Why FE believers never will show you a perfect map?

People have been able to find their way around on this Earth using nothing but a wide assortment of flat earth maps since we started practicing cartography.

To say otherwise is simply being purposefully obtuse, willfully ignorant, or an outright liar.

Maps came first.

Maps are drawn on a flat surface and a perfect reflection of the reality around us. 

People have been able to find their way around on this Earth using nothing but a wide assortment of flat earth maps since we started practicing cartography.

To say otherwise is simply being purposefully obtuse, willfully ignorant, or an outright liar.

Maps came first.

Maps are drawn on a flat surface and a perfect reflection of the reality around us.

It would be far more correct to say that maps of limited areas of the earth came first, but in those days there were no accurate ways to measure distance and longitude. Latitude could be measured with good accuracy since the inventions of the astrolabe, mariner's quadrant and the sextant.

But with the accurate latitude and longitude measurements, it soon became apparent that any flat map of the earth must have distortions in direction, shape and/or distance.

This is why there have been so many "projections of the Globe" since Mercator's time. All have their strengths and weaknesses.
Mercator's has accurate local shapes and directions, but it is well known for its gross exaggeration of size as the poles are approached.
Nevertheless, because its lines of latitude and longitude are all straight and perpendicular to each other, it is a convenient projection to see the whole world and easily "zoom in" to local areas. This is why a version of Mercator's is used for Google and OSM on-line maps.

Since no single flat map can accurately represent the whole world, early mariners often carried globes to better picture where they were. But no globe can be large enough to show the fine detail needed for navigation near land, so flat maps of limited regions are used.

This stuff is common knowledge to anyone with any interest in navigation and to deny it is to go in the face of many centuries of knowledge of sea-faring.

Go tell that to your boss Mr Lackey

lackey
noun
1. a servant, especially a liveried footman or manservant.
"lackeys were waiting to help them from the carriage"

I've got a map 

Using a metric I've derived before on this forum:

Quote from: Jane on September 01, 2016, 01:50:14 PM

The Earth is defined by the x and y axes, with the North Pole (for the sake of tradition) at 0, and the South at infinity. An infinite plane is used so that if you reach the South, you can come out the far side. Once the metric is used, the distance shouldn't actually be infinite. This is just our set.
Longitude is 0 along the line y=0, latitude is zero on the circle of radius 1 centred at the North pole.

Now then, our spectacularly awful looking metric. For points P₁=(x₁,y₁), P₂ = (x₂,y₂):

[jsTex]d(P_1,P_2) = \cos^{-1} \left( \sin \left(\tan^{-1} \left(\frac{x_1^2 + y_1^2 -1}{2x_1} \right) \right) \sin \left(\tan^{-1} \left(\frac{x_2^2 + y_2^2 -1}{2x_2} \right) \right) +\cos \left(\tan^{-1} \left(\frac{x_1^2 + y_1^2 -1}{2x_1} \right) \right) \cos \left(\tan^{-1} \left(\frac{x_2^2 + y_2^2 -1}{2x_2} \right) \right) \cos \left|\tan^{-1} \left( \frac{y_1}{x_1}  \right) - \tan^{-1} \left( \frac{y_2}{x_2} \right) \right| \right)[/jsTex]

The following map gives over half the Earth. The rest can be extended out, but it grows in size.



But remember, we're in non-Euclidean space so you have to calculate distances with the above metric.

Awesome.

Quote from: Jane on November 25, 2016, 10:35:03 AM

But remember, we're in non-Euclidean space so you have to calculate distances with the above metric.

    Please Jane, can I still use my trusty Lufkin steel tape?

You need to order on the "non euclidean lufkin tape"

Lufkins are overpriced for the quality imo, I prefer the way a stanley feels.

Edit. Couldn't resist.


Mines a little beat up.

Quote from: rabinoz on November 25, 2016, 05:53:47 PM

Quote from: Jane on November 25, 2016, 10:35:03 AM

But remember, we're in non-Euclidean space so you have to calculate distances with the above metric.

    Please Jane, can I still use my trusty Lufkin steel tape?

You need to order on the "non euclidean lufkin tape"

Lufkins are overpriced for the quality imo, I prefer the way a stanley feels.

Edit. Couldn't resist.


Mines a little beat up.

Likewise!
I got a good price on the Lufkin at Bunnings and IMHO, I prefer the way a Lufkin feels.
Besides the Lufkin metric had metric along both edges, but the Stanley (which I also have) has metric one side and feet and inches on the other.

All very technical stuff this, hey what!
But they were fresh out of this "non-Euclidean Lufkin tape" at the time.

Yeah cant use that imperial crap.

Bunnings amazes me the amount of imperial stuff they sell in a metric country.

Apparently most of their suppliers are from the US...

Yeah cant use that imperial crap.

Bunnings amazes me the amount of imperial stuff they sell in a metric country.

Apparently most of their suppliers are from the US...

Look closer at what I wrote!

Besides the Lufkin metric had metric along both edges, but the Stanley (which I also have) has metric one side and feet and inches on the other.

All very technical stuff this, hey what!
But they were fresh out of this "non-Euclidean Lufkin tape" at the time.

An look closer at the "non-Euclidean Lufkin tape" - it says .
Now,  down on bended knee and apologise for suggesting that I might use those dread feet and inches.  , or I might be forced take off my glove!
I guess I've used metric units for around 60 years - after escaping from the clutches of civil and mechanical engineering into all electrical engineering.
I often post in " Imperious  Units" so the . . . . . . Americans and Brits will understand.
Just imagine driving a French car (Peugeot 508 wagon) around the UK, with the car reading km/h, speed limits in mph and buying petrol in pounds/litre etc, etc.
Then getting to Ireland and swapping across the Ireland/Ulster border with no signs for the border other than a yellow to white centre line and speed limit change from km/h to mph.
Too bad if you're driving south in a 50 mph zone (with the car on 80 km/hr) and unknowing cross the border into a town at 50 km/hr. The joys of unit changes!

I often post in " Imperious  Units" so the . . . . . . Americans and Brits will understand.

Just stick with metric.
The smart ones will have no problem keeping up.
The dumb ones don't understand either one.

I just meant that I woulda bought the lufkin also if stanley had an imperial side lol.

Agreed stick with metric, anyone who cares will do the conversions.

I just meant that I woulda bought the lufkin also if stanley had an imperial side lol.

Agreed stick with metric, anyone who cares will do the conversions.

I'll accept that as an apology and keep my glove on - but what idiot would wear gloves when it's 36°^[1] outside?

The Stanley was a long while ago, when some still used feet, inches and sixteenths etc.
But do you remember the decimal equivalent of ⁹/₆₄" so you could transfer the measurement from the ruler (in sixty-fourths) to the micrometer (in thou), ugh!.

Then "Chickenmess" comes in with his 8"/mile², that is supposed to answer everything about curvature.

[1] I know I should have written 36C but that might not have confused those from the "Imperious Countries" into thinking 36° was quite cool.

But do you remember the decimal equivalent of ⁹/₆₄" so you could transfer the measurement from the ruler (in sixty-fourths) to the micrometer (in thou), ugh!.

Luckily you are good at maths.

What are you measuring in micrometers with a ruler?

I use callipers if I need to be more accurate than .5mm (which doesn't happen all that often.)

Actually broke them out doing my valve clearances on my duc recently.

Edit. My bad I think you are talking about the tool micrometer rather than the unit of measure.

But do you remember the decimal equivalent of ⁹/₆₄" so you could transfer the measurement from the ruler (in sixty-fourths) to the micrometer (in thou), ugh!.

You do realize that you simply divide 9 by 64 to get the decimal equivalent, right?  Is it division that scares you so much, or calculators in general?

Quote from: rabinoz on November 28, 2016, 09:43:15 PM

But do you remember the decimal equivalent of ⁹/₆₄" so you could transfer the measurement from the ruler (in sixty-fourths) to the micrometer (in thou), ugh!.

You do realize that you simply divide 9 by 64 to get the decimal equivalent, right?  Is it division that scares you so much, or calculators in general?

Of course I know that, but when I was working with ¹/₆₄'s was in die making and machining was in the 1950's.
In cases you hadn't heard, no calculators then and dividing by 64 in your head is not that easy. The first decent calculator I had was an HP-45 in 1973.
So it was easier to remember the decimals, you know the 0.015625", 0.03125" etc, etc.

Quote from: jroa on November 28, 2016, 10:44:28 PM

Quote from: rabinoz on November 28, 2016, 09:43:15 PM

But do you remember the decimal equivalent of ⁹/₆₄" so you could transfer the measurement from the ruler (in sixty-fourths) to the micrometer (in thou), ugh!.

You do realize that you simply divide 9 by 64 to get the decimal equivalent, right?  Is it division that scares you so much, or calculators in general?

Of course I know that, but when I was working with ¹/₆₄'s was in die making and machining was in the 1950's.
In cases you hadn't heard, no calculators then and dividing by 64 in your head is not that easy. The first decent calculator I had was an HP-45 in 1973.
So it was easier to remember the decimals, you know the 0.015625", 0.03125" etc, etc.

What kind of die maker works with fractions?  I have never seen die drawings with fractions on them. 

Also, a slide rule is arguably faster and just as precise as a modern calculator.  Did the slide rules scare you away from mathematics? 

Quote from: rabinoz on November 29, 2016, 02:04:31 AM

Quote from: jroa on November 28, 2016, 10:44:28 PM

Quote from: rabinoz on November 28, 2016, 09:43:15 PM

But do you remember the decimal equivalent of ⁹/₆₄" so you could transfer the measurement from the ruler (in sixty-fourths) to the micrometer (in thou), ugh!.

You do realize that you simply divide 9 by 64 to get the decimal equivalent, right?  Is it division that scares you so much, or calculators in general?

Of course I know that, but when I was working with ¹/₆₄'s was in die making and machining was in the 1950's.
In cases you hadn't heard, no calculators then and dividing by 64 in your head is not that easy. The first decent calculator I had was an HP-45 in 1973.
So it was easier to remember the decimals, you know the 0.015625", 0.03125" etc, etc.

What kind of die maker works with fractions?  I have never seen die drawings with fractions on them. 

Also, a slide rule is arguably faster and just as precise as a modern calculator.  Did the slide rules scare you away from mathematics?

A "sly drool" in a machine shop? we had enough comedians as it was, and I was only in my teens and I didn't do much die making, plenty of metal lathe-work.
I used slide rules (still have a couple in a drawer somewhere) often enough from around 1958 till I got my first calculator.
But no, slide rules (10" anyway) are only good to about 3 places and in Electrical Engineering that was barely enough. Any calculators (all HP's) I have had have been at least 10 digit.

Then you ask "Did the slide rules scare you away from mathematics?"
          Slide rules don't do mathematics! They just help with the simple arithmetic - a tiny sub-set of mathematics.
No, slide-rules were fine, but I balked a bit at non-linear differential equations, "Schrödinger wave equation" and vector solutions to Maxwell's equations, not to mention recursive and non-recursive digital filters - little thingos like that.

First, you claim that die makers use fractions, now are making the claim that they must solve non-linear differential equations.  Do you ever have discussions about things you are knowledgeable about?

Yeah cant use that imperial crap.

Bunnings amazes me the amount of imperial stuff they sell in a metric country.

Apparently most of their suppliers are from the US...

I have never quite understood why we never adopted the metric system. It just makes total sense all the way around. I'm sure there is a reason why, but it'll never be good enough.

First, you claim that die makers use fractions, now are making the claim that they must solve non-linear differential equations.  Do you ever have discussions about things you are knowledgeable about?

Your reading comprehension has fallen below zero by now!

They don't do "Schrödinger wave equation, solutions to Maxwell's equations nor recursive and non-recursive digital filters" much in any die maker's shop I have seen,
but those things do pop up in Electrical Engineering.

By the way, fractions might not be used in making the dies, but they certainly come in when measuring up larger things around the shop. But not wanting to overtax your valuable time I could hardly go into every little detail, lest I land in tl;dr territory.

But, I'll take that risk, just to get back in topic, of course, which happens to be "Why FE believers never will show you a perfect map?"
and I claim that one reason is that Flat Earther's cannot show a map that has a consistent
          distance from the Equator to the North pole, which is 6214 miles 3 furlongs 2 chains 4 yards 0 feet and 3¹⁵/₆₄ inches^[1] and the
          circumferential distance around the Equator, which is 24901 miles 5 furlongs 8 chains 9 yards 0 feet and 8²⁹/₃₂ inches^[2] - just so these Yanks and Brits can follow it!

[1] Based on the best approximation I could find of  10,001,965.72931270 metres  .

[2] Based on the best approximation I could find of  6,378,206 metres  , pretty rough, I know.

Well, I had enough for one night... Jora, nice trolling.You have added absolutely nothing to this topic. You never challenged any of the substantial evidence brought up against you, you only swiftly evaded it all with ad hominem.
Is it because you know the flat earth is a joke?

Well, I had enough for one night... Jora, nice trolling.You have added absolutely nothing to this topic. You never challenged any of the substantial evidence brought up against you, you only swiftly evaded it all with ad hominem.
Is it because you know the flat earth is a joke?

n00b

I've got a map 

Using a metric I've derived before on this forum:

Quote from: Jane on September 01, 2016, 01:50:14 PM

The Earth is defined by the x and y axes, with the North Pole (for the sake of tradition) at 0, and the South at infinity. An infinite plane is used so that if you reach the South, you can come out the far side. Once the metric is used, the distance shouldn't actually be infinite. This is just our set.
Longitude is 0 along the line y=0, latitude is zero on the circle of radius 1 centred at the North pole.

Now then, our spectacularly awful looking metric. For points P₁=(x₁,y₁), P₂ = (x₂,y₂):

[jsTex]d(P_1,P_2) = \cos^{-1} \left( \sin \left(\tan^{-1} \left(\frac{x_1^2 + y_1^2 -1}{2x_1} \right) \right) \sin \left(\tan^{-1} \left(\frac{x_2^2 + y_2^2 -1}{2x_2} \right) \right) +\cos \left(\tan^{-1} \left(\frac{x_1^2 + y_1^2 -1}{2x_1} \right) \right) \cos \left(\tan^{-1} \left(\frac{x_2^2 + y_2^2 -1}{2x_2} \right) \right) \cos \left|\tan^{-1} \left( \frac{y_1}{x_1}  \right) - \tan^{-1} \left( \frac{y_2}{x_2} \right) \right| \right)[/jsTex]

The following map gives over half the Earth. The rest can be extended out, but it grows in size.



But remember, we're in non-Euclidean space so you have to calculate distances with the above metric.

Let's go right back to here, with its spectacularly awful looking metric.

Now my question is can I whip out my trusty Lufkin Tape ( I think it's an ordinary Euclidean one  ) and measure distances from near here to a town almost exactly due West of here.

The 8 m tape was a bit tedious, so I actually have used Garmin map data, but I've driven that route so many times that I would trust those distances to certainly better than ±1%. I know my car odometer is that close. The car and map show the road distance and the map has direct distance and Lat/Long as well, so let's see what we get.

The two locations are the westerly point, Withcott at 27.553°S 152.024°E and the easterly point, Blacksoil at 27.576°S 152.706°E
 on the Warrego Highway that heads west from Ipswich.

Lat 1	Long 1	Lat 2	Long 2	Road dist	Direct dist	Avg Lat	Long  diff	Globe km/deg @ Lat	Calc Dist
-27.553°	152.024°	-27.576°	152.706°	71.6 km	67.4 km	-27.564°	0.682°	98.6 km/°	67.2 km

The "direct distance" is the map distance between Withcott and Blacksoil.  The road distance is given just as a comparison because it is not practical to measure directly "as the drone flies" and as expected it is a few kilometers more than the direct distance.

The Globe km/deg @ Lat is the expected distance for 1° of longitude at a latitude of 27.576°S

The Direct Distance agrees with the Calculated Distance as closely as can be expected.

So it appears that on the "real earth", whether "Euclidean" or "non-Euclidean", we can measure distances with our ordinary "yardsticks".

Is this what we would expect on a "non-Euclidean" surface? Does the "yard-stick" expand to fit the distance according to your metric?


     
                           

Is this what we would expect on a "non-Euclidean" surface? Does the "yard-stick" expand to fit the distance according to your metric?     

Typically yardsticks occupy space, so yep. They naturally give what the metric would give.
The easiest case of a non-Euclidean surface to visualize would be a curved surface existing in Euclidean space. Place string on said curved surface, it naturally gives the distance between those two points when limited to the surface.
Having space itself be non-Euclidean basically just cuts out the middleman. A flat stick gives the distance between two points, and said stick has a fixed length: and that length is determined by the metric. The stick doesn't expand, it's only space that's at all different.

Take the points P₁ and P₂ to be the beginning and end of your yardstick. Then the distance between them, d(P₁, P₂) would be the length of the stick, one yard, and that's fixed. Then take any values you want for (x₁, y₁) and (x₂, y₂).
You can see that taking one of them to be, say, (0,0), gives you an entirely different range of coordinates for the other point, than taking one to be closer to the edge.

Quote from: jroa on November 29, 2016, 06:44:07 AM

First, you claim that die makers use fractions, now are making the claim that they must solve non-linear differential equations.  Do you ever have discussions about things you are knowledgeable about?

Your reading comprehension has fallen below zero by now!

They don't do "Schrödinger wave equation, solutions to Maxwell's equations nor recursive and non-recursive digital filters" much in any die maker's shop I have seen,
but those things do pop up in Electrical Engineering.

By the way, fractions might not be used in making the dies, but they certainly come in when measuring up larger things around the shop. But not wanting to overtax your valuable time I could hardly go into every little detail, lest I land in tl;dr territory.

But, I'll take that risk, just to get back in topic, of course, which happens to be "Why FE believers never will show you a perfect map?"
and I claim that one reason is that Flat Earther's cannot show a map that has a consistent
          distance from the Equator to the North pole, which is 6214 miles 3 furlongs 2 chains 4 yards 0 feet and 3¹⁵/₆₄ inches^[1] and the
          circumferential distance around the Equator, which is 24901 miles 5 furlongs 8 chains 9 yards 0 feet and 8²⁹/₃₂ inches^[2] - just so these Yanks and Brits can follow it!

[1] Based on the best approximation I could find of  10,001,965.72931270 metres  .

[2] Based on the best approximation I could find of  6,378,206 metres  , pretty rough, I know.

I will give you that die shops often do some amount of fabrication, using fractions, as well as make dies, if you will agree that die makers do not use feactions in the course of making dies. 

I will give you that die shops often do some amount of fabrication, using fractions, as well as make dies, if you will agree that die makers do not use feactions in the course of making dies.

No contest, I'll gladly concede that, we did not tolerate any "feactions" at all.

But let's leave all that stuff behind us. For me, it was long, long ago.

rabby, welding as well as die making?

rabby, welding as well as die making?

"Welding"? Where did that come in. But sometimes some large dies are fabricated by welding.
I've done my share of (mainly very poor) arc welding, but mainly for fabrication on my own things, like the shelves and roll-out fridge mount I have used in the back of two 4WDs (Land Cruiser series 100 and now Landcruiser Prado - Land Cruiser LC90 in the USA).
So no, I was never a "welder"!
Mind you "dies" and "welder" does remind me of a rather tragic welding "event", when someone who died using a welder.
        He was welding in  bare feet  on a metal roof  and put the electrode holder under his arm to roll a cigarette. Nuff said  . Should have been alarm bells all the way!

But hey, apart from (un)handy-man stuff that machine shop stuff was only in my teens in a tiny shop run by my father ran making parts for various items like washing machines and dryers and later (after my time there) for mowers include ride-ons.
Sure, I can "use" lots of power tools and lighter machinery (various lathes, welders, drill presses, shapers and a tiny bit of milling machine stuff), but never as a real tradesman and that was long, long ago.

I won't try to compete with you on knowledge or skill in that area.

I only asked because, here in the US, welders tend to work in your hated fractions, while machinists work with decimals.  Just wondering. 

I only asked because, here in the US, welders tend to work in your hated fractions, while machinists work with decimals.  Just wondering.

This got  tl;dr  , so
the short answer any welders in bigger firms use metric.

The long answer is:

I cannot answer from any authority, but after using metric for so long I presume welders here all use metric measures.
We have had landscaping type work with fences and quite a big retaining wall. Not a lot of welding, but the contractor did happen do a little welding himself, but would never have thought of using imperial measure, let alone fractions.

When we were using imperial measure, I used to get frustrated with the difficulty of procuring good decimal steel rulers.

Certainly, if outside workers like that all use metric by now, any engineering work would most certainly be metric, so no chance of feet and inches - fractions or decimal.

I can sort of understand USA and the UK sticking to imperial measures as the extent of changes involved in any changeover would be massive.
But don't get me started on the "conservatism" or the USA. Admittedly it's 45 years since I was there but even then, we could direct dial to the USA from here, but had to use an operator (or send a "cable") back to Australia.

Australia changed currency in 1966 (with mixed currency for a while) and weights and measures in 1971. The transition to metric weights and measures took a lot longer than the currency change.

Engineering and building materials are now of course entirely in metric and large engineering or building firm would have done everything in metric for decades.
But a lot of "handymen" (myself included, though handy might be a stretch) still use some imperial (Whitworth of all things) nuts and bolts, just for compatibility with the things being repaired.

I imagine Chile, even though there was a fair bit of English influence earlier, has always used metric, following Spain.

Sorry, as usual my yes/no answer got to be another tl;dr.