Just for fun, lets see if we can scale down the size of the Earth a bit and figure out how much of it we can see with our eyes.
The average distance to the horizon is 3.1miles
If you were to spin in a circle, the area that you could see would be about 30.2 square miles. (pi*r^2 where r=3.1)
The radius of of the Earth is 3,959 miles.
The surface area of a spherical Earth is 3.087*10^15 sq miles. (4*pi*r^4 where r=3959)
The ratio of what you can actually see verses all that can be seen is 9.7796*10^-15. (0.00000000000097796%)
Those are hard numbers to grasp so lets scale this down to the size of a basketball.
The radius of a basketball is about 5" so the area of the basketball is 7853.98 square inches. (4*pi*r^4 where r=5)
Using the ratio calculated above, the equivalent area that a very tiny person standing on the basket ball could see would be 7.6809*10^-11 square inches.
Doing the math, that means that the distance to the horizon is 4.94459*10^-6 inches. That number doesn't mean much so lets convert it to something else.
There are 25,400,000 nano-meters per inch. So the distance to the horizon is 125.59 nano-meters. Still a very small number so lets see if we can put that in terms of something we are familiar with - a human hair.
Human hair averages between 80,000 and 100,000 nano-meters in diameter. If we use the 100,000 nano-meter hair the radius is 50,000 nano-meters.
On our basket ball, the distance to the horizon is 125.59 nano-meters so if we divide that by the diameter of the hair and express that as a percentage we get 0.25118%. That means that the distance to the horizon for a person standing on our basketball sized world is 1/4 of 1 percent of the radius of a human hair. That gives a viewing area of 49,5553 square
nano-meters. The cross-sectional area of the human hair is 7,853,981,633.97 square nano-meters for comparison. (The area that our person on the basket ball can see is only 0.0000016% of the area of a human hair!!)
How reliable can our observations of the world as whole be given that we can only see about 0.00000000000097796% of that world at any one time? This is why we need science to help us understand. The scale of the world is so great that it is beyond the ability of our eyes to accurately see it from a mere 5' or so above the ground.