Earth Time

Time reveals only one direction: toward the future.

By comparison space has few constraints. Gravity tethers us, yet we may jump. We may move in any direction in space, yet time moves irreversibly forward. While we may remember the past, we cannot not travel back in time.

Earth time is perceived as sequences of events.

"Time is what prevents everything from happening at once."
― John Archibald Wheeler

Snow Bank

Consider Earth phenomena as frames on a filmstrip that, for example, record the decreasing size of a snow bank.

As individual frames, we might detect evidence of a phase change from ice to liquid by the glint of the sun reflected on water drops.

If the frames were sped up so they were experienced in animated succession, and if the temperature was above freezing, we might imagine sublimation (the phase transition from solid to gas) as the snow bank shrunk.

"Time isn't just a label on each instance of the world; it provides a sequence that puts the different instances in order."
― Sean Carroll

Many scientists have observed the remarkable phenomena of the irreversibleness of these events. Science conceived of entropy as a framework to understand the tendency of these events to progress in a way that cannot be reversed.

Astronomers, physicists, and cosmologists call this irreversibility The Arrow of Time. The arrow metaphor captures the idea that time flows in one direction. As time flows, empirical evidence indicates that energy dissipates or disintegrates from well-ordered (low entropy) to disorderly (high entropy).

Hemispherical Sundial

On earth we experience time as repetition: Sun up, sun down.

"The Earth spins on its axis, and it's going to do so 365.25 times every time the Earth moves around the sun."
― Sean Carroll

We experience repetitive seasons. Many of earth's processes occur over and over like the water cycle.

On, above, and below the surface of the Earth, water undergoes continuous change. The changes are explained by physical processes (evaporation, condensation, precipitation, infiltration, runoff, and subsurface flow and by phase changes (liquid, ice, and vapor).

"The key to measuring time is synchronized repetition ― a wide variety of processes occur over and over again, and the number of times that one process repeats itself while another process returns to its original state is reliably predictable."
― Sean Carroll

Time feels real to us. Our hearts pump rhythmic beats. We need time to frame perception and to order and make sense of the incoming data.

"Time is an illusion."
― Albert Einstein

It feels as if time flows. However illusory it is, we sense time as the present constantly updating itself like oncoming river water approaching a bridge. We sense the future as anticipated (and unanticipated) events. The future remains distinct until it becomes the present. We sense the past as fixed and immutable.

Sensing the flow of time, we carry the framework of fixed past, immediate present, and anticipated and unanticipated future along with us like a familiar backpack that structures our thoughts and behavior.

"As if you could kill time without injuring eternity."
― Henry David Thoreau

REFERENCES

• From Eternity to Here. 2010. Sean Carroll.
• Philosophy of Space Time. Wikipedia.

Ode to Dew

Drops of water formed by the condensation of moisture in the air is dew. Dew occurs when the moisture in the air is cooled to its dew point.

Shape

Dew drops assumes the shape that minimizes the sum of its gravitational energy and its surface tension. Surface tension is expressed as force per unit length. Water has a surface tension of 0.072 N/m.

Man's life is like a drop of dew on a leaf.
- Socrates

The shape of a dew drop cannot be described by a closed form mathematical function. The governing differential equations do not have a closed form solution, so must be integrated numerically to trace the profile of a drop (cf. The profile of a dew drop).

A drop of dew cupped in the leaf of the common garden nasturtium.

The person who doesn't scatter the morning dew will not comb gray hairs.
- Hunter S. Thompson

Refraction

The term refraction describes the deflection of light that occurs when light waves travel through a change in medium (e.g., from air to water). Water droplets refract light like a lens.

When we contemplate the whole globe as one great dewdrop, striped and dotted with continents and islands, flying through space with other stars all singing and shining together as one, the whole universe appears as an infinite storm of beauty.
- Travels in Alaska by John Muir, 1915, chapter 1, page 5.

Refraction Photograph by Markus Reugels

Photographer Markus Reugels uses the refraction of light in water to create still life images in a drop of water.

REFERENCES

• Muir, John, Travels in Alaska, 1915.
• Feredoon Behroozi, Hilliard K. Macomber, Jack A. Dostal, Cyrus H. Behroozi, and Brian K. Lambert, The profile of a dew drop, American Journal of Physics. September 1996, Volume 64, Issue 9, pp. 1120.
• Liquid Art by Markus Reugels.
• Liquid Sculptures. Pictures of drops.

Rain from Clouds

Water is continually evaporating and condensing in the sky. Clouds contain water vapor and small drops of condensed water (cloud droplets). Most of the condensed water in clouds does not fall as precipitation

Potential rain forms when water droplets condense on dust, salt, or smoke particles, which act as a cloud seeding nucleus.

When the water droplets become large enough that their fall speed exceeds the updraft speed in the cloud, they fall toward the ground. If the water drops do not evaporate as they travel earthward, they reach the ground as rain.

Virga, oil on canvas by Crystal Foreman Brown

Virga is the term for visible streaks or shafts of water that fall from clouds but evaporate before reaching the ground.

After the last of the rain had fallen from the sky and come to earth — leaving the sky clear and the earth damp and gleaming — the world below grew joyful in the cool left by the rain, and the greater clarity of life that returned with the blue of the heavens furnished each soul with its own sky.
~ Fernando Pessoa (1888-1935) from The Book of Disquiet.

Rain Drop Size

Size, fall velocity, and particle density (drops per square foot of air) vary for different types of rain (shown below).

Rain Type	Intensity inches/hour	Median diameter millimeters	Fall Velocity ft./sec.	Drops per sec. per sq. ft.
Fog	0.005	0.01	0.01	6,264,000
Mist	.002	.1	.7	2,510
Drizzle	.01	.96	13.5	14
Light rain	.04	1.24	15.7	26
Moderate rain	.15	1.60	18.7	46
Heavy rain	.60	2.05	22.0	46
Excessive rain	1.60	2.40	24.0	76
Cloudburst	4.00	2.85	25.9	113
Source: Lull, H.W., 1959, Soil Compaction on Forest and Range Lands, U.S. Dept. of Agriculture, Forestry Service, Misc. Publication No.768

Rain is grace; rain is the sky descending to the earth; without rain, there would be no life.
~ John Updike (1932-2009)

References

• USGS, The Water Cycle: Precipitation