The Very Small and the Very Big

In a prior post we considered how many digits of pi are required for a calculation, and I recently listened to a Lex Fridman podcast with guest Tim Urban, where they discussed if man is smaller than we are large or larger than we are small (Lex Fridman podcast).

Let's explore both extremes of small and large. 

Starting with the characteristic size of a human, 1 meter. Most humans are taller than a meter but are thinner and not at wide as a meter so for this discussion 1 meter will be the scale of comparison we use.

Moving up in scale:

10 m            About the size of a garage or apartment

100 m          The length of athletic field or pitch

1000 m        The span of a large bridge (The New York George Washington bridge has a span of 1067 m)

10,000 m     A 10k race in which many runners have competed

100,000 m   A distance typically traveled in an hour by automobile at highway speeds 

10⁶ m            A full day's driving on a long trip or traversing the north-south extent of California

10⁷ m            The distance from the north pole to the equator through Paris (by definition of meter)

10¹¹ m          The distance from the Earth to the Sun (One AU = 1.5 10x11m)

10¹² to 10¹³ m   The orbit of Neptune is 30 AU

10¹⁶ m          The distance to the Oort cloud (the furthest extent of our Solar system)

10²¹ m          The diameter of the Milky Way Galaxy

10²⁷ m          The radius of the observable universe

View this animation on the large scale of the universe: (1535) your mind will collapse if you try to imagine this | UNIVERSE SIZE COMPARISON - YouTube

Another good visualization is given here: https://bigthink.com/starts-with-a-bang/logarithmic-view-universe/

Moving down in scale

0.1 m            A human hand width

0.01 m          A small finger width

0.001 m        1 mm or about the thickness of a credit card

0.0001 m      A fine human hair or diameter of a human egg cell (the largest human cell)

0.00001 m    Diameter of a human capillary vessel

10^-6 m           The low end of the size of a bacterium (one micron) 

10^-9 m            Size of a molecule  (one nanometer) 

10^-10 m          Angstrom - approximate size of a hydrogen atom

10^-15 m           Size of a proton

10^-19 m           Upper limit of the theoretical size of a quark

10^-35 m          The Planck length is 1.62 x 10^-35 m (smallest possible dimension)

Now, let’s consider the ratio of the very largest thing, the observable universe, to the vary smallest, theoretical size, the Planck length. The ratio is approximately:
10²⁷ m: 10^-35 m or 10⁶² to 1. Humans are somewhat in the middle but closer to large end in the comparison given above. If we only venture down to the size of a quark, then we closer to small end.