Saturday, November 30, 2013

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 20th, 21st, or 22nd.  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.

Friday, November 29, 2013

Origin of our Calendar - Part II

In my last post, we discussed the origins of our modern calendar in early Rome.  We left off with the beginning of the reign of Julius Caesar and the calendar being hopelessly out of sync with the seasons.

The Julian Calendar was a reform of the Roman Calendar and instituted by Julius Caesar in 45 BCEWhere did this new calendar come from? Julius Caesar spend time in Egypt from 48-47 BCE where he became embroiled in the Ptolemaic dynastic war (and with Cleopatra). Julius Caesar was an intelligent man who spent much of his time in Egypt learning about their knowledge and culture. It was there that he heard about the ancient Egyptian solar calendar of 365 days.

Caesar (Rex Harrison) & Cleopatra (Elizabeth Taylor) in Cleopatra (1963)

The Egyptians actually knew the year was 365.25 days long since they they had learned if from the ancient Greeks (the city of Alexandria, on the Mediterranean coast of Egypt, was a center of Greek knowledge during the Greek classical age and hosted the largest library in the ancient world).

Egyptian calendar at Luxor

When Julius Caesar returned to Rome, he decided to reform the calendar which everyone acknowledged was a mess. He called together a council of mathematicians and astronomers, notably Sosigenes of Alexandria, who pulled together the old Roman Calendar, the Egyptian solar calendar, and the knowledge that the tropical year was 365.25 days long (this knowledge goes all the way back to Eudoxus of Cnidus  (pictured at right) – a brilliant Greek mathematician who lived around 375 BCE).

Roman historian Pliny the Elder wrote around 79 CE:

"There were three main schools, the Chaldaean, the Egyptian, and the Greek; and to these a fourth was added in our country by Caesar during his dictatorship, who with the assistance of the learned astronomer Sosigenes... brought the separate years back into conformity with the course of the sun."

In order to align January 1, 45 BCE with its correct position in his new calendar, Caesar decreed that 46 BCE would be 445 days long – how far the old Roman Calendar had fallen behind the “real” date by the position of the Sun.

The Julian calendar had the following months.

   Ianuarius (31 days)
   Febrarius (28 days, 29 on leap years)
   Martius (31 days)
   Aprilis (30 days)
   Maius (31 days)
   Iunius (30 days)
   Quintilis (Iulius) (31 days)
   Sextilis (Augustus) (31 days)
   September (30 days)
   October (31 days)
   November (30 days)
   December (31 days)

The old Roman month of Quintilis was renamed Iulius in Julius Caesar’s honor after his death in 44 BCE shortly after his calendar reform (it didn’t make much sense to keep calling the seventh month “fifth”).

A popular Roman senatorial decree in 8 BCE changed the name of Sextilis to Augustus after Augustus Caesar.

“Whereas the Emperor Augustus Caesar, in the month of Sextilis, was first admitted to the consulate, and thrice entered the city in triumph, and in the same month the legions, from the Janiculum, placed themselves under his auspices, and in the same month Egypt was brought under the authority of the Roman people, and in the same month an end was put to the civil wars; and whereas for these reasons the said month is, and has been, most fortunate to this empire, it is hereby decreed by the senate that the said month shall be called Augustus.”

So by the beginning of the Christian Era, all of the months of the calendar had the names by which we know them today.

Adding up the days of the month gives us 365 days in the year. By adding a leap year every 4 years , giving 366 days, the average length of the year was now 365.25 days. Since the mean tropical year (from solstice to solstice) is slightly shorter at 365.2421897 days, this gives a difference of 0.0078103 days.

Let’s calculate how many years it will take before we have an error of 1 day (isn't math just wonderful!):

   0.0078103 d / 1 yr = 1 d / X yr [Here’s the ratio]
   X yr = (1 d) (1 yr) / 0.0078103 d [Rearrange the terms to solve for X]
   X yr = 1 yr / 0.0078103 [Cross off day units]
   128.04 yr [Solved]

So, every 128 years, the calendar is off by one day – the date of the solstice will occur one day before the actual solstice – that’s actually a lot of error! Over time, the Julian calendar was also doomed to failure for this inaccuracy.

Next post, the calendar reform of Pope Gregory...

Thursday, November 28, 2013

Origns of our Calendar - Part I

Ever wonder where the names of our months came from?  Specifically, have you ever wondered why September, October, November, and December have prefixes that mean 7 (septem), 8 (octo), 9 (novem), and 10 (decem) in Latin even though they are the 9th, 10th, 11th, and 12th months of our calendar.  No?  Just me?  Oh well, I'll explain anyway.

The original Roman Calendar was a lunar calendar similar to that used by the earlier Greeks. Since the time between new moons averages 29.5 days, months alternated with either 29 or 30 days. The first day of the month, the kalends (from which we get “calendar”) started with the first appearance of the crescent after the new moon, the nones were the two days of the quarter moons, and the ides (in the middle of the month) were the days of the full moon.
   Who is it in the press that calls on me?
   I hear a tongue shriller than all the music
   Cry "Caesar!" Speak, Caesar is turn'd to hear.
   Beware the ides of March.
   What man is that?
   A soothsayer bids you beware the ides of March.

Julius Caesar (Act 1, scene 2, 15-19)
William Shakespeare

The Murder of Caesar
Karl von Piloty (1826–1886)

At some point in history, this traditional lunar calendar was replaced by a solar calendar roughly in line with the length of the tropical year (the length of time from equinox to equinox). It was attributed to Romulus – the mythical character who, along with his twin brother Remus, was fathered by the god Mars, abandoned as an infant to die, suckled and raised by wolves, and founded the city of Rome around 753 BCE.

Romulus, vainqueur d'Acron, porte les d├ępouilles opimes au temple de Jupiter
Jean Auguste Dominique Ingres (1780–1867)

This Roman calendar started on March 1, the month containing the vernal equinox, and consisted of 10 months:
   Martius (31 days) Honors Mars, god of war (when armies marched off to war)
   Aprilis (30 days) From Latin aperire or “open” (leaf buds are opening)
   Maius (31 days) Honors Maia, Greek goddess of fertility (flowers are blooming)
   Junius (30 days) Honors Juno, goddess of marriage (why we have June weddings)
   Quintilis (31 days) Latin for five (fifth month)
   Sextilis (30 days) Latin for six (sixth month)
   September (30 days) Latin septem or seven (seventh month)
   October (31 days) Latin octo or eight (eighth month)
   November (30 days) Latin novem or nine (ninth month)
   December (30 days) Latin decem or ten (tenth month)
See, September, October, November, and December once did make sense!
Anyway, if you're like me, you'll have added up those numbers and see that they only add up to 304 day. The Romans dealt with this by having an unnamed and unnumbered winter period of about 61 days in the period of time we now call January and February.

King Numa Pompilius conversing with the nymph Egeria in her grotto
Bertel Thorvaldsen (1770-1844)
Around 713 BCE, the legendary(?) second king of Rome (after Romulus), Numa Pompilius, is credited with adding two months to the calendar, altering some of the days of each month, giving the following:
   Ianuarius (29 days) Honors Janus, the two-faced god of gates and doorways
   Februarius (28 days) Latin Februra – a day of purification held during late winter
   Martius (31 days)
   Aprilis (29 days)
   Maius (31 days)
   Junius (29 days)
   Quintilis (31 days)
   Sextilis (29 days)
   September (29 days)
   October (31 days)
   November (31 days)
   December (29 days)
This add up to 355 days, still 10 days off from the length of the solar year. To accommodate things, a complicated method was used. For religious reasons, February was split into two parts – days 1 to 23 and days 24 to 28.  Every once in a while, a leap month of 27 days (Mensis Intercalaris) was inserted between the two halves of February.
The decision to add the intercalary month was that of the Pontifex Maximus and done every 2-3 years. This position was a political appointment and many in the position abused their power by lengthening the year when it didn’t need to be in order to keep their political allies in power. By the time Julius Caesar was Pontifex Maximus around 46 BCE, the calendar was almost a full season (80 days or so) off from the date of the Vernal Equinox!

Next post - Julius Caesar's calendar reform!

Wednesday, November 27, 2013

Chazy Reef - Part II

In my last post, I discussed the geologic setting of the Chazy Reef.  Today, I'll just show some images from my visit last month to the Goodsell Ridge and the Fisk Quarry Preserves on Isle La Motte in Lake Champlain, Vermont.

The Goodsell Ridge Preserve has a visitor's center that's supposed to be nice but it wasn't open when we were there.  You can, however, park and walk around the property which is studded with low outcrops of limestone.

Some dork walking around staring at rocks

Some of the limestone shows interesting dissolution features along the fractures.

Far more interesting, however, are the ubiquitous fossils studding the rock.

Marine gastropods (snails) - Maclurites
More gastropods
Yet another (can never have too many snail fossils!)
Squid-like cephalopod shells

Swirly fossil of a stromatoporoid (type of calcareous sponge)

It's hard to show in pictures, but when examined closely, the limestone was simply full of fossil fragments (much of it difficult to identify).

We next went to the Fisk Quarry Preserve, a short drive away, and walked around this wonderful abandoned limestone quarry (most old quarries like this are posted, it's nice to see one open for people to explore).  This is the oldest quarry in Vermont, dating back to 1803.  Polished limestone from this area (incorrectly called marble) can be found in such locations as the Brooklyn Bridge, Radio City Music Hall, the National Gallery in Washington, D.C., and the Vermont Statehouse in Montpelier.

Fisk Quarry from one angle
Fisk Quarry from a different angle
Yet another view

As you can see, my family was overjoyed to be here.

See how excited they are to search for fossils on a Sunday morning!

They later amused themselves by staring at a duckweed covered pit of water and all was well.

Wonder what evil lurks beneath?

The floor of the quarry, where it wasn't flooded, also exhibited a lot of neat fossils.

Another gastropod (snail)

A squid-like cephalopod shell

Pelmatozoan columnal - a stalked echinoderm, sometimes called sea lilies

Shells at far left and right - brachipods or perhaps bivalves, not sure

Not sure.  Radial symmetry seems to indicate a coral or sponge perhaps?

The most impressive fossils, however, are the large stromatoporoid (calcareous sponge reef former) fossils in the walls of the limestone quarry.

My daughter sitting on a stromatoporoid mound.

See those white mounds in the cliff face?  Those are all stromatoporoids

 Closer view

Some fossils warranted closer inspection.

But there's a fossil half-way down the cliff!
From my wife's perspective on the other side of the quarry
Seriously, the quarry is well worth a visit if you're ever in the area.  It also tells a neat story of an ancient subtropical reef system in what's now upstate New York and Vermont.

Monday, November 25, 2013

Chazy Reef - Part I

So after visiting Ausable Chasm this past October, and spending the night in Plattsburgh, we drove into Vermont at Rouses Point, a stone's throw from Canada, and then followed Route 2 down through the islands in northern Lake Champlain toward Burlington, VT.

Cropped from Google Maps

Along the way, however, we made a detour to Isle La Motte (island just east of Chazy and the NY/VT line above) - site of the geologically famous Chazy Reef.  Never heard of it, you say?  It's unfortunate because it's one of the coolest fossil localities in the state.  And it's just sitting there - free and open for anyone to wander in and have a look.

If you go back a read my previous post about Ausable Chasm, you'll learn about the Potsdam Sandstone.  Starting half a billion years ago, when New York State was a flat featureless landscape of rock and gravel (no life yet on land), the sea began to encroach as sea levels gradually rose.  It took a few tens of millions of years, but eventually the whole of the state was covered with warm shallow seawater (we were, believe it or not, closer to the equator and in the Southern Hemisphere to boot).  The sandy seafloor (later to become the Potsdam Sandstone exposed so nicely in Ausable Chasm) gave way, after a time, to a seafloor of carbonate or lime mud - grains of the mineral calcite (CaCO3) which eventually formed limestone.  The Chazy Sea was established.

Carbonate mud seafloor in the Caribbean - just like the ancient Chazy Sea

The details are far more complex, but that summary will serve well enough for our purposes.

So here's a paleogeographic map depicting a part of the Earth some 480 million years ago during a span of time geologists call the Ordovician Period.  Look carefully at this image.  See the equator (Eq) line near the top?  See the 30° S latitude line near the bottom?  In between is proto-North America, called Laurentia by geologists, rotated clockwise by 90°.  The modern-day states are outlined, can you identify the sideways New York near the lower right?  See that red dot?  That's the location of the Chazy Reef as it was forming.

Ron Blakey, Colorado Plateau Geosystems, Arizona USA.

Note that the Chazy Reef was around 30° S latitude just offshore in a shallow, subtropical sea.  That chain of islands to the south are a line of volcanoes ominously approaching North America, eventually to collide, but nothing to worry about now.  It's all sunshine and gentle trade winds in the Chazy Sea.  A beautiful place to live if you were a marine invertebrate.

And marine invertebrates did live there, building a reef system over time that rivaled the Great Barrier Reef in our modern world.  The Chazy Reef stretched for 1,000 miles (1,600 km) from Quebec to Tennessee.  Only small patches of fossil material remain of this once massive reef and one such place to preserve it is Isle La Motte in Lake Champlain.

The Great Barrier Reef - what upstate NY looked like 480 million years ago

There are two sites on the island designated as U.S. National Landmarks and protected by the Isle La Motte Preservation Trust - the Goodsell Ridge Preserve and the Fisk Quarry Preserve.  In my next post, in a day or two, I'll show some pictures of fossils from these amazing sites.  For now, I'll leave you with this:

Limestone bedrock on Isle La Motte.  The spiral is the cross-section of a fossil gastropod (marine snail) named Maclurites magnus.  Just laying there for all to look at.  Cool, isn't it.

More to come...

Wednesday, November 20, 2013

Ausable Chasm

Earlier in the fall (during peak leaf season), my family and I took a two-day drive up to the Plattsburgh area in New York, then across the top of Lake Champlain (spitting distance from Canada) and down through Vermont.  We obviously saw a lot of pretty trees changing colors.

Since I'm a geologist, I also subjected my long-suffering family to two geological areas (one more touristy than the other) - Ausable Chasm and the Chazy Reef.  Today I'll talk a bit about Ausable Chasm (and will tackle the Chazy Reef on another day).

Ausable Chasm is a sandstone gorge through which the Ausable River (Ausable is French for "of sand") runs for a couple of miles (~ 3 km) from the area just northeast of Keeseville, NY toward Lake Champlain.  The gorge is as deep as 300-500 feet (90-150 m) in places and only 20-50 feet (6-15 m) wide.  It's a popular summer tourist attraction with walkways and overlooks through the gorge.

Not a good place for those who don't like stairs

Geologically, the gorge is pretty simple.  The Ausable River carved a gorge a little over a mile long (~2 km) down through the Cambrian-Period (about 500 million-years-old) Potsdam Sandstone since the end of the Pleistocene Epoch ice age (which ended up there around 10,000 years ago).  It was basically due to the headward erosion of ancestral Rainbow Falls which is today located near the visitor's center.

Peaceful waterfalls relentlessly cutting

A little math, just for fun...  2 km / 10,000 yr = 0.0002 km/yr = 20 cm/yr (about 8 in/yr).  To tell the truth, that seems a bit high to me but we have to realize that as the ice age was ending, there were tremendous volumes of meltwater flowing off the massive continental glaciers and water volume (and erosion) would have been much greater in the past.  Remember, while we calculate an average, erosion is discontinuous in time - for example, 100-year floods cause massive amounts of erosion in a day or two (read about the Devastating Floods of 1996 at Ausable Chasm).  Hiking the gorge this year, I still saw plenty of evidence of those floods.

I-beam from destroyed bridge in side canyon

Ausable Chasm was first seen by non-Native Americans in 1765 and, since then, has been a draw to tourists in the eastern Adirondacks.  Landscape photographer Seneca Ray Stoddard took a number of stereographic photos of the chasm in the post-Civil War era which also publicized the site (note that walkways existed through the gorge even back then).

The path of the gorge seems to be controlled in places by joints (vertical fractures in the sandstone) and faults.  A number of side canyons have also eroded out along those fractures (as in the I-beam picture I showed above).  This is especially true near the end of the chasm where the river takes a couple of extreme right-angle turns and is very narrow.

From Google Maps
The straight and narrow part at the end

In a few places, the river even changed course in the past and left behind dry canyons you can hike through (and we did).

Now a few words about the Potsdam Sandstone which makes up the walls of the chasm.  It's a great story and I could go on for pages but I'll just give a quick summary here.  Over a billion years ago, a microcontinent collided with proto-North America and thrust up a Himalayan-scale mountain range (exactly the same as India's recent collision with Asia forming the actual Himalaya).  These mountains eventually eroded away over hundreds of millions of years (as will the Himalaya - nothing lasts forever).  This eroded surface became the basement rock of New York State.

About 550 million years ago, sea levels rose and ocean water started lapping onto that bare metamorphic bedrock (no life existed on land yet).  First a sandy beach, then a shallow seas.  These sands eventually lithified into sandstone.  We call this the Potsdam Sandstone in upstate New York.

The lower part of the Potsdam contains pebbles and fragments of the underlying metamorphic basement rock.  Lower parts of the sandstone also show cross bedding indicating deposition in an environment of braided rivers and streams.  It then becomes more of a pure sandstone (in the past it was mined for its pure quartz composition) as you move upwards which has some ripple marks and a few marine fossils indicating a shallow sea.

See the ripples on the sandstone bedding plane?

Trace fossils are more common than actual body fossils (although trilobites and even a rare jellyfish fossil has been found in the Potsdam).  Here are some trackways from an ancient arthropod (there's no consensus among paleontologists about what made this track, even if it was an arthropod or a type of molluscan) walking on the seafloor (it's a slab on display near the visitor center).
Here's one of the coolest fossils from the Potsdam.  It's now on display in the New York State Museum in Albany.  These trackways on ripple-marked sandstone (looking like motorcycle tracks) were made by a large arthropod scooting along the bottom of the sea half a billion years ago.
Climactichnites tracks in the New York State Museum
Yea, yea, I know what you're thinking right about now if you're interested (and interesting - I'd probably get along well with readers who read my rambling posts on this blog) enough to have read this far.  You're thinking how I wrote this whole post of Ausable Chasm and haven't put in one "traditional" photo of the main part of the chasm.  Ok, here you go.
Pretty place
Being the curmudgeon that I am, let me add that all the websites and guidebooks rave about the elephant's head rock formation at Ausable.  Somehow we missed it.  I don't care.  I'm far more interested in looking at the real features in the rocks, the features than mean something (like ripple marks, for example), rather than artifacts of some promoter's often-limited imagination.  It always irritates me when guidebooks to natural places like gorges and caves make up cute names for all the rock features ("goblin's nose" or "devil's den") yet don't explain at least a little of the science of what they're seeing.  These aren't just featureless gray rocks that happen to resemble something.  The Potsdam Sandstone represents the first influx of an ancient sea on a rocky, barren landscape devoid of terrestrial life half a billion years ago.  That's far more interesting to me that a rock that looks like a fucking frog.  I know I'm a dying breed though when I see that Ausable Chasm has been adding all kinds of activities (tubing, rapelling, zip lines across the canyon, for example) to appeal to dim-witted, adventure seeking tourists who could care less what the hell they're zipping across.  The slow Disneyfication of America (nothing against Disney, but does every place now have to feature thrill rides to be interesting to people?).
Some grumpy old bastard with no sense of fashion looking at rocks
"As long as I live, I'll hear waterfalls and birds and winds sing. I'll interpret the rocks, learn the language of flood, storm, and the avalanche. I'll acquaint myself with the glaciers and wild gardens, and get as near the heart of the world as I can." - John Muir (1871)