Science Cantata (unfinished at this time)
By Leonard H. Berman
Part I ---- Leonardo Fibonacci
Sung:
I’ll tell you when I felt it first,
A child no more than twelve,
I stood upon a hillside,
As the twilight trickled in,
The sun was skimming off the hills,
Like a pebble off the sea,
The clouds seemed herds of orange sheep,
On hills of filigree.
I heard what seemed a golden chord,
A sound that once begun,
Would tremble always in my bones,
And fill my life with overtones,
And vibrate me till I was one,
With the sound of the setting sun.
Spoken:
Oddly enough, my romance with the universe began when I was presented with a problem about rabbits. Yes, rabbits! Actually, the original problem was presented in the 13th century by a man named Leonardo Fibonacci. He was called “the simpleton.” Some simpleton.
This is what he theorized.
Sung:
If you place a pair of rabbits in a place that is confined,
And you theorize their matings, then the numbers you will find,
Will be 2,3,5,8,13,21 then 34,
And the sequence is consistent as the numbers start to soar,
Add two numbers in the series, any place along the line,
The resulting sum was always the next number by design.
Spoken:
It’s true. Every number in the sequence is the sum of the two preceding numbers. It was remarkable but the strangest thing and the most exciting to me was that if you divide any number in the sequence from the 14th numbers onward into the preceding number, you get .618034. It was like magic. The Greeks knew about it and called it the golden proportion or .618034 to one. They may not have understood it, but they knew it was pleasing to the eye and they defined this golden mean as the point that divided a line into two parts in such a manner that the smaller part was in proportion to the larger part as the larger part was to the entire line. But I wanted to prove this for myself.
Sung:
So I took my father’s playing cards and mother’s writing pads,
And postal stamps and window pains and photographs and adds,
And by squaring off the left side just as Jake Berouilli did,
And by putting squares and rectangles proportionally on a grid,
I saw in every measurement a strange comparison,
For consistently the ratio was .618034 to one.
My appetite was whetted.
Then I looked back into history as far as I could see,
And discovered that the pyramids and Parthenon were key,
The plateau in Giza, Egypt in proportion 5 to 8,
Were just numbers in the sequence that were steady, true and straight,
And the glory that was Athens that stood high above the town,
Is harmonious perfection in proportion world renown.
And I saw in every measurement a strange comparison,
For consistently the ratio was point 618034 to one.
Spoken:
Astounding and my mathematical chase through art and architecture, oceanography, botany, biology, astronomy and music began.
Sung:
Yes, it worked in man made objects, engineering and in art,
But in nature, what of nature? Would the theory fall apart?
I took horns and claws and parrot beaks and shells from out the sea,
And with calliper and ruler, I would see what I would see,
And the curve in nature’s beaks and horns were measured by degree,
Were reflected in the sweeps of stars in the swelling galaxy.
And I saw in every measurement, a strange comparison,
For consistently, the ration was point 618034 to one.
Spoken:
You see any section of the spiral is .618034 as large as the remainder of the spiral. And everywhere along these spectacular lothorithmic curves, be it on a sea shell like the nautilus or an arm of a galaxy, the proportion holds. And then I thought of flowers.
Sung:
So I looked into a garden, looked at petals, looked at seeds,
Counted petals on the daisies, even numbered leaves on weeds,
And consistently the numbers fell within that magic range,
Swelling spirals in the sunflowers that would never, ever change.
Spoken:
Those same wonderful lothoritmic spirals of the galaxy, I saw on the face of pine cones as they lay on the ground. All around me, in every corner of my world, that same mysterious series of numbers and that divine proportion.
Sung:
Come see what I see,
Come reach out,
To galaxies and star stuff,
Swelling about.
There are no boundaries in the place where I go,
No limits or edges on the things that I know,
Dare to be great and seek the divine,
Voyage with me to the frontiers of time.
Part II ---- Steven Hawkings
Sung:
Come see what I see,
Come reach out,
To galaxies and star stuff,
Swirling about,
There are no boundaries in the places I go,
No limit on the edges on the things that I know,
Dare to be great, to seek the divine,
Voyage with me to the frontiers of time.
Spoken:
You are hearing my thoughts. I can no longer speak. As you see, I am confined to the chair by amyotrophic lateral sclerosis. You know it as Lou Gehrig’s disease. I am Stephen Hawkings. My body is paralyzed and I am exhausted by my struggle against gravity, but my mind continues to leap unchecked through the galaxy a quantum at a time. I search for how the universe came into being and if I can uncover this, the greatest mystery of the universe, I will have proven the grand unification and linked relativity with quantum mechanics.
Sung:
What if the theory Einstein taught,
You know- on relativity.
A large scale universe he sought,
Finite and set by gravity?
What if the theory, once conceived,
Quantum physics-atomic scale,
Is wedded to Einstein’s and believed,
Wouldn’t that tell a remarkable tale?
To reconcile the two as one,
In a single unity, where atoms bind,
A revelation to shake and stun,
An astounding glimpse into God’s mind.
God’s mind to know and radiant be,
Wrapped in the wonder such knowledge brings,
To know why we are and finally see,
Our existence and places in the scheme of things.
Unification is what I seek,
That great and small are somehow linked.
Spoken:
The secret hovers around the black holes in the universe. For those of you who do not know about the theory, a black hole is thought to be a region of extremely dense matter caused by a burned out star collapsing in on itself. Surrounding a black hole is a surface known as an event horizon, a kind of trap door through which matter could pass in only one direction-inward. But what if that is not always the case?
Sung:
A black hole, a black hole,
Sucking life and sucking light,
A star as black as ebonite,
Emploded so it can’t be seen,
Emitting nothing from its demesne.
But what if radiation can,
Escape into the cosmic night,
From singularities in flight
Perhaps in sub atomic cold,
The laws of nature do not hold.
What if, what if, I postulate,
A mass so infinitely dense,
A place collapsed to zero size,
Where nothing known is realized,
A place called, singularity,
Where nothing is but just might be?
I postulate, I postulate,
A theory of the universe,
A theory which some think perverse,
A single singularity,
Exploding out its own debris,
We’ve come to call the first big bang.
Spoken:
But what if there are no singularities and the universe is finite but without boundaries. And what if there are no black holes. We have no conclusive physical evidence they even exist. But what if they do but we find that sub atomic level particles do not obey the same laws that we see in natural objects around us? What if sub atomic particles were created at the event horizon and one was sucked into the black hole and the other escaped into space. They call this “Hawkings Radiation.” They named it after me. Does it exit?
Does it rally exist and if it does exist, I can marry quantum mechanics to relativity and we take a step on the road to the grand unification.
Sung:
Come see what I see,
Come reach out,
To galaxies and star stuff,
Swirling about,
There are no boundaries in the places I go,
No limit on the edges on the things that I know,
Dare to be great, to seek the divine,
Voyage with me to the frontiers of time.
Part I ---- Leonardo Fibonacci
Sung:
I’ll tell you when I felt it first,
A child no more than twelve,
I stood upon a hillside,
As the twilight trickled in,
The sun was skimming off the hills,
Like a pebble off the sea,
The clouds seemed herds of orange sheep,
On hills of filigree.
I heard what seemed a golden chord,
A sound that once begun,
Would tremble always in my bones,
And fill my life with overtones,
And vibrate me till I was one,
With the sound of the setting sun.
Spoken:
Oddly enough, my romance with the universe began when I was presented with a problem about rabbits. Yes, rabbits! Actually, the original problem was presented in the 13th century by a man named Leonardo Fibonacci. He was called “the simpleton.” Some simpleton.
This is what he theorized.
Sung:
If you place a pair of rabbits in a place that is confined,
And you theorize their matings, then the numbers you will find,
Will be 2,3,5,8,13,21 then 34,
And the sequence is consistent as the numbers start to soar,
Add two numbers in the series, any place along the line,
The resulting sum was always the next number by design.
Spoken:
It’s true. Every number in the sequence is the sum of the two preceding numbers. It was remarkable but the strangest thing and the most exciting to me was that if you divide any number in the sequence from the 14th numbers onward into the preceding number, you get .618034. It was like magic. The Greeks knew about it and called it the golden proportion or .618034 to one. They may not have understood it, but they knew it was pleasing to the eye and they defined this golden mean as the point that divided a line into two parts in such a manner that the smaller part was in proportion to the larger part as the larger part was to the entire line. But I wanted to prove this for myself.
Sung:
So I took my father’s playing cards and mother’s writing pads,
And postal stamps and window pains and photographs and adds,
And by squaring off the left side just as Jake Berouilli did,
And by putting squares and rectangles proportionally on a grid,
I saw in every measurement a strange comparison,
For consistently the ratio was .618034 to one.
My appetite was whetted.
Then I looked back into history as far as I could see,
And discovered that the pyramids and Parthenon were key,
The plateau in Giza, Egypt in proportion 5 to 8,
Were just numbers in the sequence that were steady, true and straight,
And the glory that was Athens that stood high above the town,
Is harmonious perfection in proportion world renown.
And I saw in every measurement a strange comparison,
For consistently the ratio was point 618034 to one.
Spoken:
Astounding and my mathematical chase through art and architecture, oceanography, botany, biology, astronomy and music began.
Sung:
Yes, it worked in man made objects, engineering and in art,
But in nature, what of nature? Would the theory fall apart?
I took horns and claws and parrot beaks and shells from out the sea,
And with calliper and ruler, I would see what I would see,
And the curve in nature’s beaks and horns were measured by degree,
Were reflected in the sweeps of stars in the swelling galaxy.
And I saw in every measurement, a strange comparison,
For consistently, the ration was point 618034 to one.
Spoken:
You see any section of the spiral is .618034 as large as the remainder of the spiral. And everywhere along these spectacular lothorithmic curves, be it on a sea shell like the nautilus or an arm of a galaxy, the proportion holds. And then I thought of flowers.
Sung:
So I looked into a garden, looked at petals, looked at seeds,
Counted petals on the daisies, even numbered leaves on weeds,
And consistently the numbers fell within that magic range,
Swelling spirals in the sunflowers that would never, ever change.
Spoken:
Those same wonderful lothoritmic spirals of the galaxy, I saw on the face of pine cones as they lay on the ground. All around me, in every corner of my world, that same mysterious series of numbers and that divine proportion.
Sung:
Come see what I see,
Come reach out,
To galaxies and star stuff,
Swelling about.
There are no boundaries in the place where I go,
No limits or edges on the things that I know,
Dare to be great and seek the divine,
Voyage with me to the frontiers of time.
Part II ---- Steven Hawkings
Sung:
Come see what I see,
Come reach out,
To galaxies and star stuff,
Swirling about,
There are no boundaries in the places I go,
No limit on the edges on the things that I know,
Dare to be great, to seek the divine,
Voyage with me to the frontiers of time.
Spoken:
You are hearing my thoughts. I can no longer speak. As you see, I am confined to the chair by amyotrophic lateral sclerosis. You know it as Lou Gehrig’s disease. I am Stephen Hawkings. My body is paralyzed and I am exhausted by my struggle against gravity, but my mind continues to leap unchecked through the galaxy a quantum at a time. I search for how the universe came into being and if I can uncover this, the greatest mystery of the universe, I will have proven the grand unification and linked relativity with quantum mechanics.
Sung:
What if the theory Einstein taught,
You know- on relativity.
A large scale universe he sought,
Finite and set by gravity?
What if the theory, once conceived,
Quantum physics-atomic scale,
Is wedded to Einstein’s and believed,
Wouldn’t that tell a remarkable tale?
To reconcile the two as one,
In a single unity, where atoms bind,
A revelation to shake and stun,
An astounding glimpse into God’s mind.
God’s mind to know and radiant be,
Wrapped in the wonder such knowledge brings,
To know why we are and finally see,
Our existence and places in the scheme of things.
Unification is what I seek,
That great and small are somehow linked.
Spoken:
The secret hovers around the black holes in the universe. For those of you who do not know about the theory, a black hole is thought to be a region of extremely dense matter caused by a burned out star collapsing in on itself. Surrounding a black hole is a surface known as an event horizon, a kind of trap door through which matter could pass in only one direction-inward. But what if that is not always the case?
Sung:
A black hole, a black hole,
Sucking life and sucking light,
A star as black as ebonite,
Emploded so it can’t be seen,
Emitting nothing from its demesne.
But what if radiation can,
Escape into the cosmic night,
From singularities in flight
Perhaps in sub atomic cold,
The laws of nature do not hold.
What if, what if, I postulate,
A mass so infinitely dense,
A place collapsed to zero size,
Where nothing known is realized,
A place called, singularity,
Where nothing is but just might be?
I postulate, I postulate,
A theory of the universe,
A theory which some think perverse,
A single singularity,
Exploding out its own debris,
We’ve come to call the first big bang.
Spoken:
But what if there are no singularities and the universe is finite but without boundaries. And what if there are no black holes. We have no conclusive physical evidence they even exist. But what if they do but we find that sub atomic level particles do not obey the same laws that we see in natural objects around us? What if sub atomic particles were created at the event horizon and one was sucked into the black hole and the other escaped into space. They call this “Hawkings Radiation.” They named it after me. Does it exit?
Does it rally exist and if it does exist, I can marry quantum mechanics to relativity and we take a step on the road to the grand unification.
Sung:
Come see what I see,
Come reach out,
To galaxies and star stuff,
Swirling about,
There are no boundaries in the places I go,
No limit on the edges on the things that I know,
Dare to be great, to seek the divine,
Voyage with me to the frontiers of time.