A friend and I were on a park bench earlier today discussing philosophy and the nature of reality and I brought up a subject I read about in the comments section in relation to a blog post I read about the physics of a cube shaped earth.
Imagine you are at the centre of the earth and you build a staircase at a 45 degree angle up to the surface of the earth, it would have to reach the surface eventually, however if you started at the earth's surface and built a 45 degree staircase downwards towards the centre of the earth surely the staircase would lead not to the centre of the earth but would exit at another part of the earth's surface as I assume to reach the centre of the earth one would would have to dig straight down at a 90 degree angle perpendicular to the earth's surface.
Although hypothetical It seems to me paradoxical and had a zen koan like quality to it which my friend appreciated as he is a Buddhist, but what is the actual science behind this apparent paradox?
Pic kinda related
>>8142233
???? If you are at the center of the square and you go up at a 45 degree angle you will reach the top left angle
If you are at the center of the top edge and you go down at 45 degrees you will exit at the center of the right edge.
I fail to see the problem
>>8142233
>45 degree angle up .. at the centre of the earth
You need to work on your visualization skills
after that, return to chan buddhism
>>8142233
If you're at the center of the earth, you can go through at any angle and reach the surface. However, if you're at the surface, because the earth isn't a perfect sphere, you would have to go at different angles depending on your current latitude to reach the exact center. It would have to be a very specific angle.
>>8142233
Here is a circle and a point for the center (it's not perfect, please don't expect much.
Please show how it's possible to draw a 45 degree angle starting from the center.
>>8142276
go read the OP again then delete your post
>>8142233
m8 you're retarded.
If you built a staircase a 45 degrees from the center, you would hit an edge or a corner.
If you built one from anywhere except an edge or corner, you would pass the center.
>>8142298
>Imagine you are at the centre of the earth and you build a staircase at a 45 degree angle up to the surface of the earth
I did. What he's describing is impossible. All points starting from the center of either a circle or a sphere are perpendicular from the center. A circle is simply easier to draw
>>8142319
Even thats wrong because you wouldnt hit any edges. You would hit corners or you would exit in some circumference of a circle through any side with a smaller radius than the circumference that touches the corners.
>>8142321
>about the physics of a cube shaped earth.
>>8142326
The principle is the same.
>>8142333
Clearly the bottom edge is taken as reference to calculate angles
>>8142326
OP here to clarify I am talking about the earth in it's present shape not a cube the staircase subject was in the comments section of the blog post the cube shaped earth subject was just incidental
>>8142338
and? It's still a 90 degree angle from center
>>8142343
Sorry for the shitty photo, no Internet of the laptop and this was faster than cables.
Going 90 degrees down is like rotating the stair by 45 degrees more
>>8142271
>cube
Re-read the op
>>8142363
Would a staircase to the centre of the earth be too steep to descend safely?
>>8142233
If you go down at the same angle you can from you will hit the center. You just confused yourself by measuring the angle in two different ways. Going up 45 degrees from however you are oriented at the center is not the same angle as going down 45 degrees from standing on the surface.
>>8142363
The first example isn't 45 degrees from the center, it is straight up from the center.
WTF does "45 degree angle from the center" even mean?
????????????????????????????
this is too stupid, it has got to be bait right?
>>8142557
that is my assumption, yes. Charitably, it could be a brainteaser.
>>8142363
You are visualizing the problem incorrectly. There is no such thing as a line that can be drawn from the center to the edge which is not 90 degrees.
Let's take the square example although it also works with the circle the same way.
Square 1 shows you the center.
Square 2 shows you a .... 45 degree? stair from the center.
Square 3 is the same square (ok it's not I'm working in paint here) rotated over showing the same line is actually just another 90 degree angle from center. ALL the lines you can ever draw from the center will be 90 degrees from that center. It is literally impossible not to draw a 90 degree line from center.
The only way this could work is if your staircase wasn't a line at all but a spiral like #4. Maybe then you could claim it's 45 degrees from the center? But then it makes your question irrelevant.
Hope that helps.
>>8142233
Most of the answers given are using information you don't have and failing to communicate it in any reasonable way. Let me attempt to make it simpler:
Angle is relative to a base. On the edge of a sphere, you take a tangent line from your position and measure an angle off of that tangent line. There is no tangent line to a single point. For any base in the center of a planet to measure an angle off of, the planet would have to be obloid so you could take, for example, the major axis as reference.
Your idea of "draw a 45 degree angle off of the surface, and then shift it to start from the origin" does not solve the inability to make a 45 degree angle with a point.
Besides, as should be obvious, ANY line from the origin crosses the surface if extended far enough, while only some lines from the surface pass through the origin. This is not very zen or paradoxical. There are "more" unique lines available from the surface than from the origin.
>>8142790
But how would you start in the centre of the planet and build a stairway to the surface unless you were already at the centre of the planet? How do you get there to begin with?
>>8142790
>Angle is relative to a base. On the edge of a sphere, you take a tangent line from your position and measure an angle off of that tangent line. There is no tangent line to a single point. For any base in the center of a planet to measure an angle off of, the planet would have to be obloid so you could take, for example, the major axis as reference.
The earth is an oblate spheroid.
>>8142779
i will not likely remind you tat 45 degree is just for a square and in 2 and 3 not quite a square.
I think you dont visualize good. But I do have a good visual thninking... pretty much only quite annoying tho
in 2 and 3 the 3D qube is not equal and it tends from 45 degrees to 31 degrees to hit the outer line and the inner center
>>8142233
Imagine a cube.
Imagine yourself at the center.
You draw a line 45° to the top right edge of the cube.
You're at the top right edge.
Now you travel backwards and arrive at the center again.
