“The same holds also of astronomy. For treating of the description of the celestial objects, about the form of the universe, and the revolution of the heavens, and the motion of the stars, leading the soul nearer to the creative power, it teaches to quickness in perceiving the seasons of the year, the changes of the air, and the appearance of the stars; since also navigation and husbandry derive from this much benefit, as architecture and building from geometry. This branch of learning, too, makes the soul in the highest degree observant, capable of perceiving the true and detecting the false, of discovering correspondences and proportions, so as to hunt out for similarity in things dissimilar; and conducts us to the discovery of length without breadth, and superficial extent without thickness, and an indivisible point, and transports to intellectual objects from those of sense.”

This is from his “Stromata”, Book VI, Chapter 11. The Mystical Meanings in the Proportions of Numbers, Geometrical Ratios, and Music.

More to the point, Clement writes [Stromata, Book II, Chap. 21],

“Pythagoras taught that the knowledge of the perfection of the numbers was happiness of the soul.”

That all this crusty source from the 2nd century church fathers is available online is just amazing.

One single word used by John Paul struck me as I read Redemptor hominis afresh this week in prep for next week’s seminar. That word is “unrepeatable”. There are several occasions he uses the term, each time with a fuller meaning. I’ll list them, along with paragraph numbers in brackets. First John Paul writes:

1. Christ, the Redeemer of the world, is the one who penetrated in a unique unrepeatable way into the mystery of man and entered his “heart”. [8].

And then later,

2. Jesus Christ becomes present with the power of the truth and the love that are expressed in him with unique unrepeatable fullness in spite of the shortness of his life on earth and the even greater shortness of his public activity.. [13]

These intial uses are for Jesus the Christ. But then the usage bleeds into mortal man himself:

3. Her solicitude is about the whole man and is focussed on him in an altogether special manner. The object of her care is man in his unique unrepeatable human reality, which keeps intact the image and likeness of God himself. [13]

Then his usage of unrepeatable is obviously instantiated in us all:

4. We are speaking precisely of each man on this planet, this earth that the Creator gave to the first man, saying to the man and the women: “subdue it and have dominion”. Each man in all the unrepeatable reality of what he is and what he does, of his intellect and will, of his conscience and heart. Man who in his reality has, because he is a “person”, a history of his life that is his own and, most important, a history of his soul that is his own. [14]

Why do I find this word “unrepeatable” so fascinating? Perhaps it is because, as a physicist by vocation, the word has such a rich meaning in the modern physics parlance of complex systems, where disparate parts or members of a many-body system can exhibit rich unpredictable patterns. Yes the members in the larger Body are at some level (genetic, atomic) identical, but when interacting in service of a larger Body, and higher calling and term, they each settle into a unique and precious behavior. An unrepeatable path. A vocation. Please understand I’m not pretending to reduce the sacred to the material. Rather I’m pointing out harmonies I note in what we know in ancient faith and modern physics of bodies and organisms composed of manifold members. In fact John Paul even invokes the word “organism” :

In this way, turning to man and his real problems, his hopes and sufferings, his achievements and falls-this too also makes the Church as a body, an organism, a social unit perceive the same divine influences, the light and strength of the Spirit that come from the crucified and risen Christ, and it is for this very reason that she lives her life. [18]

And then as the encyclical unfolds John Paul pulls all these notions arising from the interplay of member-body, note-symphony, one-many, together in his exposition of “Vocation.” To explain this “vocation” he invokes and unifies a slew of related terms: body, organism, unrepeatable, singular, uniqueness, principle, rule, proportion (all these terms having serious meaning in the physical study of complex systems):

5. We must however always keep in mind the truth that every initiative serves true renewal in the Church and helps to bring the authentic light that is Christ insofar as the initiative is based on adequate awareness of the individual Christian’s vocation and of responsibility for this singular, unique and unrepeatable grace by which each Christian in the community of the People of God builds up the Body of Christ. This principle, the key rule for the whole of Christian practice-apostolic and pastoral practice, practice of interior and of social life-must with due proportion be applied to the whole of humanity and to each human being. [21]

Finally, befitting John Paul’s respect and adoration of Mary we find his last and most potent use of “unrepeatable” in describing the truly singular vocation:

6. Not only is the dignity of this Motherhood unique and unrepeatable in the history of the human race, but Mary’s participation, due to this Maternity, in God’s plan for man’s salvation through the mystery of the Redemption is also unique in profundity and range of action. [22]

On Wednesday we had a “day off” from the intense reading schedule. A most awesome fellow from Wyoming Catholic College choir came to teach and play for us a sweeping history of church liturgical music from 800 – 1500 ish. Amazing. There was a period in which entire masses were set to the tune of popular songs. E.g, “The saga of the one armed man” a bizzare song which was all the rage in bars across italy, so you have (and he played them for us) these Kyrie’s chanted to tune of another song. My favorite period was during the so-called Musical Big-Bang when polyphony (many voices singing harmony. Think John, Paul and George in “Shake it up Baby” early Beatles) was rediscovered. A composer called Guillaume de Machaut, who was one of the 1st to be allowed to use polyphony in mass (available from iTunes), instead of Gregorian where all singers keep same voice. He takes the mutiple-voice liberation to such exuberant extremes it’s almost comical. But beautiful.

“I suppose it’s a coincidence…” he said, his voice trailing off, quickly changing subject to something about latest news he read on the internet about Federal bailouts.

The blank spots represent those many which die; computationally speaking they evolve to zero’s everywhere. Many others pair up into yin/yang Adam/Eve dipoles.

You can view a larger sampling of about one hundred of such paired creatures.

This sort of behavior makes you pause. That old saw “Was evolution random or designed?” seems a limited way to phrase the problem. Those two categories, random or designed don’t seem to capture all that is possibly at play. That is, I did not personally set out a plan and design the patterns above. Nor did I just tell the computer to string together random combinations of 1′s and 0′s. Instead I did something inbetween, or outside. I programmed a few simple rules for how cells on a grid would change their value (color). Then let those rules play out. Mechanically. Methodically.

It begins with 8am mass. Eleven priests all crowd at the altar and consecrate the “new beginning.” Even those who doubt such philosophical doctrines as Aquinas’s transubstantiation will have second thoughts watching eleven men intensely whisper prayers into wafers of bread and gold chalices of wine.

Then off to gather for breakfast. I sit next to a philosopher, a chemist, and a nun. The conversation ranges mostly about what “forms” science misses by assuming all is composed of atoms; as well as conversely what princples philosphers might be missing by automatically dismissing as “just a bunch of atoms” the pictures many working scientists have of structures in the world such as brains, cells, etc.

The lunchtime “address” is given by the Vice President and is more like a lecture on Greek morals. It is spectacular. He titled it “Philo and Agon” which invokes two Greek notions/terms/characters: which you might call “love and strife” in our modern terms. He translated as “friendship and arguement” and he argued that both are necessary for a community to survive. He made two good observations:

1) A new ominous myth/trend in our society is that we are being sold the idea that modern life has become so complex that it requires specialized bureaucrats to administer our lives. Worse yet, this Administration will base it’s decisions only upon information and information science, as opposed to say intellectual argument (agon) between friendly (philos) parties of regular citizens.

And his 2nd point I caught (note: I missed much since it moved at philosophy lecture pace)

2) He offered an equation relating the notions of past and future to Catholic religious ideals:

Forgiveness = our remedy to the past’s irreversibility
Promise = our remedy to the future’s chaos and unpredictability

This seems to touch on deep issues in both faith and physics, esp. entropy and chaos and how religion offers some “remedy” to these natural forces. E.g., I can’t change fact you slapped me, but I can forgive you. E.g., I can’t predict how much money I’ll make in 5yrs but I can promise to still love you and buy you food so you can get through school.

Next up was the president’s address. No philosophy here. He had the sober task of telling us how tough the times are for our university, and all universities, given that endowments run most operating budgets. Endowment is a fancy academic term  for lots of stocks and investments. So effectively most universities have seen their revenue stream drop by the same huge percentages as our retirement funds, Dow Jones, etc. His message then was since our job is to teach, we better be the best darn teachers around if we want students to continue to purchase our product. I have to agree.

Odd smell as I enter Fr. Braden’s lab. He is still on campus. Once head of physics dept. Once the president of the university even. Now he is “retired” but comes in every day to so research and writing (both homily’s and scientific thoughts). To give the quick word-picture: White-haired man in priest garb, grinning like a 4yr old child who caught a firefly:

Fr. Braden: Can you smell that!? Ozone!

All week he’d been dusting off this old piece of “equipment”, circa 1880, for storing charges in Lyden jars. Beautiful wooden base. Cherry plank holding silver wheel which spins, metal brushes in odd orientations… and two jars with silver in them.

Fr. Braden: There are only 2 or 3 days a year this works in Southern climates. All other days the humidity is too high.

He starts turning a hand-crank. The wheel starts spinning. Two metal spheres start to sizzle. Then “pow” tiny lightning bolts surge between the two silver balls. Snapping like a whip. A blue jaggy whip.

I ask if I can turn off the lights, to see the bolts better. He likes that idea. It gives him another:

He talks me into holding a fluorescent light tube to one of the jars… sure enough the fluorescent light lit up– no plugging in, no wire, nothing… just the lamp absorbing the “charge” and lighting up on it’s own…

Me: “Cool! it’s just– OUCH!”

The fluorescent tube would light up, then go dark, then light, etc… and I’d get a shock down my hand to foot w/ each cycle. Seeing my yelp Fr. Braden added, in all dry seriousness, as if it was obvious:

Fr. Braden: “Well of course you will feel a small shock as the tube’s plasma discharges through your body and into the Earth.”

Believe it of not for most of history people argued it traveled not from the object to your eye– but from your eye to the object. This seems absurd to us, living in post-Cartesian scientific world. Compared to the heliocentric vs. geocentric battles, this one is lesser known to us.

But I’ve realized that relativity has an interesting take on the question. In relativity, the space-time interval for light is minimal. In the screwy Minkowski metric of 4-dimensional spacetime (which very loosely puts the time dimension as imaginary coordinate axis) the pythagorean distance between two events is:

sqrt[dx^2 - c^2*dt^2]

Which looks like the Pythagorean theorem except that the time signature is negative, -cdt^2. Since dx=c*dt for light, clearly this interval is always zero. In some sense the “path” between object and eye is connected by an interval (in 4d spacetime) of zero length. So the question of which direction the photons travel is moot. The eye and object have zero interval between them as far as the light ray’s journey is concerned. Thus it is just as meaningful (or meaningless) to say light travels from object to eye, as eye to object.

I realize part my point is just taking advantage of some loose semantics in relativity, but I found it interesting.

ps, for a good visual explanation of this “zero” interval along lightray paths, look at Roger Penrose’s wonderful book, A Complete Guide to the Laws of the Universe.

a = v^2 / r

which always seemed a bit odd, it just an obvious consequence of a geometric construction w/ triangles of any circular motion. Here’s webcam shot of my charkboard:

my chalkboard derivation

Bottom line: the triangles swept out by position vector (r) and velocity vector (v) are always perpendicular and similar. So it immediately follows that:

ratio: delta_v / v

is same as

ratio: delta_r / r

Dividing both sides of ration by delta_t gives:

a/v = v/r

or

a = v^2 / r
Q.E.D.

As fun corrollary the a/v = v/r step means that v is the geometric mean between a and r. In more modern notation it means v = sqrt(a*r), or v is the “mean” which harmonizes the lengths a and r. Geometric mean is old greek way of doing means or averages instead of our modern arithmetic mean of adding numbers and dividing by 2. Moderns would say the mean of a and r is (a+r)/2, using arithmetic operation (+/-) instead of geometric operations (viz., multiplication of a and r, then rooting by 2, instead of dividing by 2). My son, Ray, was learning this mean in his freshman highschool geometry class, so I got to rediscover this while helping him w/ homework. How soon we sweep this math under rug to make room for calc and trig.

Perhaps an alternative *definition* of circular motion is: that ideal motion where the velocity is the geometric mean between i) acceleration towards center and ii) distance from center.

- A Latin Mass.

- One of the 10 great experiments in physical science.

I did this week. The usual noon mass at St. Thomas was in Latin today. Ten member choir Gregorian chanting every intercession, response, song and prayer. The priest said the his part in Latin also. It is an amazing slow, downshifted and lovely way to experience a mass.

Afterwards I wolfed some lunch and went to my General Physics lab. The experiment was a classic: The Mechanical Equivalent of Heat. We moderns (including me) not only don’t appreciate Latin, but don’t really appreciate the punch of the Conservation of Energy Law. We really didn’t have it until the 50years from Count Rumford’s famous military research paper on boring cannons (1798) to James Prescott Joule‘s measurement of “J” the equivalence (or conversion factor) between energy units and caloric (calorie) units. In our lab, we actually agitate water with mechanical energy and then measure the resulting heat. Dividing the two gives:

J = 4.186 Joules/cal

And one of my lab groups actually got the accepted value to within 0.05% error !

I’ve been alive about 400,000 hours on this planet. But in those mere 4hours (0.001%?!) I experienced such richness. Bless this new job.