A Musical Weekend

Friday afternoon, Christina, Kyle, Tom and I went out to Gellert Hill to watch the sunset (at 4pm). On the way up the hill we stopped at the giant slides! It had been so long since I have been on slides...These are the sorts of slides that would probably be considered safety hazards in the US, but they are great. I even saw a grandpa going down one of the slides with his grandson.

It was cold, but nice out. The sunset was pretty, and the full moon was rising just as the sun was setting. Overall, it made for a very pleasant evening.





Saturday I stayed home in the morning and one of my host mom's daughters came over for lunch. I still have not quite gotten used to the Budapesti notion of lunch... We started with soup, then had homemade french fries and some sort of fried meat patties (I think they were made from ground turkey mixed with spices, egg, and bread crumbs) and after that my host mom brought out a large pot of spaghetti. Needless to say, I was stuffed. In the evening a group of 7 of us gathered at Christina's to make American style pancakes for dinner and then to go to a piano concert. I really enjoyed the concert. Making time to just go listen to music is a very good thing and the Liszt Ferenc Zeneakadémia where the concert was held is absolutely gorgeous.

Sunday I went to church in the morning (and recognized all but one of the tunes for the hymns!), worked on HW with Christina in the afternoon, went to the organ concert at the Lutheran church in the evening, and then met up with Kyle to go to the pancake place for dinner (yes, pancakes two nights in a row, but they were very different kinds of pancakes).

The weather has decided that it is going to be clear and cold for a while. Oh, and windy - quite windy (20-40 km/hr windy). I am glad my coat is good a blocking wind. The wind chill factor has been keeping the temperature below 0 C and Monday I woke up to find the hill behind my apartment dusted with snow. It is exciting. I love having actual weather :-)

Happy Thanksgiving!

This marks the third year that I have not made it home for Thanksgiving. My freshman and sophomore years I had Thanksgiving at my dorm back at Mudd with the (23 my frosh year, 40 or so my sophomore year) of my friends that were also on campus. Last year I managed to put myself in charge of the production. Having successfully pulled off organizing Thanksgiving for 40 last year I decided that it would be a good idea to take charge of making sure it happened here in Budapest. As it turns out, organizing Thanksgiving abroad is a somewhat larger project than organizing Thanksgiving at Mudd for 2 main reasons:

1) Here we are spread all over the city rather instead of being concentrated in a small area.

2) Foods that count as traditional in America and thus show up in larger than usual quantities near Thanksgiving are not necessarily foods that are common in Magyarorszag.

The first one is not that big of a deal, it just requires a bit more logistical planning. The second...
Sweet Potatoes I love sweet potatoes. They are delicious baked and my mom's sweet potato casserole is one of my favorite foods at Thanksgiving. Hungary on the other hand is not quite so familiar with them. I had been watching for them in the various different grocery stores and at the fruit and vegetable stands and even Tesco (the closest equivalent to Walmart here) for a while and they seemed to be completely non-existent. On Monday I do not have class until noon, so in the morning Christina and I headed to the giant market. The first floor of the market consists of a ridiculous number of fruit and vegetable stands along the sides with various meat stands and baked goods stands in the center. We figured that if there were going to be sweet potatoes anywhere they would be at the market. Sure enough, at the two stands in the far back corner of the market there were unlabeled piles of what looked like sweet potatoes. One of the stand owners knew enough English that with my limited knowledge of Hungarian I was able to confirm that they were in fact sweet potatoes. This worked out fine, the process of finding them was just rather time consuming.

Cranberry Sauce
Another very traditional Thanksgiving food. At Mudd we usually end up with a homemade cranberry sauce and some sort of cranberry relish and possibly also cranberry sauce from a can. When we went to the market I was watching for cranberries, but, unlike the sweet potatoes, we did not have any luck there. Charlie and I went to Tesco to hunt later, thinking that perhaps it was just hiding somewhere strange, but no. The only mention of cranberries we found in the whole store were dried cranberries in a box of granola - not exactly useful for concocting cranberry sauce. We eventually gave up on trying to locate cranberries.

Pecans
This one was especially frustrating since Hungarians seem to like nuts. Walnuts, hazelnuts, peanuts, pistachios and almonds are all very easy to find. Things like cashews and macadamia nuts are rarer but can still be found with minimal searching. Pecans though... nincs. Rumor has it that they can occasionally be found in small quantities at exotic markets, but I did not have any luck. Thus pecan pie and pecan topping on sweet potatoes and such things were out of the question.

Pumpkin Pie
Tesco had pumpkins back about a week prior to Halloween. These days, there are no pumpkins anywhere (this was another thing I had been watching for at the market). There is what seems to be butter nut squash at every small fruit stand and a different winter squash in all of the grocery stores (it intrigues me, none of the grocery stores have the butternut and none of the stands have the other kind). The flesh of the squash in the grocery stores has a similar texture to pumpkin, so I got a chunk of it and decided to see what happened if I turned it into a pie. This involved more improvising since evaporated milk also seems to be hard to come by here - or at least I have been unable to recognize it if does exist. Despite all of the improvising, it came out great, so Christina and Alison looked for another piece of the squash when they went to the store on Thanksgiving morning. Even though they were at the same place I had bought the squash the day before, it seemed to have vanished. Thus we ended up with a single 'pumpkin' pie... such is life.

Despite all of this, the whole production went off amazingly.

As per usual, I made crescent rolls - about 100 of them. I don't know if it was the European flour, or the fresh eggs or if I just managed to do something exactly right, but they came out extremely light and fluffy. I was very pleased.





While I was working on the rolls and baking the pumpkin pie, Chelsey made deviled eggs. When we were done cooking, this meant that we now had 100 rolls, a pie and several plates of deviled eggs that we had to get from Christina's apartment to Kevin and David's apartment (where we were all meeting to actually have dinner). We decided that it would be less awkward to just walk than to try to take it on the metro, so we made quite the procession as we paraded down the sidewalk of one of the largest streets in Budapest carrying a tub-o-rolls, a pie, several plates of deviled eggs and a pot of butternut squash (Kyle had joined us by that point). I was rather amused by all of the double takes we got from the Budapesti that we passed on the way :-)



Dinner ended up starting around 4:30 and, despite the fact that the cranberry sauce was missing, it was a very impressive spread. Even after everyone had been through and taken heaping plates of food there was a LOT of food left on the tables.



All 40 or so of the people who showed up ended up stuffed and happy, so the meal was a resounding success :-)

I hope everyone else had an equally wonderful Thanksgiving!

I'm doing well, but life is rather busy at the moment. Finding everything for Thanksgiving in Budapest is quite the project - Pecans seem to be non-existant as are pumpkin and cranberries. And things like evaporated milk seem to be unknown here. It is going to be a very improv Thanksgiving dinner :-). I will give a more detailed update after Thanksgiving when I am less busy.

Happy Thanksgiving!

How to approach a math problem...

Mathy post today. I will try to get a non-mathy one up tomorrow :-)

In Conjecture and Proof:

* Define something that prevents.

* Consider something smallest.

* Consider something largest.

* Find a clever coloring.

* Try using a Hamel basis.

* Try following paths.

* Count things.

In Geometric Graph Theory:

* Turn the edges into rubber bands.

* Triangulate.

* Draw circles around *everything*.

* Apply Euler’s formula.

* Pass a line across it.

* Color the edges red and blue and find the vertex where the red edges are together

* Use physics.

In Set Theory:

* Use the sandwich theorem.

* Use ridiculous seeming approximations.

* Look at the cardinality of the sets.

* Order the sets and compare ordinals.

* Consider a representative set.

* Draw the diagrams.

* Remember that everything is a set - unless it isn’t.

In Topics in Geometry:

* Try stringing definitions together.

* Try looking at equivalent definitions.

* Play with the geometry, convert to algebra, play with the algebra, convert back to geometry, repeat.

* Look for eigenvectors/values.

* Draw pictures.

* Use symmetry.

* Look at subgroups.

Hó hó hó!

I’ve been learning about the wonders of tejfől. I did not feel like doing HW Thursday evening and my next assignment was not due until Monday, so I decided to experiment with cooking instead. My goal: to try actually making some of the delicious Hungarian food I have been watching my host mother make. I went to Kaiser (one of the local grocery stores) and obtained two large tubs of tejfől (sour cream), a small box of tejszin (really thick heavy cream) and a carton of tojas (eggs). I then obtained ket hagyma, ket alma és ket körte (two each of onions, apples and pears). I decided to start the project with nokedli.

When I asked my host mom what was in the nokedli dough she responded: ket tojas, ket deci viz, fel kilo liszt. Now, when we were making the nokedli it was clear that there was a lot more dough than would come from those proportions (and we had about 3 times as much nokedi as I was hoping to make) so I decided to just hope that she had given me a reasonable sized recipe. I beat the eggs with the water and then attempted to add something close to ½ kilo of flour (my host mom never measures anything, so I figured the exact amounts were not crucial). This resulted in a dough that resembled the dough we had used before, I figured we were off to a good start. I got a pot of water boiling, dug out the cheese grater and found a big metal spoon to force the dough through the grater with. The first blob of dough that I blopped onto the grater was difficult to force through and was resulting in very small noodle/dumplings, so I added a little more water to the dough and this corrected the problem. The only other issue was the grater. My host mom’s grater seems like it was made for making nokedli - the back has raised sides to keep the dough from falling off the grater and otherwise has no unneccesary bumps or grooves. Christina’s grater on the other hand has the raised sides, but also lots of little groves that like to catch the dough and keep it from going through the holes. I am going to see if I can find a proper nokedli grater to bring back to the States with me. Nokedli is a fun alternative to pasta and rice and I rather like the texture.

However, like noodles, nokedli is somewhat bland plain, so my next task was to create something to serve over it. While I was working on the nokedli I had a separate pot on the back burner boiling eggs (I was rather amused that the one thing I had to look up online for this meal of things I had never made on my own before was how long to boil eggs). Cartons come with 10 eggs, and I used two for the nokedli, so I boiled 8. While Christina was pealing the eggs, I diced and sauted the onions. I dumped on of the tubs of tejföl into a bowl and mixed in a largish glob of the tejszin, some flour (for thickening purposes, roughly the same amount I would have used if I had been making the kind of cream sauce I was used to) and a liberal portion of paprika (akin to the quanity of chili powder I might use when making chili). I then added two sour cream tubs worth of water to the pot with the onions and mixed in the cream mixture. While this was heating up, I chopped the eggs and added them to the mix. From this point it just needed to be stirred periodically to keep it from sticking and it came out great. It was really far easier than trying to get a normal cream sauce to the right consistency.

Now, this probably would have been enough for dinner, but I had been wanting to try my hand at fruit soup for a while now. I have not managed to be home when my host mom was making fruit soup yet, but I have asked her about it and as far as I could tell it consisted of boiling fruit until it is mushy and then adding – naturally – tejföl és tejszin és picsit cukor (a little sugar) és fahej és szegfűszeg (cinnamon and cloves). As such, we pealed and chopped the apples and pears and put them in a pot with some water to boil them. A traditional Hungarian meal would start with the fruit soup, but it made more sense to make it last given the selection of pots Christina’s apartment is stocked with (I used all of the large ones twice), so we let them boil while we ate the nokedli and tojas paprikas (I have no idea what it is really called, but that follows the pattern of csirke paprikas so I assume it works as a reasonable name). When the fruit had gotten soft, I scooped some of it out into a bowl, mashed it, and added it back to the pot. I then mixed half of the second tub of tejföl with another glob of the tejszin, a little flour, some sugar, cinnamon and cloves and then dumped it into the pot of fruit. Once I got it all blended together, I took it out and set it on the balcony to get it to cool off (using the balcony as a fridge seems to be common practice here, and when it is at least as cold outside as in the fridge it really makes sense. The concoction was delicious. It was not quite like any fruit soup I have had here, but also was not that different, more of a variation on a theme than something different.

Overall, I deem the whole project an overwhelming success and a much more productive use of a Thursday night than getting ahead on HW. Also, I suspect that sour cream may become a kitchen staple.

Friday was not terribly exciting and this is going to be quite long as it is, so I will just jump to Saturday.

Saturday morning I went over to Christina’s apartment. It felt chillier than it had been being, certainly colder than the 10 C Christina had seen on a sign when she had gone running earlier that morning. We looked up the weather report on line and found that it was 6 C feels like 2 C – that’s quite a wind chill factor. Never mind the cold, it was actually sunny. Or rather, it was about half sunny. There was a distinct line in the sky between blue and some potentially nasty looking grey clouds. Mandi came over to theoretically work on HW, but none of us could focus, so we decided that it was a good day to go up to the top of St. Stephens Basilica to see the view of the city. We collected Kyle on the way and then got to see the results of having both rainy and sunny weather at the same time – a rainbow! Not a very bright one, but still:

The view of the city from the top of the basilica was quite impressive:

After that we went back to Christina’s apartment. Christina and Mandi worked on their combinatorics and I made dinner . Every time I have gone to the zöldseg-gyümölcs recently they have had big squash and I had been wanting to try it, so I finally decided to just get one. I baked it like I would an acorn or butternut squash and then decided that it smelled like it would go really well with nutmeg, cinnamon and cloves, so I scraped it out of the skin and mixed it with some of the leftover tejfől and tejszin, a little bit of brown sugar and a liberal sprinkling of each of the above mentioned spices. It was quite tasty. I served it as a side with the left over tojas paprikas sauce and rice (since we had basically eaten up the nokedli).

After dinner the four of us (Kyle had shown up for dinner) went to a tanchaz – a Hungarian folk dance thing similar in spirit to a contra dance as Kyle and Mandi are in a class that had encouraged them to go. It was quite fun, though also exceedingly exhausting. The Hungarians and seemed to be slightly amused at the presence of American students, but were none the less very helpful and happy to dance with us. It’s really too bad that Mudd does not have any sort of folk dance class. That would be a PE class I could enjoy.

Sunday morning Christina and I went to church. The service made me very happy as I actually knew 3 of the hymns. But anyway, after the service we had tea and sweets as usual and stood around chatting with the other members of congregation. Christina mentioned that she would really like to see it snow and asked what the chances of it snowing while we were still here were. The general consensus was that the forecast is expecting this to be a mild winter and there is not likely to be much snow, if any. We then go back to Christina's apartment to eat leftovers for lunch. After lunch I went out on their balcony to check my email (it is the only place they get wireless) and it started to rain. I went back inside and started helping Christina clean up in the kitchen, watching the rain out the kitchen window and not really looking forward to walking to the busz stop at Deák in the rain. Then the rain started falling funny. At first I just attributed it to the fact that wind does strange things in their courtyard sometimes, and it quickly looked like normal rain again, so I shrugged it off. Pretty soon it had changed back to falling funny...it really did not look like rain, it really looked more like...snow! Christina and Alison and I all crowded at the window and confirmed to each other that, yes, it really was snowing! Within a minute it had changed back to rain again. I figured I should head back to my apartment to get my HW done, so I put on my shoes and collected my jacket. By the time I was ready to leave, it had once again been transformed to snow. Christina and I glanced at each other and exchanged looks that clearly said, "Do you think there is any chance...?" and shook our heads. There was no way it was going to stick. Everything was wet from the earlier rain and it couldn't even make up its mind to stay snow. I walked to the busz stop at Deák, amused by the bewildered looks I saw on the faces of the Hungarians I passed (and the huge grins that little kids had), and sat on the busz watching it snow as I waited the 5 or so minutes before it was time for it to leave.

Mother nature seemed to have decided that yes, it really was going to snow today, not rain. By I got to my stop the benches and the cars parked on the side of the road had started to accumulate snow (as was my jacket and hair).

I went up to my apartment, and by the time I had finished my geometry (which did not take long) the hill behind the house was covered in snow. I realized that it was also starting to accumulate on the street level when a snowball came flying through the grates in the window of the little balcony room and smashed into my window (I then looked out and down to see a group of kids excitedly packing snowballs and throwing them at each other and the building).

Around 4 I decided to take a break from my homework to go see just how snowy it had gotten outside and to see about getting some pictures of snow covered Budapest. Judging by the trees and castle walls we had gotten at least an inch of snow by that point.

Sometime during the night it had switched from hó back to eső, from snow back to rain, so by morning most of the snow had melted. However, I came across this on my way to school

Hó hó hó!

Suppose you have an infinite checkerboard...

Math can sometimes be frustrating, it is true. It will sometime take hours of playing with equations and theorems and such to crack through and understand how to solve a problem. Occasionally when you solve it the response is "oh, that was dumb" - those problems are annoying. Sometimes the response is "huh, thats cute" or "OH!, thats clever." - those problems are satisfying to solve. Sometimes the response is "Wow...that's...impressive..." which usually happens when the solution really is quite long, complex and/or involved - those problems leave you with a sense of accomplishment. Occasionally you find a particularly beautiful solution to a problem and the response is one of pure joy and excitement. The Conjecture and Proof club problem was one of that last category this week. It was amazing. The only problem was that I was then on such a math high that it was impossible for me to go to sleep at a reasonable hour (though I was impressively productive during that time).

Geometric Graph Theory continues to make me thankful for the Core physics required at Mudd. One of our HW problems on the last set was basically a simple mechanics problem, but really messy if you were not comfortable dealing with balancing torques and forces. We are currently playing with double circuit embeddings which result in chalkboard pictures in at least 4 colors of chalk where it is still hard to keep track of what everything is. It is a great deal of fun.

We have started projective geometry in the topics in Geometry class. It is fun to play with things that can't quite be properly visualized. It was also very interesting to see two different models - one completely algebraic in nature and the other based on adding 'ideal' points to regular Euclidean space (where 'normal' high school geometry occurs). On the surface they look completely different, but we showed that they really are the same. During the 'office hour' portion of class today I got him to give us the formal definition of homeomorphic- a notion that I vaguely understood just from the contexts where I had seen it used but which I had never seen defined. It was quite interesting.

I love set theory. The axiom of choice is very strange. It seems intuitive that it should work and there are things that are equivalent that seem very natural, but it leads to some very strange things. The idea that it is possible to put an ordering on the real numbers so that there is a 'smallest' one and any subset has a 'smallest' element seems very counter intuitive (granted, such an ordering is impossible to describe) .

Food!

Sorry about the long absence. We had last Thursday and Friday off, so my internet access was very limited over the weekend and then coming back from a long weekend seems to result in life being extra busy!

Thursday was very low key. I spent most of the day alone in the apartment getting little things I had been meaning to do done. Having time completely alone occasionally is really nice, it seems to not happen often. In the evening I went over to a Kyle's apartment (Christina was out of town all weekend) to make dinner and to just hang out and chat.

On Friday, Zoli and Adam, my host mother's grandsons, and her daughter Erika came over. This meant that my host mother had to make a big lunch for everyone, so we spent the morning cooking. The most exciting part was making nokedli - dumpling/noodle things which are formed by running the batter through a cheese grater into a pot of boiling water. We served the nokedli with a sour cream based sauce with boiled eggs.
Here is a picture of me with my host mom and Zoli :-)


On Saturday morning my host mom was cooking all out again to have food to take over to Zoli's house since EVERYONE was coming over to celebrate Zoli's birthday. I learned how Hungarians fry meat and helped make a husi paprikas (meat in a paprika/sour cream sauce) topping for the nokedli. She then got all dressed up and posed for me with one of her Christmas cacti:

When she left, I went over to Kyle's and since it was a beautiful day we headed to Nepliget (a park) to go for a walk. It is fall here - I'm really enjoying actually having seasons.
Pictures from the park:



Sunday morning I finally decided to go to choir practice before the service (I've been toying with the idea and just not getting to it for a while). The choir was desperately in need of altos, so I agreed to attempt to sing alto. It was interesting. The alto line didn't go to low, so it was ok in that regard and given that I had only seen it that morning and was basically carrying it next to a group of very strong sopranos I think it went quite well. I definitely prefer singing higher though.

When I got back from church, Zoli, Adam and their dad were over - as were one of my host mother's nephews and his wife and three little boys. My host mother had gone all out with lunch. It started with cherry soup (fruit soup here is amazing) and then there was fried meat and potatoes, and nokedli with the meat sauce as the main course and a sweet custardy soup with meringue floating in it called madartej (literally bird's milk). All of it was quite tasty. The afternoon was interesting - having 5 little boys running around is loud and exhausting. It was interesting though, and good for my Hungarian.