YouTube channel: videos,
Drone footage of cloud forest and jungle habitats in Manú National Park in Peru.
Lectures on video evidence and other information relevant to the conservation of the Ivory-billed Woodpecker.
Drone footage of swamp forests where Ivory-billed Woodpeckers were observed in Louisiana and Florida.
Articles on the Ivory-billed Woodpecker that cover evidence, flights, double knocks, elusiveness, conservation, foolishness, and politics:
“Putative audio recordings of the Ivory-billed Woodpecker (Campephilus principalis),” J. Acoust. Soc. Am. (2011),
“Video evidence and other information relevant to the conservation of the Ivory-billed Woodpecker (Campephilus principalis),” Heliyon (2017),
“Periodic and transient motions of large woodpeckers,” Scientific Reports (2017),
“Using a drone to search for the Ivory-billed Woodpecker (Campephilus principalis),” Drones (2018),
“Statistics, probability, and a failed conservation policy,” Statistics and Public Policy (2019),
“Application of image processing to evidence for the persistence of the Ivory-billed Woodpecker (Campephilus principalis),” Scientific Reports (2020),
The videos may be downloaded in raw digital format from a data archive. Individual files may be downloaded by expanding the drop-down menu under “Data Files” as shown here.
My interest in conservation was inspired by “The Song of the Dodo” by David Quammen, who
mentioned my work on the Ivory-billed Woodpecker while accepting an award from the Audubon Society. Quammen published a prescient article on the coronavirus in the N.Y. Times on January 28, 2020.
“Extinct or Alive” episode about the Ivory-billed Woodpecker on Animal Planet.
Drone video footage that shows the approaching shadow of the 2017 eclipse.
Photos and video footage that were obtained during sea trips to the north of
Norway (2014) and Alaska
(2016 and 2017). Several months of acoustic data were obtained on hydrophones that were deployed during the first Alaska trip. Some audio recordings from under the ice may be accessed through this article.
NFL Power Rankings (1945−2020)
Ivory-billed Woodpeckers in the Pearl River Swamp
In April 2005, the most exciting news in the history of conservation came from the Big Woods of Arkansas, where a group of ornithologists led by John Fitzpatrick announced several sightings of the Ivory-billed Woodpecker in an article that was featured on the cover of Science. It was the first report by ornithologists of this remarkably elusive bird in several decades. The following year, a group of ornithologists led by Geoff Hill independently reported several sightings in the Choctawhatchee River swamp in Florida. There had been many sightings since the 1950s, including David Kulivan’s report of a pair of Ivory-billed Woodpeckers in the Pearl River swamp in Louisiana in 1999, but they usually lacked follow-up sightings or evidence to back them up. The strongest evidence that has been obtained during the past several decades is presented at this website and in articles that may be accessed in the Quick Links section above. I knew that Kulivan’s report was legitimate after hearing the ‘kent’ calls of the Ivory-billed Woodpecker just across the Pearl River in Mississippi in February 2000. In the same area several years later, I found an
unusual pattern of bark scaling that appears to be consistent with the Ivory-billed Woodpecker. Between November 2005 and June 2013, I spent several months per year searching for Ivory-billed Woodpeckers in the Pearl River (and made brief visits to other swamp forests). Most of the searching involved kayaking and hiking through appropriate habitat, but I spent some time observing from tall trees that provide unobstructed views over the treetops. During a five day period in February 2006, I had five sightings, heard kents on two occasions (once coming from two directions at the same time), and obtained video footage of a perched Ivory-billed Woodpecker. A short distance up the same bayou in March 2008, I was keeping watch from one of the observation trees and obtained video footage of an Ivory-billed Woodpecker in flight. While working with Hill’s search team in the Choctawhatchee River in January 2007, I had an encounter with a pair of Ivory-billed Woodpeckers and obtained video footage of a double knock and spectacular swooping flights that are consistent with accounts by Audubon of a flight that is “graceful in the extreme” and Eckleberry of a landing with “one magnificent upward swoop.” The events in the videos show field marks, other characteristics, several types of flight, and other behaviors that are consistent with the Ivory-billed Woodpecker but no other species.
Daily logs for the 2006,
2011, 2012, and
2013 search seasons and for
visits after 2013.
of sightings, sights and sounds from the Pearl River,
photo gallery, and digital artwork.
Cartoons based on the Ivory-billed Woodpecker’s ability to frustrate bird watchers and
supposed need for old growth forest.
Flights of the Ivory-billed Woodpecker
According to the great naturalist, John James Audubon, the flight of the
Ivory-billed Woodpecker is “graceful in the extreme.” This account indicates that there must be something extraordinary about the flights
of this bird, but for many years it appeared that specific details about the types of flights that inspired the account were lost forever.
Since no flights appear in the film that was obtained at one of the last
known nests in 1935, historical accounts were until recently the only information that existed about the flights of the Ivory-billed Woodpecker. Several types of flight appear in
video footage that was obtained
during encounters with Ivory-billed Woodpeckers in Louisiana in 2006 and 2008
and Florida in 2007. These flights may be viewed in the supplemental material of
this paper. Michael DiGiorgio produced the above illustrations of flights (click here for a high-resolution version).
Swooping flights: The spectacular swooping flights that appear in the 2007 video must be the types of flights that
inspired Audubon’s account. As shown in the illustration on the left,
there are upward swooping landings with long vertical ascents that are consistent with a 1944 account by
Don Eckleberry of an Ivory-billed Woodpecker that “alighted with
one magnificent upward swoop.” The closely related Magellanic Woodpecker
has long vertical ascents that are “very similar” to the one in the illustration according to Laura Chazarreta, an ornithologist who has studied and
published on this species. The Pileated Woodpecker typically swoops
upward a short distance before landing on a surface that faces the
direction of approach (as shown in the illustration). A long vertical ascent allows time for maneuvering.
During two of the long vertical ascents in the 2007 video, the bird appears to
rotate about its axis and land on a surface that does not face the direction
of approach (as shown in the illustration). In a film of the closely-related Magellanic Woodpecker in Part 6 of
David Attenborough’s The Life of Birds (BBC, 1998), there is maneuvering during an upward swooping landing with a long vertical ascent. A downward swooping
takeoff that is followed by a long horizontal glide in the 2007 video
is consistent with the following account by Audubon: “The transit from one tree to another, even should the distance be as much as a hundred yards, is performed by a single sweep, and the bird appears as if merely swinging from the top of the one tree to that of the other, forming an elegantly curved line.”
As shown in the illustration in the middle, a woodpecker in the 2007 video takes off and accelerates with rapid wingbeats into a remarkable high-speed upward swooping flight immediately after delivering a blow that produces an audible double knock.
Cruising flight: The Ivory-billed Woodpecker has a ‘duck-like’
flight according to historical accounts, which were widely (but incorrectly)
interpreted to pertain to the wing motion. In the September/October 2005
issue of Bird Watcher’s Digest, the flights of the large woodpeckers are illustrated in a series of paintings by
Julie Zickefoose (an avian artist whose work on the Ivory-billed Woodpecker has appeared
on the cover of a leading ornithology journal). The wings
of the Pileated Woodpecker are correctly shown folding closed during the middle of the
upstroke (this wing motion is apparent in this footage).
In accordance with conventional wisdom at the time, the wings of the Ivory-billed Woodpecker are shown
remaining extended throughout the entire flap cycle. After the 2008 video revealed that the wing motion of the Ivory-billed
Woodpecker is similar to the wing motion of the Pileated Woodpecker (as shown in the right frame of the illustration above),
it came to light that a
photo from 1939 was taken at an instant when the wings were nearly folded closed.
This is one of the lowest quality historical photos, and the clue it provides about wing motion was apparently overlooked for
several decades. The description of a duck-like flight evidently pertained
to the high-speed flight rather than to the wing motion. The bird in the 2008 video has a flight speed of 15.2 m/s, which is well above the flight
speed range of 7.5 to 11.6 m/s that Bret Tobalske published for the Pileated
Woodpecker. The bird in the 2008 video has a flap rate of about 10 Hz, which
is about double the flap rate that Tobalske published for the Pileated Woodpecker. The high
flight speed and high flap rate are consistent with historical accounts,
the narrow wings and high mass of this species, and the predictions of models that relate these
quantities to each other and to body parameters. The wings of the bird in the 2008 video have a swept-back appearance, which is consistent with a
photo from 1935
and the narrow wings and high-speed flight of this species.
The wings of the Pileated Woodpecker do not seem to have a swept-back appearance
during cruising flight.
Other types of flight: According to an account by
James Tanner, the Ivory-billed Woodpecker usually flaps its wings during
short flights between limbs. This would make sense for a woodpecker that has narrow wings and is one of
the most massive in the world. The Pileated Woodpecker has a relatively
low mass and broad wings, and it makes short flights nearly effortlessly.
The large woodpecker in the 2006 video makes a deep and rapid flap during
a flight of less than one meter. According to Zickefoose, this flight is
“unlike anything I’ve seen a Pileated Woodpecker do.”
According to historical accounts, the Ivory-billed Woodpecker has
deep and rapid flaps during takeoffs. This would make sense for a massive
woodpecker with narrow wings. The deep and rapid flaps during a takeoff in
the 2007 video are not consistent with the
flaps during takeoffs of Pileated Woodpeckers but are similar to the
deep and rapid flaps during a takeoff of the closely-related
Imperial Woodpecker. According to Tanner, the Ivory-billed
Woodpecker frequently ‘flirts’ its wings (rapidly opens and closes them).
This behavior would make sense for a massive woodpecker
that uses its wings in order to maintain its balance while moving
around in a tree. In some cases, flirting the wings could be regarded as a type of flight
in which the wings are used for balance rather than to become airborne.
An Imperial Woodpecker (the most massive woodpecker in the world)
flirts its wings in the only 85 seconds of film that exists of that species.
Just before delivering a blow that produces a double knock in the 2007 video,
the bird flirts its wings several times while moving along a branch.
Double Knocks vs Drumming
Most woodpeckers signal with drumming, but the Ivory-billed Woodpecker and some of the other members of the Campephilus genus signal with double knocks. While studying footage in the 2007 video of an Ivory-billed Woodpecker delivering a blow that is accompanied by an audible double knock, I noticed that there appears to be only one thrust of the body. This didn’t seem to be consistent with my expectation that a double knock is the result of two deliberate blows. While studying video footage of a Pileated Woodpecker drumming, I noticed something that led to an understanding of double knocks and how they relate to the drumming that is typical of most woodpeckers. As discussed in Movie S1 of
this paper, the drumming of a Pileated Woodpecker is driven by periodic vibrations of the body, and there are a few additional blows of decreasing amplitude after the driving force is turned off. This suggests that a drumming woodpecker may be modeled as a harmonic oscillator in which the bird is anchored with its feet and tail and the restoring force corresponds to tension in the neck and body. The graph on the above left corresponds to a damped harmonic oscillator in which periodic forcing is turned on at the first dashed line and turned off at the second dashed line. After a brief transient, the response is periodic. After the forcing is turned off, there is a transient that is consistent with the observed drumming of a Pileated Woodpecker. The graph on the above right corresponds to a damped harmonic oscillator with impulsive forcing. The response is a transient similar to the one appearing to the right of the second dashed line in the graph on the above left. This model accounts for (1) the double knock in the 2007 video, (2) the double knock of a Pale-billed Woodpecker that is discussed in Movie S2 of this paper, and (3) the multiple knocks of some Campephilus woodpeckers, such as those of a Crimson-crested Woodpecker in this recording.
In 2007, I started using tall trees to keep watch over much larger areas than are visible from the ground. I was hoping to obtain a video of an Ivory-billed Woodpecker similar to this video of a Pileated Woodpecker flying over the treetops in the distance. The approach ended up working, but not as I had expected. In June of that year, Steve Sillett, Jim Spickler, and Michael Taylor came to the Pearl River to get me started with this approach. In this video, Steve and Jim are rigging a tree that is located a short distance up the bayou from a site where I had a series of sightings in 2006. Less than a year later, I was keeping watch from 75 feet up that tree when an Ivory-billed Woodpecker flew up the bayou and passed nearly directly below. I obtained lots of video footage and images during observation sessions in the trees, which provide stunning views of the habitats. The first step of the approach that Steve and Jim use to rig trees is to shoot an arrow attached to a fishing line over a high branch. I have used the same approach to put Christmas and Mardi Gras lights up in trees. I can still remember my first tree climbing experience, which was around 1963.
Imaging Natural Habitats with a Drone
In 2016, I started using a drone to obtain video footage and
images of habitats where there had been recent sightings of Ivory-billed Woodpeckers. In areas appearing in
this image of English Bayou in the Pearl River swamp, Ivory-billed Woodpeckers were observed seven times in 2006 and twice in 2008; video footage was obtained during encounters at sites on the lower left (February 20, 2006) and near the center (March 29, 2008). In areas appearing in
this image of the Bruce Creek area in the Choctawhatchee River swamp, Ivory-billed Woodpeckers were observed several times between 2005 and 2007 (one of the sightings was by an ornithologist); video footage was obtained during an encounter with a pair of Ivory-billed Woodpeckers near the center of the image (January 19, 2007). I have also used a drone to obtain video footage of
cloud forest and jungle habitats in Peru (the above image was obtained near Rio Madre de Dios),
the approaching shadow of the eclipse of 2017,
the Hillsborough River swamp in Florida,
fireworks on the 4th of July,
an Easter egg hunt,
autumn colors in the Appalachians,
Palisade Falls in Montana,
the Pennsylvania towns of Greenville and
and the Virginia town of Radford.
12,500 Mile USA Bird Watching Trip — Spring 1997
In the spring of 1997, I did a 12,500 mile (the distance between the North Pole and the South Pole) birding watching trip around the USA and partially into Canada.
This report contains a day-by-day account of the locations that were visited (marked on the map above) and the birds that were seen.
These reports contain accounts of some of my other bird watching trips. I started in Virginia on May 3 and headed south to Florida; then west through Louisiana, Texas, and Arizona; north through New Mexico, Colorado, Wyoming, and Montana; back to the east through North Dakota, Manitoba, Minnesota, and Michigan; and finally back to Virginia on June 13. I did the trip in my 1979 Ford Fairmont two years after rebuilding its engine. By sleeping in the car, I saved money and woke up most days near prime areas for birds. The trip cost about $800 in gas and less than $500 for food, day-use fees, and other expenses. Two of the highlights of the trip were my first visit to southeastern Arizona and seeing a Connecticut Warbler singing in its breeding territory. On a typical day, I looked for birds from before sunrise until after sunset, drove several hundred miles between sites at night, slept for a few hours curled up on the front seat, and repeated this the next day. I lived off cereal with water, juice, granola bars, raisins, junk food, and adrenaline. I had a great time while seeing 383 species of birds and lots of gorgeous places.
Wave Propagation in Geophysics and Planetary Physics
For many wave propagation problems in geophysics and planetary physics, it is necessary to take into account the fact that the medium varies in the horizontal directions. In the ocean acoustics example on the above left, the bathymetry varies in the horizontal direction. In the seismology example on the lower left, the topography and thicknesses of layers of different types of rock vary in the horizontal direction. In the Jovian acoustics example on the right, the zonal winds vary with latitude. Such problems cannot be solved with analytical methods (separation of variables), and they are often too large to be solved directly with numerical methods. When the horizontal variations in the medium are sufficiently gradual, accurate solutions may often be obtained efficiently by applying a parabolic wave equation, which accounts for energy that propagates in the outward horizontal direction (energy that is backscattered toward the source is neglected). This approach and some of its applications are described in
Parabolic Wave Equations with Applications.
Peruvian Amazon — June 2019
In June 2019, I visited Manú National Park in Peru and obtained lots of
photos, video footage, and audio recordings. I stayed at Cock-of-the-Rock Lodge on Manú Road in the cloud forest and Amazonia Lodge near Rio Madre de Dios in the lowland forest. I used a DJI Phantom 4 Pro drone to obtain video footage and images of the forest habitats and a Sony PCM-D100 to obtain audio recordings.
Peruvian Amazon — July 2003
In July 2003, I visited the Peruvian Amazon and Machu Picchu. I entered Manú National Park with a small tour group and visited Huarcapay, many areas on Manú Road, Amazonia Lodge, the river below Atalaya, and Pantiacolla Lodge. Despite having problems with my camera, I managed to get some fairly good photos such as the one above of a Golden-headed Quetzal.
Rio Marañon — April 2000
In April 2000, I made my first trip to South America. After attending a conference in Trujillo, Peru, I rented a car and drove over the Andes and into the jungle. One of the highlights of the trip was getting my first view of the Amazon River (the Rio Marañon branch) as shown in the above photo. I had an unnerving encounter with natives in the jungle, but it was an amazing experience to get my first taste of the Amazon and see stunning birds such as the Paradise Tanager.
This report contains an account of the trip and the birds that were seen.
Iguazu Falls — July 2002
In July 2002, I obtained some photos at Iguazu Falls, which are the largest in the world by flow rate. They are located in
the border region between Argentina, Brazil, and Paraguay. The falls and
surrounding tropical forest are one of the most beautiful places in the
world. Watching the water thunder over the falls in the Garganta del Diablo (Devil’s Throat) is a stunning sight. This report contains an account of the trip and the birds that were seen.
Alaska Sea Trip — Fall 2017
During the fall of 2017, I participated in a sea trip to the north of Alaska and obtained lots of
photos and video footage. The videos may also be accessed in
this playlist on YouTube. The trip began in Dutch Harbor on October 18 and ended in Seward on November 8. This map shows the trip back to the south.
I obtained photos of the aurora from the ship with a DJI Osmo+, a camera with a gimbal that can be used for long exposures on a moving platform. Among the highlights of the trip were observing sea ice, the auroras, and the amazing flights of albatrosses, going through the Unimak Pass, and seeing for the first time the Alaska Peninsula, Kodiak Island, the Kenai Peninsula, Seward, Denali, and Anchorage.
This image of an apparent Ivory Gull is from the 11:44 mark in this video (the bird is flying from left to right near the top edge of the picture).
Alaska Sea Trip — Fall 2016
During the fall of 2016, I participated in a sea trip to the north of Alaska and obtained lots of
photos and video footage. The videos may also be accessed in this playlist on YouTube. As shown on this map, the trip began in Nome on October 15 and ended in Dutch Harbor on November 11. Most of the trip was above the Arctic Circle, and we got up to 75° N. Some of the highlights of the trip were a Gyrfalcon, an Ivory Gull (see the above photo), and twenty-one Ross’s Gulls that were in migratory flights to the west. Some of the video footage was obtained with a DJI Phantom 3 Pro drone, but it was usually too windy for it.
Norway Sea Trip — Winter 2014
During the winter of 2014, I participated in a sea trip off the coast of Norway and obtained lots of
photos and video footage. The videos may also be accessed in
this playlist on YouTube. As shown on this map, the trip began in Ålesund on February 18 and ended in Tromsø on March 9. Most of the trip was above the Arctic Circle, including several days above the northernmost tip of Norway up to nearly 72° N. Only a few people went ashore during a brief stop at Honningsvåg, but it was interesting to see that town from the ship. The video footage was obtained using bino-cam, which consists of a video camera mounted on binoculars. The binoculars provide a better image than the viewfinder and make it easier to get the camera on a bird. I saw a gull that seemed different from all of the common species that were seen regularly during the trip and suspected it was an Ivory Gull while watching it through the binoculars. It was exciting to see flocks of alcids with stunning Arctic scenery in the background. I never got tired of watching fulmars in flight. The northern lights were indescribably amazing on some nights, with some of the glowing green arcs passing directly above and extending from one horizon to the other.
Cruise to Alaska — May 2014
During the last week of May 2014, I obtained lots of photos and video footage during a sea cruise from Seattle to Alaska with Holland America.
The videos may also be accessed in this playlist on YouTube. I saw lots of seabirds during the transit from Seattle to Juneau, including several Black-footed Albatrosses, lots of Leach’s Storm Petrels, a few Fork-tailed Storm Petrels, several unidentified Shearwaters (some with white underwings and some with dark underwings), and many alcids. I saw lots of whales and other sea mammals at various points during the trip. My favorite part of the trip was going up Mt. Roberts in Juneau and seeing Rock Ptarmigans. I was expecting the ptarmigans to be in breeding plumage and was initially taken aback by the stunning white plumage. I heard one of them calling and the video shows the field marks well enough for positive identification. I was amazed by the flight and rapid bursts of wingbeats of that species. It was difficult to track a pair through the viewfinder of the video camera as they passed in front of patches of snow during a meandering flight. There was an amusing photo-bombing by a Bald Eagle during the filming of a singing Fox Sparrow. I was blown away by the beauty of Glacier Bay. It was the first time I was able to really study the Arctic Tern. I was amused to see a Black-legged Kittiwake resting on a small iceberg.
Eclipse — August 2017
I watched the eclipse of August 21, 2017, near the Boysen Reservoir just to the north of Riverton, Wyoming. My primary objective was to film the approaching shadow with a drone, but I brought along a Sony HDR-HC5 video camera. Since totality would last for only a few minutes, I decided on a plan that would allow me to start the drone and video camera and then focus on enjoying the spectacle. Ten minutes before the start of totality, I launched the drone and left it hovering at an altitude of 120 meters. Immediately after the start of totality, I aimed the video camera at the Sun and left it recording from a tripod. As I had hoped, the
drone video shows the approaching shadow. I have never seen a film that really captures the splendor of how an eclipse appears to the eye, but the other video might have been better if I had taken the time to adjust the exposure and zoom. During the partial phases of the eclipse, there were obvious drops in temperature and light, as illustrated in these photos.
Mardi Gras Parades
Many of my visits to Louisiana have coincided with Mardi Gras, which occurs during the most favorable months for searching for the Ivory-billed Woodpecker. In 2013, I obtained video footage of the Endymion and
Zulu parades in New Orleans. In 2019, I used a drone to obtain video footage of the
and Slidellians parades in Slidell. I also obtained video footage of some ingenious
Louisiana Pelican Art in Slidell.
Road Trip to Montana — August 2019
In August 2019, I obtained lots of photos during a 5000 mile road trip to Montana that included visits
to the Badlands, Black Hills, Yellowstone National Park, Grand Teton National Park, Wind River Canyon, North Platte River, and Iowa State Fair.
Arizona — June 2015
During a visit to Arizona, I spent a day each in the Chiricahua and Huachuca Mountains in
the southeastern corner of the state and also visited Monument Valley and
Petrified Forest National Park. Some photos of the
gorgeous scenery are posted here. I had a bit of an adventure during a hike around Carr Peak. On the
way up a steep trail to Bear Saddle, I got severe cramps in my thighs and had to use up most of my fluids in order to stop them. I was
beyond the half-way point of the hike and decided to keep going. When the trail got steeper and the cramps returned, I decided to turn
back. The trail ahead was uncertain, and I knew there was a stream with water on the way back. I wouldn’t have
made it out of there if not for that stream.
Colorado — June 2014
I spent several days in Colorado at the end of June 2014. I obtained photos and video footage of flowers and the glass artwork of Dale Chihuly at the Denver Botanical Gardens and of wildflowers, wildlife, and scenery in the mountains in Golden Gate Canyon State Park and Rocky Mountain National Park.
1000 Islands — August 2015
In August 2015, I took a cruise out of Kingston, Ontario, that
sailed through the 1000 Islands and made stops at Upper Canada Village,
the observation tower near the international bridge, and
other locations. Some photos are posted
The Fourier Engine
I’ve always been fascinated by mechanical objects, such as the internal combustion engine. When I was twelve, I took apart and reassembled a lawn mower engine. In my late teens, I developed an interest in Volkswagen engines, such as the one appearing in the above photo from 1979, which powered a 1966 Beetle that I used to drive back and forth between Florida and Massachusetts while attending MIT. After learning about Fourier series, I came up with an idea for a new type of internal combustion engine that might make it possible to increase power by modifying the volume curve so that the duration of the intake and ignition strokes exceeds the duration of the compression and exhaust strokes. In
the Fourier engine, each combustion chamber is open to multiple pistons that operate at different rates. Different choices for the displacements and phases of the cylinders correspond to different volume curves.
Appalachian Colors — Fall 2020
In October 2020, I used a drone to obtain images of the autumn foliage in the Appalachians of Virginia, North Carolina, and Tennessee. The images may be viewed in high resolution here and in a slideshow here. This project nearly came to an end when I crashed the drone into a tree. As can be seen in this image, however, I was very fortunate that small branches gently caught the drone with no damage other than a broken prop.
Installing a Metal Roof — May 2020
Starting at the age of 15 in 1973, I spent several years doing construction work, including building fences (such as
this one at my mother’s house in Tampa as shown after a rare snowstorm in 1977) and swimming pools (such as this one, where I’m dumping a wheelbarrow in 1977). At the age of 62, I helped out in a type of construction work in which I had no previous experience — installing a metal roof. As discussed here, it was interesting to see some of the problems that can arise in roofing and how to deal with them.
Solving Puzzles with Group Theory
I didn’t have much interest in Rubik’s Cube when it first came out, but then it occurred to me that it’s a fascinating application of group theory. It was 1982, and I had recently been introduced to that topic in an algebra class at MIT. It didn’t take long to figure out how to solve it using commutators, conjugates, and the cycle notation. I was hoping that someone would generalize it to the dodecahedron. Such a puzzle, which is known as the Megaminx (shown above), was already available at the time, but I didn’t find out about it until decades later. I have posted a lecture on
solving puzzles using group theory. FORTRAN codes for solving these puzzles on the screen are available for download.
Buffalo Nickel Population Model
My grandmother got me interested in coin collecting in the early 1960s. My favorite coin was the Buffalo Nickel (1913–1938), which was rapidly disappearing from circulation by the mid 1960s. In order to gain insights into the variation over time of the population of Buffalo Nickels in circulation (relative to the total number of nickels of all designs in circulation), I used a simple model in which 4% of all nickels disappear from circulation each year. I used the number of nickels produced each year since 1866 as inputs to the model. There is uncertainty in the attrition rate, which would be expected to vary with time (e.g., attrition increases as a design becomes rare and gets pulled from circulation at a higher rate). I decided to terminate the above graph at 1964, when the interest in coin collecting increased with the introduction of the Kennedy Half Dollar and the end of 90% silver coins. The prediction of a rapid decrease in Buffalo Nickels during the early 1960s is consistent with my experiences as a collector during that period. I also applied the model to all four nickel designs (Shield, Liberty Head, Buffalo, and Jefferson) and the Indian Head Penny (1859–1909), which I never found in circulation.
Photos from the Four Corners area
Photos from Big Bend National Park
Photos from Yellowstone National Park
Wakefield Park: A Hotspot for Mourning and Connecticut Warblers
Venus transits the Sun (June 8, 2004)
Radford High School Basketball