Patterson's Pellet, Minnewaska

So, a couple of days ago I went on a hike at Lake Minnewaska State Park in the Shawangunks.

One of the interesting geologic features at the park is a large glacial erratic called Patterson's Pellet.  It's a dramatic feature along Millbrook Mountain Carriage Road where it's perched atop the cliffs above Palmaghatt Ravine.

 

Here's a picture from the backside (I climbed a short distance down to a ledge).  Another foot or two to the left and the erratic would never have lasted atop the cliff.

 

 

Here's a bad self-portrait (I was hiking alone) by placing the camera on the ground (and into the Sun!).  As you can see, the rock is about 6 x 6 feet in size.

Here's a picture of Patterson's Pellet from the other side of Palmaghatt Ravine (a place called Kempton Ledge on Castle Point Carriage Road).

 So what's a glacial erratic?  I've posted about them in the past (like North Salem Balanced Rock).  They're simply rocks that were picked up by the glaciers during the last ice age.  When the glaciers melted some 12,000-10,000 years ago in the Hudson Valley, the rocks entrained within the ice simply dropped out.  Some, like North Salem Balanced Rock and Patterson's Pellet, dropped out in interesting ways.

I'm 18 of 105 Geology Websites that Rock

So, I was listed on Geology Online: 105 Websites That Rock.  Number 18 out of the 105 websites.  There's some other interesting stuff there as well, it's worth a look around.  Including the blogs they chose is part of a marketing strategy since the site obviously exists to advertise various for-profit colleges which, as a traditional academic, I have reservations about but caveat emptor and all that.

The Density of the Earth

In my previous two posts, I described how the ancient Greek Eratosthenes calculated the circumference of the Earth by an observation of shadows on the summer solstice in 200 BCE and how English scientist Henry Cavendish calculated the mass of the Earth from a simple torsion balance in the late 1700s.  Go and read them here and here if you haven't already.

Once you know the mass and size of the Earth you can calculate its density.

Density (abbreviated with the Greek letter rho - r), is mass per unit volume (g/cm³ or kg/m³ are common units).  Imagine a block of steel and a block of cheese the same size.  The steel will weigh more and thus have a higher density (steel is about 8 times the density of cheese!).

Steel vs. cheddar cheese (not quite the same size)

So what is the density of the Earth?  Well, let's start with the circumference of the Earth which Eratosthenes has shown can be measures.  We'll use an average value of 40,075 km.  From this, we need to calculate the volume of the Earth.  The formula for the volume of a sphere is:

   V = (4/3) p r³

and the radius (r) is:

   r = C / 2 p

Substituting yields:

   V = (4/3) p (C/2p)³

Simplifying and solving:

   V = C³ / 6 p² = (40,075 km)³ / 6 p² = 1 x 10¹² km³

What about the mass of the Earth?  Well that was calculated by Cavendish and we can use the modern value of 6 x 10²⁴ kg.

Now finding the density is easy (don't even need a calculator):

   r = m / V = (6 x 10²⁴ kg / 1 x 10¹² km³) = 6 x 10¹² kg/km³

This rather nicely converts to 6 g/cm³ (a more exact modern value is 5.515 g/cm³).

So the average density of the Earth is about 5.5 g/cm³.   This poses a problem, however.  It turns out that the average density of crustal rocks is around 2.7 g/cm³ (the density of the mineral quartz which is a major constituent of many rocks).  So where is all this extra mass coming from to give this higher density?

It turns out that the center of the Earth has an iron core.  Iron has a high enough density (over 7 g/cm³) to bring the average density of the Earth up to its calculated value.

Even though we've never directly sampled the core of the Earth, there is other evidence to support the hypothesis of an iron core.  These include the fact that iron is an abundant element in the solar system (ever hear of iron meteorites?), the speed of seismic waves through the core match what's predicted for it being composed of iron, and we have a magnetic field that's generated by the movement of liquid iron in the outer part of the core.

It's pretty cool how an ancient Greek, an 18^th century British scientist, and our knowledge of the interior of the Earth are all part of an interrelated story.

Cavendish Weighs the Earth

In my previous post, I described how the ancient Greek Eratosthenes measured the size of the Earth.  Today I'd like to talk about how you can calculate the mass of the Earth.

Henry Cavendish (1731-1810) was a British scientist who made several important contributions to chemistry and physics.  He was born into an aristocratic family and his family wealth and frugality allowed him the freedom to devote himself to his academic interests.

Cavendish was also notoriously eccentric.  He reportedly spoke in a "shrill, high-pitched" voice and hated talking to people.  He left notes to communicate with his servants and built a special staircase in his home for them so that he wouldn't have to see or speak with them.  If someone did manage to corner him for a chat, Cavendish would reportedly issue a "peeved squeak" and scurry off to escape the social encounter.  His anthropophobia (fear of people) was particularly acute with women - he apparently never had a relationship or married.  Neurologist Oliver Sacks has suggested that Cavendish suffered from Asperger Syndrome.

Cavendish was also noted for his odd manner of dress.  He was known for always wearing a faded violet coat and three-cornered hat.  Clothes that had been out of fashion since his grandfather's time.  When one pair wore out, he simply commissioned someone to make another set.

Cavendish's stately home in Clapham Commons (just outside of London)

The only place Cavendish ever interacted with people outside of his home was when he regularly attended the weekly dinners and meetings of the Royal Society.  There, he lost his inhibitions when discussing his scientific work and was highly respected by his peers despite his eccentricity.

Cavendish is perhaps best known for the eponymous Cavendish experiment which he published in 1798.  He started by constructing a torsion balance which consisted of two separate suspension systems.  One held two 12-inch lead balls that weighed almost 350 pounds each.  The other system held two smaller 2-inch lead balls (weighing about a pound and a half each) attached to the ends of a six foot wooden rod which could rotate freely.  The two smaller lead balls were located about 9 inches away from the much larger weights.  As these masses attracted each other (by the force of gravity), the wire suspension system would twist (hence the name torsion balance).

Cavendish built the balance in an outbuilding on his property and meticulously measured the deflection of the masses and calculated a value for G - the gravitational constant.

Published figure by Cavendish of his torsion balance

 

Reproduction in the Science Museum, London

 

At right below is a simplified diagram of the experiment.  The formula for calculating the gravitational constant (G) from this setup is the following:

 

   G = [(2 p² L r²) / (M T²)] q

 

Where L is the length of the rod holding the two smaller masses, M is the mass of the large balls, r is the distance between the large and small balls, q is the angle of deflection, and T is the resonant oscillation period (time units) of the balance (basically a measure of how easily the wire twists and related to k, the torsion coefficient of the wire).

Cavendish obtained a value for G of 6.74 × 10⁻¹¹ m³ kg⁻¹ s⁻².  This value is only about 1% off from the value we use today.  If you're interested in the mathematics, the Wikipedia article on the Cavendish experiment has the derivation.

From G, and the Law of Universal Gravitation developed by Isaac Newton one hundred years earlier, Cavendish could then calculate the mass of the Earth by the formula:

   M_Earth = [(g R_Earth²) / G]

Where M_Earth is the mass of the Earth, R_Earth is the radius of the Earth (obtained from Eratosthenes), g is the acceleration of gravity (9.8 m/s²), and G is the gravitational constant.

From this experiment, Henry Cavendish was able to "weigh the world."  Amazing!  Now that we know the size of the Earth from Eratosthenes, and the mass of the Earth from Cavendish, we can calculate the Earth's density and that tells us something interesting about the unseen interior of our planet that I'll discuss in my next post.

Eratosthenes Measures the Earth

Here's an assignment for you.  I want you to measure the size of the Earth.  Oh, and you can't use any modern equipment.  All you have available to you is what would be around in, let's say, 200 BCE.

Stumped?

It's not a trivial problem, is it?  It turns out, however, that it is possible to do and an ancient Greek named Eratosthenes (c. 276 BCE - c. 195 BCE) figured it out (Eratosthenes really was a polymath - Wikipedia describes him as a Greek mathematician, geographer, astronomer, music theorist, and poet who, given the size of his head, must have been brilliant!).  Critics nicknamed him Βήτα ("Beta" - the second letter of the Greek alphabet) because, while knowledgeable about everything, he was always seen as being second-best.  Supporters, however, called him Πένταθλος, ("pentathlos") a word used to describe well-rounded athletes who performed well in all events.

Born in Cyrene (in Libya, today, but part of the lands conquered by Alexander the Great and a Greek city), Eratosthenes was undoubtedly recognized for his intelligence as a youth since he was sent to Athens to continue his education where he ended up studying with several famous Greek philosophers and poets.  At 30 years old, his writings on poetry and history captured the attention of the Pharaoh who invited him to work at the Library of Alexandria (the most famous library of the ancient world and a center of learning - think of being invited to work at Oxford or Harvard today).  He spent the rest of his life there becoming Chief Librarian after just five years.  He was held in such high esteem that he tutored the children of the Pharaoh (one of whom became the next Pharaoh).  Eratosthenes was a also good friends with Archimedes (another brilliant Greek).

Back to the size of the Earth.  It turns out the Eratosthenes knew about a well in the Egyptian city of Syene (called Aswan today) that had an interesting feature.  On the day of the summer solstice (the longest day of the year when the Sun rises and sets in its most northerly positions), the Sun would illuminate the bottom of the well at local noon.  In other words, on the solstice, and only on the solstice, the Sun was directly over this well in Syene.

Looking down into the well at Syene

Today, we know why this occurred at Syene.  The Earth is tilted by 23.5° and, on the summer solstice, the Northern Hemisphere is at it's maximum tilt toward the Sun.  At local noon, the Sun will be directly over 23.5° N latitude (the Tropic of Cancer).  Syene (now called Aswan) is located very close to that latitude.

In the north of Egypt, Eratosthenes also knew that on the summer solstice, the Sun was not directly overhead in Alexandria where he was located.  How could you explain the fact that the east-west moving Sun was directly over one city on a specific day but not directly over another city, further to the north, at the same time?

Alexandria and Syene (note they're not quite on the same N-S meridian)

Well, one hypothesis which would explain this observation is that the Earth is spherical.  "Wait," you might be thinking, "didn't ancient people believe the Earth was flat?"  If you go back to the Mesopotamian world view, and the Biblical world view that arose from that, the answer is yes.  As a digression, any literal reading of the Torah/Psalms/Prophets (Old Testament) clearly indicates the world is fixed, the center of the universe, and flat with corners and pillars (just as clearly as the view held by some supposedly modern religious groups that the Earth is only a few thousand years old and all life was saved by Noah and his ark).

By the time of the ancient Greeks, however, some intelligent people were wondering if the Earth might not be spherical.  Aristotle, who live 100 years before Eratosthenes, even proposed several logical arguments in support of a spherical Earth (one argument, for example, was that one saw stars in the southern sky in Alexandria, Egypt that were below the horizon in Athens on the other side of the Mediterranean.  By similar reasoning, the Sun could be overhead in Syene yet not quite exactly overhead in Alexandria.

One easy way to measure the angle of the Sun at noon is to use the shadow cast by a tall, straight object.  If the Sun is directly overhead, no shadow will be cast but if it's not quite overhead, a shadow will appear.  So what can you use for a tall, straight object?  Well, Eratosthenes was in Egypt - how about an obelisk like Cleopatra's Needle?

Painting of an obelisk in Alexandria (Cleopatra's Needle) circa 1850

Another brilliant Greek, Euclid, who also lived about 100 years before Eratosthenes, developed the mathematical field of geometry which can be used to calculate the angle between the Sun and the zenith (the point in the sky directly overhead) from the known height of the obelisk and the measured length of the shadow cast.

The well at Syene (left) and obelisk in Alexandria (right) at the summer solstice

The angle of the Sun's rays from vertical turned out to be 7.2°.  According to Euclid's geometry, this will be the same as the angle formed between lines connecting the center of the Earth to both Alexandria and Syene.  Eratosthenes also knew, by talking to Egyptian surveyors, that the distance from Alexandria to Syene was about 5,000 stadia.  There is some debate as to the length of a stadion at the time but I'll use the conversion of 1 stadion = 150 meters (0.15 km).

Now, since  7.2° is to 360° (the number of degrees around a circle) as 5,000 stadia is to the circumference of the Earth (C), we can set up the equation:

   (7.2° / 360°) = (5,000 stadia / C)
   C = (5,000 stadia * 360° / 7.2°)
   C = 250,000 stadia

Converting to kilometers:

   250,000 stadia * (0.15 km/stadion) = 37,500 km

The modern value for the circumference of the Earth is 40,070 km so Eratosthenes would have only been off by 6.4%.  That's  pretty damn good for something done over 2,000 years ago!

There are a few sources of error in this value.  Eratosthenes assumed Alexandria and Syene were directly lined up with each other in a north-south direction.  They're not (see the map above).  The value for the distance from Alexandria to Syene was not exact.  A tenth of a degree difference in the measured angle leads to a difference of thousands of stadia in the final result.  And, finally, we're not sure of the exact conversion between an Greek stadion of 200 BCE and a modern kilometer.

As a final note, when Christopher Columbus proposed to go after the spices of India by sailing west across the Atlantic, he knew the Earth was round.  King Ferdinand's advisers counseled him to turn down Columbus's proposal because Eratosthenes estimate for the size of the Earth gave an untenable distance going that way around.  Columbus, however, argued persuasively enough that this value was too high and convinced Queen Isabella to give him a shot.  The rest, as they say, is history.

Now that the size of the world had been measured, I'll explain in my next post how it was weighed.

Geology is sexy

Always looking to recruit new students into geology. Maybe if it had a sexier image...

  From XKCD comics
Geology is full of terms which have a double entendre meaning. Structural geologists like myself are always checking out cleavage, discussing thrusting, and thinking about what makes the bedrock.

Tamu Massif - Largest Volcano on Earth?

So what's the largest volcano on Earth?  I used to tell students it was Mauna Loa, part of the Big Island of Hawaii but according to William Sager, a geophysicist from the Department of Earth and Atmospheric Sciences at the University of Houston, the largest volcano is actually Tamu Massif located on the floor of the western Pacific Ocean.  Sager, who's been studying this seafloor feature for the past 20 years, named it after Texas A&M University (TAMU) where he used to teach.

Location of Tamu Massif in western Pacific Ocean

The Tamu Massif is located on a seafloor feature called the Shatsky Rise which is found 1,600 km (990 mi) east of Japan.

Other volcanic centers on the rise include the Ori Massif and Shirshov Massif as shown below.

Seismic reflection surveys (red lines on map) and cores (red dots on map) of the seafloor taken by the Joint Oceanographic Institutions for Deep Earth Sampling (JOIDES) Resolution research vessel were used to study this seafloor feature.

JOIDES Resolution

So what are seismic reflection surveys?  That's when a ship uses an instrument called an air gun to generate bursts of energy.  An array of air guns can be towed behind the ship, under water, and then charged to about 18 MPa (2,600 psi) of air pressure.  Suddenly released, this generates waves of acoustical energy which then travel down to the seafloor and then bounce back to the sea surface where they can be picked up by sensitive hydrophones.

Working on an air gun

It differs a bit from regular sonar, which uses lower energy sound waves, since the waves of energy from the air gun don't just tell us the depth to the seafloor but, being higher energy, penetrate into the sediments and bedrock of the seafloor.  Some of this energy simply reflects off the surface, but some travels down below the seafloor to reflect off the different internal layers of sediment and rock.

The timing and strengths of these reflections can then be interpreted to reveal some of the internal structure of the upper crust and provide what's called a seismic reflection profile.

Sager, et al. 2013

The seismic profiles for the Tamu Massif, along with geochemical studies of the basaltic lava flows sampled by deep-sea drilling cores, indicate that there seems to be a single eruptive center for the massif.  In other words, Tamu Massif represents a single large volcano, not several inter-grown volcanoes.  That's why it was claimed to be the largest volcano on Earth by Sager and his team.

Of course, there are different ways one could define "largest".

The base of Tamu Massif apparently covers some 120,000 square miles or so, which makes its footprint on the seafloor about the same size as the state of New Mexico.  This may be slightly larger than the base of Olympus Mons, the largest volcano in the solar system located on the planet Mars (although Olympus Mons is much higher!).

Olympus Mons on Mars

For comparison, the Hawaiian volcano of Mauna Loa has a base covering only about 2,000 square miles.  While it is taller than Tamu Massif (Mauna Loa, after all, pokes almost 14,000 feet above sea level on the Big Island, after rising over 16,000 feet from the seafloor!).

Keep in mind the diagram above has about 17x vertical exaggeration.  The horizontal scale of 100 km is shown and you can see it covers much more distance than the vertical scale shown.  This effectively exaggerates the height differences of these volcanoes.

I would think the most important factor for determining the size of a volcano is the volume of erupted material, not the area of the base or the height of the volcano.  Using this, Tamu Massif is still the largest volcano on Earth but Olympus Mons still holds the record as the largest volcano in the solar system having about 25% more volume.

Of course, Mauna Loa is much nicer to visit!

 

Mauna Loa as seen from Mauna Kea

Simple Rate Problems in Geology

One of the most-common uses of mathematics in introductory geology courses is in looking at rates.  Here are some basic examples:

1. Sediment is accumulating in a deep ocean basin at an average rate of 2 mm/1,000 years.  How much sediment will accumulate in a million years?

2. Assume an average erosional rate of rock to be 0.1 mm/yr.  How many years will it take to erode away a 3,500 m high mountain peak?

3. A basaltic lava flow cools from 1,200° C to 20° C in 36 hours.  What is the average rate of cooling in °C/min?

4. A volcanic island on the Pacific Plate has moved 200 km away from a hot spot.  The oldest volcanics on the island are 5 million years old.  What is the average rate of plate movement in cm/yr?

5. If sea level rises at at average rate of 2 mm/yr, how long before an area 25 meters above sea level will be inundated?

Now, in some ways, these are unrealistic problems because they assume average linear rates of change.  In reality, geologic processes are generally not linear.  For example, if we look at the rate at which sediment accumulates in the Mississippi Delta area, we'll see that it's highly variable based upon the flow of the river.  During times of drought, the rate slows way down and during flood stages, the rate may be incredibly high.  Nevertheless, it is still sometimes helpful to look at average rates of change because they give an idea of how long things take to happen (how long, for example, is needed to completely erode away a mountain belt?).

Anyway, these problems are common in introductory geology lab manuals and I'm always surprised that some college-level (supposedly) students will struggle with these middle-school-level math problems.  So, a few notes about how to approach such things...

First, recognize that these problems are all of the same form - they involve a rate (R) which is a change in distance (D) units over (divided by) time (T) units.  In other words:

   R = D / T

Using basic algebra, we can rearrange this to solve for either time (T) or distance (D):

   T = D / R
   D = R T

Next, and some students have trouble with this, we need to read the word problem and identify the three things - R, D, and T.  One of these we'll be solving for and the other two are given.  For example, in the five examples given above:

   1. R = (2 mm/1,000 yr); D = ?; T = 1,000,000 yr
   2. R = (0.1 mm/yr); D = 3,500 m; T = ?
   3. R = ?; D = (1,200° C - 20° C); T = 36 hr
   4. R = ?; D = 200 km; T = 5,000,000 yr
   5. R = (2 mm/yr); D = 25 m; T = ?

One that might have been a little tricky is recognizing in number 3 that the D value is the change in temperature (think of it as the distance between the starting and ending temperature).

Now we know which equation to use depending on whether we're solving for R, D, or T.

Another place where people get into trouble.  They'll plug in the numbers without thinking about the units.  For example, in solving example 5 above, they'll write:

   T = D / R = 25 / 2 = 12.5

Of course, I'll respond with 12.5 what?  Years?  No.  You divided meters by millimeters per year so your answer is 12.5 meter year per millimeter.  What the hell is that?

You MUST pay attention to units when solving these problems.  If you have one variable in meters and another in millimeters, you have to either convert to either one or the other for consistency.  You also need to pay attention to what units your answer should be in and convert accordingly.

Also, if you're not told what units your answer should be in, use common sense.  Suppose you're solving for time and the answer comes out to 4,320 minutes.  That's not useful to most people but converting it to 72 hours or 3 days is much better.

Let's solve the five example problems:

1. Sediment is accumulating in a deep ocean basin at an average rate of 2 mm/1,000 years.  How much sediment will accumulate in a million years?

   How much sediment is D = R T
   D = (2 mm/1,000 yr) (1,000,000 yr)  [Should be able to solve this in your head!]
   D = 2,000 mm
   Since units aren't specified for the answer, I'd covert answer to meters
   2 meters of sediment will accumulate

2. Assume an average erosional rate of rock to be 0.1 mm/yr.  How many years will it take to erode away a 3,500 m high mountain peak?

   How many years is T = D / R
   Problem! R is in millimeters and D is in meters.  Need to convert
   3,500 m (1,000 mm/m) = 3,500,000 mm
   T = 3,500,000 mm / 0.1 mm/yr = 35,000,000 yr
   35 million years to erode away the peak

3. A basaltic lava flow cools from 1,200° C to 20° C in 36 hours.  What is the average rate of cooling in °C/min?

   Rate problem is R = D / T
   D is difference in temperatures so 1,200° C - 20° C = 1,180° C
   We want our answer in minutes so 36 hr (60 min/hr) = 2,160 min
   R =  1,180° C / 2,160 min = 0.5462962962962962962962962962963° C/min
   Why the long number?  That's what my calculate said.  It's ridiculous, we need to round.
    Since temperature and time are only given as whole numbers, round to one digit.
    R = 0.5° C/min
   Half a degree Celsius per minute cooling

4. A volcanic island on the Pacific Plate has moved 200 km away from a hot spot.  The oldest volcanics on the island are 5 million years old.  What is the average rate of plate movement in cm/yr?

   This again asks for a rate so R = D / T
   The answer needs to be in cm/yr so D needs conversion from km to cm
   200 km (100,000 cm/km) = 20,000,000 cm
   R = 20,000,000 cm / 5,000,000 yr = 4 cm/yr
   The average rate of plate movement is 4 cm/yr

5. If sea level rises at at average rate of 2 mm/yr, how long before an area 25 meters above sea level will be inundated?

   A time problem so T = D / R
   Need to get distance and rate in the same units so let's convert m to mm
   25 m (1,000 mm/m) = 25,000 mm
   T = 25,000 mm / 2 mm/yr =12,500 yr
   It will take 12,500 years for sea level to flood this area

These are all reasonable problems and kind of neat to think about.  Sediment does accumulate in ocean basins (and other environments).  Rocks and even entire mountain ranges do erode away.  Igneous rocks cool from their molten state.  Volcanic islands, like Hawaii, do move off of hot spots with the motion of the Pacific Plate.  Sea level has been rising since the last ice age (and will continue to do so at a faster rate with anthropogenic warming of the climate).

It's interesting to think about how long those things take to happen.  While eroding a mountain in 35 million years seems like a long time, remember that in the 4.5 billion year history of the Earth, you could have eroded away well over 100 consecutive mountain ranges!  While a plate movement of 4 cm/yr seems slow, a plate could move 2600 km (the distance across the Atlantic Ocean) since the time of the extinction of the dinosaurs 65 million years ago (and, geologically, that wasn't very long ago!).  The 25 meter rise in sea level could have taken place since the end of the last ice age.

In other words, even though some of these rates seem slow, geologists have plenty of time to play with and even small rates add up to big changes over geological time spans.

Venus of Laussel - Part II

In my last post, I introduced the Venus of Laussel.  In today's post, I'll discuss some interpretations of this interesting Upper Paleolithic carving.

As mentioned in my previous post, Venus figurines shared similar characteristics showing naked females with exaggerated breasts, bellies, hips, thighs, and vulva with poorly-developed hands and feet and generally no facial features.  So why were naked obese women a popular subject for artistic expression in the Late Stone Age?

Over the years, archaeologists (and others) have proposed a number of explanations - some more widely accepted than others.  And it may well be that different figurines, which we lump together today, represented different things to the different groups they belonged to at the time.

Images of figurines and their geographic origins.  (1) Willendorf’s Venus (Rhine/Danube), (2) Lespugue Venus (Pyrenees/Aquitaine), (3) Laussel Venus (Pyrenees/Aquitaine), (4) Dolní Věstonice Venus (Rhine/Danube), (5) Gagarino no. 4 Venus (Russia), (6) Moravany Venus (Rhine/Danube), (7) Kostenki 1. Statuette no. 3 (Russia), (8) Grimaldi nVenus (Italy), (9) Chiozza di Scandiano Venus (Italy), (10) Petrkovice Venus (Rhine/Danube), (11) Modern sculpture (N. America), (12) Eleesivitchi Venus (Russia); (13) Savignano Venus (Italy), (14) The so-called “Brassempouy Venus” (Pyrenees/Aquitaine), (15) Hohle Fels Venus (SW Germany).

Some have speculated that they were representations of actual women.  A problem with this interpretation is that Venus figurines show stylized conventions and typically don't even show facial features.  Other carvings and painting have shown that our ancestors could be excellent artists and realistically depicted animals, for example, but, perhaps there was a taboo against realistically depicting people.

Others have claimed that they were ideal representations of female beauty or even primitive pornography.  I'm personally a bit skeptical of this interpretation.  Forgive me if this offends, but were our ancestors so different that men preferred obese naked women to thinner ones?  Some of the Venus figurines are more "attractive" than others (at least to my modern sensibilities) but others hardly seem to have been made to represent any standard of physical beauty.

One researcher has suggested that they represent self portraits of women and their artistic conventions are from women looking down at their own bodies and seeing them from that perspective.  Just my opinion, but this idea seems a bit far-fetched to me.

The most accepted idea regarding these figurines is that they are a representation of fertility and had a "religious" significance, perhaps representing a mother or Earth goddess (when writing was developed, we do see that virtually all cultures had a concept of such a goddess so it's certainly not a stretch to speculate that this idea was shared by our more primitive ancestors).

The Upper Paleolithic humans lived during the peak of the most recent ice age.  Europe, at the time, was a very different place than it is today.  Southwest France, where the Venus of Laussel was found, was steppe grassland with short summers and long, severely-cold winters.

Survival was tough. The diet was primarily meat-based and you had to find it and kill it in order to eat.  As mentioned in the last post, the Gravettian Culture which existed in France at the time is noted for its distinctive blades which were used for spearing big game migrating across the grasslands.

Women living to middle-age, surviving multiple childbirths, and being what we today would consider overweight were rare events.  The Venus figurines, with the large, often-sagging breasts, large belly (which may indicate pregnancy), prominent vulva, and fat hips and thighs may have symbolized the hope of tribal success in the form of fecundity of their females and an abundance of food.  What archaeologists call a fetish - an object to which is attributed "supernatural" power.  It may also represent a mother or Earth goddess who could provide such bounty.

What about the wisent horn the Venus of Laussel is holding?  Remember that?

 

So what does the horn and 13 notches represent?

Again, a diversity of opinions among archaeologists.

Since there are traces of red ochre staining the figure, some have argued that the 13 notches represent the approximate number of menstrual cycles in a year (365 days / 28 days/cycle).  Another representation of fertility (once the menstrual cycles end, so does fertility).

One interesting speculation is that the notched wisent horn is an ideophonic scraper like the güiro - a Latin-American musical instrument.  Basically, you cut notches in a stick, a gourd, a bone, an animal horn, etc. and then rub over it with a stick to produce sound.  Here's a recording of a modern güiro. Perhaps it was an instrument played in a ceremonial context associated with these Venus figurines.

The final speculation I want to discuss is the real reason I wrote this post.  I'm teaching an Ancient Astronomy course this semester and one of the topics is looking at any astronomical knowledge that may have existed in Paleolithic cultures.  The Venus of Laussel is a topic of discussion.

Alexander Marshack, a self-trained archaeologist who was appointed as Research Fellow at the Peabody Museum at Harvard (an interesting guy), presented a very interesting argument in his landmark 1972 book The Roots of Civilization: The Cognitive Beginnings of Man's First Art, Symbol and Notation.  In it, he argued that the horn symbolically represents the crescent Moon and the 13 notches represent the fact that there are approximately 13 lunar cycles in a year.  As Marshack writes:

"If this is so, then it is possible, but not yet proven, that the 'goddess' with the horn is a forerunner of later Neolithic, agricultural variants.  She was the goddess who was called 'Mistress of the Animals,' had a lunar mythology, and had associated with her signs, symbols, and attributes, including the lunar crescent, the crescent horns of the bull, ... the vulva, the naked breasts,...

The count of thirteen is the number of crescent 'horns' that may make up an observational lunar year; it is also the number of days from the birth of the first crescent to just before the days of the mature full moon."

In the book, of course, Marshak presents a lot of other evidence for lunar notation in Paleolithic artifacts.  It's an interesting speculation.  Unfortunately, given the distance of these ancestors from us today, and their lack of a written language to tell us what they really believed, these ideas will likely remain in the realm of speculation.

Venus of Laussel - Part I

In 1908, psychiatrist and amateur archaeologist Dr. Jean-Gaston Lalanne started conducting excavations in a rock shelter near the Château de Laussel in the Dordogne area of southwestern France.   In 1911, he discovered an interesting carving of a large, naked woman (other carvings were discovered as well but we'll just discuss this one today).

It was dubbed the Venus of Laussel after other so-called Venus figurines depicting similar subjects.  These figures are believed to be from the  Gravettian Upper Paleolithic culture (about 25,000 years old).

This carving was kept in Lalanne's private collection until 1960 when it was donated to the Museum of Aquitaine (Musée d'Aquitaine) in Bordeaux where it resides today.

The bas relief carving is 54 x 36 x 15.5 centimeters in size.  It was carved into a fallen block of limestone with flint implements.  Traces of red ochre (an iron oxide mineral) indicate that it may have been stained a rusty-red color.

The carving depicts a naked woman holding what appears to be a wisent horn (more on this in a minute).  There are no details on her face (which is facing the horn), but her pendulous breasts, swollen belly, large thighs ("saddle-bag" hips), and vulva are accentuated.  Her free hand is placed on her belly (womb?).

There's so much to say about this figurine I scarcely know where to start...

First, you may be wondering about the wisent horn.  Wisents are European bison (Bison bonasus).  They were hunted to extinction in the wild in the early 1900s but have more recently been reintroduced from captive specimens.

Wisents were hunted for meat, furs, and to produce drinking horns.  They would have been an important resource for Upper Paleolithic hunters.

The wisent horn held by the Venus figure has 13 inscribed notches.  We'll return to this later.

The rock, as mentioned previously, is limestone.  The region in southwestern France where it was found is characterized by a Jurassic-Cretaceous Period limestone plateau dissected by river valleys (the largest being the Dordogne River).  Since limestone is so soluble, the region is riddled with natural caves which were exploited by our ancestors who hunted in the fertile valleys.  Once of the most well-known caves in the area is Lascaux famous for its exquisite cave paintings.

The carving was found in a grotto (not quite a cave, more like a cliff overhang) near the Château de Laussel, commune of Marquay, Dordogne department, region of Aquitaine (commune, department, and region are similar to township, county, and state in the U.S.).

 Approximate area of Château de Laussel is within red circle

Château de Laussel from Google Earth (44° 56' 42" N, 001° 06' 08" E)

 

hâteau de Laussel from the ground

An old photograph of the site shows where the Venus carving was found (white cross).

A few words about the Gravettian culture that produced this sculpture.  The Gravettian denotes a toolmaking culture in Europe that existed between 32,000 and 22,000 years ago during the Upper Paleolithic (Late Stone Age).  It's characterized by specific technological advances in the manufacturing of stone blades used for the hunting of of big game such as horse, bison, reindeer, mastodons, and mammoths.  The culture is named after a type site at a location called La Gravette which is also in the Dordogne area.

The Gravettian culture is also famous for the carving of Venus figurines out of soft stones (like the limestone Venus de Laussel), bone, or ivory (from mastodon and mammoth tusks).  The figurines shared similar characteristics showing naked females with exaggerated breasts, bellies, hips, thighs, and vulva with poorly-developed hands and feet and generally no facial features.

So why were these Venus figurines so important and what specifically was being represented by the Venus of Laussel?  Short answer, no one knows for sure.  Long answer, there are a lot of speculations.

I'll discuss some interpretations in my next post...

Giant Fungi

The fossil Prototaxites was first collected, named, and studied in the mid-1800s.  The name means "first yew" and it was originally thought to be the fossil of an early conifer with a partially rotted trunk containing the remains of fungi.  Later, others argued that it was actually a type of marine alga or seaweed.  The problem with this interpretation was that Prototaxites fossils were being found in terrestrial environments.  The fossil remained problematic until fairly recently when intensive studies have shown that it's most likely a type of fungus.

Fossil at right is 12 cm in diameter (a small example) and was collected in the Netherlands.

Fungi are neat organisms, belonging to their own phylum separate from animals and plants.  While the study of fungi (mycology) is usually done by botanists, genetic studies have shown that fungi are more closely related, evolutionarily, to animals.  One of the problems of fungi is that they lack hard parts so don't leave a good fossil record making it problematic to follow their evolutionary development through geologic time.

Prototaxites is a notable exception to the lack of fungal fossils and dates from the Silurian and Devonian Periods (420 to 370 million years ago).  It's also quite unusual (for a fungus) in having a trunk-like structure that was about a meter in diameter (3 ft) and up to 8 meters in height (26 ft).  This trunk or stalk was made up of tiny interwoven fibers only 50 microns (0.0020 in) in diameter.  Some have suggested it also had an algal symbiont which would technically make it a lichen.

Digging up a Prototaxites in Saudi Arabia

What's amazing about these fungi is that they were, by far, the tallest organisms on Earth at the time.  During the Silurian and early Devonian Periods, plant life primarily consisted of non-vascular plants like mosses (bryophytes) and some primitive vascular plants (trachyophytes) that, at most, reached a meter in height.  The most advanced terrestrial animal life consisted of invertebrates like insects and eventually a few early amphibians.  Prototaxites towered over them all dominating the landscape.

Painting of Prototaxites by Mary Parrish, National Museum of Natural History

 

It would have been a truly alien landscape.  Read more about the research here.

Venus Brightly Shining

You may have noticed an unusually bright "star" in the southwestern sky these past few weeks just after sunset.  It is, of course, the planet Venus approaching its brightest aspect of the year in early December.  It's brighter than any of the other stars or planets in our night sky.

Why is Venus so bright?  For one, it's a near neighbor (the next planet in closer to the Sun).  It's also about the same size as the Earth.  And, most importantly, it's shrouded in light-colored clouds which reflect about 75% of the sunlight hitting the planet (Earth reflects only about 30%).

Venus is also only seen in the evening just after sunset or the morning just before sunrise (it alternates over the span of several months).  Why?  Because it's closer to the Sun than we are - the geometry is easier to show with a diagram.

Earth is shown in green.  Keep in mind that if you're on the half of the Earth that faces the Sun it will be daytime and you won't see Venus.  When you're just moving into darkness (on the left side of the Earth in the diagram), you'll see Venus at positions 3-6 as shown (in different phases, just like some of the phases of the Moon).

If you're just coming into dawn (on the right side of the Earth in the diagram), you'll see Venus if it's in positions 7-8 or 1-2 as shown.

If Venus is in the green areas, it won't be seen since it will be lost in the daytime glare of the Sun.

To complicate things, keep in mind that the diagram is just a snapshot.  In reality, both Venus and the Earth are moving in their orbits at different speeds (Venus is moving faster).  Right now, in early December, the situation is as shown below where Venus is approximately in position 5 vis-à-vis the diagram above.

Ever wonder where the name for Venus come from?  Venus, after all, is the name of an ancient goddess of beauty and love.  Most people are familiar with the famous painting by Botticelli shown below.

The Birth of Venus by Sandro Botticelli (1486)

The mythology of Venus, by the way, is a great story.  The Greek poet Hesiod (c. 700 BCE) wrote in the Theogeny the following story about how Chronos lopped off the penis of his father Uranus and tossed it into the sea.  From there was born the goddess Aphrodite (the Greeks earlier name for Venus).

Then the son from his ambush stretched forth his left hand and in his right took the great long sickle with jagged teeth, and swiftly lopped off his own father's members and cast them away to fall behind him...  And so soon as he had cut off the members with flint and cast them from the land into the surging sea, they were swept away over the main a long time: and a white foam spread around them from the immortal flesh, and in it there grew a maiden. First she drew near holy Cythera, and from there, afterwards, she came to sea-girt Cyprus, and came forth an awful and lovely goddess, and grass grew up about her beneath her shapely feet. Her gods and men call Aphrodite, and the foam-born goddess...

Venus was blown to shore on a scallop shell by the god of the winds, Zephyr, who is embracing the breeze Aura shown on the left side of the painting.  Walking ashore, she was recognized as the most beautiful of women and all men desired her as their wife.  She was the goddess of love and feminine beauty.

By the way, here's even more trivia, the pose shown by the goddess here, with her hands covering herself, is referred to in art as the "Venus pudica" where "pudica" is derived from the Latin pudendus which means "which is to be ashamed of" and, of course, the external female genitalia (which is nothing to be ashamed of, but people have always had hang-ups about such things).

The Greek name Aphrodite likely derives from the Greek word ἀφρός (aphrós) for "foam" recalling the circumstances of her watery birth.

The Birth of Venus by William-Adolphe Bouguereau (1879) & the featureless planet
Not too much in common...

So, how did she become associated with the planet?  Even more strangely, the ancient  Akkadians, Assyrians, and Babylonians had a goddess of love and beauty as well whom they called Ishtar.  Guess what?  She also was considered the personification of the planet Venus.

Ishtar (c. 1800 BCE) - British Museum

So, imagine yourself back in ancient Mesopotamia thousands of years ago.  Dark desert skies, no light pollution, and little to do after dark provide excellent conditions for skywatching.  A very bright "star" appears in the evening sky for a few months, disappears, and then appears in the morning sky.  Over and over again.  You know it's special, not like all of the other fixed stars.  With years of observation, you can start to predict its appearances and disappearances.  Why identify this with a beautiful female diety?

Nobody knows for sure.  One speculation that I like is that it simply is beautiful.  Venus is the brightest object in the sky other than the Sun and Moon.  On a clear dark night, it shines brightly and dazzles the eye - much as a strikingly beautiful woman.  Why not?

In any case, pop outside some evening this week around dinner time, gaze to the southwest, and find Venus.  It's unmistakable - nothing else will be as bright.  Feast on her beautiful visage for a few moments before the cold December air forces you back into your warm house.

Origin of our Calendar - Part III

In my last post, I discussed how the Julian Calendar was instituted by Julius Caesar but it had the flaw of losing a day every 128 years or so.

This inaccuracy came to a head in the 1500s when church authorities finally dealt with the problem. The push to do this came from the fact that the method for computing the date of Easter uses the date of the vernal equinox. By the 1500s, the Julian Calendar was saying the vernal equinox was on March 10 instead of March 21 where it should have been and this was causing no end of confusion.

Pope Gregory the XIII, with the assistance of Jesuit astronomer Christopher Clavius, developed a new calendar and the Pope issued a Papal Bull which decreed that the day after Thursday, October 4, 1582 would be not Friday, October, 5 but Friday, October 15! The loss of 10 days was necessary to align the new calendar with the actual date in the tropical year.

The Gregorian Calendar is now also known as the Western or Christian Calendar and is the internationally accepted civil calendar. The month names and days are familiar to all of us:

   January (31 days)
   February (28 days, 29 on leap years)
   March (31 days)
   April (30 days)
   May (31 days)
   June (30 days)
   July (31 days)
   August (31 days)
   September (30 days)
   October (31 days)
   November (30 days)
   December (31 days)

The days of the months remembered with the traditional rhyme which dates back to the late 1500s):

   Thirty days hath September,
   April, June, and November;
   All the rest have thirty-one,
   Save February, with twenty-eight days clear,
   And twenty-nine each leap year.

How is this different from the Julian Calendar?

What Pope Gregory did was institute another rule – years divisible by 100 would be leap years only if they were divisible by 400 as well. In other words, 1600 and 2000 were normal leap years but 1700, 1800, and 1900 were not (these would have been in the Julian Calendar). So every 400 years, you lose 3 leap year days. This gives the average length of the year as:

   400 yr x 365.25 d/yr = 146,100 d – 3 d = 146,997 d / 400 yr = 365.2425 d/yr [on average]

Compared to the tropical year value of 365.2421897 days, this gives a difference of 0.0003103 days. Let’s calculate how many years it will take before we have an error of 1 day.

   0.0003103 d / 1 yr = 1 d / X yr [Here’s the ratio]
   X yr = (1 d) (1 yr) / 0.0003103 d [Rearrange the terms to solve for X]
   X yr = 1 yr / 0.0003103 [Cross off day units]
   3222.69 yr [Solved]

In other words, the new Gregorian Calendar will lose a day every 3,223 years as opposed to the Julian Calendar error of a day every 128 years. From its institution in 1582, it will only have lost 1 day by the year 4805!

The above diagram shows how the date of the summer solstice shifts each year to fall sometime on either June 20^th, 21^st, or 22^nd.  Each dot represents the date (and time) of the summer solstice for that year.  Note the shifts by a day in 1800, 1900, 2100, and 2200 (because we omit January 29 since they're not divisible by 400 so are not leap years) but not 2000 (since it is divisible by 400 and is a leap year so we keep the four year leap year sequence).

People rioted in the streets in some places over the loss of 10 days when October, 5 changed to October 15 but Catholic countries relatively quickly adopted the new calendar (the Pope still had a lot of power at that time). It took over 100 years before most of the Protestant countries in Europe abandoned the Julian Calendar. Great Britain and the American colonies didn’t switch until 1752 and in Russia, it wasn’t adopted until the Russian Revolution of 1917. One of the last major holdouts, the Eastern Orthodox Church, still uses the Julian Calendar for calculating the date of movable feasts (church holy days that don’t fall on the same date each year).

When England switched (the Calendar Act of 1750), the date of September 2 was followed by September 14 in 1752.  A number of people saw the change as a "Catholic plot" and reputedly rioted apparently believing the government took away days of their life chanting "Give us back our eleven day!"  Others welcomed the change - Benjamin Franklin wrote "“It is pleasant for an old man to be able to go to bed on September 2, and not have to get up until September 14."

"An Election Entertainment" by William Hogarth (1755)

The famous painting above, according to Wikipedia, is "loosely based on the 1754 Oxfordshire elections, in which the 1752 calendar change was one of a number of issues brought up by Tory opponents to the Whig candidate for MP...  The painting shows a Whig banquet, and 'Give us our Eleven Days' is a stolen Tory campaign banner."  The banner is the small black square, with white writing, under the boot of the gentleman in the gray coat sitting on the floor at front.

No matter what you do, a calendar will always have some accumulating error due to the fact there are 365.2421897 days in a tropical year and, worse yet, that number is an average since the shape of the Earth’s orbit varies a bit year to year and over geologic time periods.