GandalfTheWise

Millard Erickson's take on this issue strongly influenced the development of my opinions on this issue. Many years ago in one version of his systematic theology book, he did a nice job of laying out the various beliefs of various systems of Calvinists and Arminians. He then summarized it as this: Calvinists believe that God determines an individual's eternal destination. Arminians believe God lets the individual make that choice. Everything else is putting details onto that single core belief. He then went on to indicate that he thought that some form of Calvinism was most consistent with scripture though there were issues with that. After years of pondering which one was right, I started to wonder if human logic (which says one or the other has to be correct and the other wrong) should be applied in this case or not. I've now come to believe that this is a false dichotomy and that scripture indeed teaches both. As Christians, we use this approach to both the Trinity and the humanity/deity of Christ. I accept the full deity and full humanity of Christ. Why? Because there are scriptures that clearly indicate Jesus was human and there are scriptures that clearly indicate He was divine. Many heresies developed because people applied a logic that said He could not be human and divine at the same time. I accept the Trinity. Why? Because there are scriptures that clearly indicate that there is one God and there are scriptures that clearly indicate that the Father, Son, and Holy Spirit are distinct Persons. Many heresies developed because people applied a logic that lead to a rejection of the Trinity. I can freely talk about Jesus as being a human being without fear of violating scripture. I can freely talk about Jesus being God without fear of violating scripture. But I cannot deny that Jesus was human or deny He was divine without violating scripture. I think that both calvinists and arminians both make the same fundamental error. They assume that human logic holds and that only one of them can be correct. Either God decides an individual's fate or the individual does. Both sides believe that only one of them can be correct. Calvinists thus reject the plain meaning of scriptures that indicate that individuals have the free will to determine their eternal destination. Arminians thus reject the plain meaning of scriptures that indicate that God determines an individual's eternal destination. When I read passages of Scripture such as Exodus 8, 9, and 10, I take them on their face value. Scripture says God hardened Pharaoh's heart means that He did. Scripture says that Pharaoh hardened his heart means that he did. Calvinists and Arminians are forced to "explain" what these scriptures "really" mean and reject their plain meaning. I'd give my opinion of both by adapting what Paul wrote to the Corinthians. "My brothers and sisters, some from Chloe’s household have informed me that there are quarrels among you. What I mean is this: One of you says, “I follow Paul”;another, “I follow Apollos”; another, “I follow Cephas”; still another, “I follow Christ.” Is Christ divided? Was Paul crucified for you? Were you baptized in the name of Paul? I thank God that I did not baptize any of you except Crispus and Gaius, so no one can say that you were baptized in my name. 16 (Yes, I also baptized the household of Stephanas; beyond that, I don’t remember if I baptized anyone else.) For Christ did not send me to baptize, but to preach the gospel—not with wisdom and eloquence, lest the cross of Christ be emptied of its power." and For when one says, “I follow Paul,” and another, “I follow Apollos,” are you not mere human beings? What, after all, is Apollos? And what is Paul? Only servants, through whom you came to believe—as the Lord has assigned to each his task." Would Paul today condemn those who say "I follow Calvin" or "I follow Arminius"? I think he probably would. Some of the more extremists of those views hold that the opposite side is a heresy. I've seen Christians of good conscience and reputable life refuse to fellowship and minister with other Christians of good conscience and reputable life over whether they answer the question, "can a Christian lose their salvation?" with the "correct" answer.

That is interesting. Fluid flow is very complicated especially when it is a compressible fluid like air. I have the feeling that there is the actual physical shape of the wing and then there is the "effective" shape of the wing (which varies with speed, angle, etc.) which includes a boundary layer of vortices and "stable" air patterns near the wing. My gut feeling is that the actual air flow patterns that do the pushing and lifting are interacting with the "effective" shape of the wing rather than the physical shape of the wing. Last Christmas, my mother got me the book about the Wright Brothers by David McCullough. It was a fascinating book. I had always thought of them as some tinkerers that were lucky enough not to get killed. They actually did a lot of high level applied engineering in order to figure out how to fly. I had no idea that they made their own wind tunnel, did many mock ups, did lots of testing, and then realized that one of the main keys to flying was the pilot having enough practice to do it right. This was a well document book that followed their family life, travels to Kitty Hawk and around the world, their engineering progress. I found it very interesting.

I just added a video showing the Coriolis effect on a merry-go-round. It's a short (sub 30 seconds) that gives a nice demonstration of what I attempted to describe in words in the OP. Here's the link to the approved video post. https://www.worthychristianforums.com/topic/212872-coriolis-effect-on-merry-go-round/ The key thing to understand about this is that the motion of the ball is quite real. It is the observers' point of reference that determines how they will measure the ball's motion. An observer standing to one side would measure a straight line and an observer sitting on the merry-go-round would measure a curve. Over the years, many textbook descriptions of the Coriolis effect (and other rotational effects) have unfortunately used words such as "fictional" or "apparent" to attempt to describe the observed curved motion. They were attempting to describe how the observer sitting on the merry-go-round could not observe a force acting on the ball to make it curve. Indeed, to most people who sit on a merry-go-round and actually try this for the first time, it does sort of seem like magic when you try to throw a ball straight to someone and you watch it curve to one side. On the earth's surface, the effect is quite small over the types of distances we are used to in everyday life. Throwing a ball on a football field or a basketball court is dominated by air resistance and gravity which are so much larger that we never notice it in day-to-day life. It is interesting to note that snipers and long distance shooters do account for the Coriolis effect for long range shooting.

I used to take this as the standard explanation. I now think it is a "truth by repetition" situation. Many years ago I was helping a colleague study for his pilot's license. He kept asking me questions about stuff like this. At first, I just repeated the standard answers until I realized I really didn't understand how angle of attack, Bernoulli's equation, and simple force diagrams applied to flight. I then realized I could not explain how aircraft can fly upside down. I went back to first principles and finally came up with some reasoning that I was comfortable with. 1. Air is a fluid. It cannot pull outward on anything, it can only push. (Strictly speaking, it can cause shear forces to the side for objects with rough surfaces. But this is really just pushing against the rough projections.) It is the pressure differential of high pressure under the wind and low pressure over the wing that causes a net force upward. 2. Bernoulli's equation does NOT dictate cause and effect. It merely states that high pressure is associated with low air speed and low pressure is associated with high air speed. In some cases, pressure differences can cause air to move. In some cases, air being blown into an object slows down and builds up pressure. Here are a couple crude schematics I just tossed together to illustrate this. In the top case, a fan starts to blow air into an enclosure. The arrows show the air speed and the coloring shows the pressure. When the fan is turned on, the air rushes into the box and is stopped by the far wall. The pressure build up against the back wall stops the air. In the bottom schematic, the fan is turned off. Air then starts to rush out of the box. The higher pressure near the back wall is pushing the air out of the box. Here is how I think of a wing in terms of cause and effect of pressure and air speed. Moving air (from the forward motion of the plane) piles into the bottom surface of the wing (which is angled upward slightly called the angle of attack). Because of the angle of attack, the air is striking the bottom of the wing and producing a region of high pressure where the wing stops the air. This builds up pressure causing the pressure under the wing to be higher than pressure over the wing. The primary effect of the rounded shape of the wing is to reduce turbulence and drag not produce a pressure difference. Now, imagine if the standard "Bernoulli" explanation of cause and effect was correct. What would happens when flaps or ailerons are used? If the "Bernoulli" explanation of air traveling faster and farther causing low pressure was correct, they'd be working backwards. Lowering ailerons would cause the air to have to travel further and faster reducing pressure and causing a wing to drop if an aileron or flap was lowered. But, if the cause is the moving air pushing into them building up pressure, they work as expected. I think it is much more intuitive and accurate to think of air movement pushing against the aircraft wings to figure out what is happening. I think that someone somewhere misapplied cause and effect in the Bernoulli equation and got the cause and effect backwards. Also, if the wing shape causes lift rather than air pushing on the bottom of the wing, the old rubber band wooden airplanes I used to have as a kid would not have worked as well as they did. Those were nothing more than cheap flat stamped wood. Here's an image I found. I recall mine had cheap wires and little plastic wheels for landing gear. It was fun winding them up, setting it on the ground, and then watching it take off. If someone has further info on this, I would be willing to reconsider my position. But thinking about things this way made it easy to answer my friend's questions about various things and he (an engineer) seemed to think that my explanation made a lot more sense than what he was reading and being told.

Since I had Mathematica up and running and playing with the atmosphere model, I decided to put out a graph showing the temperature model. I added the blue, green, and red bands show the troposphere, stratosphere, and mesosphere. The straight line segments (rather than smooth curves) are because the model is focused primarily on quantities like density and pressure which are what pilots and other uses of the information need the most. The temperature is shown as linearized between important inflection points (e.g. the top of the stratosphere) and is primarily used to generate smooth density and pressure information. Notice how cold things get very quickly as you go up. Notice that the ozone layer in is the stratosphere. Ozone absorbs some energy from the sun and causes warming in the upper atmosphere. Without the ozone layer, the temperature would continue to drop. Without the ozone layer, the stratosphere really wouldn't exist. This has a profound effect on our weather. This temperature peak is what stops warm air masses from rising indefinitely. It basically puts a cap on how high warm humid air can rise and how high thunderstorms can build up. Here's a great image from wiki showing this effect. (original link to full size image: https://commons.wikimedia.org/wiki/File:Single-cell_Thunderstorm_in_a_No-shear_Environment..jpg)

Higher humidity air being less dense seemed pretty counterintuitive to me too. When I first started researching things for this thread I ran across that and thought "What?!?". Air is mostly nitrogen and oxygen molecules, which are N2 and O2. The atomic mass of N2 is about 28 and O2 is about 32 whereas water H2O is about 18. Water molecules are much lighter than N2 and O2 molecules. A given container full of N2 and O2 will be heavier than the same container full of N2, O2, and H2O. At least, that's the way I think about it now, and it seems to match what is observed. There's stuff about partial pressures and how different species of molecules interact in fluids that I haven't looked at in ages that has something to do with this as well.

Cool question. My first thought was, "I've never heard of density altitude." Instead of giving my final answer right away, I'll use this post as an example of how I figure something out when I've never heard of it before. The first thing I did was use Bing to search for the definition. I used wiki and aopa.org sites to get the definitions. Sometimes this can be a chore sorting through people's attempts at an explanation (which may or may not be completely clear or accurate). The AOPA site was fairly clear and also gave the formula for pilots to use. I found this very useful since it's what people use in practice. From this, I was able to relate what was happening to my general knowledge of thermodynamics and mechanics. I'll try to answer this now in a way that non-pilots can follow. An airplane can fly because air pushing against the bottom of the wings causes enough upward lift. It's more complicated than that, but this basic idea covers most of what you need to know. The amount of lift generated depends on many things. The faster the plane is moving the more lift. The shape and angle of the wings affect the amount of lift. And most importantly for this example, the density of the air affects the lift. Very dense air (like at low altitudes) has many more atoms and molecules per cubic inch (or whatever volume you with to use) than less dense air (like at high altitudes). The more atoms and molecules striking the bottom of the wings, the more lift. This is why different types of aircraft have different limits on how high they can fly. Depending on the aircraft design, it will need more or less air density to properly operate. The amount of lift also affects take-off and landing distances! Taking off from sea-level is much different than taking off from an airfield in the Himalayas. There are 3 main factors that go into how dense the air is. These are altitude, temperature, and humidity. A lot of work has been done on the standard model of the atmosphere. Here is a graph I generated using Mathematica. It shows the 1976 US standard atmosphere model (which assumes a dry atmosphere at standard atmospheric conditions). In other words, this is basically the average density of air for a dry atmosphere at a given altitude. The blue line shows the density at altitude for standard dry conditions. However, higher humidity and temperature cause the density to decrease. I put in a random red dashed line to indicate what this might look like. So, if an aircraft requires at least 0.8 kg/m^3 air density to fly, under ideal conditions its maximum ceiling would be about 15,000 feet. On a hot and humid day, its maximum ceiling would be more like 10,000 feet. (It's really much more complicated than that, but this gives the general idea.) In practice, pilots do not directly use this type of graph. A pilot doesn't want to know if the air density is 1 kg/m^3 or 0.5 kg/m^3. What a pilot wants to know is what the equivalent altitude is that they are at. Density altitude is a simple formula that takes a measured pressure altitude reading and measured temperature reading and indicates what the equivalent altitude is. It is basically a way of taking the altimeter reading and saying "your plane will behave as it would XXX feet above what the altimeter says."

I was rather curious to see how atmospheric pressure changes with altitude and how that compared to actual weather data. I use Mathematica for much of my professional work. See wolfram.com for more details on it. It is a powerful mathematical package with a lot of curated data and information built into it. I used their built in standard atmosphere functions, weather data, and city information to generate an interesting graph showing how the earth's atmospheric pressure changes with altitude. The blue line shows the 1976 version of the US Standard Atmosphere Model. This model gives what is essentially the average value of temperature, density, pressure, and other quantities at various altitudes in the atmosphere. It is used for aircraft engine design, ballistics, and other applications where various properties of the atmosphere are important to know at different altitudes. This model assumes that the atmosphere is dry and there is no wind or other such effects. Users of the model must add the effects of wind, water vapor, precipitation, and other such things themselves. Various sites on the web have more information about this model. The wiki page isn't too bad of a place to start. https://en.wikipedia.org/wiki/U.S._Standard_Atmosphere The red line shows the estimated effect of water vapor in the atmosphere. This is a very complicated type of interaction that has different aspects of things to consider. The main thing to know is that it will reduce the atmospheric pressure by a few percent or more depending on temperature, dew point, and other things. The red line is set to a 5% reduction to provide a reference point for the city information. The 4 cities give the average raw atmospheric pressure measurements over a 2 year period from 9/10/2015 to 9/10/2017. I pulled this in from the Mathematica weather data set. As can be seen, they all sit a few percent below the dry atmosphere pressure curve as would be expected.

Good question as it touches upon the meaning and importance of units in mathematical descriptions. 1 foot is not the same as 1 inch is not the same as 1 pound. It is not the 1 that matters so much as the unit that matters. Writing it as (1 ft/12 in) or (ft/12 in) would be equivalent. It is an issue of keeping units well documented and consistent on both sides of an equation. In this case it clearly shows the reader that (1ft/12in) is simply a conversion factor whereas only dividing by 12in can cause confusion as to whether or not it is a fundamental distance that is part of the equation.

This is a nice short video demonstrating the Coriolis effect on a merry-go-round. Thanks.

I have a lot of respect for what it takes to actually fly a plane. Many years ago, I worked with a fellow who was working on getting his pilot's license. He's now a certified instructor and commercial pilot. I remember helping him out with various questions and stuff. My Dad was a navigator in the AF back in the late 50s (during the cold war) back in the days of dead reckoning and being able to navigate off of stars at night without GPS. Yep, the entire ocean/atmosphere system is amazing complex. And then it's fun to sit outside and look at clouds too. There are different types of "smarts". God's made us all quite different. I'm confident that there are things that you can do where you could run circles around me. I'm very serious about that. As an offer here, if there is anything you run across that you'd like me to try to explain in simpler words, or pictures, or whatever, please feel free to ask. I enjoy this type of stuff. I was a physics prof many years ago, enjoyed teaching, and picked up a few awards for it. I had planned on a career in academia but God had other plans for me.

This is kind of fun for me. I'm having to go back to stuff I haven't thought about in ages. I had to think about this one a bit. I then remembered the derivation of the acceleration of gravity at the earth's surface starting from Newton's equation of gravitation. Basically, the masses do not screen each other. For astronomical bodies like the earth and moon (which are mostly spherical), you can more or less treat them as point sources with the gravitational fields originating from the center. F = G m1*m2/r^2 where G is the universal gravitational constant, m1 and m2 are the two masses attracting each other, and r is the distance between their centers. For most purposes, it is unnecessary to worry about general relativity.

I had tunnel vision on the shape of the movement and had the merry-go-round example fresh in my mind so I was only thinking about circular motion. Wow. Take a year off in semi-retirement and I get rusty. That's why there's a peer review process. Now that you've mentioned the moon, curiosity will probably get the better of me at some point and I'll calculate that.

Thank you for pointing this out. I was incorrectly thinking of earth as the stationary reference frame, not the solar system looking at the earth. Going east at the equator, the values would be 9 times greater than what I gave. (1500/500 = 3 times faster and then squaring it.) The value I calculated would be appropriate for flying over the poles. I'll edit this into the OP. Also, strictly speaking, using 24 hours (or using the sun at the same point in the sky each day) does not give the correct speed. We should take into account the extra 1/365.25 variation for orbiting the sun. And then the sun's motion in the Milky Way, ad infinitum. Numerically speaking though, assuming a 24 hour rotation period is good enough to get a good grasp on the magnitude of the effect. Thanks again. That's an embarrassing one to miss, but not as embarrassing as having left it there for posterity.

This thread is about how a physicist approaches various physics problems. Many people do not get to see how we practicing scientists and engineers approach problems. I chose to use a few simple examples that were brought up in another thread. I'm hoping other people might have serious questions on various things. People who read it can choose to decide if I'm a person from whom they could get good answers and reasoned thoughts from or not. The initial responses also gave me an unexpected opportunity to illustrate the typical life of a scientist and engineer when dealing with sloppy non-technical information and assertions dressed up in inaccurately used scientific jargon when their conclusions do not meet preconceived notions. One of the challenges to practicing scientists, engineers, and analysts face is when their work is not "convenient" and it forces people to face errors and problems with their positions. I have no desire to waste my time dealing with either true-believers or trolls on fringe ideas such as flat earth nonsense. True-believers rarely change their minds until something major arises and causes them enough cognitive dissonance to rethink things. Trolls simply enjoy wasting people's time and trying to goad them into anger or negative emotions. This thread is not about debating flat-earth nonsense. When the discussion could be focused on mathematics and physics (including fixing typos) and trying to understand what something meant and if it made sense or not, I was willing to continue on the tangent as an illustration of how to approach things with an open mind to understand them better. When it reaches the point of saying two equations that are algebraically different and give different numbers are really identical and a misleading equation might not be corrected in the future, this indicates to me that the intended purpose of the responses is likely either an unending true-believer ideological monologue or a trollish waste of my time. I refuse to engage anymore whichever the case may be. Speaking as a Christian, I believe that God has created each of us uniquely and to reflect His glory to the world. He has made us each to be skilled at different things and have different passions and interests. I believe that as we each walk with God and become closer to Him, that we will more and more live in a way that He can use us to change the world around us for His glory. I do not know the motivation behind all of the flat-earth advocacy. I merely wonder if it is a fruitful use of time and energy that is advancing spiritual growth or if it is a time-consuming diversion that is taking time and energy away from other activities and study that could be unique and powerful that could make a much bigger impact in the world. I now request that this thread return to its original purpose.

The dimensionally correct form of this equation would be: (500 mi)^2 (8 in/mi^2) (1ft/12 in) = 166667 ft. I'd recommend writing (8in/mi^2) instead of 8in and (1ft/12in) instead of /12in. People will more clearly understand what is intended. From the description given, this can be rewritten as L^2 (8in/mi^2)(1ft/12in) = X where L is the distance traveled by the plane (in miles) and X is the drop (in feet) The equation in the diagram is X = R-R Cos(ArcSin(L/R)) (5280 ft/mi) where L is the distance traveled by the plane (in miles), R is the radius of the earth (in miles), and X is the drop (in feet) where I have added the conversion factor from miles to feet. Why is the original equation different from the equation in the diagram? How do we decide which, if either, is correct?

Could you please clarify the first equation given here? What is the underlying formula? Is there some type of diagram available showing the geometry or a description of how these quantities are related? Where do the 8 inches and the 12 inches come from? Why is the distance the plane travels in one hour being squared? Also, as posted here, the units in the first equation are inconsistent. The units on the left are square miles and the units on the right are feet. This equation says that an area is equivalent to a distance. Is this a typo?

Few people ever get to see the real workings of physics and math. I'm a physicist and mathematician (by education) and have spent decades of my life professionally as an applied scientist, engineer, data scientist, and computer scientist. This has forced me to learn to do things correctly. By correctly, I mean that my work has to match what happens in the real world. I cannot simply make up a few numbers and generate some colorful graphs. I have to correctly predict what will happen and give solid recommendations that people can depend on. Here's how a practicing physicist approaches a few trivial examples. (Unfortunately, I couldn't figure out how to trivially cut and paste some graphs and diagrams into this post. ) Example 1: What type of acceleration does a passenger in an aircraft experience in flight due to the curvature of the earth? My approach to this is to clearly define the motion, use the appropriate mathematical formula, and produce a comparison to other effects for reference. A typical airliner cruising at 500 MPH at an altitude of between 30,000 feet and 40,000 feet (I'll call it 7 miles or 36,960 feet to round out the numbers) will follow an arc of a radius equal to the earth's radius plus its altitude. I'll use the average value of 3956.5 miles for the earth's radius. Any object traveling in a circle experiences centripetal acceleration. This is simply v^2/r (the velocity of the object squared divided by the radius of the circle). This is true for someone on a merry-go-round, spinning a rock in a sling, a flywheel, or a spinning circular saw. Any circular motion requires the object (or parts of the object) to constantly be forced toward the axis of rotation to change its direction to move in a circle. This is a simple consequence of mathematics. There is nothing complicated about this. For a person in an airliner, we have a centripetal acceleration of (500 MPH)^2/(3956.5+7 miles). Converting this into feet/sec^2 we have 0.0257 ft/sec^2. For comparison, the acceleration due to gravity is 32 ft/sec^2. Some of the world's most intense roller coasters generate up to 5 or 6 g's of acceleration (or over 150 ft/sec^2 of acceleration). Now, over the course of 500 miles, the plane's arc will move about 30 miles off of the original tangent. However, the centripetal acceleration associated with this is rather gentle compared to the accelerations associated with takeoff, landing, and any turbulence that is encountered. EDIT[Thank you to @hmbld for a later post pointing out an oversight in this example. We need to consider the plane's motion relative to the center of the earth and from the view of an observer out in space watching the earth rotate. Depending where the plane is at on earth and what direction it is traveling, a ground speed of 500 MPH will need to include the speed of earth's rotation. This will be at a maximum on the equator heading east. The ground speed of 500 MPH needs to be added to the approximately 1000 MPH tangential eastward velocity due to the earth's rotation. This gives a centripetal acceleration 9 times greater than the number above or 0.231 ft/sec^2. The number calculated above is appropriate for over the poles. At the appropriate N or S latitude heading west, it would be possible to get this down to zero. At it's maximum 0.231 ft/sec^2, this is still less than 1% of 1 g of acceleration. ] Example: What is the Coriolis effect? My approach to this one is to use a simple physical example to illustrate the main principles. I then use this example as an analogy to show that observed phenomena are consistent with this in a much more complicated system, the earth. The easiest way to think about this is with a thought experiment. Imagine sitting on a merry-go-round. (The old type that used to be on playgrounds where you had to run around the outside and push it in circles.) You have a basketball. When the merry-go-round is still, you can roll the ball straight toward the center of the merry-go-round and you will see it roll toward the center. However, when the merry-go-round is spinning, you will see the ball curve to one side. When the merry-go-round is still, the ball leaves your hand straight in the direction you roll it. The ball's initial velocity (speed and direction) is straight away from you. If the merry-go-round is rotating (let's assume toward your left), the ball leaves your hand with a composite velocity, the straight velocity you are rolling it with PLUS the velocity you are moving toward your left with. To someone standing on the ground watching, it will look like you rolled the ball at an angle toward your left instead of straight. As you rotate around, the ball will appear to you to move in a curve to the left and it will miss the center of the merry-go-round. Now, imagine that the merry-go-round is spinning at a constant rate. If you sit on the edge and roll the ball toward the center, you'll see a large curve. If you sit halfway in toward the center and roll the ball in the same way, you will see a smaller amount of curving. This is because as you move closer to the center, the less the spinning motion affects you. EDIT[Here's a link to a video showing this. https://www.worthychristianforums.com/topic/212872-coriolis-effect-on-merry-go-round/] On earth, land at the equator is about 4000 miles (earth's radius) away from the axis of rotation. At the poles, you are on the axis of rotation. This is sort of like moving from the outside of the merry-go-round to the center. The tangential velocity at the equator is about 1000 MPH and at the poles it is 0 MPH. In other words, air that is stationary above the equator is following along with the earth at about 1000 MPH toward the east along with the earth. Air that is stationary at the poles is just sitting there. As this equatorial air moves toward the north or the south, the eastward motion of the air causes it to move toward the east (in much the same way that you would see a ball curve on the merry-go-round). A look at typical wind flow patterns on earth illustrates this. Near the equator, people see a general pattern of east to west winds. This is consistent with earth's surface applying a shear force to the atmosphere to keep it moving along with the direction of rotation. At the equator, the earth's rotation to the east is a bit faster than the air as the earth drags it along. People standing on the equator are moving toward the east a bit faster than the air so it seems that the air is blowing from the east. This means that people near the equator see predominantly east-to-west wind patterns. Both the earth and air are moving toward the east, it's just that the earth is doing it a bit faster so that the air appears to be moving east-to-west. As air masses move from the equator toward the north or south, it is similar to the ball on the merry-go-round. The air starts to "curve" and move toward the direction of rotation as it gets closer to the axis of rotation. From our perspective on earth, it looks like air moves in a west-to-east direction as we have moved from the equator nearer to the poles. This pattern we see on earth of east-to-west near the equator and west-to-east toward the farther north and south parts of earth is what is observed in actual weather patterns. As a point of comment, when dealing with the Coriolis effect mathematically, we must clearly define our fixed and rotating reference frames. In the case of the merry-go-round, the merry-go-round is the rotating frame of reference and the ground is the fixed reference frame. In the case of the earth, we treat the fixed stars in the sky as the fixed frame and the earth as the rotating frame. Trying to mathematically use both the earth and atmosphere as two reference frames makes as much sense as using the merry-go-round and the basketball as the two reference frames. In order to properly use the rotational mathematics for earth, we need to use a fixed reference frame such as that provided by the fixed stars in the sky. Example 3: How much wind shear is there at different altitudes due to earth's rotation? My approach to this one is to use basic geometry and the definition of speed being distance traveled by time. We'll go to the equator and round some numbers. I'll use 4000 miles for the earth's radius. The speed of a point moving in a circle is equal to the circumference of the circle divided by how long it takes to go around once. For example, if I am on a merry-go-round with a 10 foot radius that goes around once every 10 seconds, I am moving with a tangential velocity of 2 Pi 10 ft/10 sec or about 6.28 ft/sec. The circumference of the earth is about 2 Pi 4000 miles and it goes around once in 24 hours. At the equator, this corresponds to 2 Pi 4000/24 MPH (or about 1047 MPH). At an altitude of 20 miles above the earth, the speed of air that is stationary above the earth would be 2 Pi 4020/24 MPH which is about 1052 MPH. In other words, there is about a 5 MPH difference due to rotational effects. Example 4: How does atmospheric pressure vary above the earth? My approach to this one is to grab some readily available data to clarify what is really observed. In the same way that gravity pulls down on water (making the pressure greater at the bottom of a swimming pool or at the bottom of the ocean), gravity pulls on the atmosphere making it denser near the ground. I did a quick look up on the raw atmospheric pressure readings available for the past two years at 4 locations, New York City (10 meters above sea level), Chicago (180 m), Denver (1600m), and Leadville, Colorado (3100m). The average readings at these locations are 957.1 millibars, 929.7 millibars, 728.1 millibars, and 658.9 millibars of pressure. I use Mathematica as my primary analysis package and I pulled in two years of data (from 9/10/2015 to 9/10/2017) from the Wolfram.com curated data site and processed it myself. Many years ago as a grad student, as part of a problem set in statistical mechanics, I recall deriving the actual formula for the change in atmospheric pressure assuming only gravity as a constraining force and the atmosphere as a compressible fluid. It came out to an exponential drop with altitude which tracks well with observed measurements. It is arbitrary to define where the atmosphere "ends" because it just slowly becomes less and less dense at higher and higher altitudes. I tried to cut and paste some graphs and schematics into this post but couldn't. At this point, I've put in enough time on this. Basically, this post is just scratching the surface of the type of stuff applied physicists do. This is the type of stuff I'd do on the back of an envelope in a meeting on the fly when someone has a question. Most of what I do is much more complex mathematically and computationally. The real key is having the mathematical and technical ability to actually understand what is happening and to make successful predictions from it. People who can do this are the ones that I respect and have some degree of confidence in what they say.

There are some things we can help others with; there are some things that they must decide to do themselves. When you say you are his "caretaker", is he disabled in some way? Or is it just that he doesn't take care of his medical condition? How is the rest of his life? Is he satisfied and content? stressed? Is work going good? or unemployed? I spent many years way too stressed out about work and other things and it affected my health. The simple act of leaving my last two jobs due to stress and poor working conditions and I've lost about 60 pounds in the past few years without changing my diet or lifestyle much. There can be emotional or other things in life that affect our health and ability to take care of ourselves. If there are spiritual or emotional things that are dragging him down, those could be having an impact on his health and motivation to do things.

There are two steps to something like this. The first is taking steps to mitigate the damage to prevent as many long-term consequences as possible. It sounds like you are actively doing that. The second is trying to find the root cause(s) of this. Why do you want or need or crave the attention so badly? Until that is dealt with, you are probably going to struggle with this. I'm not a counselor or anything, just someone who has read a lot and observed a lot of people over the years. I'm just going to toss some things out as food for thought and meditation. Sometimes, the behaviors that have our attention are symptoms and not the real problem. Sometimes the real problem is buried deep within us and we cannot see it for what it is. We can do many things to reduce a fever, but until an infection is dealt with, the fever will keep returning. Sometimes we have spiritual wounds inside of us that affect us. This could be from emotional hurt from abuse or neglect or deep loss or grief. The sort of things that either keep us awake at night or the sort of things we bury away and refuse to think of. These are things that God needs to take us on a path of healing. Often, we may need to forgive someone for something. Sometimes we need to realize being a victim was not our fault. Sometimes it would be helpful to talk to an experienced Christian counselor or pastor for some things. Sometimes we have spiritual lies embedded into our hearts. There is a world and enemy that hates God and hates every beautiful creation He has made and does not want any human being to become what God wants them to. We often end up with lies and accusations embedded deep within us that we are not what God created us to be. At times when we are young and spiritually vulnerable, those lies get stuck inside of us and become reality for us. You are worthless. You are stupid. You are ugly. You are clumsy. You can't do anything right. You'll never amount to anything. God hates you. You deserve everything that happens to you. No one could ever love you. You deserve to be alone. What start out as accusations and lies start to become parts of our identity as we believe and accept them. I am worthless. I am stupid. etc. Sometimes, we need to let God shine His light and truth inside of us to see these lies for what they are and reject them. I'd suggest praying that God would show you what He wants to change inside you. Maybe a few questions to ask yourself and prayerfully consider. When do you remember first feeling this way as a child? How do you feel without attention? Do you struggle with negative feelings of some sort ( for example, feeling worthless or ugly or stupid or lonely)? Do you have any particular phrases that you constantly repeat to yourself? (Here are few real ones I've heard people talk about. I'm a loser. No man could ever love me. God made me stupid. I don't know what I'm doing.) Are there particular scenes in movies, books, songs that you hear, paintings that you see, whatever, that cause an unexpected strong emotional reaction that catches you by surprise? Sometimes those types of things unexpectedly put a mirror to our face and something inside of us peeks out at us. Sometimes these are positive things, the person God created us to be stirring to life and trying to break out of the masks we put on. Sometimes these are negative things, the pains and lies that are buried inside that sneak out. Ask God to bring to your attention to what He wants to work on. Sometimes we may need to talk to a Christian counselor or pastor for assistance in this. God created you to be special person made to reflect His glory in a way unique to you. You need to learn to walk closely with God as that person He created you to be. You need to learn how spiritual disciplines (such as Bible reading, prayer, meditation, getting together with other Christians) work best for you. I suspect you may be like me and need to move from season to season with such things. Some people can get onto the same spiritual schedule for these things for decades and grow. I can do something (e.g. bible reading) in an intense way for perhaps 4 to 6 months and then I don't get much out of it anymore. Then I need to move to the next thing. Over the years, I've learned how to follow God's leading as to next thing I need to be doing to grow. Learning to embrace variety has helped me grow.

I would reduce the initial chart to a single entry: Who determines an individual's salvation? Calvinists say God does and Arminians say the individual does. Many years ago, I was reading one of Millard Erickson's theology books. He summarized the fundamental difference between all the varieties of Calvinists and Arminians as this: Calvinists believe that an individual's salvation is God's decision whereas Arminians believe that salvation is the individual's decision. Erickson's conclusion was basically that while there were problems with both, Calvinism seemed the more consistent with scripture. I would add one further point that never seems to be considered. Calvinists and Arminians both believe that human logic dictates that only one or the other is correct and hence centuries of Christian infighting over the point. It is a belief in this logic that it is simply assumed to be common sense and accepted without question. However, is it Biblical to simply accept that it has to be one or the other? Neither side is willing to consider that it is possible that sovereignty vs. free will is perhaps one of those mysteries of the faith such as Jesus being fully human and fully divine or the Trinity where God is at the same time one God but 3 Persons. We accept Christ's full humanity and full deity and we simply say that Bible passages which point to His humanity do not disprove His deity nor do Bible passages which point to His deity disprove His humanity. We accept both as true. In the same way, we do not use verses pointing to God being one God as disproving He is not 3 Persons, nor do we use verses clearing showing 3 Persons as proof of tri-theism. We take passages showing God's unity as well as 3 Persons on their face value and accept both as something we as finite beings cannot wrap our heads around. We comfortably talk about Jesus being human. We comfortably talk about Jesus being God. We do not use logic to prove that we must choose between the two options as many heresies that either reject the humanity or the deity of Christ (or force a modality where He was first human and then divine or talk about a human "Jesus" and a divine "Christ"). Over the years, I've come to accept scripture passages both dealing with God's sovereignty and human free will to be taken on their face value and not to explain them away. I've come to accept both as true and fit this under the same category as the Trinity and the Humanity/Deity of Christ. It does make reading the Bible much more enjoyable. I don't have to spend my time worrying about whether Pharaoh hardened his heart or God hardened Pharaoh's heart and which of those verses are the "real" ones and which need to be "explained". I just take both as written and say that it seems that the Bible teaches both are equally true statements. I've decided to reject logic that says one or the other is correct and go with the preponderance of Biblical evidence that seems to say that both are true. So, basically this means everyone thinks I'm a fruit cake that needs Biblical correction because I now refuse to join either side in a centuries long schism.

I think an important thing is discernment as to what the real issue is. Often, many of the things we are most concerned about in ourselves and other people are *symptoms* of a deeper cause. For example (hypothetical case only, I'm not suggesting this is actually what is happening), if your sister is angry and frustrated and rebellious towards your parents and the church, this is going to result in a lot of different behaviors that are not good. If the root issue is anger and bitterness, getting her out of the current relationship is damage control and isn't dealing with the real problem. More issues would continue to emerge in the future. Continuing on in the hypothetical case, is this just rebellion and stubbornness gone too far, or was your sister hurt in some way by your parents or the church? In that case, apologies, reconciliation, and forgiveness may be needed for healing and change to occur. I'm not suggesting that is the actual case though I've seen that in a few people. I'm just trying to generate food for thought as to if this relationship is indeed the main issue or if there is something deeper that God wants to work on. When something is going on with someone, I prayerfully try to discern what the real issue is that God wants to deal with at present. I then focus my prayers and interactions with that person on addressing that deeper issue. I've at times seen that the most obvious stuff we are most concerned with are symptoms rather than root causes. Of course, that's not to say we don't try to minimize consequences of what's going on, but we need to focus on what God's priority is for change in someone. If we do not deal with the root issue, we're going to see a range of different problems keep emerging and we end up fighting a bunch of different battles without ever fixing the real problem. Sometimes what we see is the real issue; sometimes not. In this case, the main issue might be the relationship itself, or the relationship might just be a symptom of some deeper spiritual battle going on inside your sister.

Here is one book I'd recommend for anyone to read. I first read it back in early 1980s when it first came out (and still have my original copy). It's a very good introduction to learning to interpret scripture from a historical standpoint. What this book is great for is learning to answer the question, "What did this mean to the original hearers of the message?". For a time, I used this method exclusively, but then eventually realized it is a major part of good study but not all of it. "How to Read the Bible for All It's Worth" by Gordon Fee and Douglas Stuart. I just noticed it's on a 4th edition. The reality is that every time anyone of us quotes a Bible passage and says "this is what it means" or "this is how we should apply it", we are taking upon ourselves the role of interpreter and spokesperson for God. Furthermore, we are taking a tremendous spiritual responsibility upon ourselves if in this role we determine who is and who is not pleasing to God by whether they match up or not with our interpretation. We need to be extremely careful that we are NOT just expressing our own opinion (or the opinion of our denomination or church) as being equivalent to the authority of scripture. If I say Matt 5:29 (If your right eye causes you to stumble, gouge it out and throw it away. It is better for you to lose one part of your body than for your whole body to be thrown into hell.) is NOT meant to be taken literally, I am taking upon myself the role of interpreter. I am telling someone addicted to pornography NOT to take this verse literally as a means of stopping the sin. This is a case where all Christians would agree NOT to take scripture literally. If I say Matt 28:19 ( Therefore go and make disciples of all nations, baptizing them in the name of the Father and of the Son and of the Holy Spirit...) means baptism the way MY church practices it (and that all other methods are at best ineffectual and at worst a spiritual perversion), I have become an interpreter and enforcer of my interpretation. (But that's okay because my church is right and the others are wrong. ) This is a case where there are extremely passionate opinions where some Christians feel it is the proper spiritual thing to do to have nothing to do with people who have different opinions about it. If I choose sides on what a particular verse means and use that choice as a standard of determining if someone is "in error", "not pleasing to God", "under a curse", etc., I had better be sure of two things. First, I'd better be sure that I'm on the right side and that I indeed am taking God's view of it. Second, I'd better be sure that this is as important to God as it is to me. I first became acutely aware of this when I was involved in a church plant with an inexperienced pastor. In our initial planning meetings and small group meetings, I came to observe that he would not tolerate any questions when he said something. If anyone questioned him about a particular verse or anything or expressed a contrary opinion, his response was "well that's what the Bible says. Don't you believe the Bible?" As I quickly came to see, this was not wisdom, learning, and great discernment, but rather it was arrogance, insecurity, and stubbornness. His Bible study lessons and teaching were often full of conjectures and peripheral issues that few Christians would all agree on. The "discussions" were not discussions. Basically, anyone who did not toe the doctrinal line in each and every detail he held "didn't believe the Bible". My family and I were the first ones out the door. Within about a year, all of the original people involved (except for the pastor) had left as well. In my opinion, we all need to examine ourselves very carefully that we are both 1. rightly interpreting scripture and that 2. we are rightly enforcing it in the way God would (or would not) want us to.

This has been interesting for me since I've long known this verse and never really dug into it until now. The last big thing I see of interest is the word order in Greek. It's roughly: the one believing in me, the works which I am doing, that one will (future tense) also do, and even greater (than my works) they will do, because I am going to the Father. Sometimes, there is a tendency in Greek sentences to start with the familiar and move toward the unfamiliar. If so, this would run in the following chain of thought for the disciples hearing this. "The one believing in me will do the works I am doing." This would be no surprise since the 12 (and others) had been sent out by Jesus to do miracles and proclaim the kingdom of heaven. To some extent, it's a statement of fact of what's been happening. But then we move to something different. "And even greater works that one will do". This is somewhat different. What they've been doing for a few years and watching Jesus do is not all that is going to happen. Works and deeds beyond what Jesus and the disciples had been doing would happen. And finally, He says that the reason that this will happen is because He is going to the Father. Jesus had already given authority to the 12 and they had done and seen many things, but because Jesus was leaving to return to the Father meant that something more would happen beyond what they had already seen. The context of this verse in the last supper is also interesting. The following verses including asking for things in prayer as well as keeping His commands and the coming of the Holy Spirit. A further context that is interesting is the entire book of John. The author obviously included many things that he thought that the works of Jesus included. Water into wine at the wedding, the clearing of the temple courts, talking to Nicodemus, talking to the Samaritan woman at the well and staying for a few days to talk to the Samaritans in the town, healing the official's child, healing the lame man, debating the pharisees and lawyers, ministering and then feeding the 5000, walking on water, teaching the crowds about God and the Kingdom, preaching at the temple, and other things. Within what is recorded here (not counting the other things in the synoptic gospels) we have miracles, teaching, dealing with crowds and individuals, ministering to individuals, and the explicit statement that He did many more things that weren't recorded in this book. Moving forward into the book of Acts, we have a further list of works and deeds we can add such as conversions, the coming of the Holy Spirit at Pentecost and at other times and places. In addition, Acts and the Epistles contain many references to the new life in Christ wherein believers are a new creation and not merely people trying to do good things. My sense of this verse is that it applies to all Christians individually (since the verse is explicitly singular not plural in Greek). The works include everything (mentioned in the NT) from answered prayers to miracles to a transformed life to ministry. This verse basically states the works of Jesus and early believers in the early church in Acts are meant for "one who is believing in me" without limitation and (from context) is because the Holy Spirit is sent to dwell in believers.

Many times Christianity is misrepresented as being a system of rules and laws; of punishment and reward; and of doing the best we can. Christianity is not about that, but it is about revolution and transformation. We see those things that we despise and abhor in the world such murder, genocide, rape, disease, natural disasters, and things that seem unfair and unjust. We see those things that we admire and like about the world, friendship, love, compassion, and the beauty of nature. We think that the world would be a better place if we got rid of the bad and kept only the good. Indeed, God is going to get rid of all of the evil and harmful things. He's going to take all of those things and chuck them onto the garbage heap and burn them away forever. Heaven will indeed be a place where all of those harmful and hurtful things will be gone. The issue is that each one of us is contaminated with this evil. It is not about being mostly uncontaminated. It is that we are all carriers of it and have been touched by it and have touched others with it. Adam as patient zero contaminated us all. Some of us have a lot more symptoms than others, but we all have it. We have all hurt people (in spite of our best efforts, we have hurt people). We all have addictions and compulsions and urges we cannot control. We have all been wounded by it, and we all carry it and spread it. Heaven being a good place is not about trying to triage and quarantine people into those with fewer symptoms and those with more symptoms, it is about being completely healthy and free of it. Having fewer symptoms than someone else or taking a few aspirin to reduce the fever does not make us disease free. The reality is that each of us would be a source of contamination that cannot be allowed in. Christianity is about being transformed and changed from within. The purpose of Jesus' work was not just forgiveness, but transformation. The revolutionary thing about Christianity is that God has decided to live inside of us. It's not about being given a free pass to Heaven as we are; it is about being changed into a person that is becoming a good person and fit into Heaven. The Bible says that the fruit of the Spirit is love, joy, peace, patience, kindness, goodness, gentleness, self-control, etc. Being patient does not mean taking anger management classes, learning to count to 10 before speaking, or learning how to bottle up our anger; being patient means that we do not get angry. This is not something we teach ourselves to do; this is something that happens as God changes us from inside. The message of Christianity is that as we walk with God, we will be transformed and changed into the unique person He intends for us to be, and be able to live life to the fullest in a grand adventure of walking with Him. So, how do mass-murderers, pedophiles, rapists, etc. fit into this? The issue is forgiveness. Forgiveness does NOT mean that nothing happened. Indeed, something happened. Sometimes something unspeakable and unfathomable happened. Forgiveness does NOT mean those things are right or will ever be right. Forgiveness means that we let it go and don't let it have a hold on us. Forgiveness means that I have decided that what happened will not continue to affect my emotions and thoughts. I will not dwell on it at night when I cannot sleep. I will not have this bottled up rage that it isn't fair. I will let it go so that the original event(s) and act(s) no long have their claws buried deep within my soul continuing to poison me. (As a practical matter, it doesn't mean I have to trust that person or reconcile with them. In some cases, they haven't changed, I do not have to endanger myself or others.) The key to us forgiving people is that we do not let past events continue to be an infected wound that slowly poisons us emotionally. We treat it, let it heal, and are left with a scar that is a memento of something that we survived and moved on from. Lack of forgiveness is an infected wound that slowly poisons us (and others around us). Forgiveness is a way of treating that wound so it can heal over. If there is a particular person or group that we see and react to, our blood boils, we become sick to our stomach, we relive the events, we want justice and revenge, we want something to happen to them, it means that we are bound with chains of bitterness and anger. No amount of justice or revenge or anything will heal us or free us. It may give momentary satisfaction to see them suffer. However, only forgiveness will bring the healing we need. When Jesus was on the cross, His words were "Father forgive them". When Stephen was being stoned, his dying words were “Lord, do not hold this sin against them.” Forgiveness is not about declaring what someone did as being okay. It is about letting it go. When God forgives us and others, He is letting go everything we've done that has hurt others. Compared to Hitler or Stalin, I'm a saint. But I know I've done things to people that has caused them pain and hurt (and I'm sure there are many more I don't know about). I know I'm part of groups that have hurt people. We are all guilty of this. It is not the question of whether we are more or less guilty of being part of the problem with the world, it is the issue that we all contribute to the problems in the world. Christianity is about God's plan and means to transform all of us so that we are no longer part of the problem but part of the solution. It doesn't mean we become perfect overnight. It means that over time He transforms us so that the unique person we were created to be can start to be the person He means for us to be in ever increasing freedom. It means that we are being changed into people suitable for Heaven who can enjoy and contribute to it being a good place. Some of us have a head start and are on this journey most of our lives; others start at the last possible moment.