The statement that a single speck of dust is halfway between the size of an atom and the entire planet Earth is a fascinating way to think about scale, and it’s based on a logarithmic, not linear, scale.
A fun fact
On a linear scale, the size of a dust speck is nowhere near the midpoint between an atom and Earth. However, if we consider a logarithmic scale, which compares things in terms of orders of magnitude rather than absolute size, the idea becomes more meaningful.
Midpoint equals 30g
- The mass of a carbon atom is approximately 1.67377×10 to the power of −24 kilograms.
- The mass of Earth is about 5.9736×10 to the power of 24 kilograms.
- On a logarithmic scale, the midpoint of these two masses would be around 10 to the power of −1.5, which is roughly 30 grams.
While 30 grams is heavier than what we’d typically consider a speck of dust, it’s not too far off when we’re looking at the vast difference in scale between an atom and the Earth.
So, proportionally speaking, a speck of dust’s mass is closer to the midpoint on a logarithmic scale, even though it’s not exactly halfway.
It’s a way to visualize and understand the immense range of scales in our universe, from the very small to the very large. It’s not meant to be a precise measurement but rather an illustration of the concept of scale.