Dealing with "Things Unseen"

Science deals with unseen things like black holes by developing a testable hypothesis, which essentially describes what we would expect to see if there were black holes. When we observe behavior which matches the prediction, the hypothesis is confirmed. If not, it is rejected. Same for microwaves. When we observe behavior (thermal excitation of water molecules) consistent with energy transfer of microwaves, we confirm the theory! Religion on the other hand, takes an unexplained thing and blindly asserts #GodDidIt.  When the tests for god's existence fail, believers make up excuses for *why* it failed rather than reject the hypothesis. You're likely well aware of this method. The Bible provides many objective tests for the Christian god's existence, all of which demonstrably fail: - Matthew 7:7 “Ask, and it will be given to you seek, and you will find; knock, and it will be opened to you. - Matthew 21:22 And whatever you ask in prayer, you will receive, if you have faith.” - Mark 11:24 Therefore I tell you, whatever you ask in prayer, believe that you have received it, and it will be yours. - John 14:13-14 Whatever you ask in my name, this I will do, that the Father may be glorified in the Son. If you ask me anything in my name, I will do it So as a devout Christian, the first time you pray for something and it doesn't come true, you can know that the Bible is wrong. However, instead of admit their assumptions might be wrong, religious people blame themselves ("I must not have enough *faith*!") or make empty platitudes ("God works in mysterious ways.")

Geometry and a Flat Earth

We're told that the sun disappears over the horizon for the same reason that airplane contrails reach the horizon (which ironically is due to them following the curvature of the earth).  So let's consider perspective at night.  According to a Flat Earther I asked, Australia is about 10k miles from the US in a Flat Earth model.

We know that:

• $ \theta_{ele} = atan(h/d) $ Where h is the height of the sun off the flat earth and d is the distance to the sun's nadir point (directly below the sun). 
• When the sun is over Australia, it's dark in the united states.
• It's 10,000 miles from US to Australia.

Flat Earthers generally report that the sun is 3000 to 4000 miles in elevation. This is probably because if you tried to triangulate the sun (at approximately infinity miles away) from a curved surface you erroneously believed to be flat, you'd find that it appears to be about $ r $  miles away.

But how can that be?! $  atan(3000/10000) = 16.7  \degree $ !!. That's a pretty good elevation. About one and a half fists above the horizon! That would be pretty obvious! 

Making the small-angle approximation, these angles and distances scale approximately linearly.  To get as low as half of a fist above the horizon, we need 1/3 the height (let's say 1000 miles!). To get as low as one degree (still 2 sun widths) above the horizon, we'd need to be just 100 miles up. That's just at the edge of space. The sun could be hit with an amateyr  rocket!! 

With that, I've got no way to try to rescue this theory. The angles don't make sense.  Anyone got a way to make this problem work?

Collection of Satellite Images and Videos

I keep getting asked for pictures of satellites by #FlatEarthers I'm talking with. Rather than find them each time, here's a collection. The gif was from reddit.

Amateur Videos Showing Satellites

I'm not sure which satellites these are, but they're geostationary over Switzerland.  This sort of imaging is surprisingly easy to do (this guy does it VERY well!).  Just get a camera, a tripod, and take  5-10 sec exposures all night of the plane where the moon, sun, and planets pass.  Stitch them all together and you'll notice that some don't move.  Those are geostationary satellites.  You can figure out which ones they are with a bit of extra math.
Geostationary satellites in the Swiss Alps from Michael Kunze on Vimeo.

This guy wasn't even really trying, but when he co-adds frames (go make the streaking effect), it jumps right out.There's a clear GEO satellite near the top of the frame, about 40% in from  the left.

A Starry Night of Mt.Kilimanjaro from kwon, o chul on Vimeo.

This photographer isn't taking exposures long enough and has too much city light to see the satellites clearly. The "flashes" are likely glints off the solar panels or an aliasing artifact in his video conversion.  Longer exposures could cause streaking, but would bring the satellites out more clearly.
Geostationary Satellite Flashes, Night of March 7-8, 2013 from Ken Musgrave on Vimeo.

The folks at ExoAnalytic have some great professional videos through robotic telescopes.

Why not from other satellites?

I'm also often asked why we don't see satellites take pictures of other satellites.  To someone naive about otbits, this might seem like an easier task. You're closer, right? No. Space is very big, and satellites moving 17,000 mph, not all in the same direction!  Nevertheless, It's been done. An imaging satellite named Pléiades 1A took a picture of SPOT 5. 

Comparing Flat Earth Models to Reality

I finally found a video which helped me understand the flat-earther model of a sun circling a flat earth. Thanks to p-brain for helping me out here.

Setting aside his disastrous misunderstanding of perspective, he has a decent point regarding how distant points converge at long distances.  The "plane" that the sun would orbit within would indeed appear to approach (though never quite cross) the horizon.

I suspect this claim falls apart when we start examining distances necessary to accomplish this.  Clearly the Sun isn't flying along at 30,000 ft like the contrails p-brain uses as an example.  Rather, it would need to be flying a minimum of 2-3x higher. My intuition is that the angles will come closest to working if we set the sun at an altitude equal to the radius of the earth (4000 miles) .  

So let's compare the two approaches. For the sake of simplicity, I'll assume the curvature of the sun's path is so slight that we don't notice it curving northwards. That's right, I'm going to give the Flat  Earthers a pass on the fact that we don't see the sun curving to the north! No "Where's the curve?!" from me.  

So anyways, the distinction is really easy to make. If you believe in a Flat Earth, simply measure the angle to the sun throughout the day and compare the following plot of arctan(1/x): 

If it's straight, the angular rotation is constant, which matches the spherical earth model:

1. If the solar angle matches the plot of $ arctan(1/t) $, then it's a flat earth. 
2. If the solar angle is a straight line, it's a sphere.

Note: The angle you need to measure is called the "Right Ascension" (RA).  Align a pole to point to the North Star at night. Measure the angle to the sun about this pole.  This could be done with a protractor oriented perpendicular to the pole on the back side (away from the sun). Note the angle where the shadow is cast.  Here's my attempt to draw the experimental setup.

Flat Earth Misconceptions

I'm so tired of repeating myself to Flat-Earthers. It's like they revel in doing their math wrong, but there's not enough characters in twitter to send them the proper equations. So I'll address a few classic pics here to explain how it's done.

The distant mountain picture

This is a favorite among flat-earthers, and it's pretty easy to show they get the math wrong.  Someone told this guy that he can use a simple linear fit for earth's CURVED surface (8 inches per mile or some such tripe). I'm not sure where this approximation came from, but it obviously doesn't fit a curve very well. Anyhow, here's an example:

Here, we have the classic flat-earther example of a "mountain that's too far away to see." First, let's check the facts. After a bit of digging, I figured out that they're claiming this is Mt. Denali.  That's 140 miles away, with an elevation of roughly 20,000 ft.

It's actually 700 ft at the summit of the Hilltop Ski Resort, but it turns out that won't matter in the end.  

Anyhow, let's assume they're right and it's Denali.  First, calculate the distance and angle to the horizon from an elevation of 700 ft.  I'll let WikiHow explain how to do it. I'm using the arccos formula: 

$ d = r  \arccos(\frac{r}{r+h}) $

The horizon from Hilltop is calculated here at 32 miles.

The horizon from Denali is calculated here at 174 miles.

Suppose the picture were taken from the parking lot of Hilltop instead of the top.  The horizon is still 27.5 miles away, well within the range of Denali's summit. 

32 + 174 means you can see the tip of Denali from as far as 206 mi at an altitude of 700 ft (assuming there's no mountains in between and neglecting atmospheric lensing, of course). This is obviously not a problem for observation from 140 miles away.

Just for convenience, we could figure out how tall an object needs to be to see it from a distance, x. We simply add the horizon distance to the solution to our first equation for h:

$ \cos( \frac{d}{r} ) = \frac{r}{r+h} $

$ h = \frac{r}{cos(\frac{d}{r})} - r $

d = 140-32 = 108

h = 7700 ft tall. 

This means we should be able to see the top 12,300 of Denali. 

Time Zone Solar Models

This is another flat earther hand-waving explanation for time-zones.  

Even the most casual thought regarding this picture and you'll realize that since the sun is above a flat earth, you'll be able to see it at all times from any location on earth. Turn this model on its side and draw a vector from any point on earth to the sun and you'll see that it never sets.  The figure below shows this and explains the problems.

If there's some other way to interpret the animation above, I sure can't think of it.  Send me a comment or tweet to help me understand.
I'm left wondering if flat earthers lack all spatial reasoning. It sure seems that way.

Pilots Would End up in Space!

This one is so bizarre that it takes a little work to wrap your head around.  Essentially, the argument is that airline pilots would need to adjust their elevation by 1 degree every 6 or 7 minutes to keep from climbing higher and higher and crash into the firmament or flying into space.  There's some specious assumptions here:

• That airplanes fly along laser-like straight lines
• Airplanes will continue climbing at the same rate for a given angle of attack even as the air thins.
• That the pilot has the sensitive equipment to recognize one-degree drift over 6 minutes

In the same way as you might make minor course corrections along a straight road to keep your car centered in your lane, the autopilot (or the real pilot) is constantly adjusting to maintain a reasonably constant altitude and heading.  These corrections are happening at a rate of tens to hundreds per minute.  To the pilot or autopilot, this feels like maintaining altitude.  In reality, it's conforming the flight to the curvature of earth.  This publication described the typical roughness of a commercial flight.  I've pulled out the "rough cruise" section because the constant readjustment of altitude is more clearly apparent.  Same thing happens in "smooth cruise", but more gradually.

Where's the curve?

Simple computer models can help us understand when and where we'll be able to observe curvature of a sphere.  The key factors which affect the appearance of curvature are:

• Altitude above the surface
• Camera Focal Length (or field of view)
• Radius of the sphere

I'm sure someone could write an expression  for the apparent curvature versus these parameters, but it's easier to just show you. I'm using an open-source tool called Celestia which accurately presents the position, sizes, and velocities of celestial objects.  I highly recommend it. It's fun to play with.

Changing the Field of View

Here's the  same view as the Field of View is altered.  This is like zooming out on your camera.  The FOV is reported in the bottom-right while the location (constant) is presented in the upper-left.

Changing the Altitude

This one is a little more obvious.  As you move to higher and higher altitudes, the curvature becomes more apparent.

Note that the Distance is 30 km. That's a decimal place, not a comma.

Radius Matters Too

This one is just for fun.  Here's some spheres of different radii from the same distance.

Mythbusters are shills?

Well, as we've shown, the curvature isn't expected to be visible at low altitudes. Here's Adam Savage  at a 12 mile altitude witnessing the curvature for himself.  So I suppose he's got to be a liar now, eh?

The Moon / Spinning Earth can't be felt!

Moon: The gravitational acceleration of the moon on the surface of earth is given by $ a = G m_{moon}/r^2 $ or roughly $ 3.6 \times 10^{-5}  m/s^2  $ compared to the $ 9.8  m/s^2 $ I measured in high school for earth's gravity.  That's less than one part in a million.  A hard thing to measure.

Rotation: The acceleration of an object on the equator due to circular motion from the rotation of the earth is given by: $ a = \omega^2 / r $.  This also tiny at $ 0.034 m/s^2 $. This effect (0.34%) MIGHT be measurable by exceptionally sensitive equipment and a skilled scientist, but these are the sorts of people the Flat Earth crowd seems to consider untrustworthy.

Edit: I fixed my math above. Rotation is actually much more important than I originally calculated. Thanks to @TheOlifant for catching my error:

@haplesspete @AtheistEngineer Thanks for the link! That's a great read. 1 q.: Where is my mistake in this? pic.twitter.com/3M6QtVGG37

— The Olifant (@TheOlifant) May 2, 2016

Mentality

The mentality of flat-earthers seems to be very similar to that of anti-vaxers and deeply religious.  The believer thinks they've figured out that most of humanity is wrong, and that their answer is the right answer. They often tell you to "research it," and couple commands with insults "stupid" or "dummy" or "sheep." 

These believers think they've figured out what "they" don't want you to know.  The "they" varies between people, but it seems to be illuminati, the government, or the Free Masons. For devout Christians or Muslims, the "they" is Satan, heretics, or demons.  

These believers pride themselves in being different. They think they're visionaries for knowing the truth when everyone else has it wrong.  Despite having no formal training in the specific scientific claims they reject, they feel sure that all the professional scientists have been deceived by the "they."
What's particularly interesting is that these people seem to blindly follow (IMO obvious) quacks. Some guy with a YouTube channel is seen as more reliable than all the world's scientists. They wave off these brilliant scientists by presuming they've never actually TESTED any of the claims they learned in science text books without seeming to notice that:

1. The YouTube quack has never tested his flat earth claims. At best their "evidence" seems to be that they find actual physics hard to understand or inconsistent with scripture.
2. Scientists actually do verify the basics. They build more complex experiments on top of them, so if the basics weren't right, nothing would work.

A quick review of the usual apologetics

A Christian apologetic video called "10 INCREDIBLE BIBLE FACTS to blow your mind" was posted to the "Philosophy of Religion" G+ Group.  Bible click-bait is not "Philosophy of Religion."  But I took the time to respond anyways.

1: So what? Harry Potter sold a lot of books too.  Doesn't make it true.

2: Lots of authors, but "the Bible does not contradict itself" Yes. It does.  Lots. There are whole indices of the contradictions. http://infidels.org/library/modern/jim_meritt/bible-contradictions.html
But even if it were, a cursory understanding of how the Bible was formed (by committee, from a much larger set of texts) shows that it could be just good editing, not good writing.

3: Again. So what? This is just false. Book of Mormon says that god said things too. https://www.lds.org/ensign/1988/01/the-book-of-mormon-is-the-word-of-god?lang=eng

4: What a cute legend.

5. We're going down-hill here. This is pretty wildly speculative and vague. I wrote a blog about how this sort of post-hoc rationality works. The prophecies of Dr. Seuss
http://www.atheistengineer.com/2015/06/the-of-dr-seuss.html
"Jesus is Coming Back Soon." This has been the Christian claim

6. The Bible is true?! LMFAO. Where are the four corners of the earth? Stop pretending a circle is the same as a sphere.
Wow. Look under the water and you can see rocky formations that resemble what's over the land.
You're doing science just like the Muslims do it!
https://twitter.com/AtheistEngineer/status/671157215210766336
   Step 1: Look at what's real.
  Step 2: Find places where the Bible can be interpreted to suggest those things.

7. Ha ha ha. So there's some facts which agree with history? I'll defer to the usual "Spider Man happens in New York, but it doesn't make Spider Man true."
The Biblical writings are "viable"?  Might not be false isn't a very good basis.

8. Accurate to what?!  Oh. The disagreements between different scribes are "minor" in the opinion of some biblical historians? The 31,000

9. Methamphetamine has also changed people's lives.  People who use it are transformed. They become committed to methamphetamine.  Does that make it true?  The video goes on to cite a few anecdotes about people who were born and raised Christian, then happened to do good things anyways.  Lots of people find Jesus at their lowest -- because that's when they're most vulnerable to indoctrination.

10. There's a corrupted Bible? God hasn't protected "his word" very well, eh?  Imagine if that happened EARLY in the Bible's history. The result would be an unreliable Bible today!

I Don't Understand What You Think God Is. And Neither do You

What is God?

This is definitely not God.

Ask google, and you'll be flooded with thousands of sites which exude confidence. But dig a little deeper and you'll see that they're peddling platitudes.

God is the creator of mankind and He loves you.
You were created by Him and He knows everything about you.

Note: Some of them seem to have identical content: http://myranchlandchurch.com/god-is-real and http://mastersmen.com/who-is-god-answers-about-life-and-god/ haha.
The site contains claims about the things we ought to credit god with, but not a single observable property of this god.

• “Jesus said to him, ‘I am the way, the truth, and the life. No one comes to the Father except through Me’” (John 14:6).
• “Sanctify them by Your truth. Your word is truth” (John 17:17).
• “You have known the Holy Scriptures, which are able to make you wise for salvation through faith which is in Christ Jesus. All Scripture is given by inspiration of God, and is profitable for doctrine, for reproof, for correction, for instruction in righteousness” (2 Timothy 3:15-16).
• “No one has seen God at any time. The only begotten Son, who is in the bosom of the Father, He has declared Him” (John 1:18).
• “All things have been delivered to Me by My Father, and no one knows the Son except the Father. Nor does anyone know the Father except the Son, and the one to whom the Son wills to reveal Him” (Matthew 11:27).

These are presented by one of the more credible articles as "very logical answers to what is God, and what is He doing." Yet even the most cursory review and it's clear that they're empty dogmatic claims, not observable properties of a anything.

You don't know either

So here's the hard point. Not only are Christian apologetics and ministries unable to articulate any tangible properties of their god, but neither are you. Most Christians think of god as a personality they can interact with and a place-holder for the unanswerable questions of the universe.  But can you identify any tangible properties? Before you get angry, consider some practical questions:

• If a person introduced themselves as god, how would you know if they're lying or honest? 
• When a fortunate event occurs to you or a loved one, how can you tell if it's an action  of a god or just good fortune?
• Suppose find yourself in a place devoid of features. There's a person-like entity there which knows your name and speaks to you. The implication is that you've died and are in some sort of afterlife. The usual cues are missing.   No puffy clouds and halos, no firey pits and horns.  How do you determine if the entity is a god or a demon?
• That voice in your mind seems to always know what you need to hear. How can you tell if it's a god or just your own imagination?

In short, there's no good way to tell whether these characters are gods or someone else. I don't understand what you think god is, and neither do you.

Epilogue

In researching this post, I came across this post, which starts out surprisingly well. It's not the usual hateful misrepresentation of atheists. But it makes the usual mistakes regarding their own beliefs. Once they start describing the Bible, the claims quickly go from "the authors said" to "it's true."  Here's the paragraph where it happens:

There is a book that has existed longer than the philosophies of materialism and humanism. Those who wrote this book claimed that they were personally in contact with the one, true Creator God. They say, in fact, that this God actually inspired what they wrote, and they claimed to know Him personally. Furthermore, they wrote that God has a plan—a purpose—for each human life. They claimed that what they wrote in this book called the Bible is truth—from the God of truth. They staked their lives on it! 

Another way to understand God is to be willing to take a close look at what He reveals about Himself in the only book that can be seen as a legitimate source of information about Him. Most people own a Bible, but most people—even Christians—have never really honestly or thoroughly examined the Bible to see what it reveals about God. You will likely be very surprised to see what God says about Himself!

Oh well.  It's  a train-wreck from there.