181

Flat Earth Investigations / Re: Antipodal journeys

« on: November 03, 2018, 09:52:45 AM »

I don't agree that...

when you take a flight with a stop over that stop over is unlikely to be exactly on the great circle between the two places.

On the contrary, because the two endpoints are antipodal then there must always exist one great circle route which passes through both the endpoints and the stopover. Only one great circle passes through the departure and stopover and only one through the stopover and destination, so they must be one and the same great circle.

Put it another way. Pick any two non-antipodal points A and B and there is one great circle route between them. Extend that route all the way round and you must necessarily pass through the antipodal points of both A and B.

Right. Yes, you are correct. Again, taking my example because it's easier to think about. If you're at the North Pole then you can, as I said above, go down any line of Longitude to get to the South Pole. And since you must go through every point of Latitude as you do so you can go to any place of Longitude and Latitude on earth on your way between the poles.
That remains true for any antipodal points on earth. The way to think about it is imagine a ring around the earth going through the two points A and B which are antipodal. That ring is a great circle. You can pivot that ring around points A and B so it goes through any point on earth.

Note to certain people. This is how grown ups discuss things, actually conceding points and admitting error when shown to be incorrect. It's not that difficult...

I like the pivoting ring analogy and I love the "grown ups" comment, but in the spirit of this forum, perhaps we should really have thrown at least a few insults at each other along the way ;-)

182

Flat Earth Investigations / Re: Antipodal journeys

« on: November 02, 2018, 11:11:29 PM »

On the contrary, because the two endpoints are antipodal then there must always exist one great circle route which passes through both the endpoints and the stopover. Only one great circle passes through the departure and stopover and only one through the stopover and destination, so they must be one and the same great circle.

Still don't follow. Suppose I travel down the meridian (0 longitude) from London A to some point on the equator B. Then suppose I travel along the equator (which is another great circle) to somewhere else C. It clearly doesn't follow that ABC is 'one and the same great circle'. Clearly there is a third great circle AC, but B does not lie on it.

Perhaps I misunderstand.

I think it's more likely that I'm not explaining this very well. I'll have another go.

In your example you have points A, B and C, but you don't have two antipodal points and that difference is crucial. So let's fix that and make A and C antipodal.

Travel down the meridian (0 longitude) as you did before to get to B (on the equator). Now you need to head for C, but C is constrained to be directly opposite A, which means it must also be on the 0 longitude line somewhere, so basically you just carry on in the same direction until you get to C.

Hope that helps.

Yes it does. I was reading 'antipodal' as meaning 'in the antipodes'. You see my mistake.

Yes indeed, sorry - I could probably have explained better.

Now we're on the same page, do you see why I think this is an interesting challenge for the flat earth?

On a flat earth it makes no sense to me that flying from London, one route could start out heading north-west, another due east, with stopovers thousands of miles apart and yet they meet up at the same place and take the same amount of time. These routes exist.

183

Flat Earth Investigations / Re: Antipodal journeys

« on: November 02, 2018, 07:26:04 PM »

On the contrary, because the two endpoints are antipodal then there must always exist one great circle route which passes through both the endpoints and the stopover. Only one great circle passes through the departure and stopover and only one through the stopover and destination, so they must be one and the same great circle.

Still don't follow. Suppose I travel down the meridian (0 longitude) from London A to some point on the equator B. Then suppose I travel along the equator (which is another great circle) to somewhere else C. It clearly doesn't follow that ABC is 'one and the same great circle'. Clearly there is a third great circle AC, but B does not lie on it.

Perhaps I misunderstand.

I think it's more likely that I'm not explaining this very well. I'll have another go.

In your example you have points A, B and C, but you don't have two antipodal points and that difference is crucial. So let's fix that and make A and C antipodal.

Travel down the meridian (0 longitude) as you did before to get to B (on the equator). Now you need to head for C, but C is constrained to be directly opposite A, which means it must also be on the 0 longitude line somewhere, so basically you just carry on in the same direction until you get to C.

Hope that helps.

184

Flat Earth Investigations / Re: Antipodal journeys

« on: November 02, 2018, 05:05:28 PM »

I'm still keen to get an answer to the original point which is that if I'm travelling between say UK and New Zealand, on a globe I believe I can head off in any direction I like

I don't think you can head in any direction you like. Only one great circle passes through any two points, and the haversine formula above gives you the distance along that great circle.

Hmm. But if those points are antipodal then you pretty much can, can't you? Imagine the two poles, if you're standing at the North Pole you can follow any line of Longitude you like and you'll end up at the South Pole.

Obviously when it comes to flights there are practical considerations like where there is a conveniently placed airport part of the way and when you take a flight with a stop over that stop over is unlikely to be exactly on the great circle between the two places.

Ah yes, and that's exactly what I'm trying to get at. UK to New Zealand flights do in fact offer a very wide choice of conveniently placed airports serving as stopovers in very different locations across the globe, from North America (e.g. Los Angeles) through the Middle East (e.g Dubai) and the far east (e.g. Tokyo).

I don't agree that...

when you take a flight with a stop over that stop over is unlikely to be exactly on the great circle between the two places.

On the contrary, because the two endpoints are antipodal then there must always exist one great circle route which passes through both the endpoints and the stopover. Only one great circle passes through the departure and stopover and only one through the stopover and destination, so they must be one and the same great circle.

Put it another way. Pick any two non-antipodal points A and B and there is one great circle route between them. Extend that route all the way round and you must necessarily pass through the antipodal points of both A and B.

185

Flat Earth Investigations / Re: Antipodal journeys

« on: November 02, 2018, 03:19:21 PM »

I'm still keen to get an answer to the original point which is that if I'm travelling between say UK and New Zealand, on a globe I believe I can head off in any direction I like, following a great circle route for 12500 miles and I will arrive at my desired destination. Does anyone disagree that if we are on a globe, that assertion would hold true?

The only assumption being made is that a great circle distance is the shortest distance between any two points on a sphere and that flights on a globe would presumably follow such routes where practicable (and with minor adjustments for weather) for efficiency. Is there agreement on this or not?

I've read Tom's ENAG link and I'm not clear at all whether Rowbottom is disputing that a great circle distance is always the shortest on a sphere or if he's simply saying sailors in the 19th C and earlier aren't sailing great circle routes so that means we're not on a globe.

186

Flat Earth Investigations / Re: Antipodal journeys

« on: November 01, 2018, 10:52:32 PM »

There is a chapter on Great Circle Sailing in Earth Not a Globe.

OK thanks for the link, I read through that and a lot of it seems more to do with the practicalities of 19th C sailing, so I'm not really clear whether Rowbotham is actually claiming that there is a shorter distance on a sphere (not talking about the Earth here, just a plain old sphere) than a great circle distance. If he is claiming that, then it begs the question - what is this shorter route?

Put plainly, on a sphere, is the shortest distance between any two points a great circle distance or not?

187

Flat Earth Investigations / Antipodal journeys

« on: November 01, 2018, 03:14:31 PM »

One of the problems with flat earth discussions is that there is no consensus behind any particular flat map, however the one thing I assume everyone does agree on is that whatever it looks like, it will be flat.

On any flat surface, there can only be one shortest route between any two points - a straight line - and therefore only ever one sensible direction of travel if you want to get to your destination via the shortest route.

On a sphere, the shortest route between two points is a great circle arc and in general there is only one great circle passing through both points and hence one shortest route. The exception occurs when the two points are antipodal (directly opposite each other). In this case many great circle routes are possible so there is no longer a single shortest route, there are many.

So for example, on a globe earth, the UK and New Zealand are almost antipodal, therefore you can head off in any direction you like from the UK, follow a great circle route for about 12500 miles and you will be more or less in New Zealand. On a globe travelling in opposite directions yet ending up in the same place makes perfect sense, on a flat earth it doesn't.

In reality, from the UK, I can fly west via Los Angeles to New Zealand or I can fly east via Tokyo and there are plenty of other routes to choose from such as via Hong Kong, Dubai, Manilla etc. These routes all have similar flight durations and cost similar amounts of money.

Anyone care to try and explain?

188

Flat Earth Theory / Re: Requirements elements for a FE map

« on: September 25, 2018, 11:13:32 AM »

The starting point for a map is a model and then a coordinate system, so if you pick a model and can draw lines of latitude and longitude then the rest follows from that.

A while back I was teaching myself the basics of 2D and 3D graphics in the C# programming language for fun and wondered if I could generate my own maps. I came across http://www.geonames.org/ which has a massive database of freely downloadable "features". A feature could be anything, a building, a road, river, gas/oil platform, you name it. Each feature has an associated country code and latitude/longitude location info.

To cut a long story short, I basically wrote a program to read the "all counties" features file (11 million odd features) and plot each feature as a dot on a map with a different colour for each country. What you end up with is a nicely coloured world map based on the model of your choice. I made a spherical 3D globe plus north and south pole centric mono-pole 2D maps and they looked pretty good.

I discovered a few interesting things along the way. Antarctica you can barely make out because so little of it has any features. Parts of the US and Australia are similarly sparse. The interior of Brazil is fascinating because presumably everyone lives on or near the banks of the Amazon or its major tributaries, so pretty much all you see is the spidery outline of the rivers.

For larks, I also added point of view and zoom features to my 3D globe and had a go at recreating the original "Blue Marble" Apollo 17 photo - basically set my point of view 18k miles away and zoomed in - pretty damned perfect match.

Anyway, I digress, the point is forget about a map, with a bit of programming know-how, that'll draw itself. Come up with model and a diagram with latitude/longitude on it that works and the countries can draw themselves.

189

Flat Earth Investigations / Re: Flying from UK to New Zealand - Possible experiments?

« on: September 23, 2018, 10:33:29 PM »

We had a long debate about this this past summer, about how the "tilt" of the moon might help distinguish between a round earth and a flat earth, either when viewed simultaneously by two observers from different locations, or by the same observer at different times.

I read through some of this and I think the difficulty with that particular thread is that the OP muddied the waters somewhat by stating at the outset what they believed FET would predict, without actually asking anyone and from there on it all seemed to go downhill and as you say, by the end it was clear that nobody was going to agree on the premise, so I'd say no point in re-hashing that debate, trying to convince anyone of anything based on rotation angle of the moon is a non-starter.

I am however still interested to hear anyone's explanation as to how it is possible to choose pretty much any route you like to travel to NZ and take the same time/travel the same distance (more or less) under FET, or if this has been discussed before, if someone could point me to the right thread topic.

In this case, the OP and his mate are setting off (from the UK) in almost completely opposite directions (one via Singapore the other via LA), presumably by the shortest route (within reason) and yet they end up at the same destination (NZ) having been in the air for a similar amount of time. This makes complete sense under RET, you just pick a direction and follow a great circle route, but I can't visualize this in a flat earth model.

190

Flat Earth Investigations / Re: Flying from UK to New Zealand - Possible experiments?

« on: September 23, 2018, 04:44:19 PM »

In theory if I were to go outside in an hour and a half (18:50 UK time) and look ESE I might just make out the moon rising - assuming I could find an unobstructed view and no clouds(not from where I am right now).

If I ask my son to do the same from where he is (but look WSW instead), he might be able to make out the moon just setting, although it will be 05:50 his time.

I can't honestly think that it's going to be easy to get a photo at all, let alone a good one with the moon so low on the horizon and at sunrise/sunset.

But assuming we could, what would be the point. What is FET predicting here that contradicts RET?

I'm expecting to see the moon "the right way up" and my son will see it "upside down" (relative terms obviously), beyond that, can't think of anything unusual I would expect to see and I assume that FET will also predict the same for my son and I.

191

Flat Earth Investigations / Re: Flying from UK to New Zealand - Possible experiments?

« on: September 22, 2018, 01:11:41 PM »

We went as a family from the UK to New Zealand 20 years ago. When we were booking flights, I remember how surprised I was at the wide choice of routes available. Then it dawned on me - because the UK and New Zealand are virtually opposite each other (globe model), you can in theory pick any point of the compass and any great circle route will get you there just as quickly as any other, so the choice comes down to where you want to change planes. We considered LA, Tokyo, Bangkok, Hong Kong, Singapore, Dubai and in the end plumped for Hong Kong. Various members of the family have been back since and taken different routes and my son is out there now - he went via Manilla a few weeks back.

This all makes perfect sense on a globe, but I'm struggling to see how it would work out on a flat earth.

As far as experiments go, unless you have window seats, can't think of any, but if you do, I believe android phones will allow you to use GPS in airplane mode, so perhaps some kind of GPS tracking app might allow to you at least confirm your ground speed and roughly where you are (see if it agrees with what you see on the in-flight route map and through the window). My understanding is that the fuselage will act like a Faraday cage so you'll have to rely on whatever limited signal gets through the window, so don't expect great accuracy. Altitude data will probably be useless. Time in the air should be similar for the two routes (give or take a bit for wind).

What you really want here is a proper flat earth believer to suggest some achievable test you could do which, depending on the result, could change their mind - good luck with that.

Enjoy New Zealand - great place to visit.

192

Flat Earth Theory / Re: On a globe Earth the horizon should not curve

« on: April 20, 2018, 01:52:57 PM »

I’m new. I just heard about this flat earth stuff and was curious.

Am I being thick? Surely if you’re standing on a small island looking at the horizon all around you, you cannot tell whether you are standing on a ball or a plate. The horizon forms a sharply-defined circle all around you, 5 miles away. Because it’s 5 miles away it looks like a horizontal edge, whether it’s a large ball or a large plate.

The one way to find out whether it’s a ball or a plate is to step onto on a chair or go up a hill. If the plate stays the same size then you are on a 10 mile diameter plate.

But if the horizon recedes with elevation, what other conclusion can there be but that this plate must be domed or ball-shaped?

I must be lacking in my logical facilities not to be able to conceive of any other explanation - can someone help me understand how that can point to the earth being flat?

Oh and I read earlier someone saying the horizon rises to eye level. What does this mean? That the earth is actually concave? Or that when you look directly down at the horizon from a height then, well, you are looking directly at it so it meets your eye level? Or that it physically moves? Surely anything you look at meets your eye level, whether you have to look up at it or down at it? I just can’t grasp these concepts.

Agree with all of that. I'd also add that since you are standing in the exact centre of a 5 mile radius circle, if you decided to move a mile or so away, the circle would apparently move with you. A bit like one of those old Victorian era dresses that move around the floor with you. That rules out the simple plate idea, but is precisely what you'd expect to see on a sphere. A very simple explanation for what you see. You don't need to complicate this explanation with atmospheric effects, refraction, perspective, lens distortions. As an explanation it works just fine on its own.

193

Flat Earth Theory / Re: On a globe Earth the horizon should not curve

« on: April 09, 2018, 01:58:14 PM »

A common argument against a GE is 'the horizon doesn't curve'. But why would we expect it to curve? Where would the highest point on the curve be. The fact is that the horizon would not curve on a GE:
All points on the horizon are at the same level and the same distance from the observer in all directions, thus forming a straight line. Yes, it is that simple.

mathematically: The projection of a circle is a line, only if the observer is at the same level/same plane of the circle. If the observer is above the center of the circle, he would see part of an ellipse.
Theoretically, but this circle, the horizon, compared to the hight of the observer, is huge. So in practice it's not distinguishable if you see a line or part of an ellipse.

An example: You know a Soccer field? There's a big circle in the center of the field. If you stay in the middle of this circle, you can see, that this is a circle around you - All points on the horizon this circle are at the same level and the same distance from the observer in all directions.

The points on the circle are all on the same horizontal plane. Standing up I can see the ellipse, yes, but that is not a curvature of the plane on which the circle is. It is the same elipse one would see standing close to the edge on a FE. It is also what we see in images of the Earth taken from space. We see the Earth is round, but because it is so far away it's reduced to the 2 dimensional shape of a circle, and we can't determine, from still images, that we're looking at a globe. From the Moon the Earth might as well be a flat disk

I've been following this thread with interest, so decided to register and join the party so to speak, to add a few observations of my own.

It just so happens that I spent a very pleasant couple of hours at a cafe by the seaside yesterday. A very clear day with a clearly defined horizon and calm sea. Based on the few boats I could see at various distances, I'd estimate the horizon at about 3-5 miles (let's say 5) distant and I was about 15-20 feet above sea level. If I looked directly ahead, I could see the horizon, it looked flat and perpendicular to my line of sight, however I had a very clear field of view of the sea approximately 180 degrees from left to right and no matter where I looked, I saw the horizon the same apparent distance away, perpendicular to my line of sight. So if I can turn my head through 180 degrees and see a horizon line at about 5 miles everywhere I look, then logically I'm looking at a semi-circle with a 10 mile diameter and me dead centre.

My eyes tell me I'm looking at a straight line, no curve, but I turn my head around and my brain tells me I'm clearly looking at a semi-circle. Lesson learned, I simply can't trust my own eyes to detect a curve on this scale from this viewing position.

Past experience also tells me that I could have moved to pretty much anywhere along the coast and I'd still find myself at the centre of a circle (or rather semi-circle). Also if I were to choose a higher vantage point, I'd see further - the circle would grow. As a pure exercise in geometry, ignoring any other factors, if I ask myself what kind of geometric object am I likely to be looking at if I find myself at the centre of a circle, no matter where I move to or look, but at the same time the size of circle grows when I increase my altitude, then the simplest explanation is that I'm in close proximity to a reasonably large sphere. It perfectly explains everything I see. Of course I'm ignoring all other factors such as refraction here, I'm just looking for the simplest geometrical explanation for what I saw. I'm not trying to go beyond that and speculate how or why the sea would curve away from me, just using my eyes and brain.