We live in an amazing time - Ilon Musk launches sports cars towards Mars, satellites land on comets and transmit photos and data about the composition of the soil from there, and at the same time the Internet is filled with videos, sites, communities in social networks on the subject of flat earth. It would seem that it is impossible, in 2018, to believe and actively try to convince the whole world of a theory that was rejected several thousand years ago. What is this lack of education? Desire for light fame or money? Or is it just that these people are much more developed than us and can see what the rest of humanity does not have? I invite you to go on a Friday journey through the measurements and find out - is this earth really really spherical ...
In depth measurements
And we start with the simplest, one-dimensional space. Let's imagine for a while that we are a scientist-point living in a one-dimensional space! All that we can operate in one-dimensional space is a point, a segment, a ray and a straight line. But can we see them? Point - yes, it is zero-dimensional, but we, being in one-dimensional space, we can never see all other objects. The only thing we can see is the point from the “end” of the segment. In order to somehow explore the object and make an idea about it, we will have to “walk” along it and, say, measure the distance. That is, we can understand that the segment is in front of us, because here it began, we walked along it, measuring the distance, and came to its end, but we can’t see the whole of it until ...
We rise a little higher
Until we get to the plane! Now we are scientists in two-dimensional space and objects from one-dimensional space become simple and clear for us, we can look at them “from the side” and embrace the whole at a glance! It seemed cool, but to live in two-dimensional space surrounded by one-dimensional and zero-dimensional (point) objects is somehow boring. The bonus to the plane is that we can work on it with closed flat figures, such as a circle or a polygon. And here in this place a 2D scientist can feel himself in the role of a one-dimensional one - instead of any “complex” object we can only see its one-dimensional projection in the form of, again, the same segment. That is, we can describe a complex two-dimensional object only in terms of one-dimensional space — insulting.
To understand what the object is in front of us, we will have to go around it from all sides, good, we can now, and somehow document what we have seen, only in this way we can understand that the circle is a circle, and the rhombus is a diamond. Thus, in order to enjoy all the objects of their world, two-dimensional residents have to develop their imagination well.
Meanwhile in our space
Well, finally, we emerged from these incomprehensible, truncated dimensions and turned out to be in our own - three-dimensional! Welcome home! But now let's understand a little our visit to one-dimensional and flat scientists, how can their experience be useful for us to expand our understanding of our own space? Now we can easily see 2D objects as a whole, and ... and that's it! We cannot see three-dimensional objects in their entirety, all that is available to us is again a pathetic projection! Well, at least not one-dimensional. We falsely think that our vision is three-dimensional, but this is not so, our vision can be described by the word "stereo" - we see the objects of our space in the form of two projections from a slightly different angle and our brain transforms this vision into a solid "three-dimensional" picture. Thus, we feel ourselves inside three dimensions, we can orient ourselves in them and manipulate three-dimensional objects, but we cannot see these objects entirely! We can formulate the traveler's law between measurements: in n-dimensional space in its entirety, we can see only n-1 dimensional objects, or objects of a lower dimension, we see as “flat”. In whatever measurement you are in, there will always be a reason for dissatisfaction.
Let us return to our landowners and sharovers
And now the most esoteric part of our journey begins. Let's try by analogy to rise above our three-dimensional world and imagine that we are residents of four-dimensional space! And here the gap of the pattern happens - for us the earth will become “flat” in the sense that from the side we will see it entirely from the side and we will not have to imagine something or fly around it! Just as for a two-dimensional little man it is inconceivable to see the entire circle as a whole, it is also physically impossible for us to see the entire surface of the earth with one glance, but for four-dimensional creatures this is something taken for granted. Just imagine!
In conclusion, I want to note that one should not be so biased with respect to the landowners, perhaps they are higher beings and have four-dimensional vision and it is obvious to them that the earth is flat, and we, the underdeveloped sharovers, simply cannot see anything beyond what we allow imperfect feelings.