Fides et Fig Trees

A priest down here showed me a giant thriving fig tree. He said a few years back the tree was dying, so one evening he poured upon it some holy water from Lourdes France. He does not believe in any of this nonsense about holy water vis-a-vis healing. But he thought he’d do it, on a whim one late evening in dark courtyard of the Basilian fathers residence. He admits he is very puzzled how it resurrected a dying fig tree, and even made it grow huge, bursting w/ juicy figs.

“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.

2d creatures

Order seems limitless. I’m messing w/ some cellular automata. Below is snippet of different “creatures” which arise:

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.

Philo and Agon (Peace and War)

St. Thomas formally begins each semester  with a “Faculty Study Day” where all professors officially arrive on campus and begin the semester. Even though most of us have been working already prep’ing for classes this formal start is fun.

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.

Fr. Braden on a shockingly cool, dry day in Houston

Grading lab notebooks… Thursday morning… very boring… Then I hear out in the hall a sound like sparks… like electrical equipment is exploding… I go out to hall.

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.”

Which way does light travel?

How fast does light travel? This question is not nearly as old the more fundamental question: Which way does light travel?

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.

Circular motion (for Greeks)

I’m really thinking of writing (someday) a retro physics textbook for greeks. No trig. Just similar triangles, etc. Doodling w/ circular motion, and some old text I put together a few things. E.g., the centripetal acceleration:

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.

High Mass and Energy

How many places in Houston– let alone the planet– can you experience in a 4hr span:

- 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.

Kepler’s laws and Atwood machines

Had great weekend. Saturday afternoon I “proved”
Kepler’s harmonic law from Newton’s laws and Euclid’s geometry (similar triangles crucial). Quite a pump to my ego. My brain felt like a stallion!

Last night I went on to other chapters, which had these problems with pulleys and weights on pulleys. I spent all night and couldn’t solve a simple pulley! My brain struggled– how could this simple machine be more complex than the solar system!!! (Atwood machine: 2 masses on pulley, where the pulley itself has a mass and moment of inertial so problem isn’t totally trivial). I finally solved it at 1am, and realized how beautiful this machine really is. It’s supposedly how/why elevators in buildings work, among I imagine 100’s other machines going back to Alexander and his armies, etc.