Re-Romanticizing Valentines Day: Hearts, Flowers, Bunnies, Ballads, and of course Quantum Mechanics

St Valentine's Day

The history of Valentine's Day is really obscure.  Its roots are in an ancient Roman festival called Lupercalia, a fertility celebration commemorated annually on February 15, and most scholars believe that St. Valentine of the Catholic Church was a priest who was executed/ martyred for performing secret marriage ceremonies.  Before he was executed, he allegedly sent her a letter to his own true love signed..."Your Valentine."

The Heart

The heart symbol we use to express our affections today can be traced back to Cro-Magnon hunters in Europe who used the symbol in pictographs. 

Cave painting from Cueva del Pindal

Cave painting from Cueva del Pindal

The Egyptians crafted a stylized heart symbol to represent the center of life and morality. 

               Illustrations of Egyptian artifacts

               Illustrations of Egyptian artifacts

And the ancient Greeks decorated with a heart shaped symbol to represent the division between the physical and spiritual realms; as pictured here in a threshold mosaic.

Mosaic uncovered in Ancient Ephesus

Mosaic uncovered in Ancient Ephesus

The heart symbol has also been found on old Roman coins and artifacts like this one, which apparently depicts a seedpod from the extinct plant Silphium.

The Silphium seedpod is the most likely candidate as origin for our modern heart shape.  It was used medicinally to treat infertility, and as a contraceptive.  It was also a well know treatment for mental illness, in particular the "madness of love".  In fact most historians believe that the Romans did not relate the symbol to love at all but rather to sex and carnality, it's form reminiscent of the vulva, breasts, butts, testicles... you know, real Roman currency.

And so, through the centuries the heart came to represent not just sex but love.  And in any case,  a symbol referencing the relationship between human and natural history.

The Garden of Earthly Delights by Hieronymus Bosch, 1500

The Garden of Earthly Delights by Hieronymus Bosch, 1500

Modern society has an obvious and longstanding affection for the symbol, and we seem to imbue places and things that exhibit this symbology with particular meaning.  A quick online search will turn up troves of photos of found hearts everywhere:  Islands and ponds, ferns and swans, leaves and puddles, where you seek so shall you find.

                     Heart-shaped Lichens (Crustose), Audubon Corkscrew Swamp Sanctuary‬

                     Heart-shaped Lichens (Crustose), Audubon Corkscrew Swamp Sanctuary

                                               The 130,000 square yard islet of Galesnjak, Croatia.

                                               The 130,000 square yard islet of Galesnjak, Croatia.

This private and uninhabited Croatian island once contained only wild plants, trees and untouched beaches.  However since it was "discovered" on Google Earth in 2009, the island has become a major tourist destination.  In fact there are at least 25 heart shaped islands in the world, all of then famed for their shape and it's connotations. 

This got me thinking about universally understood and universally attractive shapes and forms.  And by the way, what is the MOST infinitely ancient and universally tangible image or form? 

I submit to you:

The Golden Spiral, or Fibonacci’s Spiral

        Flowers

        Flowers

The first written record of the Fibonacci's Sequence comes from around 200BC in the Sanskrit tradition of prosody; basically a study of phonetics.  In the West, the Fibonacci sequence first appears in the book Liber Abaci by Leonardo of Pisa, written in 1202. Leonardo was known as Fibonacci. 

Bunnies

Fibonacci's equation was based on an idealized pattern of rabbit reproduction, which consisted of mating pairs of rabbits reproducing at optimum efficiency.  Because rabbits begin breeding when they are one month old,  the sequence looks like this. 

Image Credit: Curiosa Mathmatica

Image Credit: Curiosa Mathmatica

Begin with one Female rabbit, one month old

At the end of the first month a female mates, but there is still just her and her mate, 1 pair.

At the end of the second month the female produces a new pair, so now there are 2 pairs of rabbits.

At the end of the third month, the original female produces a second pair, making 3 pairs in all.

At the end of the fourth month, the original female has produced yet another new pair, the female born two months ago produces her first pair also, making 5 pairs.

And so on.  Adding the sum of the previous two numbers to get the following number creates the sequence.

1+1=2

1+2=3

2+3=5

3+5=8

5+8=13...

And on into infinity.

It is no accident that Fibonacci came across this pattern studying nature, because this pattern is everywhere in nature.  You can calculate it in pine cones, sunflowers, even hurricanes...

                                                                         Sunflower with Fibonacci sequence imposed

                                                                         Sunflower with Fibonacci sequence imposed

                             Hurricane Sandy with Fibonacci's Spiral Imposed

                             Hurricane Sandy with Fibonacci's Spiral Imposed

When the sequence is translated geometrically, it is a rectangle.  If you continue to create successive squares and spiral out of the first rectangle, the quadratic equation of the sides becomes closer and closer to 1.618033, which is Phi or the Golden Ratio.  That Golden Ratio has been romancing artists, scientists, musicians, and mathematicians for centuries.

                                                             Mona Lisa with the Golden Ratio imposed

                                                             Mona Lisa with the Golden Ratio imposed

If you would like to check out further applications and implications of the sequence, I would start here with Arthur Benjamin.  He is a truly inspired mathematician and teacher.

If you are a hack like me, let's continue...

If you take that series of rectangles and plot a spiral by drawing a 90-degree curve through each square, you have the Golden Spiral, also known as Fibonacci’s Spiral.

                   The Golden Spiral expressed in a Nautilus shell

                   The Golden Spiral expressed in a Nautilus shell

                                          The Golden Spiral expressed in the human ear

                                          The Golden Spiral expressed in the human ear

 

Ballads

It is not just physical/ visible objects that carry the sequence.  Fibonacci Numbers are also the underlying structure of the worlds most played and universally adored music. 

There are 13 notes in the Chromatic Scale, broken into 8 white keys and 5 black keys, the 13th note being the first note in the following octave. There are 8 notes in the Diatonic Scale (just the 8 white keys of the Chromatic Scale) the 8th being the first note in the following octave.  When we stack the two scales on top of each other visually, you can see how the Fibonacci numbers correspond with cords. 

I will not elaborate on this right now, but if you are interested, please check out this great video from Sylvain Lalonde:

Fibonacci and phi relationships are found in the timing of musical compositions as well, from Mozart to Pink, the climax or bridge of a song is most often found at roughly the phi point (61.8%) of the song.  Further, the typical three or four chord structure of most songs in any key, is made up of the key cord along with it’s Fibonacci & Phi partner plus one or two.  This is analogous to the “A is to B as B is to C” basis for the golden ratio.  It makes you wonder how many of our aesthetic values and personal expressions are based on these ancient and fundamental systems. 

Dave Carlton, one of the contributors to Hooktheory, a modern music theory site, analyzed 13,000 popular songs for patterns, and published the results in an online article you can read here:

Hooktheory

He found, as you might expect, that C/Am and G/Em are the most popular key signatures.  With G, F, C and Am the most popular cords.  But more interesting to me, is the relationship of cords to each other in the songs he analyzed.  Such as, what cord is most likely to come next in popular music?  Well he found in the case of C with and Em, 93% of the time the other cords will be F, Am or both. 

Not surprisingly, the most popular songs are also the most emotive, through a combination of effects.  To illustrate this divine musical situation, I submit to you the following video snippet from comedian, Owen Benjamin.  Owen is a musician, and has done several hilarious bits about the absurdity and homogeneity of pop music.  In this one he provides a heartfelt exploration of Coldplay, and shares his own ballad OTPHJ (in a Walgreens). 

As a side note, Owen’s ballad, is in fact a golden ratio composition, complicated a bit by the use of 2 bridge moments at measures 17 and 27 (double climaxes), the median of which is 21.7…61.8% of the 35 measure song. 

Now we have seen the same mathematical sequence equally applied to visible and audible phenomenon.  If you ask me, this is a brilliant opener to talking about the nature of existence. 

Quantum Mechanics

All things in existence can be thought of in two ways:

Atomic particles like Atoms, protons and neutrons 

or, Vibrations like Electromagnetic fields and sound-forms. 

Whether you choose an atomic or vibrational world view, the same rules will always apply.  I think music is a key starting point to this exploration because it is vibration made tangible through the tools we use to express it.  And, if you will agree (for the moment) to impose a vibrational world view of waveforms onto musical theory, we can begin to talk about dimensions and infinity.

Dimensional levels are simply different base rate wavelengths. It is not really the difference between line, shape, form and time as many of us were taught.  Those are three-dimensional expressions of vibration. In fact, the only difference between this dimension and any other is the waveform we express through vibration.  More dense life forms like crystals and plants have a much lower base wavelength, and as you travel dimensionally upwards the base wavelength increases. 

To illustrate the beauty of this we can think again about the Chromatic scale.  If you look at a piano’s keyboard, it has 8 white keys and 5 black keys in each octave.  The last note in the scale, is the first note of the next octave.  This musical system theoretically goes on infinitely in both directions, we just happen to prefer an instrument with a set number of octaves that sounds great at our level of vibration.

If you picture yourself as any key on that piano, and think about how big we perceive the universe to be from that one point, our one key perspective in an infinite set of harmonic possibilities… Imagine how much more is out there, and how much more we have yet to perceive.

 Now a message from our sponsors

Hubble Ultra Deep Field

Hubble Ultra Deep Field

 

This photo titled Hubble Ultra Deep Field, was captured in 2003 by The Hubble Telescope.  To create it astronomers pointed the Hubble near constellation Orion and opened the shutter for 11 days. Using sensitive detectors and specialized filters, the telescope was able to capture an image with over 10,000 galaxies.  And this was in just one tiny speck of sky that appears completely void of, even stars from earth.  This year scientists went further with a 23 day exposure of a much smaller section of the Ultra Deep Field image, and titled it eXtreme Deep Field. 

 

This image shows 5,500 individual galaxies, some of which are one ten-billionth the brightness of what our human eyes can see.  Giving us a little glimpse of the infinity of existence we are more or less aware of.

I love these images in ways I cannot even clearly express; they excite and mystify me.  So, I decided to create a couple of Valentines based on my own romance with creative expression and space exploration titled...

“Infinitely Yours”

The images are taken from photos of the Barred Spiral Galaxies NGC 986, and NGC1365, located 56 million light years away in the constellation Forenax.

NGC 986

NGC 986

NGC 1365

NGC 1365

Thanks to free image licensing from NASA, I edited these galaxies together with the Fibonacci Spiral, and a lot of love.

                    NGC 986

                    NGC 986

NGC 1365

NGC 1365

If you want to share these images with your Valentine, you can of course grab the low res version here for free,  or go here to download a larger file. 

I also have posted cards, stickers, tshirts, iphone cases, pillows and travel mugs in my Redbubble store.

 

Here's wishing you the most titillating February, whether you celebrate Valentines day or not.                 

 Infinitely yours,

E

 “If the doors of perception were cleansed, everything would appear to man as it is - infinite.”
William Blake
 
“Only love can be divided endlessly and still not diminish.”
 Anne Morrow Lindbergh