Details...

[Art Blade]

"Sorry, Rightenant, you are completely left about that, sir. I won't let you up, sir, if you don't make me eat the rightovers of your MRE again, please."

[mandru]

 :-\\  At least there weren't a load of pulldowns added as punishment for PVT Fragger.

[fragger]

 

Geez, you lot... Maybe we should start a new topic for this... ????

Just as well I'm not below being sent down or I might get up in the dumps about it all ;D

[fragger]

Incidentally, the world's cartographers have gotten it all wrong - this is how a map of the world is supposed to look:

Spoiler

[smg id=4445 width=600]

[nexor]

Which means I been walking on my head all the time, no wonder I have such a shitty outlook on life,
it's all the s#!t in my brains............... ??? :'(

[PZ]

Funniest topic in a while !

[Binnatics]

 ^-^ :-X

[Art Blade]

 :-() :-X

[mandru]

I was watching a program earlier today about the discoveries and technologies of ancient civilizations and it was either in India or China (or possibly Turkey or Persia... OK!  I wasn't watching it.  I just had it turned on for background noise.  Sheesh!  :-\\  It was one of them anyway) where it was discovered that lodestone when suspended by twine would always turn to re-orient itself in the same position but in a rocking boat there was too much movement to make it reliable for finding their direction.

It was only later when someone discovered that is a fine needle of iron was rubbed against the lodestone in one direction that the needle would become permanently magnetized and when suspended on a small piece of wood floating in water that two very distinct directions were indicated by the needle.  At that time as their map makers began to use of the newly discovered compass South was the principal orientation for all of their maps.

Quite some time passed before it was switched probably because of the prominence of the North star so that the direction North became the accepted standard for the top of the maps.

[nexor]

damn,  and all the time we thought it was fragger that had his directions screwed up!
So we humbly appologise to our friend Under Down???????  aw what the hell................  :-D

[fragger]

 :-D

Well... Whether I'm upside down or upside up, I still get east and west confused sometimes... ;D

@mandru, that's very interesting, I wasn't aware of that. You're probably right, it makes sense seeing as how there's a bright star sitting almost right smack on the northern celestial pole but none at all on the southern one.

On that tack, if one looks at star maps one will notice that the constellations in the northern sky are mainly named after deities and mythological figures, but many constellations in the south are named after scientific instruments, such as Circinus (The Compasses), Telescopium, Microscopium, Sextans (the Sextant), Octans (The Octant), and Reticulum (The Reticule or Eyepiece). The reason is that by the time European astronomers and star catalogers began travelling to the southern hemisphere in numbers the Scientific Revolution was well under way in Europe, and in light of this new-found "enlightenment" it was considered passé to continue naming groups of stars after outdated folkloric characters. So the names of scientific apparatus were used instead to reflect the new scientific outlook and mindset. The further south the constellation, the more likely it is to be thus named because the southern constellations closer to the equator can still just be seen from the lower latitudes of the northern hemisphere and thus got tagged much earlier with the mythological nomenclature.

It's an interesting indication of the progression of scientific thought coupled with exploratory discovery, the two going hand in hand. For example, Captain Cook wasn't just mucking around in the south Pacific looking for the Great South Land, he was sent there with a cadre of astronomers to the newly-discovered island of Tahiti to observe the transit of Venus across the Sun (which happened again just a few days ago). Another team in the northern hemisphere would also observe this transit, and triangulation of the two sets of observations would yield an accurate distance from Earth to the Sun. Cook's secondary mission was to then head west (west? yes, west) and attempt to locate and map the vaguely perceived islands of New Zealand (which he did) and, if time permitted and at his own discretion, continue further west and see if he could bump into the Great South Land (which he also did). Cook's map-making skills were incredible, his maps are just as accurate as anything produced today (he's a bit of a personal hero of mine - at least until he lost the plot in Hawaii, had an attack of the stupids and got himself killed).

Sorry to get all serious there, but what can I say - I've been up so long that it looks like down to me ;)

[Binnatics]

Interesting piece of history there Fragger!  :-X

I'm up with that! :-D

[mandru]

Since we've drifted a bit off topic discussing North and South, upside down or not I'll toss out something I've been thinking on for a couple weeks and reached no overwhelming conclusions but only arrived at headaches because of the higher maths involved.

Something I've been told as truth and that I've seen the sense of so I've always accepted at face value is that:

If I am standing exactly at the North pole any direction I face will be South

Expanding on that concept the line of my view (following the curvature of the earth) will pass through the South pole becoming a great circle that is completed by wrapping around the earth returning to precisely the spot where I am standing.
The given is that no matter where I look (staying in place but rotating through 360 degrees) this will be the rule.

But logic also tells me that there is a paradox in that or at the very least something huge mathematically that I am overlooking.

Let's say that as I am walking up to the North pole I remove my backpack and set it down on the ice three feet away before reaching the pole.  There will be exactly one great circle that will include myself, the South pole and the backpack but here's where the logic in this thought experiment gets fuzzy and my head starts to hurt.  ????

As I rotate through the 360 degrees of a circle (staying right on the pole), for every possible direction that I can face there has to be a straight line (following the curvature of the earth) directly to the backpack instead of returning directly to me by way of the South pole.

So the first example "all directions are due South" creating a great circle doesn't leave room for my second example "there is a straight line between two points" to be possible yet logic says that it must be so.

I make no secret of the fact that high school geometry kicked my backside.  Paraphrasing Euclid's 11th postulate "Through a point outside a line there is only one parallel to that line".  I visualized a "line (A-B)" suspended in space with a "point (C)" drifting past it and concluded that there had to be an infinite number of parallel lines being created as "point (C)" passed (probably also incidentally defining a whole new plane) and that Euclid was one big dope.

No one had bothered to explain that everything described in Euclidean (Plane) Geometry is static and by convention always flat in two dimensions.  There's no time or movement (drift = time + movement) allowed.  I got stuck on my misinterpretation and by the time I'd realized the foundational error in my line of thinking I was too far behind the class to ever catch up.  So maybe I'm mixing different fields of mutually exclusive geometries here or throwing in a spacial aspect that's not supposed to be in geometry.

I'll toss this into the pond of collective reasoning here at OWG and either ripples will come back with enlightenment or it will sink, lost to the deep no longer being my problem.  ;)

[nexor]

That reasoning is something to think about for sure  ???

While is school I also came up with a puzzle, If one is able to dig a hole right through the earth, how will you come out the other end, head first or feet first? My reasoning is that you're on your feet while digging, therefore you should emerge feet first, throughout my school career all my teachers reckon the earth's magnetic field will turn me around at the halfway mark, but I'm not convinced  :-D

[Art Blade]

Mandru, hehe :)

Quickly looking at your problem tells me that there are two points to consider.

1) If you were at the North pole, "on top" of the world, and consider it a large tower, imagine taking a look down. You'd of course be looking "down" to the south, no matter which direction your body is actually facing. So of course there will be directions other than "down" or south.

2) If you had to start a journey from the North pole and had a compass in your hand, that needle on a piece of wood floating in water.. do you think it would never change directions? Half way down to the South, perhaps around the equator, ask any local to tell you where North, South, East and West are by using a compass. Do you think if putting your compass next to the other compass, they'd show different directions? :) Of course once you're out of reach of the very North your compass will start to move following the magnetic field, which is all it does.


Nexor :)

Take an orange and a pencil. Stab the orange right in the middle so the tip of the pencil sticks out to the other side. Any problems envisioning that, so far? I guess not. Well, if the rubber end of your pencil sticks out on the other side despite having stabbed the orange with the tip... then you're challenging Houdini in fame :)

Imagine William Tell shooting an arrow through an apple and it came out feathers first..  :-D

[Dweller_Benthos]

That reasoning is something to think about for sure  ???

While is school I also came up with a puzzle, If one is able to dig a hole right through the earth, how will you come out the other end, head first or feet first? My reasoning is that you're on your feet while digging, therefore you should emerge feet first, throughout my school career all my teachers reckon the earth's magnetic field will turn me around at the halfway mark, but I'm not convinced  :-D

Digging down, you'd experience less and less gravity as more and more of the earth's mass is above your head. In the center, there'd be no gravity (and a lot of pressure, but let's ignore that). If you can still maintain your sense of direction and dig in the same line, you'd start out digging "above your head" until enough of the earth's mass was below you, you'd have nothing to stand on, right? You've dug a hole beneath your feet. So let's say you put in a ladder as you dig. You are still digging above your head, adding ladder sections, until you reach the surface.

I'd have to agree with your teachers, you'd dig out the other side head first, you have to keep your feet facing towards the center of the earth's mass, "down", all the time, unless you like standing on your head while you dig through the other side.

Just like standing at the north pole, if you're in the center of the earth, then all directions are "up" and it wouldn't matter which direction you dug, if you want your feet under you to stand on, you need to dig above your head, and you'd emerge head first once you reach the surface.

[Binnatics]

Mandru, You Kick a$$ right here. I was already replying with a useless line (quoting your post etc.) when realising you just hit the paradox of the fact that you found a way to look south without looking south.

I think you try to look in curves then. Imagine you didn't drop your backpack three steps away from the north pole, but a bit earlier; on the equator. If you still want to look directly towards it (without just looking back) you'd have to look in a spiral; towards the south, but with a bending constance towards the backpack. So that you will miss the south pole and head on curving until you reach your backpack.

... I think I'm still not hitting the answer. All I know is that spirals are mathematical terrors. Imagine, a good spiral will keep expanding forever, just like the universe, but will keep forever shrinking as well. Reaching endlessly smallments in the centre. Meanwhile, it's bending angle is changing equally.

One more thing about the backpack; when you try to look at it by looking in a circle (via the south pole) you're not looking in a straight line anyhow. So don't confuse straight lines with circles. That will make your head clear again ;)

[fragger]

...all my teachers reckon the earth's magnetic field will turn me around at the halfway mark...

???? I can't believe "teachers" told you that. To paraphrase D_B, it's not the magnetic field that affects you, it's the Earth's gravitational influence - and even then it won't "turn you around" unless you choose to turn yourself around. If you fall off a cliff, Earth's magnetic field won't automatically orient you to land feet-first, or if you stand on your head, you won't feel as though the magnetic field is trying to turn you right side up again. Gravity will try to pull you down towards the centre of the Earth, but the magnetic field with have absolutely no effect on your physical orientation, since you're a non-metallic object and thus have nothing for the magnetic field to act upon.

Sounds like some of these teachers need to go back to school themselves ::)

@mandru, I get your conundrum. So I employed a little 3D modelling to try and put the following concept across:

The fact is that any straight line drawn from your position at the north pole, at any angle, will always go through the south pole - it's unavoidable. In the picture below, you are facing directly away from the backpack, and as a result, a line that continues in the exact direction you're facing will go through the south pole and pick up the backpack on its way back to you:

[smg id=4446 width=600]

If you're not facing the backpack, a line continuing directly from your facing will still go through the south pole but will miss the backpack:

[smg id=4447 width=600]

The only way to get a straight line to go from you to the backpack when you're not directly facing or facing away from the backpack is if the line is drawn at an angle to your facing - and even then, it will still ultimately go through the south pole:

[smg id=4448 width=600]

Try this: get a ball of some sort, like a basketball or soccer ball and call the air valve the north pole. Anchor one end of a piece of string to the valve, and then try connecting the string in a straight line to any arbitrary point on the ball's surface. Continue the line of the string and you'll see that the string will always go through the point opposite the valve, i.e. the south pole.

I think where you're getting confused is in believing that a straight line can be drawn around the curve of the Earth to the backpack without going through, or at least pointing towards, the south pole. It actually can't. As long as you stay right on the pole, any straight line will always go through the south pole eventually, no matter what angle you draw it at.

Hope this helps :)

[PZ]

What an interesting thread; just goes to show the varied interests of OWG members. Great visuals fragger  :-X

[mandru]

Fantastic fragger!

It made my day that you had gone to the trouble of whipping up computer generated graphics for your example.  :-X

While your explanation does perfectly meet the conditions of my first described perceived truth (slightly adjusted here for clarity), "If I am standing exactly at the North pole (point A) any direction I face will be South (that is a line of sight that will pass through the South pole point B)".  I'm still swayed that the addition of the backpack (point C) creates a new "Frame of reference" that has to be considered when examining geometry on a globe for the thought exercise I proposed.

The Frame of Reference from the position of the backpack is not constrained by the special conditions that the North pole (point A) is forced into by the human imposed imaginary limitation that "all directions leading away must be South".  The directions that can be selected from the backpack's position (point C) are potentially unlimited if smaller and smaller moments of arc are employed.

The threads of a bolt are nothing more than a geometrically imposed straight line in the form of a ramp skinned to meet the profile of a rod.  A bolt's threading is a line through topography that is parallel to itself otherwise a nut would never be able to be mated.

I still think that there must be a straight line (A-C) between two points on a globe that does not pass directly (at least not immediately) through the South Pole (point B).  It's probably tied up in orbital calculations or ballistics maybe even ratios of irrational numbers.  I tried to create a proof using ballistics and your most excellent graphics but quickly became so bogged down in the numbers that I had to give it up.  :-[

The conditions I would have employed required a planet (globe) cue ball smooth, No rotation, no atmosphere, constant gravity and instead of the backpack an artillery gun capable of firing a round precisely at at orbital velocity for the proposed globe.  An observer at the North pole facing South at exactly Zero longitude (Greenwich meridian) the artillery gun positioned 3 feet away from them sits directly on the 90 deg West longitude line.

There's got to be at least one (more likely innumerable) orbital/ballistic arc that would directly reach the North pole that can be achieved by aiming the artillery gun parallel to the globe's surface at an undetermined distance from the South pole that will cross -90 deg East longitude at its nearest approach to the South pole before meeting its mark in the North.

Then again I may just be heavily deluded.  September and FC3 is too far away.  :-\\  See what happens when I don't have a fresh game to keep me occupied?  >:D

Now my heads ringing like a gong.  I think I'll have a couple aspirins and go lay down.  :-D

[PZ]

Now my heads ringing like a gong.  I think I'll have a couple aspirins and go lay down.  :-D

Perhaps a trip into Africa will soothe the soul.  :-()

[Binnatics]

Mandru, Take an apple, and try cutting it in half. Do it so that you cut both your backpack and yourself (the stem) on the North pole. Make sure not to hit the south pole (the crown). If you are able to do that, you're right. Good luck ;)

[fragger]

Whoa mandru, you spun me out too... As much as I love thought experiments, I had to go to Africa myself and blow away some jungle trash to get my head back together after reading your post ;D

I'll have to grapple with what you put forward for a bit...

Btw, it was no trouble making the pictures. I love doing that kind of stuff and was glad for the opportunity 8) The graphics programs I use are so user-friendly that it only took an hour or so - and it was a horrible, cold wet day outside, perfect for bumming around at the PC :-D

[nexor]

Man, now I'm clever, damn..........   :-\\ :-\\

I guess those teachers never had anyone ask such a weird question so they just responded with the first thing that came to mind     :-D

[mandru]

 :-[

Too much skull sweat.  I'm wrong, you were all correct.  :(   :bow

When you lob something over the horizon in a stable orbit on a non rotating sphere regardless of the position of its starting point (North pole or the backpack) it will always return to cross directly over its point of origin bisecting the sphere into two equal halves.  Even if a sphere is rotating and the orbit is independent of that rotation there's no way that the orbiting body (mandatorily traveling in a straight line) can cross the North pole without also crossing the South pole exactly one half orbit later.  :-\\

There might be some weird geometric shape that my thought might w@&k on but a sphere isn't it.  Sorry for the wild goose chase.  :D