Public Is Invited
Marietta Natural History Society
Fall 2005 Newsletter
.
All programs are in room 143,
Rickey Science Center, 4th St.,
Marietta College campus.
7:00 PM
Butterflies in Winter
Thursday, October 13
Presenter: Jim Davidson
Jim is a repeat presenter. He is an amateur
naturalist and volunteer with Division of Natural
Areas and Preserves and with Columbus
MetroPark. He also is active with the
Appalachian Land Alliance.
Thursday, December 8
Presenter: Brian Riley
Brian Riley, of the Ohio Department of
Natural Resources, Division of Forestry,
is Mr. Ohio Champion Tree. Even as a
student he was tracking down the big ones.
Now, the Emerald Ash Borer, is currently
threatening
many trees in
Ohio and he will
be able to give
us an update.
Flying
Squirrels
Thursday, November 10
Presenter: Ed Michael
Ed Michel also is making a return
visit. He has done research on both
the southern and northern flying
squirrel and will provide lots of
information about these fascinating
animals. He will also entertain
questions about snapping turtles
(about which he spoke last time) – and
he may have copies of his book “A
Valley Called Canaan: 1885-2002”.
Page 2
Marietta Natural History Society
Web Threads
Fall 2005
1, 1, 2, 3, 5, 8, 13, 21 . . .
A site you can count on. MathWorld is a comprehensive and interactive mathematics encyclopedia maintained by Eric W.
Weisstein and intended for students, educators, math enthusiasts, and researchers. The site is continuously updated to include new
material and discoveries. You can find discussions of technical areas of math such as Algebra, Calculus, Geometry, Number Theory,
etc, while the Recreational Mathematics section may have widest appeal. Here you can find mathematical Games, Illusions, Art,
Humor, Puzzles and Sports. If you can never have too much math, visit http://mathworld.wolfram.com/about/mathworld. html.
Winter Birdfeeder Watch
Begins Again in November
Members of the MNHS and other residents have
been monitoring local bird populations. The
Winter Bird Feeder Watch is modeled on a
similar program started by the West Virginia
Department of Natural Resources. The feeder
watch offers an opportunity for bird feeder loyalists,
“armchair ornithologists” and anyone interested in
birds to contribute to long term tracking of resident
and migratory bird species. Participants record the
species and number of birds frequenting their
bird feeder(s) every other weekend from
November to mid March. Even if you cannot
watch each weekend, data you can collect are still
valuable.
The feeder watch is a great way to involve kids! Neonaturalists can fulfill school, scout and 4-H projects.
Involvement in a real monitoring program sparks
children’s interests and builds enthusiasm for birding and
nature. With your help, children can learn to identify
many of our local bird species and behaviors. If you
would like to participate, a printed tally sheet is available.
Other information can be recorded that can reveal
important ecological information about our local bird
populations.
For example, how does your residential setting
(suburban, urban, or agricultural), local trees or forests
(conifer, mixed deciduous, or predominantly oak/hickory)
and type of bird feed that you provide affect the diversity
and vitality of local bird populations? Very little is
presently known about these factors. Correlations with air
quality measurements may also reveal valuable
information about the influence of our local environmental
conditions on indigenous bird species. Establishing long
term records will be important to drawing meaningful
conclusions.
This is a great opportunity to turn your backyard bird
feeder into a satellite research station. If you want to
participate call either Ava Bradley (373-5790) or Bird
Watchers Digest (373-5285). Tally sheets and directions
are available to all participants.
Recycled Paper
100% Post-Consumer
Johnson Grass
by Marilyn Ortt
Many native grasses such as big bluestem, little
bluestem, switchgrass and Indian grass are warm season
grasses and, ecologically, are much preferred over
fescue and several other cool season grasses.
Warm season grasses are in flower now and are
quite attractive. There are a few bad actors
though.
Chinese silk grass or eulalia (Miscanthus
sinensis) has already been written about in this
series and is a large threat becoming larger
because it is still being sold by landscape
nurseries and purchased by unaware customers.
Doubters have only to look along both sides of I-77 in
West Virginia after crossing the Ohio River Bridge and, if traffic allows, take a look at the open area on
Buckley Island on your way back across the bridge.
Another prominent grass at this time of the year is
Johnson grass (Sorghum halapense). Much reviled by the
agricultural community because of its persistence and
aggressiveness, it is now moving into flower and
vegetable gardens and wildflower meadows. An overnight
eruption will occur if you recently purchased rich top soil
came collected from a floodplain.
Johnson grass is a coarse perennial that will grow to
eight feet tall in large dense clumps. It accomplishes this
by having very stout rhizomes - up to ¾" in diameter!
See Johnson, page 7
Suggestions,
Comments or
Contributions for the
MNHS Newsletter?
Send them to the
Editor:
625 5th St Marietta, OH
45750
374-8778
spilatrs@marietta.edu
Page 3
Marietta Natural History Society
Fall 2005
Good Works Department
Marietta Natural History Society provided the paper
for four Birding in Washington County brochures.
The four driving routes are Western Washington
County, Eastern Washington County, Marietta and
Birding the Muskingum River. Information was
compiled by Lynn Barnhart, Brad Bond, and Marilyn
Ortt. Elin Jones designed the brochures. The
brochures are available at the Marietta Visitors’
Center and the information center near the Bank
One Drive-Through on Acme St. They will also be
available on-line. Call 373-3372 for more
information.
Page 4
Marietta Natural History Society
Fall 2005
Scandanavian Pachyderms, Italian
Lagomorphs, and the Beauty of Numbers
by Dr. Mark Miller, Department of Mathematics and Computer Science, Marietta College
Some have posited that mathematics is a universal
language and that if we were to discover intelligent life on
other planets, mathematics there would be the same as
mathematics here. This is a rather bold claim. Is
mathematics a system of truths that hold independent of
human experience? Or did mathematics simply evolve
with the rest of the human condition? The answers to
these questions are, respectively, “Yes” and “No – well
sort of”. Consider the mathematical parlor game shown in
the box.
Repeated trials of this little puzzle show that the
overwhelming majority of participants tend to end up with
gray elephants from Denmark, although from time to time
a green eel from Djibouti may appear. (I once
encountered a student who ended up with a green eguana
(sic) from the Dominican Republic – whether the student
was displaying his wit or ignorance was unclear.)
Of course the secret to this puzzle lies in a fact most
grade school children learn: When a number is multiplied
by 9 its digits add up to 9 or a multiple of 9. But why
nine? What – if anything – makes nine so special? The
answer, it ends up, is more anthropological/anatomical
than it is mathematical. The anthropologists tell us that
our counting systems likely developed the way they did
because people found it easy to count on their ten fingers.
Since we have ten digits anatomically, we developed ten
digits mathematically (0,1,…,9). Thus, this “trick” works
because 9 is the largest of the digits.
Thus it might seem natural to conclude from this that
the mathematics that we have today is the result of
evolutionary forces. However, a second, deeper, look at
mathematics leads to a different conclusion. It is true that
if people had eight fingers instead of ten, that our
arithmetic system would be different. However this is
profoundly different from saying that mathematics would
be different. Arithmetic is a human invention;
mathematics is not.
This leads us to the question, “What is mathematics?”
At its most basic level, mathematics is the study of
knowledge. Hence mathematicians often ask the
question, “What is true?”As opposed to philosophers or
theologians who might ask, “What
is Truth?”, or natural scientists
who might ask, “What appears
to be true based on empirical data?”,
those of us in the mathematical
community often concern ourselves with
questioning what conclusions
could be true given a set of
agreed upon postulates.
So in this sense, mathematics is
A Mathematical Parlor Game
Choose your favorite whole number bigger than 1 but
less than 10. Now multiply this number by 9, add up the
digits of this new number, and then subtract 5 from this
sum and write down the result. Once you have done
this, find the letter of the alphabet that corresponds with
the number you have written down (1:A, 2:B, 3:C, …).
Now, write down the name of a country that starts
with this letter. Move one letter forward in the alphabet
and write down an animal that starts with this new letter.
Finally move two more letters forward in the alphabet
and write down a color that starts with this letter.
a universal language insomuch as logic itself is universal.
Some properties of arithmetic, on the other hand, are
relative (particularly if the other hand has only 4 digits).
The “gray elephant in Denmark” puzzle referenced above
fails to be universal because it depends not only on
properties of numbers but also on the way we represent
these numbers.
Mathematicians tend to be more interested in numbers
themselves than in their decimal representations. In fact,
many of the numbers that have intrigued mathematicians
over the past three thousand years do not have a decimal
representation. I will consider three such numbers which
give me particular intellectual pleasure – is there any
other kind?
The first such number is that ubiquitous number, π.
Most people will recall that if a circle’s circumference is
divided by its diameter, the result is constant, i.e. the ratio
is independent of the size of the circle itself. This
constant, which is approximately 3.1416, is what we call
π. This number, π, finds its way into all sorts of
applications which on their face seem to be completely
unrelated to circles.
For example, start with the positive whole numbers: 1,
2, 3, 4, 5, 6, 7, 8, 9, 10, 11, … Now square these
numbers: 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, …
Next, consider the fractions whose numerators are 1
and whose denominators are these squares: 1/1, 1/4, 1/9,
1/16, 1/25, 1/36, 1/49, 1/64, 1/81, 1/100, 1/121, …
What would happen if you started adding up these
numbers? Is there some sum that you would approach?
Let’s see what we get:
1/1 + 1/4 =1.25
1/1 + 1/4 + 1/9 = 1.36111…
1/1 + 1/4 + 1/9 + 1/16 = 1.4236111
1/1 + 1/4 + 1/9 + 1/16 + 1/25 = 1.4636111…
Cont. on page 5
Page 5
Marietta Natural History Society
Numbers, Con’t from page 4
It may not seem obvious, but these sums are actually
approaching some threshold. If you add the first few (say,
20,000) such fractions, you will see this sum approaching
something close to 1.6449. What’s so special about that?
To see, multiply it by 6; you should get 9.8694. Still
not impressed? Now take the square root; your result
should be approximately 3.1416. Easy as π! (To see why
this works, sign up for Calculus II at your nearest liberal
arts college.)
In fact, the number π shows up all over the place. And
while it is true that π is approximately 3.1416, this is only
an approximation. There is no possible way to represent
the value of π using our decimal system. Put another
way, π cannot be written as a ratio of two integers. For
this reason, we say that π is “irrational” - that is, not
lending itself to be expressed as a ratio of whole numbers.
Think for a moment about what this is saying. On the one
hand, π is defined as the ratio of a circle’s circumference
to its diameter. On the other hand π cannot be the ratio of
two whole numbers. Ponder what this says about the
existence of “perfect circles” …
The second ubiquitous number to be considered here
is φ. Like π, φ was first encountered by considering
geometric ratios. The Greeks concerned themselves
with ratios in rectangles. They observed that while
some rectangles looked pleasing, others looked
too “fat” or too “square”. Just what was it that
made a rectangle pleasing? The Greeks settled
the question this way. Call the longer side the
“base (B)” and the shorter side the “height (H)”.
A rectangle is pleasing if the ratio of the base to
the height is the same as the ratio of the sum of
the base plus the height to the base [more simply
B/H should equal (B+H)/B .] Any rectangle with
such ratios was called “golden”, and this ratio was called
φ, the “golden ratio” or “golden mean”. This ratio ends up
being approximately 1.61803. Examining architecture,
one can find this golden ratio, φ, time and time again.
Many artists used this ratio to give their art a “good” sense
of proportion. For example, the golden ratio can be found
in many of Leonardo Da Vinci’s works.
Another Italian Leonardo discovered this same golden
ratio in a seemingly unrelated scenario: Leonardo
Fibonacci proposed the following: Suppose rabbits take
one month to mature and then begin multiplying regularly
each month thereafter. Further suppose that these are
good moral rabbits with monogamous practices and that
each litter contains two off spring – a male and a female.
Finally suppose that each offspring pair imitate the
practices of their parents. Leonardo then asked how many
rabbits there would be at the beginning of the nth month.
Since this was Fibonacci’s question, we will use Fn to
indicate the population for at the beginning of month n.
Some quick calculations show that F1 = 1, F2 = 1, F3 = 2,
Fall
2005
F4 = 3, F5 = 5, F6 = 8, … In general, Fibonacci noticed
that the population for any given month equaled the sum
of the populations in the previous two months. Put more
succinctly, Fn = Fn-1 + Fn-2.
What does this have to do with the golden ratio?
Fibonacci further observed that examining ratios of
successive Fibonacci numbers gives the following ratios
which we will label with Rs: R1 = 1/1, R2 =2 /1,R3 = 3/2, R4
= 5/3, R5 = 8 /5, R6 = 13/8, .... An examination of these
fractions shows that these ratios are bouncing around
1.61803. R1 is smaller than φ, but R2 is larger than φ. R3
is bigger that R1 but less than φ; R4 is less that R2 but
bigger than φ. In general, Rn is a fraction between Rn-2 and
φ, and the larger n is, the closer Rn is to φ. So while
rabbits love each other, they also seem to love the golden
ratio.
π and φ are not the only interesting irrational numbers;
and not everyone shares my love for rational numbers.
The Pythagoreans were quite disturbed to learn that
irrational numbers existed. They were so disturbed that
legend tells us they murdered the person who made this
discovery. At the risk of upsetting any modern day
Pythagoreans, I will discuss just one more irrational
number – the number e.
To find e, once again list out the positive whole
numbers and divide these numbers into their
successors: 2/1, 3/2, 4/3, 5/4, 6/5, 7/6, 8/7, 9/8,
10/9, 11/10, …
Finally, raise the first fraction to the first power,
the second fraction to the second power, and so
on to get:
(2/1)1, (3/2)2, (4/3)3, (5/4)4, (6/5)5, (7/6)6, (8/7)7,
(9/8)8, (10/9)9, (11/10)10, …
This list begins to level off somewhere near
2.71828. The exact value of this leveling off point
is called e. Like π and φ, e is an irrational number – it
has no exact decimal representation. Also like π and φ, e
shows up in some rather strange places. To see just one
such example, consider the “elevation-slope” relationship.
Suppose you were hiking hills and that periodically
there were markers that told you your elevation at given
points as well as the incline at those points (incline =
slope= Rise/Run). Of course, these numbers measure
different things. If the elevation is 200 ft, you would be
200 ft above the base; if the slope is 200, that would mean
that for every 200 feet of vertical assent, you have
achieved 1 foot of horizontal distance. Again, these are
two different things. But could there be a point on the hill
where your incline slope number was the same as your
elevation number? The answer is yes (and is not that
surprising ... Why?) But now we consider a related
question: Could you construct a hill so that at every point
the elevation and the slope were identical? The answer to
this is a somewhat surprising yes, and in fact there is only
cont. on page 6
Page 6
Marietta Natural History Society
Numbers, Con’t from page 5
one such type of hill: it is one whose shape is of the form
Run
y = ex (or Rise = e ), where e is the same e described
above.
Irrational numbers like e, π, and φ, show up all over the
place. In fact, it ends up that there are more irrational
numbers than there are rational numbers. This means
that if you were to randomly select some number from all
the real numbers out there, you would most likely pick a
number whose value could not be expressed
using our base-ten decimal system. While
this may seem disconcerting at first blush,
this is actually quite reassuring. What this
means is that most numbers cannot be
expressed with numerals – put another way,
most numbers represent notions that are
independent of our human experience.
For me, this makes mathematics beautiful
… more beautiful than that old gray elephant in
Denmark.
Change for the Better
1. When you have doubts about a question on a multiple
choice exam, it’s best to stick with your first answer.
A. This is always true
B. This is generally true
C. This is always false
D. This is generally false
Researchers have recently endeavored to answer this
question empirically. They tallied the consequences of
answer-switching on over 2000 exams given over a two
year period in an undergraduate psychology course (J.
Pers. Soc. Psychology 88, 725; 2005). Changes were
detected as erasures on an answer form.
They found that when students changed answers, twice
as often students switched from an incorrect answer to a
correct one than from a correct answer to an incorrect
one. Thus, statistically, students were more likely to
get a question right when they changed an answer.
So why the common perception that it is better to
stick with a first choice? Follow-up investigations
suggested that the frustration of having thrown out a
correct answer leaves a deeper psychological impact
than switching to a correct one. (Is self-reprehension
emotionally stronger than self-congratulation?)
The effect is similar to the hesitation many
people have to switching checkout lines at the
grocery. Our instincts tell us not to do it because
we believe that the other line will end up moving
even slower than the one we’re in (probably due to
Devine retribution for lack of fortitude), even
though the other line is just as likely to move
faster.
Thus, answer ‘D’ above is the correct choice.
. . . or is it ‘B’?
Fall 2005
Of Migrants and Magnets
The navigational skills of migratory birds allow many to
travel hundreds to thousands of miles. All the more
wonder that some species, such as grey-cheeked and
Swainson’s thrushes do so at night! How they orient
themselves has been of great interest to ornithologists
(and, who knows, probably the military as well).
Two common hypothesis to explain their navigational
skills are that birds use a biological ‘compass’ guided by
star patterns or the earth’s magnetic field. However, to
maintain proper nocturnal flight over long distances, either
system would require periodic recalibration, since star
patterns and orientation of the magnetic flux lines vary
over different regions of the earth’s surface. One way to
recalibrate these compasses might be accomplished using
the position of the setting sun.
Using captured birds and some clever experimental
manipulation, these speculations were recently sorted out.
To perform the experiment the researchers captured
several dozen thrushes and outfitted them with radio
transmitters. Before releasing the birds into the nighttime
sky, some were exposed to artificial aberrant magnetic
fields rotated 80O to the east.
‘Thrush-chasers’ followed the birds in an old Oldsmobile
packed with tracking equipment, and despite periodic
interruptions by suspicious police officers, the flight
pattern was determined over several days.
They found that thrushes migrate in a generally
northerly direction, but those exposed to the artificial
magnetic field followed a more westward course for the
entire first night.
Experimentally treated birds did not return to
a normal flight pattern until after sunset
the following night. The results indicate
that during their nocturnal flight the
birds follow a magnetic compass, and
that magnetic compass is calibrated
to the solar azimuth (position of the
setting sun).
Twilight-calibration of the
magnetic compass also explains one
enigma of song-bird migration, that
being how they can cross the
magnetic equator without becoming
disoriented. [The magnetic equator is
where the dip or inclination of a
compass needle is zero. The
magnetic equator deflects above and
below the geographic equator and is
not fixed, slowly changing over time.]
Page 7
Marietta Natural History Society
Fall 2005
Smart Birds Stick Around
by Jamie Tidd, Bird Watcher's Digest
A study from Spain shows that birds that tough out the winter months up north may be smarter than those that go to
the Bahamas for a winter getaway.
Daniel Sol of the Independent University of Barcelona in Spain has found that short-distance migratory birds have
smaller brains than nonmigratory birds. Long-distance migrants, in turn, have even smaller brains than short-distance
migrants. Those that stay behind are also more inventive foragers.
Sol and his colleagues studied previous observations of 134 bird species in Europe, Scandinavia, and western
Russia. They examined data on brain size and the number of times researchers had seen birds using unique feeding
techniques.
One possible explanation for the size difference is that migratory birds use most of their energy to voyage south,
which means less energy to build and maintain brain tissue. So migratory birds benefit from having smaller brains, but
those small brains may be the reason they began migrating in the first place. With less brain tissue migrants are not
smart enough to forage in harsh winter conditions.
Stationary birds seem to be more innovative feeders. The blackbird, Turdus merula, has been spotted using twigs to
move snow to find food. The bullfinch, Pyrrhula pyrrhula, has been seen tearing flesh from chicken and duck carcasses
for nourishment. Nonmigratory birds have been seen using an average of four innovative feeding approaches, compared
with three for birds that migrate short distances, and around one for species who travel below the Sahara desert.
Unfortunately, Sol and his colleagues believe that migratory bird species will have more trouble adapting to future
changes in environmental conditions. With humans causing climate and landscape disruptions, they will be at a greater
risk for extinction than the smarter stationary species. [Thanks to Bird Watcher’s Digest for letting us use this article.]
A ROAD
I think that I have never knowed, a sight as lovely as a road.
A road upon whose concrete tops, the flow of traffic never stops;
A road that costs a lot to build, just as the City Council willed;
A road the planners say we need, to get the cars to greater speed;
We've let the contracts so dig in, and let the chopping now begin;
Somebody else can make a tree, but roads are made by guys like me.
– Mike Royko
Johnson, con’t from page 2
If a stem is pulled from the ground, many fresh budded rhizomes extend in all directions from the roots. Mission: to
fill all voids between this and the next clump of Johnson grass. It also spreads by seeds which ensure there are always
outlier clumps to spread toward. .
Leaves up to 20" long are smooth except for rough margins and have a prominent white center-vein. The coarse
stems are often rusty red near the base changing to a faded pink further up. The panicles of flowers are quite large and
symmetrical, loosely branched, purplish in color and have small hairs on most flower parts. Seeds are about 1/8" long
and purplish also. The stems die back to the ground each winter but things are happening beneath the ground during
mild weather
Johnson grass is native to the Mediterranean area but now occurs in all warm-temperate regions of the world. It is
especially common in cultivated floodplains including pastures, crop fields, forest edges, rights-of-way, abandoned fields,
and streambanks. If succession from old-field to forest is the desired future outcome, Johnson grass will short-circuit the
process. It can engulf small trees and then inhibit germination and growth of new woody plants.
Johnson grass does not begin to grow until late spring but it is flowering by the first of August in Washington County.
In small areas, hand pulling of smaller clumps is an option especially after a rain has softened the soil making it easier to
get most of the root material. Any adventive rhizomes left in the soil will make new plants so a follow-up-pulling about a
month later is necessary and then another a month after that.
Farmers dislike Johnson grass because of the direct competition with row crops such as corn and soybeans. Invasion
of pastures creates a problem because it contains a glucoside that yields hydrocyanic acid which can cause poisoning of
livestock under certain conditions.
Although it has been grown horticulturally, it is unlikely anyone would do so today. But this is just another example of
why native grasses are superior to non-native species and are just as beautiful.
Invite a Friend to Join the
Marietta Natural History Society
Wood Thrush — Individual $15
River Otter — Family
$25
Monarch — Friend
$50
Why not give a gift membership?
Mail check to address given below
Benefits of
Membership
L Monthly programs
L Field trips
L Quarterly newsletter
L Educational experiences
for kids and adults
L Conservation Projects
The MNHS Mission
i To foster awareness of and sensitivity to our environment and its biodiversity
i To provide a place where people with these interests can gather for information and activity
i To create a presence in our community representing these ideas
Marietta Natural History Society
P.O. Box 1081
Marietta, Ohio 45750
(740) 373-5285