Łyczyn, Dębówka, and Polish Mathematicians

I had two interesting questions this week, not unrelated to one another. The first was: "What do you think about when you're on the bike?" The second: "How do you decide what to write about in the blog?" As to the first, I don't really 'think' about anything. Cycling is a moving meditation (usually) and, as such, on country rides I am focused on my breath, my heart rate, maintaining a precise power output or my pedaling dynamics. The choice of which depends on where I am and what aspects of training I'm interested in for that period of time. I also pay keen attention to the landscape and sounds around me, without fixating on any one thing.

Focusing on these nuanced cycling details is much less possible in an urban setting where there are immediate road hazards, traffic and other things to respond to. That requires a different kind of outwardly focused, active awareness. Both types of environments give rise to thoughts, of course. I usually don't dwell on these, but when thoughts or feelings persist or resurface, I consider writing about them. Everything I do end up writing about had an initial stimulus that came from out "on the road".

More than one local has told me that we've had a very unusual September to date. It has been generally warmer and drier, which, of course, is great for cycling. Today was a continuation of that pleasant trend and we rolled out around 9:15 AM. The plan was to hit that third little hill climb north of Słomczyn (at Łyczyn) and then head back towards the Vistula River. There is a road marked on the map east of Dębówka that extends to the river, but I had serious doubts that we could negotiate it. If it were ridable, we'd have a spectacular view of the Vistula from the shore itself; if not, well, we've turned around before.

Pałac w Wilanowie.

One of the downsides of writing a blog in conjunction with my cycling activities is that it excludes the many other experiences I've had here in Poland. A good case in point is a particularly magnificent experience in our own backyard, which borders on a large green belt which, in turn, borders on the vast, manicured grounds of the beautiful Wilanowski Palace (Pałac w Wilanowie). There is not a ride I go on that doesn't skirt the palace grounds, and yet we can't ride on those grounds. Still, since this "thought" about the palace "persists", I should at least mention the place in the blog, don't you think? That's it, in the picture above.

As I implied, bicycles are not allowed on the palace or garden grounds and the picture above is from the closest point that I can get with Kościuszko. If you ever do get to Poland, be sure and check out the Wilanowski Palace museum and grounds. Plan to spend about 3-4 hours wandering about.

The construction of this palace, built in the Baroque style to honor King John III Sobieski, began in 1677 and was completed in 1696, the year of the good King's death. It is often called the Versailles of Poland. This palace miraculously managed to survive both World Wars and all the turmoil in Poland prior to then, as well. Unfortunately, although the exterior survived, the interior, which was filled with paintings, sculptures, art, furnishings, etc., was looted by the successive waves of conquerors that hit Poland after the Second Partition in 1793 (See a history of all three partitions here). Today the Palace is a comprehensive museum that showcases Poland's cultural and political heritage.

Cruising south and near the Palace grounds, we turned onto Ruczaj (a street), our go-to exit from Wilanów. Clearing the urban setting we became aware of how strong the winds really were today. They were whipping around from a variety of directions, so we couldn't count on a strong wind in a particular direction to plan the ride. We adjusted our speed downwards accordingly to conserve energy for the remaining 45 km (28 miles). We pushed ahead to Gassy and then turned West and went to Obory, where we turned south and headed for our new climb. The road gradually turned upward, providing a nice relief to the flat plain. We scurried to the 'summit' and continued onward, enjoying the "C" ticket ride (see my last post about 'tickets') at Słomczyn. All in all, the climb there is much longer and shallower than the other two, and therefore, much easier.

Last week, I hope you recall, I brought up the topic of topology (Not topography, although I do love that topic as well and have mentioned it en passant when talking about the North European Plain and the Vistula River). Topology is a branch of mathematics that deals with the deformations of spaces. It is a fascinating field of study and I loved talking about topological issues in my Philosophy class. In particular, I enjoy non-orientable objects such as Klein bottles and Möbius strips. These are fascinating, one-sided structures that are--to the uninitiated--mind-blowing. Now I wonder, though, is it possible to have a one-sided bicycle? What would that look like? Food for mathematical thought. In any event, I encourage you to read a little bit about these things, although they don't relate directly to Poland or cycling. Knowing something about topology might make you the center of attention at the next party you attend. I kid you not.

While I am on the subject of mathematics, I'd like to mention Alfred Tarski (born Alfred Teitelbaum, 1901-1983), who was a Polish-Jewish mathematician of some repute and of some personal importance to me. He led an interesting life (that included conversion to Catholicism). He was able to immigrate to America in 1939, sparing him the horrors of World War II in Poland. Tarski was one of those mathematicians who made lasting impacts in a variety of mathematical fields, including topology, metamathematics (one of my favorites), logic and set theory (another favorite). He was an especially important influence when I was working on my doctorate; his ideas about logic, set theory, and mathematical modeling (and undecidable theories) were particularly important foundational research for my dissertation.

Tarski is but one of many, many famous and dedicated Polish mathematicians. Another mathematician (and cryptologist) from Poland I want to mention is Marian Rejewski. He is not a household name, but along with two other Poles, Jerzy Różycki and Henryk Zygalski,  Rejewski reconstructed sight-unseen the German Enigma Cipher Machine some eight years prior to the outbreak of the Second World War! This remarkable accomplishment eventually enabled the Allies to decipher German coded messages throughout the war, and undoubtedly is responsible for shortening the war by at least a couple of years. Interestingly, in the West, we recognize and praise Alan Turing and the Bletchley Park crew for their work in cryptology, but we seem to have overlooked the Polish contribution to the process: namely, how all those messages were encrypted in the first place. Although Alan Turing is an interesting figure, and The Imitation Game is an interesting bio-drama that covers part of the Enigma story, I hope you will always remember that there was a crucial Polish contribution to this endeavor! But I digress...

Last week I mentioned topology as an entry point to a discussion of the hill climbs we've been searching for. Now that we have three known climbs, the question is how can we most efficiently climb all three hills in one ride? This gives rise to the kind of problem that was a forerunner to the field of topology. So, below you will find a map of the region with our three little hill climbs. We'd like to be able to climb all three hills on one ride without retracing the route. It will be up to you, Dear Readers, to help me find the right course. Your task is to look at this map and chart out a route that Kościuszko and I can take that meets the following conditions: (1) We must enter at the top of the map (where it is marked "Enter") and leave by the road marked "Leave", (2) we must climb all three hills (marked in red) in the direction indicated on the map, and (3) we can't ride over the same road twice in the same direction (opposite direction is OK).

What do you think? Will Kościuszko and I be able to do this according to the given parameters? If not, can you prove (mathematically speaking) that we cannot? If you believe we cannot, then what route would you suggest to us? Let us know, we are waiting for your responses!

After leaving our climbing area, we headed to Dębówka. As anticipated, the road turned into a bed of pitted, overgrown, rocky concrete slabs that gradually headed down towards the Vistula. We decided to persist, trying to ride just off the edge of the concrete where it was sandy, but not unduly rough on tires and frames (bicycle and human). Five minutes of frame jarring, white-knuckle riding, which seemed like an eternity, got us to a bend in the Vistula, where a movie crew was busy working. I had seen this same crew working before on two occasions several weeks ago and was surprised they'd made the trip down to the river in their large trucks and vans.

Dębówka Crossing.

I dismounted Kościuszko and carried him through the deep sand down to the banks of the Vistula. What a great view, and well worth the trip. This place appears to be an old ferry crossing or, perhaps when the river is very low, an actual ford. There were some fishermen on both sides of the river and it was a very quiet and serene place. (The movie people were actually filming down river and into the woods.) We had a bite to eat and I checked out Kościuszko's mechanicals. At that point an older man approached me, but my Polish was unable to sustain any conversation beyond immediate pleasantries. I asked (in Polish) if he spoke English. "Nie." Means 'no', oh my! In Polish and very cautiously, "How about Russian?" "Well, yes, of course!" he said enthusiastically in Russian. We continued in Russian. I explained I was an American who spoke Russian, a fact which intrigued him to no end. We had a very peasant conversation about the beauty of Poland, cycling, and the difficulties of growing old--see how quickly people can find a common language? We finished with the weather, both wishing for a continued summer that was not meant to be. We parted, I speaking in Polish and he in English. These encounters are so, so important.


Setting off from Dębówka, I was very pleased with the whole ride, but knew the return trip would be made much more challenging due to the wind and, as avid followers might surmise, at least 5 kilometers worth of gnats. Still, that is par for the course and not to be shunned. We worked our way north and home. Pulling into the courtyard I saw on my bike computer that our average speed was down (to be expected), but that my weeks of riding had paid off: my computer flashed the rare message that it had calculated a new (increased) VO2 max (Volume of Oxygen maximum) for me. An increased VO2 max means that my aerobic capacity (rate at which muscles and lungs effectively use Oxygen) has increased. It is no wonder, with all this wind to provide resistance! Remember, Dear Readers, it is never too late to improve your fitness.