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Andrew Ferguson dot NET

I am an enginerd: I excel at awkward.
  • Photography
    • Photos on Flickr
  • WordPress Plugins
    • Countdown Timer
    • Dunstan-style Error Page
    • Blockquote Cite
  • Colophon
    • About AFdN
    • History
    • Some Rights Reserved
    • Contact
    • Dereference Request
  • Archives

Search Results for: explor

Dateline: Santorini, Day 1 – Another 24 Hours

  • July 2, 2009July 27, 2009
  • The Events that are: My Life

Santorini, Greece
2 July 2009

We had an entire morning to explore the others parts of Paros before we had to leave for Santorini. We headed to the north part of the island, into what looked like a fishing village.

We walked around for a bit before we booked it back to our hotel to checkout and catch our ferry.

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18.0 mm || 1/2500 || f/4.5 || ISO200 || NIKON D70
Naousa, South Aegean, Ελλάδα


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70.0 mm || 1/3200 || f/4.5 || ISO200 || NIKON D70
Naousa, South Aegean, Ελλάδα


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70.0 mm || 1/1250 || f/4.5 || ISO200 || NIKON D70
Paros, South Aegean, Ελλάδα

The plan for getting to the ferry and returning the bike was thus, load up all of our stuff (two large backpacks, two day packs, one camera bag, one bag of food) and both of us onto one 50cc scooter and make our way to the ferry. I would drop Charlie and all the stuff off at the ferry terminal, go return the bike, and then walk back to the ferry on foot. As executed, the plan went really well, and looking something like this:

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18.0 mm || 1/2500 || f/4.5 || ISO200 || NIKON D70
Paros, South Aegean, Ελλάδα


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18.0 mm || 1/3200 || f/4.5 || ISO200 || NIKON D70
Paros, South Aegean, Ελλάδα


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27.0 mm || 1/2500 || f/4.5 || ISO200 || NIKON D70
Paros, South Aegean, Ελλάδα

One of the interesting things about riding on the ferry is that while you’re given a ticket for a particular class, no one seems to actually enforce it. This was probably a good thing because knowing where we could sit was no easy task. Our tickets said “Deck,” just like they did for the trip to Paros when we actually sat on the deck, outside, for the entire trip. I was pretty miserable and was determined not to have a repeat, damn the consequences. I found some seats inside in an area marked “Economy” and decided to stake our claim. No one cared or questioned our being there, and so it was: an air conditioned seat for the ride to Santorini. Hooray!

Santorini is much like Paros, except it’s built on a the reminants of a volcano. However, the middle part has sunk back into the ocean, creating a crescent shaped island with a small mountain island in the middle.

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Thira, South Aegean, Ελλάδα

And just like Paros, we were inundated with people at the dock with signs for hostels, hotels, and camping sites. This time though, we were a bit more prepared, having done more through research. After consulting with several people, we settled on Youth Hostel Anna, a hostel recommended in the Lonely Plant guidebook. Bonus points were awarding by being placed in a room with all girls1.

A couple of girls from Vancouver, BC, who were staying in our dorm recommended a place to grab lunch and rent a quad-ATV. I went over to check out the wheels while Charlie grabbed something to eat.

Then it was off to explore the island of Santorini. We made our way toward the northern part of the island, going to the archeology museum and exploring the various tourist spots.

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18.0 mm || 1/3200 || f/4.5 || ISO200 || NIKON D70
Thira, South Aegean, Ελλάδα


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Thira, South Aegean, Ελλάδα


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Thira, South Aegean, Ελλάδα


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Thira, South Aegean, Ελλάδα


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Thira, South Aegean, Ελλάδα

And yes, those are donkey and mules you see. There’s an entire line of them, ready to take you up and down the mountain for a fee so you don’t have to stand in the looooong line for the gondola.

On Charlie’s insistence, we stuck around for the sunset, which also afforded me a change to teach him all I know about two source lighting (in this case, the sun and the flash).

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18.0 mm || 1/100 || f/13.0 || ISO200 || NIKON D70
Thira, South Aegean, Ελλάδα


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18.0 mm || 1/200 || f/8.0 || ISO200 || NIKON D70
Thira, South Aegean, Ελλάδα


Setting Sun
70.0 mm || 1/60 || f/8.0 || ISO200 || NIKON D70
Thira, South Aegean, Ελλάδα


Earth to Space
18.0 mm || 0.6 || f/3.5 || ISO200 || NIKON D70
Fira, South Aegean, Ελλάδα

Then it was a night ride back to the hostel in the cool ocean breeze. For dinner, we had moussaka, a sort of lasagne-type dish with eggplant instead of meat. It’s actually rather good.

0
  1. No, nothing scandalous happened, thanks for asking. ↩

Dateline: Paros, Day 1 – 24 Hours on Paros

  • July 1, 2009July 24, 2009
  • The Events that are: My Life

Paros, Greece
1 July 2009

We (Charlie and I) bid our farewells to Finn and Cecilie and then made our way down to the ferry terminal. The ferry boats they use to island hop are something else and not anything like the ones we use in Washington. They are specially designed and highly manuverable cruise ships with space for vehicles inside. To dock, the ferry will head straight for the dock, and then, only minutes before docking, will execute a 180 degree turn and back in. It’s pretty insane. Several ramps on the back of the boat unseal and lower for passengers and vehicles alike to disembark. Within 30 minutes, an entire boat can be unloaded, loaded, and on its way again. Perhaps the only thing more impressive than the Greek ferry system is the Russian train system.

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Samos, North Aegean, Ελλάδα


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Samos, North Aegean, Ελλάδα


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Samos, North Aegean, Ελλάδα


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18.0 mm || 1/1250 || f/3.5 || ISO200 || NIKON D70
Paros, South Aegean, Ελλάδα


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18.0 mm || 1/2500 || f/3.5 || ISO200 || NIKON D70
Paros, South Aegean, Ελλάδα

When we got in to Paros, we were inundated with people at the dock with signs for hostels, hotels, and camping sites. We had done our research and knew the price range for most hostels this time of year, about €20, give or take 5. Unfortunately, most of the hostels were full up, so we went with Hotel Francisco, at a ghastly €25/person/night (so far the highest we’ve paid for a room).

After settling in, we headed back into town to try and rent a scooter. We were able to rent a 50cc scooter with my Washington State Drivers License, and so off we went to explore Paros!

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35.0 mm || 1/3200 || f/4.2 || ISO200 || NIKON D70
Paros, South Aegean, Ελλάδα


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Paros, South Aegean, Ελλάδα


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Paros, South Aegean, Ελλάδα


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Paros, South Aegean, Ελλάδα

We made it to the back side of the island to one of the beaches, Charlie went for a dip in the Aegean Sea while I relaxed on my beach chair and edited photos. It was actually pretty awesome. Also, please take note of my amazing farmers tan.

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300.0 mm || 1/1000 || f/5.6 || ISO200 || NIKON D70
Tsipidhos, South Aegean, Ελλάδα


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95.0 mm || 1/1250 || f/4.2 || ISO200 || NIKON D70
Tsipidhos, South Aegean, Ελλάδα

Photo by Charlie Wyman.

Photo by Charlie Wyman.

As we rode back, we stopped on the side of the road to admire yet an other amazing sunset. It’s really too bad this was our only night on Paros.

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18.0 mm || 1/800 || f/3.5 || ISO200 || NIKON D70
, South Aegean, Ελλάδα

0

Dateline: Samos, Day 1 – Down Day

  • June 29, 2009July 22, 2009
  • The Events that are: My Life

Samos, Greece
29 June 2009

Well, last night I ended up not going straight to bed. First, I wanted to get some blogs posted (still playing catch, ugh). Second, Charlie needed to call his bank to get his withdraw limit changed. And then Caitlin1 called on Skype, so I had to let the two love birds talk.

In any event, I got to bed around 3am, just in time to get four hours of sleep. We woke up, packed, had a quick breakfast, and walked down to ferry. We went through customs easily enough and were off on the ferry to Greece.

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18.0 mm || 1/1600 || f/4.0 || ISO200 || NIKON D70
Kuşadası, Aydın, Turkey

I spent the first part editing photos on the outside desk, before getting tired and dozing off. I spent the last half wishing I had something more to eat. I did “splurge” on two sandwiches, a €1.80 ham and cheese toast sandwich for breakfast, and a €3.80 ham and cheese and lettuce sandwich for lunch. Neither were filling.

Meanwhile, Charlie had found Finn and Cecilia elsewhere on the ferry.

We disembarked in Samos and promptly found food and, with the help of Anthony and Pedros at ISTA, a hotel.

I ended up calling in a down day and spent the afternoon in the hotel room recharing my batteries, so to speak, while Charlie, Cecilie, and Finn went exploring.

We met back at the hotel for an amazing sunset dinner before heading to the roof to enjoy the evening. Charlie thought that we should come up with a name for our group. After some discusion, it was settled: Cecilie and the Three Musketeers (Finntaro, The Hawk, and Ferg).

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Samos, North Aegean, Ελλάδα


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Samos, North Aegean, Ελλάδα


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Samos, North Aegean, Ελλάδα


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18.0 mm || 1/50 || f/4.0 || ISO200 || NIKON D70
Samos, North Aegean, Ελλάδα


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18.0 mm || 2.5 sec || f/4.0 || ISO200 || NIKON D70
Samos, North Aegean, Ελλάδα

0
  1. Charlie’s girlfriend ↩

Dateline: Cappadocia Region, Day 1 – You Rock My World

  • June 26, 2009July 22, 2009
  • The Events that are: My Life

Cappadocia, Turkey
26 June 2009

I’m going to start by appologzing profussely for all the pictures of rocks. Cappadocia is, in essence, a giant collection of cool looking rocks and I’m pretty sure I got a picture of every single one of them. Out of 215 photos I took today, I ended up only rejecting 84 of them. Typically, I reject just over half. Not today.

Anyway, the bus ride was less than ideal. Charlie smelled like a sweaty rugby player after an all-day round robin tournament and the bus driver refused to keep the AC on. We awoke in Nevsehir and were called off the bus. A bit dazzed from just waking up, Charlie and I got off, thinking this was the guy who was going to take us to the hostel from the bus depot.

As it turned out, we think it was just a way to get tourist to purchase a tour of Cappadocia, as the guy quickly put us back on the bus once he found out we had already booked a tour. Still super confused about what happened, we finally did off at the right stop.

We got to the hostel and learned that both Michael Jackson and Farrah Fawcett had died while we were in transit. Sad times.

A quick turn around and we were off to explore the northern region of Cappadocia with our guide, Esra.

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Üçhisar, Nevşehir, Turkey


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Üçhisar, Nevşehir, Turkey


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Üçhisar, Nevşehir, Turkey


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Ortahisar, Nevşehir, Turkey

Many of the holes in the rocks were for roosting pigeons. The previous inhabitants used the guano as fertalizer.

We spent most of the day hiking around. One kilometer here, another four there. For two guys who barely got any sleep, I thought we did pretty good. We befriended Shazia, another traveler from the States who was on vacation with her mother; had an amazing buffet lunch (that’ll teach them to let to college grads eat all they want); and, toured a pottery shop, among other things.

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Ortahisar, Nevşehir, Turkey


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Ortahisar, Nevşehir, Turkey


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Ortahisar, Nevşehir, Turkey


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Ortahisar, Nevşehir, Turkey


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Üçhisar, Nevşehir, Turkey


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Üçhisar, Nevşehir, Turkey


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Üçhisar, Nevşehir, Turkey


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Üçhisar, Nevşehir, Turkey


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Üçhisar, Nevşehir, Turkey


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Üçhisar, Nevşehir, Turkey


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Avanos, Nevşehir, Turkey


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Avanos, Nevşehir, Turkey


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Avanos, Nevşehir, Turkey


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70.0 mm || 1/30 || f/4.5 || ISO200 || NIKON D70
Avanos, Nevşehir, Turkey


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Avanos, Nevşehir, Turkey


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Avanos, Nevşehir, Turkey


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Avanos, Nevşehir, Turkey


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Avanos, Nevşehir, Turkey


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34.0 mm || 1/3200 || f/4.2 || ISO200 || NIKON D70
, Nevşehir, Turkey


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Ürgüp, Nevşehir, Turkey


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Ürgüp, Nevşehir, Turkey

For dinner, we walked into town and had pide (a Turkish pizza) and a beer at a restraunt that Shazia had recommended for their kunefe, which is amazing by the way.

We wandered back to the Bat Shoestring Cave and promptly fell asleep.

0

Dateline: Tallinn, Day 2 – T and D

  • June 15, 2009July 22, 2009
  • The Events that are: My Life

Tallinn, Estonia
15 June 2009

I woke up early today, actually using my alarm clock for the first time on this entire trip, to meet a T, a good friend from work, and his wife D. T follows my blog and let me know a couple months ago that they would be on a Baltic Sea cruise about the time I would be in the Baltic states. It happened to work out that we could hang out for the day in Talllinn.

Unfortunately, today’s weather has been downright crappy: rainy and cold. But we made the most of it. D had Rick Steves’ Scandinavia book, so we did the walking tour that Rick details. Afterward, we grabbed a bite to eat before going to explore more of Tallinn.

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18.0 mm || 1/15 || f/3.5 || ISO1600 || NIKON D70


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18.0 mm || 1/15 || f/3.5 || ISO1600 || NIKON D70

We first tried going to the Estonian Museum of Occupations, however it was closed (on a Monday). I looked through the ripped out pages of my Europe on a Shoestring book and thought that going to the Tallinna Linnamuuseum (Tallinn City Museum) would be the next best bet.

We started working our way up to the opposite end of town, weaving our way through the streets to find whatever might be off the beaten path.

The Tallinna Linnamuuseum open and was a pretty neat little museum of Tallinn’s history. It was getting close to 4, and T and D needed to leave to get back the boat. We said goodbye and parted ways.

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18.0 mm || 1/30 || f/3.5 || ISO1600 || NIKON D70

I went back to the hostel and took a nap before heading back out on my own. I was pretty hungry, but nothing looked terribly exciting. Because of the weather, no one was eating outside. I walked down through the town square, out of Old Town, and to the shopping center across the way. It was mostly a mix of western foods that I’ve been desperately trying to avoid, usually in vain. Nothing looked particularly appetizing, so I started walking back toward Old Town.

I eventually settled on McDonald’s, again. Although, this time I had a Chicken Bacon Onion (CBO). It seemed like a local offering, seeing as they didn’t have it either of the McDonald’s in St. Petersburg, and certainly not at any McDonald’s I’ve in the US.

It was decent, and certainly better than having a биг мак1 again.

0
  1. Big Mac ↩

Dateline: Tallinn, Day 1 – Meandering About

  • June 14, 2009July 22, 2009
  • The Events that are: My Life

Tallinn, Estonia
14 June 2009

Sleeping on the bus was proving to be hit and miss. I was definitely feeling much better than I was on the train, but the bumpy Russian roads were doing me no favors. I think I managed to fall asleep for about an hour before we arrived at Russian Passport Control. My final hurdle.

We got off the bus, gathering up all of our belongings and got in line to go through Passport Control. It wasn’t anything special, I just showed the lady my Russian Visa and Entry/Exit card. She typed stuff in, scanned my passport and visa, stamped my visa, and off I went. No questions, no searching, no fuss.

While we were passing through Passport Control, the bus was getting a thorough looking over by the Russian military. Everything checked out though and were were shortly on our way. We had a short trip through what I will call the DMZ before arriving at the Estonian Passport Control.

The Estonia Passport Control was much easier than the Russian. For one, we got to sit on the bus the entire time while military officer collected all of our passports. For another, there was a cute looking Estonian medic out my window. I’m just sorry I didn’t get her number.

Getting in to Estonia went without a hitch, for me at least. There were a couple of Chinese (I think) girls up front who had some issues and were escorted off the bus. Everything (apparently) got worked out as they were allowed back on a short time later. There was also a gentleman who had something from his suitcase confiscated, I think it may have been a sausage.

The rest of the ride was really smooth, much smoother than the Russian roads, and I ended up sleeping for most of the way into Tallinn.

Once I arrived at the bus station, I decided to take a taxi to my hostel — seeing as it was 6:30am, I wasn’t feeling in a position to navigate the bus system.

I got to my hostel, checked in and then crashed on the couch (again) as the bed wasn’t ready yet (again).

After I woke up from my nap, I dropped of my luggage and then was off to explore Tallinn. First though, I had to take care of my foot that was killing me and had developed quite a nasty blister whose fluid was turning a nice tinge of yellow. With my toe all bandaged up, I grabbed a huge pancake at Kompressor.

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A friend from work, T., is coming into town tomorrow, so I though it would be prudent to find out where to meet him and his wife. I found the location with ease and then wondered around a bit more.

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Tallinn, Harjumaa, Eesti


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Tallinn, Harjumaa, Eesti


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Tallinn, Harjumaa, Eesti

For dinner, I went to the Hell Hunt pub, which is just around the corner from the hostel. At the end of the meal, a couple girls sitting behind me began flicking pieces of paper at me in an, what I’m going to call juvenile, attempt to get my attention.

Olga and Anna were two sisters, separated by about 11 years. Despite the fact that they were both born in Estonia, they both had Russian passports (Anna, the youngest, was born only a couple years after Estonia gained its independence). We had a nice chat about what I was doing and what my thoughts were on various topics1.

We got into a conversation about English, including what the word “fuck” actually means23

It was pushing 11:30pm and I had to wake up early. As best I could, I politely excused myself and headed home.

0
  1. I try to avoid discussing politics ↩

  2. I swear I’m not making this up ↩

  3. Short aside: All foreign language instructors teach kids the swear words, it’s really the only thing we care about. Apparently, though, they don’t provide the etemology. See also: Usage of the world Fuck (NSFW, natch)  ↩

Dateline: St. Petersburg, Day 1 – The Amber Room

  • June 10, 2009July 22, 2009
  • The Events that are: My Life

St. Petersburg, Russian Federation
10 June 2009

Sleeping on the train was one of those worthless endeavors that I still attempted anyway. It wasn’t because the train was bumpy or loud; on the contrary, it was smooth and quiet. I really blame the short length of the bunk (my feet easily hung off, and I’m no Michael Jordan) and the fact that I was sick, which made sleeping in general uncomfortable.

Thus, sleeping for the night consisted of me rolling into and out of consciousness.

We arrived in St. Petersburg pretty much right on time, and I made my way to the metro. The St. Petersburg Metro is exactly like the Moscow Metro, except deeper (the deepest in the world by average depth of all stations, according to Wikipedia) and they also use a coin token system instead of the RFID system that Moscow uses. The stations are also less conveniently located.

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18.0 mm || 1/2000 || f/3.5 || ISO200 || NIKON D70

I took the metro for one stop and popped off. Finding the Crazy Duck hostel was pretty easy, especially considering my state of sleep deprivation. I checked in, chatted with a couple of friends back in the States, and then promptly crashed on the couch until a bed was ready.

Around noon, Evan, Jared, and Max showed up and we all checked in and got beds.

Shortly thereafter, Greg and Mike, two brothers from the Seattle area invited me to come with them and Kennon from California and Gianni (pronounced Jonny) from Italy (but living in Germany) to Tsarskoye Selo.

After a bit of walking and a 30 minute bus ride to the outskirts of town, we arrived. Tsarskoye Selo is a former Russian residence of the imperial family and visiting nobility1 and houses, among other things, the Catherine Palace and Park, home of the Amber Room.

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The line to get in was over an hour long. Fortunately, there was also the park to explore. Greg and Gianni held our place in line while Mike, Kennon, and I went to explore the gardens. The entire grounds, garden and palace, is very western looking; often times I would completely forget that I was still in Russia!

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Aleksandrovka, Saint Petersburg Federal City, Russia


Roses are Red
70.0 mm || 1/80 || f/4.5 || ISO200 || NIKON D70
Aleksandrovka, Saint Petersburg Federal City, Russia


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18.0 mm || 1/160 || f/11.0 || ISO200 || NIKON D70
Aleksandrovka, Saint Petersburg Federal City, Russia


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Aleksandrovka, Saint Petersburg Federal City, Russia


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34.0 mm || 1/40 || f/4.2 || ISO200 || NIKON D70
Aleksandrovka, Saint Petersburg Federal City, Russia

Then we switched. And it started to rain. And then pour.

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18.0 mm || 1/400 || f/3.5 || ISO200 || NIKON D70
Aleksandrovka, Saint Petersburg Federal City, Russia

The entire palace is magnificent really, the Amber Room particularly so, although I was pretty fond of the front stair case with it’s stark white walls contrasted by red curtains and blue-faced clock and barometer.

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Aleksandrovka, Saint Petersburg Federal City, Russia


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18.0 mm || 1/25 || f/3.5 || ISO1600 || NIKON D70


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18.0 mm || 1/30 || f/4.0 || ISO1600 || NIKON D70


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18.0 mm || 1/20 || f/4.0 || ISO1600 || NIKON D70

It was still raining by time we left. We made a quick dash for the bus stop and then rode back in to town. This would, fortunately, be my only real experience on the roads of Russia (save my overnight bus trip). Traffic, even in St. Petersburg, is pretty horrendous and drivers take on an every-man-for-himself approach. Not terribly bad, just moderately concerning.

On the way back to the hostel, we decided it would be a good idea to get something to eat. Armenian was the choice and I sat down to a feast of cold-seasoned beans, a bread boat with egg and cheese, and beef medallions with a beer.

I called it an early night (at 11:30pm) and headed to bed.

Update: Removed hanging sentence from third-to-last paragraph.

0
  1. http://en.wikipedia.org/wiki/Tsarskoye_Selo ↩

Shooting Salida

  • May 15, 2009
  • Photography

I went to Salida with my family this past Tuesday so that Brian could check out the church he would be working at as their Youth Intern.

While driving through town, we came across a set of abandoned railroad tracks. Having wanted to do some urban1 exploring, I took the opportunity to wander about.

DSC_8488
50.0 mm || 1/8000 || f/1.8 || ISO200 || NIKON D70
Salida, Colorado, United States

DSC_8493
50.0 mm || 1/5000 || f/2.8 || ISO200 || NIKON D70
Salida, Colorado, United States

Blue White Red
50.0 mm || 1/8000 || f/2.5 || ISO200 || NIKON D70
Salida, Colorado, United States

DSC_8522
50.0 mm || 1/8000 || f/2.5 || ISO200 || NIKON D70
Salida, Colorado, United States

DSC_8531
50.0 mm || 1/1250 || f/2.8 || ISO200 || NIKON D70
Salida, Colorado, United States

DSC_8544
50.0 mm || 1/5000 || f/1.8 || ISO200 || NIKON D70
Salida, Colorado, United States

Calco Inc
50.0 mm || 1/3200 || f/4.5 || ISO200 || NIKON D70
Salida, Colorado, United States

As always, you can see the rest of the photos on Flickr: Exploring Salida

As a side note: Brian will be working with Hilary Downs, who fellow UPC folk may recognize as the Ministry Coordinator for The Rock and The Edge back In The Day™. After graduating from Princeton, Hilary became the Associate Pastor at First Presbyterian Church of Salida. As Jeff noted, “Wow, small world… (or UPC is just that huge…).”

As yes, I love alliterations.

0
  1. although I’m not sure I’d call Salida urban ↩

Notes From The Annex, Part 4

  • May 15, 2009
  • Christianity

Several months ago, November 4th, 2008, to be exact, Gordon MacDonald came and spoke at The Annex. To say he was amazing would be an understatement.

The Annex listed some of his books, which I’m now listing here, so I check them out at a later date (and I can throw out this piece of paper I’ve been holding on to for the last 6 months).

  • Renewing Your Spiritual Passion
  • Who Stole My Church?: What to Do When the Church You Love Tries to Enter the 21st Century
  • Ordering Your Private World
  • Mid-Course Correction: Re-Ordering Your Private World for the Second Half of Life
  • When Men Think Private Thoughts: Exploring The Issues That Captivate The Minds of Men
  • A Resilient Life: You Can Move Ahead No Matter What
  • Rebuilding Your Broken World
  • The Life God Blesses: Weathering the Storms of Life That Threaten the Soul
  • The Effective Father
  • Restoring Joy
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A Short Guide to Robot Path Planning

  • April 6, 2009
  • Mines

Editors note: For my Advanced Robot Control midterm, I had to write a report answering four questions related to the class. For your reading pleasure, I now present the fruits of my labor. Note, super technical content to follow. Also note, this post is paginated. You can also download the PDF.

In Chapters 2 through 7, Choset has presented a number of different approaches to path planning. Explain in your own words the progression from Chapter 2 to 7. Include brief (synopsis) explanations of each approach (i.e., the main topic of each chapter).

Chapter 2 covers the two bug algorithms, Bug 1 and Bug 2. The Bug 1 algorithm is perhaps one of the most basic of navigating algorithms. The robot begins at the start and proceeds toward the goal until an obstacle is encountered. Once an obstacle is encountered, the robot will completely circumnavigate the obstacle before proceeding toward from the point on the perimeter that has the shortest distance to the goal.

The Bug 2 algorithm is very similar to the Bug 1 algorithm. The primary difference from Bug 1 is that an imaginary line, the M-line, is draw between the start and goal. When the robot encounters an obstacle, it will circumnavigate the obstacle until it reaches the M-line. Once it reaches the M-line, it will start moving toward the goal again; it does not completely circumnavigate the obstacle.

The primary benefits of Bug 1 and Bug 2 is that very little information is needed: a starting point, goal, and a series of touch sensors to determine when the robot runs into an obstacle.

A more advanced version of Bug 2 is the Tangent Bug. Tangent Bug utilizes a sensor of some range from zero to infinity to detect obstacles. When an obstacle is detected, the robot will start moving around the obstacle. The robot will continue its motion-to-goal routine as soon as it has cleared the obstacle.

In order to describe more complicated path planners, we need to be able to specify the position of the robot and the space it occupies. This is known as the configuration space and is the primary topic of chapter two. We used the new idea of configuration space to develop a set of equations that allow us describe the position of multi-joint planar arms. We extended the equations we used to define the movement of planar arms to define points in both R2 and R3. These equations allow us to define the position and orientation of a single point, as well as one point relative to another.

With our new ability to describe robots in a workspace, we can now begin working with more complicate path planning techniques. Path planning is quite different from the previous navigation algorithms we discussed, such as Bug 1, because path planning requires foreknowledge of the obstacles before the robot begins movement. Chapter four starts with a brief discussion on gradients. Gradients are a well studied mathematical function in undergraduate engineering university, which makes them a great introduction for more complex path planning methods. Gradients work by changing the repulsive potential as a robot gets closer to an obstacle. The start point is given a medium gradient potential, the end point is given a low gradient potential, and the obstacles are given high gradient potentials. All the robot needs to do is “roll down the hill.”

The Brushfire Algorithm is a discrete version of the aforementioned gradient algorithm and involves the use of a grid to determine the potential of cells. A variation on the Brushfire Algorithm is the Wave-Front Planner.

The Wave-Front Planner uses a grid, just like the Brushfire Algorithm, and assigns a “1” to each cell that has an obstacle (or part of an obstacle). The start point is labeled “2” and the “wave” propagates from that point. Each adjacent cell, if empty, is given an incrementally higher number until all the cells have a number. If the goal has a number in its cell, the goal is reachable in that many moves minus one. Adjacency can be computed using either four-point connectivity (where only the north, south, east, and west cells are considered adjacent) or eight-point connectivity (where north, south, east, west, and the diagonal cells are considered adjacent).

Sphere space and Star space are essentially extensions of the generalized potential path planning method with one critical difference: they only have one local minimum. Having one local minimum is a desirable quality as it greatly aids in path planning and avoiding dead ends.

Chapter five introduces roadmaps, which is effectively a way to break up the workspace into distinct stages or paths. The Visibility Graph plots straight line paths between the start, goal, and all the vertices of the all the objects in the workspace. The paths may cross over each other; however, they may not intersect an object. Once constructed, the visibility graph can be searched for the shortest path from the start to the goal.

The Generalized Voronoi Diagram extends the idea of the distinct paths by drawing equidistant “roads” between obstacles and the boundaries of the workspace. A similar technique to the GVD is the Silhouette Method, which works by determining the critical points of obstacles within the workspace. A tangent line extends from each critical point, and around the workspace edge. The path from the start to the goal “snaps” to these paths.

Trapezoidal Decomposition, which is the start of chapter six, extends the concept of the Silhouette Method. However, the obstacles (and workspace) must be represented as trapezoids. A vertical extension marks each vertex, separating the workspace into cells. The cells are mapped from the start to goal using an adjacency graph. The path planner plans a path by connecting the midpoints of the vertical extensions. Morse Cell and Boustrophedon Decomposition follow the same concept as Trapezoidal Decomposition. However, the goal in Morse Cell and Boustrophedon is path coverage rather than path planning.

Path coverage, which seeks to optimize the coverage of the workspace, leads into visibility-based decompositions for pursuit and evasion, which deals with how a pursuer attempts to capture prey and how the prey attempts to evade the predator. Specifically discussing how to clear rooms to make them “uncontaminated” and how to determine the number of predators that are required to check a system based on the number of edges in the workspace.

As this point, the path planning algorithms are becoming fairly complex and computationally intensive. So far, our examples have been using small workspaces with only a handful of obstacles. As the workspace size and number of obstacles increase, the time required to find a solution also increases, usually exponentially. Sampling-based Algorithms work by using a best-guess and check method. A path is calculated and then checked to see if it collides with any obstacles. Specific types of planners include Probabilistic Roadmaps (PRM), Randomized Path Planner (RPP), Expanisve-Spaes Trees (EST), Rapidly-exploring Random Trees (RRT), and Single-query, Bi-directional, Lazy collision-checking (SBL). In all examples of sample-based path planning, the chances of finding a successfully path approach zero as the number of samples increase.

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Andrew Ferguson

A 30-something electrical engineer. I am for God, against the status quo, an enginerd. Lutheran (LCMS). I excel at awkward and problem solving. Seattle native, former expat in 🇬🇧. Married to @fergiepants. We have a dog. And a child. And another child. This is the story of me: My hopes, my dreams, my aspirations. My trials and tribulations. My life.

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