Math and Science Ritual

Heather, Michelle, and I (Trevor) planned and led this ritual during Dragonfest, 2003. Heather is a microbiology student, Michelle a physics student, and I'm a computer scientist; we all attend The University of Colorado at Boulder (and met through the Pagan Student Alliance). We don't believe that science and religion must be separate disciplines and regularly employ scientific metaphors in religious and spiritual contexts and vice versa. Many Neo-Pagans dismiss science; many others think it is dry and unrelated to spirituality. We wanted to lead this ritual to share how we mix the two together. We're light-hearted, but we take our fun seriously. There's lots of accurate scientific and mathematical factoids cast in a tone familiar to practicing Neo-Pagans.

Topically, the ritual is divided into four domains -- the fundamental forces (electromatnetism, nuclear weak force, nuclear strong force, and gravity); states of matter (solid, liquid, gas, and plasma); types of numbers (rational, irrational, imaginary, and real); and divisions of biology (genetics, neurology, metabolism, and anatomy). Michelle wrote the first two sets, I wrote the third, and Heather wrote the fourth. Thanks to chance encounters, our ritual also featured a Bose-Einstein Condensate Call for the center.

We hope this ritual can provide inspiration for mixing your own religious beliefs and practices with your own scientific perspectives. If you would like to lead this ritual, let me know and I can answer any questions you have. For inspiration, you can check out a few pictures from the event. (You'll have to poke around to find the ones specific to this ritual.)


Calls: Forces

East/Electromagnetism

lightning snaps
atoms coalesce
planetary trap for solar wind
protection from radiation

South/Weak Force

up and down quarks
beta decay
of neutron to proton and electron
and highly energetic neutrino

West/Strong Force

binding nucleons in the nucleus
quarks in the nucleons
variety of elements
stairstepped up from hydrogen

North/Gravity

keeping our feet on the ground
bodies dancing together
acknowledging each star and galaxy
no matter how distant

Dismissals: Forces

North/Gravity

ground and center
feet glued to the Earth
to provide a full experience
of stable attachment

West/Strong Force

quarks conglomerated
nuclei nucleated
atoms accumulated
and here we are

South/Weak Force

beta decay
shifting elements
curious phenomenon
cultivates the question

East/Electromagnetism

dipole of the Earth
protecting us from harm
your auroric beauty
evokes awe and respect

Calls: Matter

East/Gas

diffuse and random
Brownian motion
collision creating heat
heat creating chaos

South/Plasma

nuclei stripped of electrons
seething swarm of particles
ionization
solar corona

West/Liquid

adhesion and cohesion
flowing toward the center of mass
spherical droplets in space
cradle of life

North/Solid

seemingly unmoving
but spinning on itself
dense collection of matter
long-term changes

Dismissals: Matter

North/Solid

standing on the firm earth
we are inspired to be stable
you stay as we will
a component of the Earth

West/Liquid

you flow away from us
and inspire us to flow
conforming our body shapes
we are mostly liquid

South/Plasma

brightly burning flame
small version of the sun
you inspire us to action
and electron independence

East/Gas

disperse as we will
collide as we will
random motion
you inspire us to chaos

Calls: Math

East/Rational

Rational numbers; all that is digital,
Inform us with high entropy!
Prime us for quantization!
Divisible, with operations and accuracy for all.

South/Imaginary

Imaginary numbers; square root of minus one,
Enigmatically give us complexity!
In impossibility, solve problems!
i becomes e if right after sine.

West/Irrational

Irrational numbers; finite infinity,
May our circle have pi!
May e not continually confound us!
We use you, but cannot speak your full name.

North/Real

Real numbers; irrational punctuated by rational,
Give us continual life in space and time!
Describe to us the world!
Powerful, you are really useful.

Dismissals: Math

North/Real

All that we touch
And all that we feel
We'll keep in touch
With all that is real.

West/Irrational

The wheel still spins,
Interest marches ever on.
We now understand the irrational,
Though we haven't finished writing it.

South/Imaginary

We thank i, our imaginary friend
For simplifying with complexity.
But we now bring two i's together
Returning to reality.

East/Rational

Rational numbers, how do we thank you?
Let me count the infinite ways.
Whole now divides
But not by zero.

Calls: Biology

East/Neurology

Sense the world around you
Neurons flash, carrying signals
Action potential flows effortlessly
Brain and body communication

South/Metabolism

The fires within are fed always
Big molecules break into small ones
Cells know what they need and take it
Mitochondria catabolize cell's food

West/Genetics

Mama egg and Papa sperm
Each code unique and special
Love brings them together to forge
New life Uncle Mendel's way

North/Anatomy

Bones giving structure
Muscles to do the work
Magical organs act so wisely
Mama Earth builds bodies strong

Dismissals: Biology

North/Anatomy

Now we lie down and rest
Mother Earth knows us best
All that has gone before
Now works to build us more

West/Genetics

The double helix folds into itself
The cozy afterglow fades
The match has been made
Rest for the new growth

South/Metabolism

We have eaten and are full
Simple molecules rush on
Toward their destination
The fire is never quenched

East/Neurology

Nerves sing with sensation
We move with grace
Smooth reflexes soothe the soul
Neurons depolarize once more

Call: Central Dogma Goddess

Along the double helix
Travels wise molecules
Creating life anew each day
Governing each tiny change

Under the double helix
Ancient code still lives
Going ever onward
Chromosome becomes protein

All of life
Carries her touch
Down to amoebae
Each tiny thing
Feels her, feeds on her
Grand scheme birthed
Here in codons
Introns and exons
Kept or recycled
Long lines of text
Mutations both sense and
Nonsense making
Permanent alterations
Quickening evolution's progress
Returning to the source of life
Sacred sister, crone, and mother
Teacher, architect, conduct the dance
Visit our minds
Welcome to this place
You are inside all of us.

Call: Formal Language (The Word) (Inspired by John 1:1-23)

In the beginning was the flesh, and the flesh was with Earth, and the flesh was god. It was in the beginning god; all things were made through it, and without it was not anything made that was made. And the flesh became word and spread among us, full of grace and truth; we have beheld its glory, glory as only speech from the mouth.

And the word became symbol and the language became logic and math. And Gödel bore witness to it, and cried, "This was it of which I said, 'All things may be made with it or something that is made cannot be made with it.'" And from his incompleteness we all received, grace upon grace. For the law was given by Gödel; grammar and hierarchy came through Noam Chomsky.

Call: "Cakes" -- Chessmen

Chess, a game with perfect information.
A solution can be found
If only we could climb a tree
With more branches than atoms in the universe.
Blessed be.

Call: "Ale" -- Water

Bent polar molecules hydrogen bonding to form liquid, solvent of life, water gave us birth and maintains us until we die. Perfect thirst-quencher of plants and animals, refresh us as a summer shower refreshes the air. Blessed be.

The Human Finite State Machine

Set up a table in each cardinal direction with instructions (below) for one domain from each discipline on each. Everyone receivs a piece of paper to record their output; other people used their body as an output device. Each person chooses a "state" (domain/element) at which to begin. He or she reads the description and follows the directions under "Activity." He or she then walks to a state indicated in the "Transitions" section. Everyone is traversing a 16-node finite state machine in which every state is both a start and end state. For convenience, the state machine is depicted below. A person in one state can transition to the one pointed to by a connecting arrow. Some (but not all) transitions go both ways.

[Elemental Finite State Machine]


Rational Numbers (East)

Description:

Any number that can be expressed as one integer divided by another (except division by zero) is a rational number. All numbers expressed digitally must be rational, unless the base itself is irrational. Computers thus cannot accurately represent most numbers -- they only know a reasonable approximation. There are countably infinite rational numbers -- there is no end to them, but they are distinct.

Activity:

Good work! Take a star! (Did you realize your teacher gave you a golden pentacle for good work?) You have one star, the basic rational number. If you tear off one of the points, you have four fifths of a star -- still a rational number. If you take another star, you have one and four fifths of a star -- a rational number yet again. If you throw them both away, you have zero stars -- the fundamental rational number. Stick a rational number of stars on your paper. Alternatively or additionally, draw some of your favorite rational numbers on your paper or on your body. Some of my favorites are 0, 1, 2, 3, -1, 42, 1/10, . 5, and all powers of 2.

Transitions:

Genetics (West)
The interdisciplinary study Bioinformatics examines the relations between digital computation, information theory, and genetics interact.
Neurology (East)
A neuron either fires or it doesn't. With the right time increment, firing rates can be expressed as a rational number.
Imaginary Numbers (South)
Taking the square root of -1 (or any negative rational number) produces an imaginary number.

Imaginary Numbers (South)

Description:

The square root operation reports the number which, multiplied by itself, produces the number under operation. When you multiply two negative numbers or two positive numbers, you get a positive number. So what's the square root of negative one? The answer is "i," the basis of the imaginary numbers. The most general form of a number is A + i*B, where A and B are real numbers. Their sum is called a complex number.

Activity:

i is most useful in Euler's formula -- eix = cos x + i*sin x. Since sin π = 0 and cos π = -1, e + 1 = 0. This equation relates the five fundamental numbers in mathematics. Write this equation on your paper or body and feel the power you harness. You may also draw an "i" in the center of your forehead. This is your third i, locus of the imaginary.

Transitions:

Irrational Numbers (West)
i is related to e and π by the equation e = -1. This equation is tied to sines and cosines, most of which are irrational.

Irrational Numbers (West)

Description:

All numbers that cannot be expressed by two divided integers are irrational numbers. There are uncountably many infinite numbers between any pair of rational numbers. Two of the most important irrational numbers are π and e. π (which begins 3.141592653) is the ratio of a circle's circumfrence to its diameter. e is the base for the natural logarithm and begins 2.718281828. e is the rate of continual compounding -- if you have $100 in the bank with an anual interest rate of 5%, after two years you have e.05*2 ≈ $110.52. After 20 years, you'll have $271.83. This principle applies to population growth and radioactive decay.

e ≈ 2.71828 18284 59045 23536 02874 71352 66249 77572 47093 69995
π ≈ 3.14159 26535 89793 23846 26433 83279 50288 41971 69399 37510

Activity:

Cut a strand of string and tie it in a circle about a part of your body. You are now covered with pi! Alternatively or additionally, draw the curve for ex ("exp(x)") or ln x (“log(x)”) on your paper or body.

Transitions:

Weak Force (South)
The weak force governs radioactive decay, which is described by e-r where r is the rate of decay.
Electromagnetism (East)
sine and cosine, and hence e, π, √2, and √3 are fundamental to electrical engineering.
Imaginary Numbers (South)
e +1 = 0 relates the five fundamental constants of mathematics. Two are irrational, one imaginary.

Real Numbers (North)

Description:

The real number line is made up from all rational and irrational numbers. Without the two together, functions cannot be continuous. Real numbers describe space, time, motion, and any other phenomena that encompass a range of numbers. There are uncountably infinitely many real numbers; math logicians debate whether there are more real numbers than irrational numbers (since rationals are real) or whether the sets are the same size.

Activity:

Move all or part of your body around. Note its fluid motion -- to get to one place, it must pass through all intervening positions, of which there are infinitely many. Yet your limb arrives at its destination in a finite amount of time! Draw your favorite shape or curve.

Transitions:

Gas (East)
Gas is molecules separated by space. The real number line is rational numbers separated by irrational numbers.
Gravity (North)
In some gravity equations, you perform a complex calculation and take the real part.
Anatomy (North)
Bodies move throughout real space, as in the activity.

Gas (East)

Description:

New Latin, alteration of Latin 'chaos' space, chaos.

Activity:

Breathe deeply, all the way into your belly. Continue until you are fully aware of the space you are making for gaseous air to fully fill. Draw on the parts of your body that change/move with the intake of air.

Transitions:

Liquid (West)
Decreased temperature or increased pressure transmutes gas to water.
Real Numbers (North)
Gas is molecules separated by space. The real number line is rational numbers separated by irrational numbers.

Plasma (South)

Description:

German, from Late Latin, something molded, from Greek, from 'plassein' to mold. Plasma is ionized gas, as found in the sun.

Activity:

Light the candle if it is not alraedy lit. Focus on the flame. Imagine the flame expanding to the size of the sun. The sun is also plasma. Draw a flame on skin that is often hit by the sun (or on your paper).

Transitions:

Gas (East)
Decreasing temperature cools plasma into gas.
Weak Force (South)
In the center of the sun, where lots of plasma resides, is lots of radioactive decay, which is governed by the Weak Force.

Liquid (West)

Description:

Middle English, from Middle French 'liquide', from Latin 'liquidus', from 'liquére' to be fluid; akin to Latin 'lixa' water, lye, and perhaps to Old Irish 'fliuch' damp.

Activity:

Create a watery design using your finger as a brushand water as the medium. Sitting or laying down may help if you are drawing on yourself.

Transitions:

Gas (East)
Increased temperature or decreased pressure transmute liquids to gas.
Solid (North)
Decreased temperature or increased pressure solidifies liquids.
Genetic (West)
Sperm and egg meet in fluid. Early land plants had to spread their seeds in water, so fog often leaves an odd-looking residue on the trees.
Metabolism (South)
Water is required for digestion.

Solid (North)

Description:

Middle English 'solide', from Middle French, from Latin 'solidus'; akin to Greek 'holos' whole.

Activity:

Hold the green serpentine rock in both hands. It comes from the pacific coast. How long did it take to become so smooth? Draw your favorite rock or rock formation.

Transitions:

Liquid (West)
Decreased pressure or increased temperature melts solids.
Metabolism (South)
Metabolism turns solid food into cellular building blocks.

Electromagnetism (East)

Description:

Fundamental physical force acting between charged particles; 100 times weaker than the strong force, but extends over infinite distances, though it is dominant over atomic and molecular distances.

Activity:

Orient yourself with the compass. Together, Magnetic North and Magnetic South exist as a dipole. By convention, magnetic field lines point out of N and wrap around to point into S. Draw something from one side of your body or paper to the other.

Transitions:

Gravity (North)
Equations for electromagnetism and gravity often have the same form.
Neurology (East)
Neurons communicate via electrical pulses.
Weak Force (South)
At high energies, electromagnetism and the weak force are the first to unify -- that is, they become the same force.
Irrational Numbers (West)
sine and cosine, and hence e, π, √2, and √3 are fundamental to electrical engineering.

Weak Force (South)

Description:

Fundamental physical force acting between hadrons (such as protons and neutrons) and leptons (such as electrons), responsible for particle decay processes in radioactivity (such as beta decay: n g p + e + neutrino); 105 times weaker than the weak force, acting over distances smaller than those between nucleons (protons, neutrons) in an atomic nucleus.

Activity:

Tkae on the highly energetic activity of the neutrino: run around, dance spastically. Run into and around nearby trees. Draw/paint something high-energy.

Transitions:

Strong Force (West)
Both the Strong and Weak forces act on the nuclear scale.
Electromagnetism (East)
At high energies, electromagnetism and the weak force are the first to unify -- that is, they become the same force.

Strong Force (West)

Description:

Fundamental physical force acting on hadrons (such as protons and neutrons), responsible for binding together particles in the atomic nucleus and for particle creation in high-energy collisions; strongest fundamental force, but acts only over distances comparable to those between nucleons.

Activity:

The nearest location at which atoms are densely enough packed together for the strong force to act constantly is the interior of the sun. Draw a depiction of the sun.

Transitions:

Weak Force (South)
Both the Strong and Weak forces act on the nuclear scale.
Rational Numbers (East)
Strong Force acts on subatomic particles (like quarks) which have quantum (rational-valued) states, such as half-spin.

Gravity (North)

Description:

Fundamental physical force which occurs because of the mass of a particle or collection of particles; 1039 times weaker than the strong force, but extends over infinite distances, though it is dominant over macroscopic distances.

Activity:

Plant your feet squarely, with equal weight on all four corners of your feet. You are always directly above the center of the Earth. Paint your feet if you desire.

Transitions:

Real Numbers (North)
In some gravity equations, you perform a complex calculation and take the real part. Gravity acts on all bodies within real space.
Electromagnetism (East)
Equations for electromagnetism and gravity often have the same form.

Neurology (East)

Description:

This branch of biology concerns itself with nerves and their functions, both sensory and motor, to and from the brain and body. Much of what we know about nerves, we have gotten from studying giant squid neurons, and lobsters, which have the most highly developed nervous systems.

Activity:

Add a drop of scent and consciously open your senses to the world around you.

Transitions:

Genetics (West)
Much of your brain activity is devoted to attempting genetic recombination.
Electromagnetism (East)
Neurons communicate via electrical pulses.
Rational Numbers (East)
A neuron either fires or it doesn't. With the right time increment, firing rates can be expressed as a rational number.

Metabolism (South)

Description:

From grain to carbohydrates, proteins, and fat, the body breaks stuff down into energy to run its processes. Carbohydrates and starch break down into glucose, the main food the body uses. Proteins break down into amino acids. Fats break down into lipids, used for every cell membrane.

Activity:

Take a piece of candy and eat it with awareness that you are feeding your cells the nourishment they require. Attach the wrapper if you'd like. Carbohydrates and starch break down into glucose, the main food the body uses. Proteins break down into amino acids. Fats break down into lipids, used for every cell membrane.

Transitions:

Anatomy (North)
Metabolism produces body parts.

Genetics (West)

Description:

Shows the ways individual traits are passed from generation to generation. The Human Genome Project has completed it's search for the basic genetic code. Now we just have to learn to read the books that are contained in that library. The search is not over!

Activity:

2 options #1: Share a kiss or caress (PG-13 max) with someone, and make note of the passion involved. #2: Write or draw something using your non-dominant hand to let your inner child say something.

Transitions:

Liquid (West)
Sperm and egg meet in fluid. Early land plants had to spread their seeds in water, so fog often leaves an odd-looking residue on the trees.
Anatomy (North)
Genes determine a being's anatomical properties.
Rational Numbers (East)
Genes can be thought of as sequences of four-option bits. Researchers are working on computers that use genes rather than transistors.

Anatomy (North)

Description:

The study of the structures that make up living beings, this discipline covers everything from cells to bodies, to trees and yeast. Considered by some to be a dead branch of science, not only for the cadaver work that is a part of it, but because some think we know everything there is to know about the human body. Does that seem arrogant to you too?

Activity:

Draw or trace your favorite body part, or paint something directly on yourself.

Transitions:

Gravity (North)
Bodies exert gravitational force on each other. (Jupiter exerts a greater gravitational force on a newborn child than does the midwife a foot away. However, the difference in gravitation between Jupiter at its furthest and nearest is less than the difference in gravitation caused by the presence or absence of the midwife.)
Real Numbers (North)
Bodies move throughout real space.