Growth and Beauty

a exploration of logarithmic spirals and symmetry

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Growth

An early thought of mine, as a child, was to wonder, “How large does a person grow?” If growth was perpetual, there was no end to how large I will become; yet, tested against observed reality, “Why was it the case this was unlikely?” Years later, when recalling this, I understood my intuition touched upon the logarithmic spiral and mollusk shell.

Three Scallops and One Tallin

Sea Oat stalk, photographed above, after it dries slowly in the sun and wind, curls into a logarithmic spiral. One two dimensional spiral may be compared to another by measuring the rate and direction of opening, the increase in distance between the part closer to the source and the outer swirl. The growth of all shells follow a logarithmic spiral in three dimensions where the progression from a staring plane, as well as the direction, up or down from the plane, is an element.

Sea shells give evidence to my question of “how large can one grow.” The size of each of the millions encountered on a beach is an example of a life ended. Each of record of the length and character of the organism. For example, a close inspection of the bottom shell of the above photograph, a tellin of the family Tellinidae, reveals the spiral is growing toward the surface of the sand. Imagine wrapping your hand around the outer edge of the tellin with your thumb pointed down.

Each of the four shells of the above photograph had a mate, were one of a pair. Types of shells share characteristic pair symmetries. For example, a pair of tellins display a type of asymmetry called chirality, also called “handed-ness” after the same property of your right and left hands. One shell half (from the same individual) is the mirror image of the other, each unbalanced as the growth spirals toward opposite directions.

Asymmetry, halves from different individuals

When I started beachcombing, examining collected shells I did not have a pair from the same individual and incorrectly concluded direction of growth was unique to an individual. The ribbing of the above two shells illustrate three concepts: the logarithmic spiral growth pattern, chirality, as well as how I came to that wrong conclusion: that two individuals can grow in different directions. It was a logical hop to understand how, to make two shells hinged at the source of the growth spiral, each individual requires two halves, each a mirror image of the other. That every member of the species demonstrated the same asymmetry, each half grows in the opposite direction.

Asymmetry, attached matching halves

The above photograph shows attached matching halves. The attachment point was a surprise: the apparent source point is not attached to the ligament joining the halves? I have yet to understand this. Do you?

Beauty

The association of beauty with scallop shells bridges thousands of years. For example, a fresco of the Roman goddess Venus, born from the ocean riding a shell, was unearthed from Pompeii. The living organism is not part of the story, just the shell. Why the scallop? My answer is, “Each half is completely, in itself, symmetrical.”

The top three shells of the first photograph are scallops. The first and last, broken by the waves, are missing parts. The middle scallop, small and off-white, is complete. Place an imaginary line down the center and each side is identical. Applying the real world (i.e., physics) to myth, a scallop shell allows the goddess to move forward in a straight line. Sailing an asymmetrical shell, she moves in an eternal circle.

An object with symmetry is visually complete unto itself, self-contained; functionality aside, one scallop does not required a partner. The paired shells are interesting in they do not match, one is deeper, it encloses more volume. The deeper side rests under the surface, allowing the top halve to present a lower profile the better to hide from predators.

Calico Scallop Shell

The scallop echoes the beauty of Venus. Symmetry enhances human features (earch “Venus (mythology)” for images of her face through the ages), though it does not define beauty. An overly symmetrical face seems strange. I will close with an extreme example, the other day I came upon this beach crab wandering around in the daylight. Symmetry does NOT enhance its features.

Dreams, Stories and Things from the Vanderbilt Museum

a spring day on the former gold coast of Long Island

The Dreams

For 32 years of work dreams about work visited occasionally, then when retirement approached and overtook me these became an almost nightly visitation.

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Northport Harbor from the Vanderbilt Museum

Last week, a few months into retirement, the haunting stopped, replaced by adventures by and on the ocean.  

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It brings to mind, a few years ago Pam and I took lessons at Cornell’s Merrill Family Sailing Center followed by several seasons of memberships.  We’d take out sailboats the size on the one enjoyed by the fellow above in Northport Harbor.

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Fountain and Pool
Fountain and Pool of the Mansion Garden

We’d spend entire days on the water, looking up at the people driving the hill up and down route 13.  “How lucky we are here and not there”, I’d say.

The Stories

Willy Vanderbilt named his Centerport estate “Eagle’s Nest” after his first yacht, “Eagle” that was anchored in Northport harbor along the estate shoreline.  In 1932 the German Krupp Germaniawerft company build a new yacht named Alva, after his mother.

Fountain and Pool
The mansion garden features several fountains and pools. Northport harbor and Long Island Sound are the view.

Willy had a “thing” about the infant Baccus.  My first Vanderbilt Museum posting “A Taste of Gatsby: details from the Vanderbilt Museum”included the following depictions of the infant Baccus.  the name preferred by the Romans.

Museum Garden Statue
Statue of a young Bacchus in the Mansion Garden with Northport Harbor and the Long Island Sound reflection

To the Greeks he was Dionysus.  Also known as the “twice born” from the myth of his being carried in his father Zeus’ thigh after Hera, the jealous wife, plotted the death of his mother, the mortal Semele.  

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Fountain Figure

The infancy of Dionysus was perilous, with Hera plotting revenge Zeus found safe haven for the child at a place of earth called Mount Nysa, with beings named Rain Nymphs.  The fascination of Vanderbilt with the story continued with the acquisition and display of a statue of the infant Dionysus with a protective nymph.

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Dionysus and protector, a Rain-nymph of Nysa

The Things

The statue and plinth are at the stairs into the garden.

Mansion Garden and Fountain from archway.

 

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Mansion Garden with Red Maple

 

Window and Red Maple
Garden of the mansion with window, red maple and early growth of tiger lilies

 

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Ornate Grating and Flowers
The mansion garden with an ornate grated window, azelia and bleeding hearts.

Copyright 2018 All Rights Reserved Michael Stephen Wills

References
Wikipedia “Dionysus” and “Willy Vanderbilt”

Bridging the Lethe

notes from November 2231 AD

Origin Date

November 6, 88 NE

Hook

Ancient legends speak of the River Lethe, crossed by departing souls.  The waters of the Lethe wash away memory, allowing for spiritual rebirth, reincarnation, a return to the world in new form.

SycamoreGrove20170404-10

This memory implant represents a bridge over the Lethe.

Footbridge over Enfield CreekFor those chosen to cross over to the new land in return for

Sycamore Grove

their treasure, lives and selves.

Sycamore Grove

Description

This virtual monoculture glade from the long time of forests,

Sycamore Grove

a place of happy gatherings, of families, plentiful food and water.

Sycamore Grove

These sycamores grew over centuries, through thousands of days, wider than 10 people,

Sycamores

white with age as the outer covering, called bark, falls away.

Sycamores

forked, trunks

Sycamore Trunk

climbing to the sky.

Sycamore Sky

Copyright 2017 Michael Stephen Wills All Rights Reserved