have we ever come up with the two new directions needed to navigate in 3 dimensions?
have we ever come up with the two new directions needed to navigate in 3 dimensions?
"Occam" is the name of the alien race that will enslave us all eventually. And they've got razors for hands. I don't know if that's true but it seems like the simplest answer."
Stephen Colbert.
"The problem with quotes on the Internet is that it is hard to verify their authenticity." — Abraham Lincoln
I say there is an invisible elf in my backyard. How do you prove that I am wrong?
The Leif Ericson Cruiser
Up, down, left, right, forward, backward. Or cephalad, caudad, left, right, anterior, posterior. Or +X, -X, +Y, -Y, +Z, -Z.
Reading through the Apollo mission manuals (as one does), you'll find they defined a fairly large number of coordinate systems for 3D navigation--different systems made sense at different parts of the mission.
Grant Hutchison
"The problem with quotes on the Internet is that it is hard to verify their authenticity." — Abraham Lincoln
I say there is an invisible elf in my backyard. How do you prove that I am wrong?
The Leif Ericson Cruiser
I was thinking, north south, east, west, ??, ??
"Occam" is the name of the alien race that will enslave us all eventually. And they've got razors for hands. I don't know if that's true but it seems like the simplest answer."
Stephen Colbert.
Also, as an aside, though up and down are not objective directions, since the actual direction depends on where you are, the same is true for east and west. If you want objective universal directions you’d be better off using x+/-, y+/-, z+/-. You’d have to set on arbitrarily, and the second to be perpendicular to that, and the third to be perpendicular to the other two. Since the universe doesn’t have objective directions you can set the first as you like.
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As above, so below
Yes, though if you do want coordinates with respect to a planet, you might want to look at spherical coordinates:
https://en.wikipedia.org/wiki/Spheri...rdinate_system
"The problem with quotes on the Internet is that it is hard to verify their authenticity." — Abraham Lincoln
I say there is an invisible elf in my backyard. How do you prove that I am wrong?
The Leif Ericson Cruiser
All directions are relative. Up and down are relative to the local orientation of gravity; IE, towards the center of the Earth in our case. Otherwise we might say dorsal and ventral.
"I'm planning to live forever. So far, that's working perfectly." Steven Wright
This really is a begging question like “what if birds could fly.” If there really is a question in the OP it needs rewording.
sicut vis videre esto
When we realize that patterns don't exist in the universe, they are a template that we hold to the universe to make sense of it, it all makes a lot more sense.
Originally Posted by Ken G
I think what you are asking is would it be easier to navigate if we had access to a fourth or fifth dimension. The answer is not at all. I took a survey class where we had plot out a 100 foot long by 50 foot wide geometrical shape using a theodolite and a steel tape. All very close to naked eye measurements in decimal inches. The space we were given was chosen so that up and down were not much of a factor. We had to have between 4-7 corners in the shape, but other than guideline, the shape was arbitrarily chosen by the students.
You can calculate the area using a very simple formula where you're just comparing the distances between the corners. However, when you're in the middle of it, good luck! The point of the task was to force people to know the limits of their equipment, accuracy, precision and the process. Simply going from one point to another all the way around the shape is like 25 pages of neatly written, super basic math. Trig is barely a factor. Even with simple multiplication and division, you start getting an arbitrary number of digits past the decimal. If you forget your sig-figs your done.
And adding a fourth or fifth dimension is totally intuitive. The process and formula is completely valid if you want to add in any number of dimensions. It's not fun for just two-ish dimensions. More dimensions just means more work. And probably less accuracy.
There have been several large scale area studies of many countries. They set out with a measurement system and pick reference points along the way. They are good enough for navigation but you wouldn't want to build something using those measures. They are wildly off. And they only tell you where you've been, not where you are going. The measurements are the definition of a space to the limits of the measurements.
Theoretically, you could take measurements in New York and London and seemly have enough reference points to plot for navigation between the two. But if you had to walk/swim that distance, you'd notice a lot of discrepancies. Its significant enough that they do these large scale land studies every two decades. The point is, there is no overreaching "frame of reference" to define where you are from the start.
Now you might think that GPS would change that. Not really. That gives you fast measurement to a high degree of accuracy. When you start to link those locations together over an areas, things can go wrong. Very wrong. In orienteering, nothing makes a mess of things more than having a machine tell you a number. It's a number that might have some bearing on where you are, but only if it's the right number at the right time and place. I cannot tell you how many times that one tiny observation goes wrong and you can see a sign that says "this is the target" and people will want to walk away from it because the machine is "right". It is, but you skipped a step in the process and don't know what it means.
Last edited by Solfe; 2021-Jun-08 at 12:28 PM.
Solfe
I dunno. Jens pretty much answered it
so I don't think I need to reword it now.Also, as an aside, though up and down are not objective directions, since the actual direction depends on where you are, the same is true for east and west. If you want objective universal directions you’d be better off using x+/-, y+/-, z+/-. You’d have to set on arbitrarily, and the second to be perpendicular to that, and the third to be perpendicular to the other two. Since the universe doesn’t have objective directions you can set the first as you like.
"Occam" is the name of the alien race that will enslave us all eventually. And they've got razors for hands. I don't know if that's true but it seems like the simplest answer."
Stephen Colbert.
For the surface of the Earth, this Wiki article on benchmarks may be helpful:
https://en.wikipedia.org/wiki/Benchmark_(surveying)