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Saturday, May 20, 2017

Angling Mathematics: Fishing For Complementary Angles

      Our late-spring trip along the North Platte River from Waterton Canyon to Deckers, Colorado, and on to Wellington Lake, was filled with angles and anglers. According to the link cited above, 

  "There are physical properties associated with the bending (refraction of light) which have significant effects on what a trout could possibly see.  The trout’s world consists of a window, the diameter of which is determined by a thing called the Snell’s equation."

    "In simple terms the window is 2.26 times as wide as the trout is deep. So it can clearly see things on the surface over a wider area the deeper the fish is. At one meter the fish can clearly see things on the film in a 2.26 meter wide circle above its head."

      "Many angling writers have made much of this, because a relatively small increase in depth radically changes the size of the window. At 0.5 meters the window has a diameter of 1.13 meters, but at a depth of a meter that window grows enormously to 2.26 meters across. If you take the area of the window the results are all the more dramatic. At 0.5 meters depth the area of the window is 1 square meter, at one meter in depth that window jumps to 4 square meters. Double the depth and you effectively quadruple the size of the window."

      Ah, look at this sky window near Wellington Lake.

       The term angler derives from one who uses an "angle, or, originally "angel," i.e., fishhook for fishing with a line.

     A bit of both angles and angels might be involved in angling mathematics.

       Much better angling earlier in the week than on May 18 during the intense Colorado snowstorm. . .

      Big flakes abound in Colorado this month ;-).

      Are you an angler?

Fishing for complementary angles,

Monday, May 8, 2017

Birdsong and Creativity: Songbirds Name Their Offspring!

      The vocal learning of songbirds is the subject of much ornithological research. Did you know songbirds name their offspring, who are called by that specific sound all their lives? (I wonder if they have middle names, for when they're in trouble. . .)

      Nearly half of bird species are songbirds. They learn songs from a mentor, like humans, and then practice the melodies.

      The baby songbirds learn "grammar and syntax" from these mentors, who are often, but not always, their parents. The songbirds' use of different tweets (the original, non-140-character kind) is more complex than the signals (or typings) of monkeys. 

       According to this bird-brained article, "New neurons grow in breeding and singing season and then die back to save energy. A signal of the dying cells stimulates the new cells."

       "Songbirds prefer singing in harmonic series similar to humans even though anatomically they could sing many other ways. They choose to sing in a particular key and with consonant intervals, octaves, fifths, and fourths like humans. Songs are used for mating and defending territory."

       The study of birdsong is a delicate balancing act. And the study of bird brains (especially songbirds vs. birds like chickens) compared to humans and monkeys is even more complicated.

       Songbirds have more interconnectedness and feedback loops comparable to the parts of the human brain, especially the striatum. Study of songbird chromosomes adds both to the complexity and understanding.

       Zebra finches are useful in understanding how birdsong phrases are learned and how they can be changed and analyzed.

        Of course, you can just listen and enjoy Birdsong, too. This recording was made at daybreak along the Mississippi River near Birdsong, Arkansas, population 41. Temporarily 42. . .

      Be glad and sing out if someone calls you a Songbird Brain! Tweet about it ;-). 

     And this goes right here. . .

"Ah" would be better. . .but close enough.

Sunday, April 30, 2017

Gaiman, A Fun Guy, on Beatrix Potter, Science, and Art: You Can't Have One Without the . . . Others

         The scientific illustration of mushrooms and other fungi by Beatrix Potter, children's book writer and mycologist, is part of the inspiration for a poem by Neil Gaiman, "The Mushroom Hunters."

        The blending of science and art is described in Gaiman's poem, which begins:

      "Science, as you know, my little one,
is the study
of the nature and behaviour of the universe.

      It’s based on observation, 
on experiment, 
and measurement,
and the formulation of laws to describe the facts revealed."

     "The Mushroom Hunters" is read by Amanda Palmer in its entirety here.

      Mushrooms, which are closer to animals than plants in their origins, are both mysterious and mundane. The poem continues (after a break):

      "Before the flint club, or flint butcher’s tools,
The first tool of all was a sling for the baby
to keep our hands free
and something to put the berries and the mushrooms in,
the roots and the good leaves, the seeds and the crawlers.

      Then a flint pestle to smash, to crush, to grind or break.

      Some mushrooms will kill you,
while some will show you gods
and some will feed the hunger in our bellies.


      Others will kill us if we eat them raw,
and kill us again if we cook them once,
but if we boil them up in spring water, and pour the water away,
and then boil them once more, and pour the water away,
only then can we eat them safely. 


Observe childbirth, 
measure the swell of bellies and the shape of breasts,
and through experience discover how to bring babies safely into the world.

Observe everything.

And the mushroom hunters walk the ways they walk
and watch the world, and see what they observe.

And some of them would thrive and lick their lips,
While others clutched their stomachs and expired.
So laws are made and handed down on what is safe.


The tools we make to build our lives:
our clothes, our food, our path home…
all these things we base on observation,
on experiment, on measurement, on truth.

And science, you remember, is the study
of the nature and behaviour of the universe,
based on observation, experiment, and measurement,
and the formulation of laws to describe these facts.

The race continues. An early scientist
drew beasts upon the walls of caves
to show her children, now all fat on mushrooms
and on berries, what would be safe to hunt.

      The men go running on after beasts.

      The scientists walk more slowly, over to the brow of the hill and down to the water’s edge and past the place where the red clay runs.

     They are carrying their babies in the slings they made,
freeing their hands to pick the mushrooms."


Have you hunted for mushrooms? My friend described finding some 'shrooms that helped him see the earth breathing. . .

Saturday, April 22, 2017

Novaculite: 99 Percent Pure Microcrystalline Quartz, the "Ivory Soap" of Napping Stones

      Novaculite is a 99 percent pure, microcrystalline quartz mineral, similar to chert or flint, found only in the Ouachita Mountains of western Arkansas and eastern Oklahoma. So-called "Arkansas stones" or "Ouachita stones" are used as sharpening tools or whetstones (and in these colorful nail files).

     Novaculite was also used by native Americans in tool napping and sharpening. 

         The extremely thin edges of napped novaculite are very sharp; they were used in early medical scalpels. The word “novaculite” is derived from a Latin word meaning “razor stone.”

      The striking outcrops are seen here in western Arkansas, exposed in the Benton-Broken Bow uplift which runs from Broken Bow, OK, to Benton, AR (near Little Rock).

      The color of novaculite varies widely depending on minor impurities.


     Arkansas novaculite samples have, on occasion, been imported to Colorado ;-).

Arkansas rocks: sharp, very sharp!

And a few images (after the rain) from Denver's March for Science today:

Sunday, April 16, 2017

Blue-Gray Limestone, Crinoids, and Large Quartz Crystals in Western Arkansas

     Yes, this is Maizie and me licking our lips (or nose, in her case) at the striking roadcuts of the Ozark Mountains (actually plateaus) of northern Arkansas and the Ouachita Mountains of west-central Arkansas.

       The western part of Arkansas includes, from north to south: the Ozark Plateaus or Mountains, the Arkansas River Valley, the Ouachita Mountains, and the West Gulf Coastal Plain. The Ouachita Mountains are one of the few east-west-trending ranges in the U.S. (The Uinta Mountains in Utah and Mt. Tom/Mt. Holyoke Range in Massachusetts are two of the other east-west-trending features.)

      The geologic units are outlined below, including shades of blue for blue-gray Mississippian rocks. (NB: unless one is a geomorphologist, most geologists just gloss over anything coloured yellow for the Tertiary and Quaternary.)

       The Mississippian Pitkin Limestone is 360 to 320 years old and is chucky-jam full of fossils, including crinoids and bryozoans. The crinoid stems (which resemble rolls of Smarties candies) are parts of animals called sea-lilies that attached to the seafloor. In this rock sample, which may or may not have travelled from northern Arkansas to Colorado, shows the unweathered fossils.

        Here are some weathered out crinoid stems.

        And here is the stem and the less-often preserved top of a crinoid animal.

       The photo below shows weathered-out screw-shaped bryzoans, commonly referred to as Archimedes screws (in the right bottom part of the photo.) The upper left part of the photo shows the crinoid stem pieces. The crinoids are so plentiful in the Pitkin Limestone that some people apparently fling them on the ground like pop-rocks. We did not partake of that practice.

      The Pitkin Limestone overlies the Fayetteville Shale as seen in this roadcut. The "tight" shale is the source of much gas development in Arkansas via hydraulic fracking.

      One of the most spectacular parts of our Natural State of Arkansas journey was traveling south along state route 7 from Russellville to Ouachita Hot Springs National Park, right through the heart of the Ouachitas.

         Here's the view (with Maizie) toward the Arkansas Valley:

        Ouachita Hot Springs National Park:

       Pictured below are some large quartz crystals from Blue Springs, Arkansas, which are now at the Crystal Bridges American Art Museum grounds in Bentonville.

       . . .And a few images incorporating geology and art from Crystal Bridges:

      And lastly, a beautiful morning with cool mist in the Ozarks somewhere between Mountain Home and Eureka Springs:

Have you explored Arkansas? Hoping you had/have a traveling companion and navigator as amazing as Maizie. . .