London, Revisited

We woke to cool weather in Ireland, but it was only 4:30 am.  We got our stuff together and headed to our bus stop, about 3 blocks away.  Our bus came a few minutes after we got there and took us to the airport.  We dropped off our bags, headed through security (wearing our shoes), and stopped for breakfast.  We made it to the gate with plenty of time to spare.  The plane was an A319 with 3-3 seating.  It was not very full, so we had two seats together by ourselves.  The plane landed roughly on time and we did not have to go through customs.

The plane flew into Gatwick airport, which is quite a ways south of London.  We were able to get a train ticket into the city that included a 1 day Underground pass for only a quid more.  The train took us into Victoria station, which we had been to several times.  We made it to our hotel just after noon and checked into our room.  We are staying the same place we stayed last week and the staff recognized us and seemed happy to see us.

Our hotel is on this street.

A church near our hotel.

It was interesting to see Google's doodle today recognize the accomplishments of Rosalind Franklin.  I found it fun to read that she was born in Notting Hill, near our hotel.

Our plan was to visit the National Gallery and get lunch along the way.  We got sandwiches at Subway and ate them in the subway as we waited for our train, which came as we finished eating.  Subs were the way to go today.

We walked through Trafalgar square to get to the museum.  The square was packed with people, a precursor for what we experienced in the museum.  Despite the crowds, we saw some great masterpieces from Cezanne, Van Gogh, Manet, Monet, Serrat, Caravaggio, Rembrandt, Rubens, Van Eyck, Da Vinci, to name a few.  Amy's favorite was Music in the Tuilleries by Manet.

After leaving the museum, we headed to a knitting store.  Part of our route took us through Green Park where there was a gun salute for the recent Royal baby.  We also shopped along the way.  We came to Harrod's again and decided to do some additional shopping.  It is quite an amazing store and we saw quite a bit more tonight than last time.  It is a bit like Meijer, with just about everything, except very upscale.  Today we walked through the pet area and saw dog collars for 250 pounds.  Amy was impressed by the full sized Santa made from Legos.

The crepe restaurant we ate at the other day was so good and close to where we were, we stopped there for dinner.  Once again the crepes were great.  A quick walk brought us to the tube station, and we took the train to our hotel stop.

Well, this was our last full day together in Europe.  Amy flies home tomorrow and I head off to two conferences in The Netherlands.  It has been a great trip so far.  Amy was a big help navigating the Scottish roads - I could not have seen all the things I did without her help!  While there is always more to see and do, I was able to accomplish everything and more than when I originally planned this research trip.

Irish eyes are smiling

We started the day with a cab ride to suburban Dublin for some mathematical history.  We took a cab ride for a few miles outside the city center where we a staying to see the spot of a famous mathematical moment.  As he was walking, Irish mathematician Hamilton discovered quaternions and, without pen and paper to record his discovery, he used the stones of the nearby bridge to record his breakthrough.  This is commemorated on the bridge with a stone plaque.  The plaque is a bit hard to read, but states:

Here as he walked by
on the 16th of October 1843
Sir William Rowan Hamilton
in a flash of genius discovered
the fundamental formula for
quaternion multiplication
i² = j² = k² = i j k = −1
& cut it on a stone of this bridge

Quaternions are numbers that extend complex numbers, having 4 parts rather than 2, as a 4-dimensional entity.  The directions for each component are indicated by the numbers 1 and the letters i, j, and k. They have applications in physics and mathematics, particularly in modeling rotations in three-dimensional space.

The commemorative plaque.

Broombridge, where the plaque is located.  This bridge crosses over a rail line and the Royal canal.  A multiple use path follows along the canal, making this a pleasant little spot.  There were swans and ducks in the canal, but were a little camera shy.

Our next destination was the National Museum of Ireland - Decorative Arts & History.  This museum contains decorative art from Ireland and is housed in an old army barracks.  There is also some historical military displays and information about Ireland's partial independence from Britain.  There was some Celtic interlace, but not like the archaeology museum we visited yesterday.  We also had a late lunch at their cafe.

We walked from there back towards the hotel and did a little shopping along the way.  This is the first day we have had where it has been cool enough to walk around without breaking a sweat.  Amy's Irish eyes were smiling!  I bought a compass for my wristwatch strap to help with orientation in the ancient cities of Europe.  The GPS on my phone works most of the time, but does not always show the correct location or direction, especially in buildings or narrow streets.  We walked by the Jameson Distillery, but opted out of the tour.  We stopped for drinks and a snack at the local Hard Rock Cafe instead.

A view of Dublin.

River Liffey.  This river runs through Dublin and its bridges are quite busy.

Our final stop was at the Chester Beatty Library.  This library, now a public collection, was acquired over the lifetime of Chester Beatty.  He had a particular interest in ancient books.  We saw some of the earliest known versions of New testament writing, dating back to about 200 AD.  There were also many illuminated texts, etchings, and paintings on display.  This we adjacent to Dublin Castle.

Part of Dublin Castle.

We came back to the hotel to rest a bit then had dinner at a local pub.  We need to leave the hotel at 5 am, so we spent some time packing and getting organized.  Amy has expanded her suitcase with lots of items we have picked up over the past 10 days.  It seems doubtful the suitcase will close.  "I think I'm going to make it." says Amy.  Tonight it closed.  We'll see after one more day in London!

I have been hearing rain falling as I finish this post.  There was also a flash and the sound of thunder.  This is the first rain of any significance since we arrived.  Hopefully we will not have to wait in the rain for our bus to the airport tomorrow morning.

Celtic knot walk

Today was our first easy day in a number of days.  This is our first night where we did not have to pack since leaving London.  We were able to sleep in and get some additional rest.  We are staying within walking distance of everything we are planning on seeing, so we don't need to worry about public transportation.  It has also cooled down, with cloudy weather and temps in the mid 70s.

We headed out to find some breakfast along our way to the museums.  We found a little cafe and had coffee (me), tea (Amy), and some cinnamon rolls.  We also did some window shopping at little shops along the way.

Here was a Mexican restaurant we saw along the way.  Want some ass?
That was their catch-phrase.  As you might assume, me and my fair lass decided to pass.

The first and most interesting museum we visited was the National Museum of Ireland - Archaeology.  It contains artifacts from the earliest peoples of Ireland up to the medieval time period.  My interest in here is related to mathematical connections and themes in the development of the interlace and knotwork that is most associated with Ireland.  The museum had a large number of fantastic pieces in stone, bronze, gold, silver, antler, leather, and wood.  There was an influence of the vikings, frequent visitors to the British Isles,  on the development and usage of decorative interlace patterns.  There are many cultures that have used interlace patterns and there is no clear history on the spread of this ornamentation.  Also, there is no record of how Celtic interlace was made, but there are some theories and modern working techniques.

Gallagh man - a bog body found in 1821.  These are found occasionally
as peat from former bogs is dug.  This fellow lived around 400-200 BC.

Some stone spheres from the same time (3300-2800 BC) as the Scottish carved stone balls.  The larger
spheres are about the same size as the Scottish carved stone balls.

A decorated bronze piece from 100-200 AD.

Interlace on a Crozier from about 1100 AD.

The Cong Cross from about 1200 AD. 

Detail on the Cong Cross.

Bone with test carvings.

Another piece showing under crossings with simple hatched.
MC Escher also used this element to show over and under crossings.

We then headed to the National Gallery.  On the way we stopped at the National Library and saw exhibits on Yeats and another on the 50th anniversary on JFK's visit to Ireland.  We also had a late lunch across the street from the National Gallery.  After seeing the artwork, we headed back to the hotel via a "shortcut" I had mapped.  For those of you who don't know, a "shortcut" tends to be quite the opposite.

We walked through St. Stephen's Green and Iveagh Gardens, both nice public park spaces south of where we are staying.  We stopped in a few shops along the way.  There were several pedestrian streets along our route filled with people.  Some shops were unique to Dublin, but there were also the multinational corporate giants as well.

St. Stephen's Green.

Roses in Iveagh Gardens.

Despite this being an easy day, we are tired.  We decided to head back to the hotel to relax and just have some sandwiches again.  We still have a some items from yesterday.  Amy brought along a highly packable nylon bag that is convenient for groceries.  The picture count for today was 234.  At this point I have taken about 1400 pictures.  I still have room on my memory card for over 4000 more, so I am not worried about running out.  Like a Celtic knot, we started at the hotel, meandered quite a bit, crossed over our path a few times, then ended back at the hotel.

Ireland

Today we flew from Glasgow to Dublin, Ireland.  We got up at 5:30 to catch our 8:20 flight. We returned the car without a full tank, despite other intentions.  We did not see a gas station on the way to the airport.  Where do they hide them in Scotland?  We saw an electronics store at the airport and found a new charger for Amy's phone.  It is a nice international charger that will work all over the world.  We'll put it to the test!  At breakfast we saw the buzz on TV about the royal baby.

Ireland, unlike the UK (England, Scotland, Wales, and Northern Ireland) uses the Euro, despite both being in the European Union.  So we have put away our pounds and have been using Euros.  Amy was able to get 100 Euros cash before leaving, so we have been able to pay for a few cash-only items, such as our bus tickets.  I will also need Euros in The Netherlands.

We landed in Dublin late morning.  The flight took just under and hour on a small turbo prop plane.  We had a very smooth flight especially considering our travel over water.  It has been hot here as it has in Scotland and England.  No sweaters or raincoats needed.  We took a bus from the airport to downtown to our hotel.  We took the scenic route to the hotel that included retracing some/many of our steps.  The hotel did not have our room ready as it was way before check-in time, but they stored our bags and we headed to see some things.

The first major site was to see the Book of Kells, located in an old library at Trinity College.  The Book of Kells is an elaborately illuminated Latin Gospel from about 800 AD.  It is impressive to see the amount of effort that went into making this book.  I am particular interested in the decorative interlace and mathematical connections.  There was a long line to see it and the exhibit area was pretty crowded, but we got to see everything on display.  We then had a nice lunch at a cafeteria on campus.

Most museums are closed on Mondays in Dublin, so we went to the Guinness Storehouse for their brewery tour experience.  I was underwhelmed by the tour.  It was not free, it was self paced, it was not in a working building, and it was dark for no apparent reason.  It did tell the story of beer making, but definitely nowhere near as good as the Sam Adams tour.  The tasting room, on the other hand, was excellent!  We each had an average of one pint of Guinness on the 7th floor Gravity Bar with 360 degree panoramic views of the city.

A gate to the factory.

The brewery commemorates the important contributions of an employee to the field of statistics.

A view from the Gravity Bar.

It was getting late so we headed back to the hotel.  I had found some yarn shops that I thought Amy would like.  We passed through some areas that seemed a little seedy, but eventually got to the yarn shop.  We had a nice time visiting with the owner and Amy purchased some yarn.  Just two blocks away from the yarn shop was St. Patrick's cathedral.  It was fun to see.  We found another yarn shop, but not much of interest, so we headed for the hotel.  We also stopped by a small bakery for a sweet treat and another place for a frozen treat.  Traffic here is nuts.  I am thankful not to be driving, as are most others in Dublin including Amy!

St. Patrick's Cathedral

Hot and tired from traveling, we decided to get some food from a local market and make sandwiches, hang out, watch some TV, charge our electronics, and do some blogging.  The hotel is HOT.  We have no air conditioning, because it never gets this warm.  I was able to get ice from the hotel bar, so we at least have cold drinks.  We also have a fan.

Amy was excited to hear the news about the royal baby.  That is all that the news stations here are talking about.  Lots of buzz in London and Buckingham and Kensington, places we have just visited.  It was interesting to see them on TV having just been there.

Scottish Highlands

We woke up in Aberdeen hoping for power in our electrical outlets for our electronics.  Amy had hoped for a hair dryer.  That was not the case, and the hotel was apologetic and gave us a free breakfast as they tried to fix the problem.  Today the haggis blood pudding were too much for my tastebuds.  The finally found the closet that likely contained the circuit, but could not find they key.  By this time, we needed to go.  They finally got the electrical working just before we left our room.  Having low power on our phones was a little bothersome, as I was using GPS to help navigate.

Luckily, the hotel staff was kind enough to print directions to our first destination, Oldmeldrum, a small town northeast of Aberdeen.  Our reason for visiting was to see a public art piece The Eternal Present by Janet McEwan.  Like the sculpture in Edinburgh, this sculpture is a large scale version of three carved stone balls.  It pays homage to three carved stone balls found nearby.  They are beautifully carved and are situated on a downtown corner.  We seemed to be the only people interested in them.  She has a nice blog about their creation.

Eternal Present by Janet McEwan

We decided to return to Glasgow via the Scottish Highlands.  The mountains were visible in the distance as we approached Oldmeldrum, so I was excited to see them.  It was a beautiful sunny day, a rarity in Scotland we have been told by many people.  We took a wrong turn, spun around and around a round-about or two, but finally got on the right road.

A view of the highlands from Oldmeldrum.

Malt whisky is one things for which Scotland is known.  Many of the distilleries are in the highlands, so we thought it would be fun to stop at one.  Glenfiddich was just off the road so we decided to stop there to stretch our legs and learn about their product.  We had a very nice tour with a great guide.  We finished with a sample to calm our nerves before continuing deeper into the Scottish hills.

The distillery.

An old delivery truck.

Pot stills.

One of about a dozen Ferrari's visiting the distillery.

Many malt whisky distilleries, including Glenfiddich, are within 25 miles of Dufftown.  On a mathematical note, the latitude of Dufftown is 57.4408° N, which is quite far north. It also very close to 1 radian, which  is 57.2957795°.  For you less mathematical, 1 radian of angular measure on a sphere corresponds to an arc that has the same length as the radius of the sphere.  This means that in Dufftown we are about as far from the equator as we are from the center of the Earth!  Could this be part of the magic of the area for making malt whisky?

We then took a road that had spectacular views.  It was also very steep, twisty, and narrow.  There were also domestic sheep grazing near the road, similar to cattle in some western US mountain areas.  The road was only one lane for a number of miles, with passing turnouts.  These were so you could wait for oncoming traffic to pass or vice-versa.  Frequently times the visibility was less than 100 yards.  I had to back up a few times to a passing area to let an oncoming car pass.  One place the road sign indicated a 20% climb.  It was an exciting drive, but we did not make great progress.  We could see snow in some of the mountain passes.

The highlands.

Mountain road.

Down and around we go!

Beautiful day.

Along the way, we stopped at Balmoral Castle, the royal home in that part of the country.  We did not get to see much, but the exterior and grounds were pretty fantastic.  The castle is on a clearing in some deep woods near a mountain river.

The Dee river near Balmoral.

Balmoral Castle

The gas gauge in the car had been getting lower, but I had only seen one gas station since leaving Aberdeen and that was in Oldmeldrum.  It was closed.  I thought we would see another one, but it was Sunday evening by now, and most stores were closed.  So we continued our drive.  The nearest big town was 60 miles and the gas range on the car said 60 miles.  I thought "this seems doable" and we pushed forward.  As we went along, we started climbing one final pass before leaving the highlands.  The range indicator went lower much quicker than we were making progress.  Soon our range had reduced to 30 miles with about 50 to go before getting to a large town.  At the top of the pass, there was a ski resort (closed) and restaurant that was open.  I asked about gas and they said the nearest gas was 22 miles in the direction from where we just came and 25 miles in the direction we were going.  I explained my low fuel and they were kind enough to say they would help if they saw me stranded, as they were heading that way in a few minutes.  Luckily it was mostly downhill, and we did not have a lot of fuel weight, so the car was lighter.  We got into town looking for the station, but did not see it, so we asked someone as we stopped at an intersection.  He pointed down the road in the direction we were headed and we took off.  Out of the corner of my eye I caught the sight of the gas station, but it was too late to turn, so we had to zip around the block.  I was glad the gas station was downhill, as the car was still running, but I did not know how long that would last.  Finally we got to the station.  We had made it!  That was a little close, but I was glad we had a little more excitement in our Scottish driving experience.

Once through town the road became a freeway and we had a relatively easy drive into Glasgow.  We only upset one drive enough to honk at us in town.  Our hotel was the same one we stayed at a few nights ago.   The hotel had parking behind the hotel, but it was full.  That means we would need to parallel park.  Now I am usually don't mind parallel parking.  I've done it with a 15 passenger van on a number of occasions.  This was the first time parking on the right and sitting on the right.  To make things more interesting, just as I started, one car then another came up behind me on the one-way street, so they got to watch me.  What I thought was a good job was actually pretty poor after seeing it from outside the car.  So I got in the car to improve the location.  Too bad the steering wheel wasn't on the side I had gotten into.

After checking into the hotel, we had dinner at a crepe restaurant two blocks away.  This time the hotel was full, so we were stuck with a small room without a bathroom.  It was only for the night and we were leaving early, so we settled in and were able to charge some electronics.  It was good to be out of the car!

Scotland Museum Crawl

We finalized our plans for the day as we had breakfast at our hotel.  I decided that I would try a wee bit o' haggis.  Amy declined.  I was expecting the taste of scrapple I had in Pennsylvania a few years ago, but much to my surprise it was actually quite tasty.

Our first stop for the day was the St. Andrew's museum.  This was about an hour from our hotel and situated in St. Andrews, of golf fame.  The museum was nice and the desk workers were very helpful.  They have two carved stone balls in their collection.

Our plan was to visit the golf museum also, as it is the home of golf.  It was a bit challenging to get there: several wrong turns, going completely around a roundabout, and stalling the car doing a u turn on a street that suddenly became one way.  I wondered what par for getting to the museum was?  We learned more about the history of golf, which was fun.

The next destination was the McManus museum in Dundee.  This is a large city (156,000) on the way to Aberdeen.  Let's just say we are probably not liked by everyone in Scotland today.  I went twice around one roundabout and maybe drove down a pedestrian lane.  Still no fiery car crash.  I have also negotiated several parking structures and tight parking lots.  Once we got to the museum, we saw their collection of carved stone balls and headed for some lunch.

A one-lane bridge we crossed.

A small Scottish town.

Much of the countryside was just a blur.

Montrose was our final museum of the day.  They had a really nice collection of carved stone balls.  They also had some other interesting items such as a hat worn by Napolean and a death mask of Napolean.  Like every small museum we have visited, the staff have been very friendly.

We saw quite a few roses.  The bees were all abuzz.

On the road to Aberdeen we saw signs for Donnattar Castle and decided to stop.  It is perched high on an outcropping in the North Sea.  Also a perch for hundreds of gulls.  The weather had become cloudy, making the view very nice.

Donnattar Castle

We wound our way around Aberdeen until we found our Hotel.  It was conveniently located in a nest of one-way streets, and others under construction.  Parking a couple blocks away.  Luckily we were able to unload our bags.  We had dinner at the hotel, as there was not much else close open.  Our hotel was generally nice.

It was also time for laundry.  We used some time in the laundry room to work on email and blogging.  Then, BAM!  Amy was charging her cell phone, as she had several times on the trip, and the charger circuits fried, tripping the electrical breaker for the room outlets.  Luckily the lights were on a different circuit.  The hotel staff could not find the breaker (even after much searching), so we were without electronics in the room for blogging or email, so we called it a night, hoping for power in the morning.

I have a message for you from the hotel management

Anyone who knows Amy will know of her propensity for trashing hotel rooms ala her favorite movie What's Up Doc. This trip is no different as whilst charging my phone last night I managed to blow the circuit breaker for all the electrical outlets in the room. And blowing up my phone charger as well. I will have to find another charger if I am to recharge my phone after today. But since we will be dashing about the highlands like William Wallace, there will no need of a phone until later. Arrghhhhhh!

DNALTOCS - Day 2

Today (well Friday) we began our adventure in our hotel room.  It did not have a hair dryer.  No worries Amy brought one we purchased before our trip that would work with the higher voltages in Europe.  That is great as long as you remember to put it on 220V rather than 110V.  If you don't, it will only work for a a few seconds before it dies.  Luckily our hotel tonight has a hair drier.

We needed to rent a car today, so after breakfast we hired a cab to take us to the airport.  We figured we would have a better selection there and better return options, as our flight leaves Glasgow early on Monday.  We were able to rent (or Hire as they say here) a VW Polo.  It is a nice little car that is big enough for us, roughly the same size as our Aveo.  The fun thing is that it has a stick shift and the steering wheel on the right side, opposite of the US.  I think the last time I drove a car with a manual transmission was several years ago when my parents had a car.  Otherwise it has been 17 years since I regularly drove a stick.  Because the driver sits on the right side of the car, the stick is on the left.  Luckily the pedal positions match what we have in the US, clutch, brake, and gas from left to right.  Driving on the left side of the road is pretty weird.  There are roundabouts to negotiate plus other cars, bikes, and pedestrians.  I did not stall the car, but did not always have the best gearing.  Starting in second and third gear is much harder than first!  I am happy to report that we had no fiery crashes or other major incidents.  It took several hours outside the car to get Amy's nerves back in the normal range.

We took some wrong turns but eventually made it to our first destination, the Auld Kirk Museum in Kirkintilloch.  They have a carved stone ball found in a nearby town.  We spent a few minutes talking with the pleasant staff there.  One had cousins from the Toledo area come visit her recently.  Then it was on our merry way through the Scottish countryside to Edinburgh.  Amy only screamed and shrieked a few times as I was driving.

Edinburgh Castle

Edinburgh Castle

A view of Edinburgh.

The next stop for the day was the Nation Museum in Edinburgh.  We parked in a lot near the spot I remembered the the museum being located.  I should have printed a map before I left, but I did not so we stated walking uphill.  After asking directions, we arrived at the museum.  They have a collection of carved stone balls, including the Towrie sphere, a particularly striking ball with four knobs and some intricate patterning.  I also got some additional information from the friendly staff at the museum's library.

The museum also contains several Lewis chessman.  

Dolly.  Not a replica, the real clone.

The first cloned sheep, Dolly, was stuffed and on display.  The straw and droppings in the exhibit added to the case's ambiance.  Note, if for some reason you decide to stuff me and put me in a museum, I think the viewers will be fine without simulated feces.

Jackie Stewart's Formula 1 Tyrrell 003 racecar.

Amy is always interested in going to yarn stores.  We found one on the way back to the car.  Amy purchased a couple skeins to make a hat.

How much is that piggie in the window,
he one with the crispy ears?

First Conundrum

Another item I saw online was a public art installation of large stone balls carved in a manner similar to the stone balls in the museums.  The artwork, called First Conundrum by Remco de Fouw, is at one side of a public square in downtown.  The local kids were having a great time playing on them.  The plaque states "Ancient carved stones believed to have been formed during the neolithic period have been found throughout Scotland. ... They remain a uniquely Scottish mystery and continue to inspire thousands of years later..."

We are about to cross the First of Forth.  As you can see, we waited
for rush hour so we could better enjoy the driving experience.

We experienced another exciting drive as we left Edinburgh for our hotel on the north side of the Firth of Forth.  Amy took some pictures as we drove across the bridge, which was a large suspension bridge.

The hotel is a very pleasant place in the middle of nowhere about 100 yards from the firth.  We had dinner at the restaurant hotel and discussed our plans for tomorrow.  We then walked outside a bit.  The weather is still very pleasant.  Our hotel for the night is a nice little place in the country.

Our hotel for the night.

A view of the firth bridge from our hotel.

One of the local residents.

The lane where our hotel was located.

Another view near the hotel.  I wish I had a bike!

A nearby building.

A view across the firth.