, and then back up to the North Pole.  Each turn would be a full 90° turn, so that's 270° total.  This is trivial to verify on your own, just make each line 1/4 of the total circumference of whatever sphere you have handy.

Now, draw the same 1"x1"x1" triangle on one of those GIANT beach balls (or any other large sphere).  It's going to look almost exactly like a normal 180° triangle - because it barely curves around the ball at all.  If the ball is a perfect sphere it WILL be slightly more than 180° but so slight you couldn't tell with your eyes.

But no matter WHAT the size of the sphere is, the minimum is 180° and the maximum is 540° or 900° depending on which side of the triangle you are counting.   I will cover each case in detail...

Now let's draw a "triangle" made of 3 points, but all three points are EXACTLY on the Equator of our ball.  That means each of those "angles" is 180° and we have 3 of them so that's 540° total.  Easy.

Exact same answer regardless of the SIZE of the ball BUT, hopefully obviously, the length of the line would have to be longer to make it all the way around.  Ok so far?

But what happens when you move one of those points a little "further" past the equator?  Do you only count the "interior" as being the smaller angles or do you allow it to continue past 540°?  You can do both of course.

This next bit will explore that further....

Ok, let's start with a microscopic, itty bitty, triangle on a HUGE GIANT sphere billions of miles around and nanometers for each leg of our triangle.   That's going to be so close to 180° we could never measure the difference.  So that is the minimum size (180°) and no matter how big our sphere or tiny our triangle it will always be every so slightly more than 180° total.

Let's make the triangle bigger and bigger and bigger... the sum of the angles will grow... they will hit our 270° mark, grow and grow bigger and now we hit 540°... but let's allow it to keep "going" past this part but STILL count the sum of angles on the SAME SIDE of the triangle.  Now our 3 points get closer and closer and closer together on the other side... eventually they are microscopically close and the EXTERIOR angle is back very very close to 180° right?

So what is the OPPOSITE of 180°?

Well, each point has 360° around it so that 3 x 360° -- and we subtract out the 180° which leaves just shy of 900°.  So that is the maximum angular sum for a triangle and the size of the triangle doesn't change that.  It DOES change how long your lines need to be to get to almost 900° but it doesn't change the maximum value.

So the answer is >180° and <=540° or <900° depending on which angles you want to count.

These values hold regardless of the size of the sphere BUT you do need to know the spherical radius along with the lengths of the sides to figure out the actual angles.

Hopefully breaking it down this way helps you and/or your readers.

And since I certainly COULD be wrong or even have made a typo/error here each person must work to understand what I've said sufficiently to PROVE IT to themselves.  That is the only way understanding grows.

Flat Earth Follies: Great Circle Lies of the Flat Earth

Flat Earth Claim

Mr. Thrive & Survive has a YouTube video "MAJOR LIES EXPOSED By TRIANGE RESEARCH" (sic) about how Great Circles are a lie and he used to sail and they never sailed a Great Circle path and his triangle research somehow proves all this.

The Facts

As per usual, it is an unnecessarily long and rambling video (I might ramble but I try to stay on point) that ultimately fails when it tries to make its point.  Let's cover a few of the more obvious misconceptions from the video...

Great Circles vs Rhumb Lines

A Great Circle path is the 'straight line' of a sphere. It doesn't mean that you go in a circle on the surface, you go in a radial circle around the Globe itself.  The length of the Great Circle is the circumference.  That's all it is.

If you put a string between any two points on a globe and pull it taunt it will mark out the Great Circle path.  That's all the more "math" you need to plot one on a globe and it works for every pair of points.  There is NO FLAT MAP in existence where you can draw a straight line between two arbitrary points and have that be the shortest path - period.  You can make special maps where SOME straight lines are the shortest distance; for example the Gleason Map is actually the azimuthal equidistant projection where every point on the map to the center AND ONLY THE CENTER is accurate, every other path is distorted to make that fit.  This is why this map utterly fails when you try to look at flight paths in the Southern Hemisphere.

The Equator is a Great Circle for example, it takes you all the way around.  Every line of longitude is a Great Circle - but the only latitude line that is is the Equator -- all the other lines of latitude get shorter and shorter.  It's called a Great Circle because it always goes all the way around the globe, never shorter.   So the Longest possible route around the Globe is also the shortest path between two points that fall along that line.

Before we had satellite navigation and computers ships traveling shorter distances (maybe 1000 miles) would often take a path called a loxodrome (or Rhumb Line) because this is a path with a constant compass bearing so it is easier to manually navigate this way.  However, over greater distances these paths become significantly longer than the Great Circle paths and it becomes very inefficient to continue to navigate using a Rhumb line route.

All modern, long haul shipping now uses Great Circle routes.  You can see this in how the routes that are further north/south of the Equator appear as arcs on the Mercator projection.

Here is an example of a Great Circle (in Red) route using Google Earth showing why this is so:

This diagram shows the issue with the Rhumb line distances compared to the Great Circle path.  The Rhumb line path turns out to be a spiral towards the pole.

The nice thing about Rhumb lines is that if you are navigating using a Mercator Projection they are the straight lines. [more info]

So my question to Mr. Thrive & Survive -- do you have any evidence for your claims about what routes you sailed and why?

Ancient Trigonometry

He then argues that since non-Euclidean geometry wasn't invented until the 1800's ancient navigators couldn't POSSIBLY have used spherical trigonometry and offers this as "proof":

The problem is that isn't the WHOLE story.

Eder, Michelle (2000), Views of Euclid's Parallel Postulate in Ancient Greece and in Medieval Islam, Rutgers University, retrieved 2008-01-23

Shows that Ibn al-Haytham contributed to alternative geometries as far back as the 11th century and...

Boris A. Rosenfeld & Adolf P. Youschkevitch, "Geometry", p. 470, in Roshdi Rashed & Régis Morelon (1996), Encyclopedia of the History of Arabic Science, Vol. 2, pp. 447–494, Routledge, London and New York:
"Three scientists, Ibn al-Haytham, Khayyam and al-Tusi, had made the most considerable contribution to this branch of geometry whose importance came to be completely recognized only in the nineteenth century. In essence their propositions concerning the properties of quadrangles which they considered assuming that some of the angles of these figures were acute of obtuse, embodied the first few theorems of the hyperbolic and the elliptic geometries. Their other proposals showed that various geometric statements were equivalent to the Euclidean postulate V. It is extremely important that these scholars established the mutual connection between this postulate and the sum of the angles of a triangle and a quadrangle. By their works on the theory of parallel lines Arab mathematicians directly influenced the relevant investigations of their European counterparts. The first European attempt to prove the postulate on parallel lines – made by Witelo, the Polish scientists of the thirteenth century, while revising Ibn al-Haytham's Book of Optics (Kitab al-Manazir) – was undoubtedly prompted by Arabic sources. The proofs put forward in the fourteenth century by the Jewish scholar Levi ben Gerson, who lived in southern France, and by the above-mentioned Alfonso from Spain directly border on Ibn al-Haytham's demonstration. Above, we have demonstrated that Pseudo-Tusi's Exposition of Euclid had stimulated borth J. Wallis's and G. Saccheri's studies of the theory of parallel lines."

The Greek astronomer and mathematician Hipparchus produced the first known table of chords in 140 BCE. His work was further developed by astronomers Menelaus (ca. CE 100) and Ptolemy (ca. CE 100). The average sailor used tables and things like the ASTROLABE (often attributed to Hipparchus) - they didn't do the math by hand.

[See also: The Oxford Encyclopedia of Philosophy, Science, and Technology in Islam]

But the deeper answer here is simple, Spherical & Conical geometry are NOT the same as formal non-Euclidean geometry -- non-euclidean geometry is a very abstract form as opposed to simply understanding spheres and basic trigonometry.

It takes about 5 minutes to research Hipparchus, Menelaus, & Ptolemy sufficiently to see that he is simply mistaken in his assessment.

This argument is the same as saying "Quantum Mechanics uses division so they couldn't have been using division 2000 years because that's Quantum Mechanics which was invented in the 20th century!" He confuses one component with the whole.

Horizon Rises To Eye-Level?

This is the simplest claim to completely debunk (as I have in this post which goes into more detail and has some video examples as well).  I have personally taken images from airplanes that disprove this absurd claim that is just so blatantly false it's hard to believe that even Flat Earthers keep repeating it.

This first image is to show the Theodolite application works and that it works well.  You can see that CAL is not activated so I have NOT recalibrated it, I'm using the default in all images.  But, by all means, don't trust me, get the Theodolite app (or some professional instrument) and make your own observations.

To explain this a bit, the red square+cross reticle here marks out LEVEL from my position and you can see that, despite my purposefully tilting the phone, it nails the actual horizon here from ground level.  The white cross-hairs just mark dead center.

This next image is from about 25,000 feet and I've pointed the 'dead center' cross hairs at the horizon and you can see this is marked as being 2.8° below level.   This is exactly where it should be on a Globe of 3959 miles radius.

And as we go up to 38,000 feet the horizon drops to about 3.4° - again, exactly where it should be on a Globe of 3959 miles radius.



He doesn't prove anything in this video except that he doesn't actually understand sailing, spherical geometry, trigonometry, history, what the horizon actually looks like, or anything else that I can tell.

Friday, December 2, 2016

Flat Earth Follies: Clouds Lit From Underneath Prove Flat Earth, say what?

Flat Earth Claim

Sunlight hitting the bottoms of clouds proves Flat Earth and yet (somehow) is impossible on a Globe (even though on a Globe it would be much further away and so the same argument would actually apply in both cases-except that argument is just Flat Out wrong and absurd as I will show).

The Facts

I wish these guys would just get to the point -- this is 42 minutes of mind-numbing rambling.

There are a whole slew of errors in this video, I'll hit on a FEW of them.  Feel free to post more in the comments.  I had to skip forward... like a lot...

At around 13:15 he shows a diagram with a greatly over tilted Earth.  He even notes this is tilted too far, but he still uses it to make the point that "all this area" would be in total darkness.  Well yes, it is in winter... but it's far LESS area than shown and this actually matches reality.

At 13:58 he goes on a numerology rant about it being tilted at 23.3333° "which leaves 66.66666° off of 90°" --- Um.... that math doesn't even work, it would be 66.6667, but it's even more wrong than that because the ACTUAL tilt of the Earth is ~23.439281° if you don't round it, which irrelevantly leaves 66.560719° which is... well nothing.  Not that it really matters if a 2/3 happens to show up somewhere.   Oddly enough when you have physical processes that vary over time they often have to cross 2/3 somewhere along the way in SOME unit of measure or another.  Have you ever driven at 70 km / hour?  Then YOU have gone 66.6 km /hour!  You must be Satan himself!  That is exactly how stupid most of these arguments are.

I asked him to correct this in his video notes.  Will he?

His statements around 15:59 are also false because he forgot about refraction which bends the light about half a degree around so slightly more than 50% of the face towards the Sun would get some light.   Since the angle is very steep at the edges that half degree bend actually covers a significant distance.

I asked him to correct this in his video notes.  Will he?

His drawing is extremely misleading and in error - the clouds aren't on the sunny side.

Here is a better one -- the clouds are NOT way out in front -- they are behind the Earth.  This isn't to scale or anything but I tried to put at least SOME sense of proportion into it.

Look at his absurd version and then he says "see, the sun rays would be going way UP like this" and draws lines from the sun to the cloud...

There is so much wrong with this I'll just leave it at that.

I asked him to correct this in his video notes.  Will he?

The Oblateness is actually only 0.3% which makes it almost impossible to see in images that are not very high resolution - if you get the Himawari 8 images you can count the pixels and see the oblateness matches since Himawari 8 takes a full frame image from a great distance.

I asked him to correct this in his video notes.  Will he?

I cover crepuscular rays in this post on my blog.

They absolutely do not "point" to the sun any more than railroads "point" to a point on the horizon where they converge.  You are viewing parallel lines at an angle and perspective makes them appear to converge.   I doubt you will understand or be convinced by this alone so I don't expect a retraction on this one as it requires some understanding and isn't a simple fact.

Where is the Sun here?  Not one single Flat Earther seems to have the answer for this (so far).

Here is a 3D model in SketchUp where the rays are absolutely parallel.  When viewed at an angle they also APPEAR to converge, just like the railroad tracks and exactly like the rays of the Sun.

After he rambles on some more about 'perspective' (and gets most of it wrong) he offers his Flat Earth model... Oh boy...

This just is not how Perspective actually works, as I explained in my post about it.

Perspective WOULD allow a distant object to APPEAR below the level of a near object but this appearance would NEVER allow the light from that object to illuminate the near object FROM BELOW.

It doesn't change the ACTUAL physical relationship of things FFS!

This is their failure, in a nutshell.  They literally think that because something is far away it is magically able to light something from underneath it even though it is actually higher than that object.  Just Wow.


So Busted.

Thursday, December 1, 2016

Flat Earth Lies - Lake Pontchartrain Causeway

You should pretty much never trust anything a Flat Earther posts. Always verify every detail.

This meme came across my timeline today...
Here is the full sized meme:

So I do the thing where you compress the width of the image to make any horizontal change stand out:

Ok, wow, that is VERY flat.  Maybe a little too flat?

Although I have no idea if their distance measurements are correct.  I seriously doubt that is only 2.9 miles to the horizon, my bet is closer to 10 miles total although the last several miles of that is going to be just a few pixels in this image and you can probably only make out details for about 1 mile.

But I don't trust memes, Flat Earther memes least of all, so I did an image search and found this was the Lake Pontchartrain Causeway taken by Robert Holmes.

You can find that image in several locations, for example, at Travel and Leisure here:

Image Credit: Robert Holmes/CORBIS
I bet you can ALREADY see the issue.  When we compress the width down to 10% on this image we can readily see the curve in the image, as plain as day.

So someone took this image and FAKED IT to make their little meme work.  That had to be a purposeful act so this is a Flat Out Lie.

Now, is this ACTUAL curvature or some lens distortion?  I don't know - seems a bit much for that Field of View so I think only a small part of this is actual curvature but that's not really the point.

But here is what I know for a FACT...

My horizon does NOT extend out forever in a flat line left and right - it CURVES around me in a 360° circle and regardless of your altitude you'll see that horizon circle

curving around you in every direction... Every Time.