| Limits of the world perceived by the human eye | |
|---|---|
| resolution of the human eye: | 1' |
| smallest size recognizable at 30 cm distance: | 0.1 mm |
| max. distance to distinguish a 3 m tall subject: | 10 km |
| max. visibility in clear weather: | 100 km |
During most of human history people's normal world consisted of what could be seen with the naked eye. The angular resolution of the human eye is in the order of one arc minute, the 60th part of one degree. At this resolution, the size of the smallest object that can be distinguished with the naked eye is 0.1 mm, and the maximum distance at which a 3 meter tall subject, say an elephant, can still be perceived is 10 kilometers [1] . If the maximum visibility from a mountain on clear days is assumed to be about 100 km, one might assume that a range from 0.1 mm to 100 km, spanning 9 orders of magnitude, was probably the world of prehistoric people. Today, air travel around the globe has become part of our lives, extending the scale of our 'normal' world to 11 orders of magnitude, ranging from 0.1 mm to 10,000 km.
For the table presented in Scale, the picture of a pinhead (2 mm) in a stadium (200 m) is used as a yardstick to illustrate a scale of one in hundred thousand (5 orders of magnitude). In an imaginary voyage into the invisible micro world, starting at the lower limit of the visible world (0.1 mm), we have to zoom in three consecutive times at this scale before we can 'see' elementary particles [2] . Conversely, in an imaginary voyage into the macro world, starting at the upper limit of our normal world (diameter of the globe), we have to zoom out four consecutive times at the same scale to 'see' the entire known universe [3] .
We can also use our entire normal world, ranging from the human egg (0.1 mm) to Earth's diameter (10,000 km), a scale of one in 100 billion (11 orders of magnitude), as a yardstick for comparison with the micro and macro worlds. In terms of linear scale, the micro world is then thousand times larger than the normal world and the macro world is 100 million times larger than the normal world [4] .
After the first zoom, a human egg would take on the size of a stadium, and a molecule the size of a pinhead. After the second zoom, the molecule is enlarged to the size of the stadium and an atomic nucleus to the size of the pinhead. Only after the third zoom we could possibly 'see' electrons and quarks, maybe at the size of pinheads (we can only deduce their size, if any, from theories and particle accelerator experiments).
After the first zoom, we arrive at a picture where the Earth is shrunk to the size of a pinhead in the center of a stadium, while Jupiter orbits near the fringe of the stadium. With the second zoom, the Jupiter orbit shrinks to pinhead-size and some local stars are dispersed in the stadium. With the third zoom, that collection of local stars shrinks to pinhead-size, the Milky Way to a disk of few meters diameter in the stadium center, and the Andromeda galaxy appears at the rim of the stadium. Only after the fourth zoom, we could fit the entire known universe into the stadium.
In linear dimension, the micro world spans 14 absolute orders of magnitude, 3 more than our normal world, and the macro world spans 19 orders of magnitude, 8 more than our normal world. If the comparison is made in terms of volume, the micro world is billion times as 'vast' as the normal world and the macro world is trillion trillion (1024) times as vast as the normal world (see Scale and Excel workbook).