# Funny things about the number 108

by G. Lathoud, September 2019

$108$ is a number reverred in the Yoga domain, and has some approximate properties:

• (1) $108$ is about the ratio: $$\frac{sun\ diameter}{earth\ diameter}$$
• (2) $108$ is about the ratio: $$\frac{distance\ from\ the\ sun\ to\ the\ earth}{sun\ diameter}$$
• (3) $108$ is about the ratio: $$\frac{distance\ from\ the\ moon\ to\ the\ earth}{moon\ diameter}$$

Because of (2) and (3), during eclipses, sun and moon almost exactly overlap (here the value $108$ does not play so much a role as the equality between the two ratios).

### km/h

Now, choosing a unit ($km/h$):

• (4) $108\ 000\ km/h$ is about the speed of the earth, rotating around the sun.
• (5) $1\ 080\ 000\ 000\ km/h$ is about the speed of light.

### Prime decomposition, and "friends" of $108$

Further, look at the prime decomposition, $108=2^2 \cdot 3^3$. If feels like a series. Let's have a look at it:

• $2^2=4$ the quaternity, much beloved by C.G. Jung.
• $2^2 \cdot 3^3=108$ described above
• $2^2 \cdot 3^3 \cdot 4^4=27\ 648$ not sure what to say about this one. Somewhat close to the estimated current value of axial precession.
• $2^2 \cdot 3^3 \cdot 4^4 \cdot 5^5=86\ 400\ 000$ is exactly the number of milliseconds in a day.
• $2^2 \cdot 3^3 \cdot 4^4 \cdot 5^5 \cdot 6^6= 128 \cdot 364.5 \cdot 86\ 400\ 000$ is slightly less than $128$ years, approximately the maximum age of a human (think of Jeanne Calment).
• $2^2 \cdot 3^3 \cdot 4^4 \cdot 5^5 \cdot 6^6 \cdot 7^7$ is then about 105 millions of years (in milliseconds). One remarkable thing I could find was this:
105 million years ago: Early Cretaceous. Ceratopsian and pachycephalosaurid dinosaurs evolve. Modern mammal, bird, and insect groups emerge [source].

### Conclusion

Taking this all with a grain of salt, still, there are amazing coincidences around $108$, and its "friends". In any case I learned a few things.