Friday the 13th — Be Forewarned

This winter season has been unseasonably pleasant…until today. Last night we went to sleep with the sound of the wind howling through the wooded ravine behind our house. This morning we awoke to perhaps a couple of inches of wind driven snow and much cooler temperatures. The first real winter weather of the season had restrained its appearance until the 13th day of the New Year. I know that it is just a coincidence that today is a Friday but “Yikes!!!” you might say, “It’s Friday the 13th!”

Yes, it is. A day, just like any other day except that in some culture(s), possibly including even our own very sophisticated culture here in the United States, both the number and the day are considered unlucky. There is a great deal of folklore surrounding this unlucky day, so much so that Jean Meeus apparently devoted a chapter in his book “Mathematical Astronomical Morsels III” to it entitled Friggatriskaidekaphobia — Friday-thrirteen-fear. While I have not read the book, it is referenced in the 2012 Astronomical Calendar by Guy Ottewell which I do read often.

The Astronomical Calendar points out that there are actually three occurrences of Fridays the 13th this year, the others being in April and July. These dates are the 104th and 195th days of 2012 respectively, perhaps making 2012 extraordinarily unlucky. “Why is that?”, the curious might ask. It is that this year, the Fridays the 13th are 13 weeks apart.

You have now been forewarned…good luck in 2012.

Of Pond Scum and Wall Street Bankers

I woke up at 3:00 in the morning a couple of weeks ago and couldn’t get back to sleep. I was thinking about biodiversity and beyond. This has happened to me a number of times since I read an article earlier in the millennium entitled “The Forest and the Trees: Romancing the J-Curve” by A.K.Dewdney. in The Mathematical Intelligencer (Volume 23, Number 3, 2001, pp 27-34) . The unfortunate consequence of reading that article is that the more I think about it, the more I am drawn into it and the problem expands into deeper and more far reaching questions about the complexity of the world. After some time I reach an impasse…some limit to my ability to comprehend it, some limit to the amount of time I can spend on it…some limit and I move on without resolving anything. It is at the same time both intriguing and frustrating. Now here it was again. This time I got up and wrote down a couple of simple experiments I could do to help me look at it again. I hope to describe the experiments and results on my website at http://amateurgeophysics.wordpress.com in the future.

If you think about an ecosystem, say a pond or a woodlot, you might think about all of the species that occur there and how many individuals represent each of those species. You would realize that there were more individuals in some species than in others. If you have some basic statistics in your background you might visualize something like a normal distribution, a bell curve, of species abundances with a mean and standard deviation…many species having an average abundance with some having more and others having less. At this point you would be wrong.

What you would really see is a distribution with many species having low abundances and a small number of species with great abundances. The rest would fall somewhere in between. This histogram is what Dewdney calls the J-Curve. While Dewdney spends a lot of time pursuing the best mathematical function to fit to biodiversity data, two aspects of this “J-Curve” capture my attention and lead me elsewhere. First is the simple ecosystem model that Dewdney describes which when run on the computer yields a “J-Curve” species-abundance histogram. His model is one of mutual predation among species with predator and prey being selected at random. “Well,” you might say, “that is not a real system!” to which I respond that no model is a real system. Models are created to help you think about a real system and that is exactly what Dewdney’s model does. It will form the basis for one of my experiments.

The second aspect of this “J-Curve” is that it falls into the class of power law  distributions having the same general shape that shows up in many diverse applications. From what I read, actually proving a fit to some power law is difficult but for me that is secondary to the ubiquitous occurrence of the general trend of the histogram. Power law distributions describe situations in which small events are common while large ones are quite rare. A few examples of possible power law distributions:

• In ecosystems, a few species have high abundances while many have only a few members.
• There are many villages with small populations but only a few very large cities.
• A few words show up many times in a large document while many words show up rarely.
• Small earthquakes are quite common whereas the largest ones are quite rare.
• Financial wealth is disproportionately held by a small number of people relative to the great masses of poor.

Aside from the observation that certain species found in pond scum and Wall Street investment bankers may occupy the same part of their respective distributions, what underlying features and drivers can cause such a diverse range of naturally occurring phenomena to all show this kind of distribution? And what are the implications that these distributions apparently result from stochastic processes? Do we live in a mostly random world over which we have little control? While there are many deterministic processes in the physical world, I think this might be more true than most people want to admit. I think that Dewdney’s simple model will suggest that, contrary to what the Occupy Wall Street movement would like to believe, even if the nation’s wealth was evenly distributed among the people, after some period of time the wealth would naturally return to its current uneven distribution. Some species are going extinct? Yes, that would be expected looking at the J-Curve species-abundance histogram. I suspect that we cannot change either of these examples any more than we can change the distribution of earthquake magnitudes.

This is the kind of thing that, every so often, keeps me awake at night!

Climate Change??

The photograph shows an iris blooming on November 10 in northeastern Ohio. Climate change? Maybe, maybe not.  Individual and isolated observations are not valid indicators of anything.  Will this become the new normal sometime in the future?  Certainly we have had an unusually warm and wet autumn. And an iris blooming in November is pretty unusual right now.

 

The October issue of Physics Today has an article by Steven Sherwood titled “Science controversies past and present – Reactions to the science of global warming have followed a similar course to those of other inconvenient truths from physics”  comparing the present state of acceptance of climate change to that of the Copernican heliocentric model of the solar system and Einstein’s general relativity. His conclusion: “… history tells us that, in the end the science will probably come out fine. Whether the planet will is another matter.” The article is available on line and is an interesting read.

 

Time again…

Grandfather's clock (this one really is)

I may think about time more than the average person. It is not uncommon to be going about my ordinary daily activities when something as common as a wooded ravine or a cicada’s song will remind me of how narrow and limited our human perspective of time is. This year that seems to be happening a lot.

When my mom died this spring, I looked around the hospital room and realized that I knew her longer than anyone else there except my dad. She was ninety one years old. She grew up in a tiny town in southeastern Ohio and used to tell of Mrs. Barnes, the old woman who live next door to them. Mrs. Barnes told a story about a native American Indian coming up through a hole in the floor of their cabin when she was a little girl. Now I admit that this could have been a tall tale that Mrs. Barnes told the little neighbor girls or that it changed (for the better) over years of retelling but it still reminds me of the changes that have taken place in just two or three human lifetimes.

Earlier this summer I noticed in my Astronomical Calendar that as of July 12th, the planet Neptune has just completed its first complete orbit since it was discovered in 1846. That was only 165 years ago but that is one Neptunian year…two human lifetimes.

Those examples are both from modern history. The ancient history of human development in the middle east may span only 5000 years and of other people perhaps 20,000 years or more. Those pale in the light of geological time, of hundreds of millions of years, during which the continents drift around the surface of the Earth crashing into each other, raising up mountain ranges that then erode away and species evolve, proliferate, and go extinct long before anything resembling a human being even exists.

The largest period of time for which we have a common formal time-keeping device, is the year with its associated calendar. I guess that helps us keep our appointments and remember important dates in our lives.

But it is not very useful in helping us think about time…

Columbus Day, 2011

After lunch on Monday, my dog and I took our daily walk down the lane to get the mail. She went off to check the groundhog holes in the woods by the pond. I continued down the lane to the mailbox. I crossed the road and opened the mailbox. Empty. Not even my weekly invitation to subscribe to Dish Network or Direct TV. Then I remembered. No mail delivery today. It’s Columbus Day!

On my walk back to the house, empty handed, I thought about what a ridiculous holiday Columbus Day is. Five hundred nineteen years ago, more than half a millennium, Columbus and his little band landed in India. Well not quite. Instead they had discovered a new world! Well not quite. To his credit they had embarked on a voyage into the unknown. There was some fear that they might sail off the edge of the world in the night and be lost forever. But there have been a lot of other courageous explorations in history that are not honored by a special holiday…Is Columbus the best example we can find in the last five hundred years?

The dark side of his landing was the beginning of the extermination of the native people already living here that would last for…five hundred years. Is that part of the celebration too?

My first thought was that Columbus Day was an anachronism, a holiday from another era that should be discarded. After all, most of us don’t even think about Columbus Day, until we check our mailboxes. My second thought was to keep it, with the same name, as a day to reflect on our current national actions. To ask ourselves whether the things we do that are so courageous today are in fact cruel, exploitative, demeaning, destructive to other cultures and worldviews…and maybe even to ourselves.

Mathematics, Beauty, Mystery, Spirit

I had a co-worker, a young engineer, many years ago who designed turbines using a modeling method called finite elements. Computational fluid dynamics is not a field for the mathematically challenged. These mathematical methods would produce models describing pressures, velocities, mass flow, etc. of fluids, in this case air, within the turbine. Those values allow the engineer to ultimately predict how much power could be derived from the turbine. Very utilitarian, just a means to an end, you might say.

Yet on more than one occasion, this engineer would talk at length about the beauty of mathematics. I was reminded of this the other day when I analyzed the recording of the sound of an agricultural aircraft making a seeding run over a field near our house. The recording converted the sound at the microphone into a sequence of numbers representing the pressure fluctuations as a function of time. In my analysis, I load the sound file, the list of numbers, into a computer program called Raven Lite which converts the first list of numbers into an array of other numbers representing the frequencies of the sound as a function of time. The conversion is made mathematically using Fourier methods. The output of the analysis shown in the image above is, in my opinion, visually beautiful. The family of smooth curves, the subtle shadings, and variation in color representing the amplitude of sounds at different times and frequencies combine to elicit an emotional response in me when I look at it. (here is a description of what it means) And beneath the visual surface there is the beauty of the logic, the methods, the rigor, and the universality of mathematics itself.

But still deeper is the mystery of a natural universe that is so ordered that it can be described by mathematics, in fact giving rise to the whole human idea of mathematics in the first place. And the mystery that phenomena as disparate as swinging pendula and electrons coursing through certain electronic circuits can be modeled using the same basic methods…and that those models will work on a planet a million light years away as well as they work right here on earth. In my world view, those mysteries extend deep into the world of the spirit.

My co-worker understood that even though he would not have used those words…

Another Downpour

It was a little cool today so I was working inside. I heard some noise in the backyard and looked to my right to see it raining there. When I looked to my left out the north window it wasn’t raining. Within a few seconds the heavy downpour moved over our house and into our north yard. Within a few minutes we had close to a quarter inch of rain. Many large drops falling vertically. It was gone as quickly as it had begun.

This is the soggiest spring I can remember for some time. The nearest weather service office at the Akron-Canton Regional Airport shows the total precipitation for the year so far to be 27.89 inches. The normal there through June is 18.82 inches.

There are parts of our yard that I have not been able to mow yet…just too wet. Some people are complaining.  Not me.  I am glad that it is raining…and not snowing.

This is for the birds…

We have been enjoying the birds this spring. Several weeks ago I walked 600 yards or so out into a soybean field to a drainage way to service an instrument platform that I use in my research. Just as I got to the instrument I was buzzed by some creature several times. It seemed too large for an insect but I couldn’t see it because it was so fast. Finally I was able to see it just as it landed on the branch above me…a hummingbird. I’m not sure what caused its behavior but after that initial attack it was content to sit on the branch and watch me work.

A week or so after that my wife and I were bicycling on the Holmes County Trail north of Millersburg when I spotted a Trumpeter Swan with a neck collar in an encounter described here. I submitted a report online but haven’t received any information on the banding location yet.

Closer to home, we have a wood thrush singing in the morning and evening down in the woods behind our house…in my opinion, one of the most beautiful bird songs. We also have Eastern Towhees and phoebes singing clearly throughout the day and Carolina wrens singing from our deck railings. Bluebirds are nesting in our backyard boxes and sit on an old grounding wire attached to the deck that rattles whenever they take off. Two flickers are active in the backyard as I write. Yesterday, a Baltimore Oriole made his appearance and, as a matter of fact just now, flew through the woods chasing another bird. A pair of yellow warblers were looking for bugs in the same tree.

The Barred Owl in the photograph flew up out of the ravine a few weeks ago in the middle of the day. I took one photograph through the deck railing before he saw me and returned to the deeper woods. Two days ago, I heard several crows coming through the backyard as I was working on the deck. I looked down on the crows as they chased a Barred Owl across the yard.

A barn swallow swooped around me as I was mowing on Monday reminding me of the joy they will bring later in the summer when I clip the pastures.

My sister-in-law considers birdwatching to be something that old people do. That’s her loss. I have enjoyed watching the birds since I was young and still do. And will continue to when I get old!

Clean Energy

Leah and I have made a Mother’s Day trip to western Lake Erie for the past several years. This year we went the weekend before the actual holiday. Our usual path is to drive up to Marblehead, visit the Lakeside Daisy preserve, drive through Lakeside, finally stopping at Port Clinton for a Lake perch lunch. We did all of those things but this year continued westward along the lake out to Crane Creek and Magee Marsh wildlife areas. The route takes us past all of the things that we associate with the lakeshore…lots of marinas, campgrounds, trailer parks, shacky little shacks, and large, expensive condominiums and vacation homes. These things are all transient. We drive by and they are gone. The exception is the Davis-Besse Nuclear Power Plant. Situated right on the lakeshore its cooling tower and associated vapor plume are visible for tens of miles in all directions.

Nuclear fission reactors are often touted as our best long term clean energy source. I am skeptical, as usual. While they are carbon free, they are not clean. They generate waste that will be dangerous for ten thousand years. Ten thousand years is a long time…ten thousand years ago, the last great ice sheet was receding from northern Ohio. I am not afraid of radioactivity. When I was in school, I worked in radioactive environments, creating short-lived isotopes in a subcritical reactor, performing scattering experiments with a small particle accelerator…not fearful but respectful of it. Ten thousand years is a long time…

Power reactors are complex operations. Pumps, motors, sensors…people. They all need to work reliably. Most of the time they will but every so often multiple, unexpected combinations of failures show up that can develop into a real bad situation. That happened in the Japanese nuclear power plant after the Great Earthquake and tsunami. An unusual situation to be sure but I wonder what an EF-5 tornado would do. I am sure the designers thought about that but I wonder if they are thinking about it again after the Japanese reactor failures.

I am not opposed to nuclear power but I am skeptical. Again, there are proponents, the “True Believers” and there are opponents the “Non-believers”. The truth is somewhere in the middle between them. In the end, the cleanest energy is the energy we use most efficiently…we waste a lot, as witnessed even by the vapor plume blowing off the Davis-Besse cooling tower.

Smoke Pit Maple Syrup

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Last Sunday after church Gary said they were going to start boiling sap on Monday and invited me out to see their sugar bush. He started making maple syrup in small batches a couple of years ago. A few other guys in the church got interested and they decided to build a sugar bush. They designed and built the evaporator and the supporting equipment using an old wood stove, mostly scrap metal and re-purposed dairy equipment.

The syrup can be had for a donation to their projects in Honduras.