Transit

From Ukraine, on the road to Romania, where my scout troop and I went for a camp in the second half of August.

Candy wrappings with writing in the Cyrillic alphabet, scattered somewhere around Grandpa’s house, in the vast storages of my memory. That’s about as much as I had seen of Ukraine prior to my first, albeit only passing, visit to the country this year. On retrospect, Ukraine is very much like that candy wrapping – the shops and restaurants and trains are all almost home-made in that they lack the uniformity of mass production, but they are dulled and grayed about the edges with poverty. I find it all very picturesque, even when I realize that I’m thrilled by all the same things that bother me so in Poland – the old, dilapidated cottages or ladies, each and every one built in a different style or wearing different-colored shawls and flower-patterned skirts, contrasting so sharply with the pseudoWestern and modernistic villas or girls with overdone make-up and provocative mini-skirts they border on. Yes, all this fascinates me here, whereas in Poland, present on a much smaller scale, it’s already too much. The paradox of open-mindedness: I want you all to stay in your backward cultures for years on end, so that I can enjoy experiencing them, but as for myself – culture is just a convention, and let’s not get too caught up in one particular one; to Freedom and the West with me. But don’t you dare follow in my footsteps!

The candy wrapping can give us no hint as to the nature of the Ukrainian population. We have to get past the wrapping, into the gooey candy inside – ah, so sweet, so sweet, except when it gives you an unimaginable stomachache. Ukrainians are the best of people, and they are the worst of people.

The ladies in the various little stores around Lvov are surely of the best kind. Had they been born in England, they would’ve said “here you go, dear” while handing you your receipt; but because they hadn’t been, they say something in Ukrainian with the same gentle smile and give you a scrap of paper with hand-written figures instead. That’s if you specifically ask for a receipt; otherwise, adding up your dues on a pocket calculator or sometimes even on an abacus (droplets of color from a world long gone in the black and white candy wrapping photograph... we gasp in amazement at this treasure), they can’t imagine you could need proof of anything.

There’s an immigration card that needs to be filled out on the Polish-Ukrainian border. There’s also a lady that comes with it, explaining exactly what we need to write.

Or what she thinks we need to write. But not, apparently, what the immigration officers in the train from Lvov to the Romanian border think.

“Why is it filled out in the Latin alphabet?! That’s not allowed.”

“But there are instructions in English here, in the Latin alphabet! Surely if the instructions don’t have to be in Cyrillic, then neither does the part we fill in?”

“Oh... Right, we’ll let you get away with it this once. But... Ah, you didn’t fill in the ‘receiving company’ part!”

“The lady at the border said we didn’t have to...”

“She was wrong then. You should have written ‘Romania’ in there. And now we have no choice but to deport you back to Poland.”

Sinking hearts and powerless indignation. This can’t be, isn’t happening.

“Isn’t there anything we can do? We’ll pay a fine, anything, just don’t send us back to Poland...!”

“Ah, a fine.” A glow of unhealthy contentment lights up their faces. What else could this have been about, if not money?... They motion for us to enter a secluded room... A few minutes later, hryvnias in hand, they disappear with a whispered “we didn’t see you, you didn’t see us”, not even bothering to check if we filled in “Romania” in the immigration cards like they told us to.

But all in all, the Plackartna (the Ukrainian night train) is a terrific thing. Seats that fold into beds; your own clean (or semi-clean) sheets, pillow, and even towel; boiling water in each wagon and tea for a small fee (needless to say, each cup is different, often decorated with pictures of the train line). People wandering about half-clothed, clad in pajama bottoms and the like; a casual, if sleepy and unbearably humid atmosphere all round . Windows that if you’re lucky open after the combined effort of the strongest members of your party, and which half the ladies of the train staff feel it is their duty to close. The other half is stupendously nice, smiling in a grandmotherly sort of way, always asking you if you need anything.

Darkness, blissful darkness, the gentle rocking of the train. “We’re getting up, fold your sheets and bring them to the front of the wagon!” Of all the torturous ways of disturbing one’s sleep, this “we’re getting up” is possibly the evilest. “We’re getting up”?! You bloody well aren’t. You’ve already gotten up at least a full ten minutes previously, and can no longer envision the agony of lifting your eyelids, the despair of sitting up, the resignation of putting on your socks...

But this particular awakening was even viler than the usual “we’re getting up” ones. It was a whole hour before the train was to reach its destination, so I shall never understand why we were already awoken. And the man who woke us up – well, shouldn’t he treat us like humans, like customers? To wake up with the feeling that you are a little child who has done something wrong, who didn’t get out of bed fast enough and bring her sheets to the right place – that’s not something that happens very often in the West.

This child-like feeling is perhaps the key to understanding the mentality of Ukrainian staff and clerks. Unlike the West, where they are in a position slightly subservient to yours, here the servant is always the master. Or rather the parent, who has the right and the duty to stand guard over prime moral values – for bringing your sheets to the front of the wagon and writing “Romania” in appropriate columns are such important things! This paternal (or maternal) quality is also what allows some Ukrainians to be so supremely nice – they are, remember, of the type that calls you “dear”, not the type that says “how ya doin’?” or “thank you, madam”.

On the bus from Lvov back to Poland, a lady comes up to Krzyś and me and asks if we could let her sit in our seats for five minutes to allow her to pack her bag. Puzzled, we nonetheless let her do so. At this, instead of sitting down, which is surely the most reasonable position for packing, she dives down under the seats and lies down on her back...

We later realize that she’s smuggling cigarettes across the border. Hiding some of them around the bus (mostly under seats...; the bus was so old and had so many holes it wasn’t difficult to find a good hiding place), sticking others with tape to her body under her clothes – and all this so, so openly! It soon became apparent that one of the bus drivers is also mixed up in the business...

Not surprisingly, we were stopped at the border for some two hours, missing our planned train from Przemyśl in the process... “You should change the picture in your passport, you don’t look similar,” said the customs officer to Paweł, and though she didn’t call him “dear”, she said it with the air of one who is giving good advice to a child.

Going through customs was rather fun. No X-ray machines here, obviously. They put their hands into our backpacks and felt for bombs and such. “Is it a helmet or bread?” the officer asked when encountering a mess tin. “A spare pair of shoes, right?” another one ascertained after touching a bottle of gasoline we used for cooking our dinners on in Romania (technically, we shouldn’t have been taking it across the border...). I wouldn’t be surprised if after these two hours of searching they hadn’t discovered the smuggled cigarettes at all; but we never actually found that out.

In a little bar in Lvov, where you could stuff yourself with pierogies for the equivalent of a single pound, a smiling lady bid us farewell with the words “come back again when you visit Lvov next time”. Farewell then, beautiful, crazy Lvov, remarkable Ukraine. Maybe I’ll return some day; for now let me remember the smiling faces of your kind matrons and laugh at your over-zealous clerks.

Fact vs Fiction

And then, as the crowning event of this feast, I would devour the tranquility of Claude Monet’s garden in Giverny. Nah, too impatient and too gluttonous to leave the crowning event for last. No, we’ll go to Giverny right at the start of our stay in France. Three years’ worth of waiting is enough towhet my appetite; I don’t need another three days of starvation.

But as the long-awaited piece of iced cake looms on the horizon, I start feeling nervous. What if I’ll be disappointed? Why on earth had I wanted to see this house and garden so desperately? After all, what could be so special about yet another house and garden? Yes, I will be disappointed, no doubt about it.

The houses bordering on Claude Monet’s property are clad in the most adorable ivy. Pah, disappointed, indeed!

Color, light, beauty. Yup. Couldn’t sum up the place more accurately. Flowers on all sides, with an overwhelming multitude of hues, and yet softened, ordered, with slightly blurred edges. Whoa, I didn’t even remember I wrote these words, and yet... yes, that’s the way it was! Blurred edges? Everything was blurred, middle, top right-hand corner, edges and all; the multitude of flowers was such that you could never get more than an impression of anything, as if someone had placed a wet, translucent tissue over your eyes (it was slightly humid as well, blurriness of sight coupled with blurriness of atmosphere).

From the moment I set foot in Monet’s garden, I ceaselessly grin like an idiot and Mom has to remind me to close my gaping mouth a few times. But she does it with a smile rivaling my own and a mock-insulting comment of “Tut, tut, tut, this is what happens when a painter starts a garden...” And what happens is that everywhere you look, there’s something worth looking at – a thrilling juxtaposition of colors, sizes and textures.

In the splash of white roses I find again the stateliness of the Alps. Yeah right. Well obviously that was just a typical use of retrospective to make my text more interesting. (How many times do we lie just to make things more interesting or nice...) No one in their right mind would expect me to retrospect on other places I had seen when faced with something as magnificent as Giverny. Besides, there weren’t even any roses here, but there was a plethora of exquisite splashes of things, white and otherwise.

And finally... I see, after all these years of dreaming, a small Japanese bridge over a pond studded with water lilies. Ekhm... The matter’s not as simple as all that. There’s actually quite a few Japanese bridges in Giverny, and at least two of them look as though they could be the bridge. No matter, the water garden itself is more than anyone could have dreamt of. A forest of bamboo trees, gently glowing a silverish green, a stream endlessly rushing by, everything green, green, green and watery – how it soothes after the myriad sparkling colors of the flower garden. And the water lily pond... It goes on and on, into a pure abstraction of beauty.

When after a few hours I shall leave this place.... My family would’ve died of boredom if I had stayed here for a whole few hours; no, about an hour and a half sufficed. ...I will – I am sure of it – see a small haystack in the distance. I admit it, the “I am sure of it” part was Mom’s suggestion – there’s not that many things I am sure of, and seeing haystacks in the distance is definitely not one of them. Unsurprisingly, the nearest thing to a haystack we had the pleasure to see was a pile of compost a few miles from Giverny...

2 + 3 = 5

From Madame Tussaud's wax figure museum in London.

(The amazing thing about Madame Tussaud’s is not how realistic the wax figures look (you can tell they’re not alive all right), but how unrealistic the people that stand next to them are. That figure over there, next to Michael Jackson, posing for a photograph – what an unnatural smile, what waxy skin, what improbable proportions! One wax figure unfreezes and walks away, the other stays on, smiling interminably. Aren’t humans the most unnatural animals?)

I never believed in following the crowd. In fact, I seem to have a mild case of crowdophobia, with a gathering of more than thirty people causing discomfort, headaches, and suicidal thoughts. The first few rooms of Madame Tussaud’s – a teeming mass of bodies, all swarming to take pictures with figures of people I’ve never even heard of – are therefore something of a nightmare. I want to scream for help, to run away to a medieval castle or abbey that no one visits. Instead, I try to join the idiots surrounding me, to take a picture next to one of those celebrities I don’t give a damn about. Oh why oh why don’t they have civilized lines you could stand in, why does it have to be push your way through and the fittest survives? I take a step toward the figure, already five people jump in to have their pictures taken first. In the process I stand between someone’s camera and the scene they’re trying to take a picture of. “Sorry”, I mumble almost inaudibly, too stressed out to be truly polite.

(As I look at the fifth or so figure of a supermodel that I’ve obviously never seen before, I realize that they all look like Barbie dolls. Yeah, I know, Barbie dolls were based on supermodels, not the other way around, but what of it? In my life, the appearance of the doll came chronologically before the model. And why anyone would want to look like a Barbie doll is beyond me. Humans are the strangest animals, aren’t they?)

But Madame Tussaud’s is not just for the crowd. In the room which exhibits historic personae, the clumps of human mass gathered around wax figures thin out noticeably. I happily dive toward each and every “unpopular” wax model. I can’t resist the urge to look through the prism Newton is holding, to stand on tiptoe in order to reach Oscar Wilde’s eye level, and, most of all, to ruffle Einstein’s hair. Vincent Van Gogh makes a particularly strong impression on me, with a face just like the one in his self-portraits, only realistic. With bittersweet amusement I notice that they placed King Charles I next to Oliver Cromwell. You couldn’t have two more different men – the short, curly-moustached dandy on the left, and on his right the ungainly Puritan, seemingly hacked out of a large and gnarled piece of wood, with two warty knobs on his face. To think that it was not the tree-like one that was eventually cut down!

When I come to the room dedicated to musicians, I rush past the Britney Spearses that everyone’s lining up to see, and head instead toward the Beatles, upon seeing whom I feel a queer desire to shriek my head off. I do wonder what I would have thought of them if they had been popular in my time. “I never believed in following the crowd, do I believe in running away from it at all costs?” I ask the figure of the young Mozart as I look him in the eye. He looks back down to his violin, clearly thinking “don’t be silly, you came here, didn’t you?” And so I did, my dear Mozart, so I did.

Stuck-on smiles

I chanced upon this text I wrote in Polish during the first few days of our stay in Bristol, when I had too much free time on my hands. As we're leaving Bristol in a week and the text isn't too bad, I thought it was appropriate to translate it and add a few ending sentences.

"This is a very important test," says the n-th lady with a wide smile I see that day. "But it’s nothing to worry about," she adds, seeing my not-too-enthusiastic expression. "Just try to do it as quickly and as carefully as possible," she smiles even more widely.

With a deep-set belief that there is some internal contradiction to her words, I start the test. It turns out that it’s an insult to my intelligence. Which makes the situation all the worse, since, deeply insulted, and strained by two hours of trying to sign up to a British school on top of that, the aforementioned intelligence decides to abandon me completely...

I press the “play” button on the computer screen for the third time. While I manage fairly well on the conventional, written questions, to which I’m used from Polish school, my thoughts are already miles away halfway through the problems that necessitate the use of headphones.

The test is disgustingly practical, and therefore presupposes knowledge of British reality. I’m supposed to click on the check which is filled out correctly – and no one gives a damn about a Pole that might not know what a British check looks like.

I’m being unfair. Oh yes, everyone gives much more than a damn about me. If it hadn’t been for the chemistry teacher that had been helping me out for the whole day, I would’ve been running from one part of the school to another not for two hours, but for five, and my frustration would’ve reached its heights after five, not ninety minutes.

Yes, the first hour-and-a-half was alright, and at times even pleasant. At each turn I was struck by how “American” the British are – smiles almost never leave their faces and kind words almost never leave their lips – words such as “That’s lovely!” and “How can I help you?”. A Pole finds a smile so wide for such trifling reasons difficult to believe, so he says loftily and sarcastically: “How fake!” . I reply that it’s just good manners. It’s hardly reasonable to accuse someone of “fakeness” when, for example, being angry, he doesn’t show his anger.

Besides, if I’m to be sincere (and that, as you can see, is a prime virtue for a Pole), I don’t care much whether the waitress that serves me is really happy or not. I only want her to smile at me and ask me if I have everything I want, because that’s part of her job. And sometimes the mask can become the face; I think that a waitress that smiles more often turns happier. During our first few days in England it felt as if everyone here took a deep liking to us personally. I find it hard to believe that a completely insincere smile could have caused such a feeling.

All this doesn’t alter the fact that after two hours of signing up to school my smile felt unskilfully stuck on and I would’ve liked everyone to just leave me alone, instead of constantly asking me if everything was alright. I was beginning to run short of synonyms for the word “yes”...

It seems that the turning point was somewhere in the office of the maths (not “math”, this is Britain, after all) teacher. I tried to persuade him that I’m really capable of finishing a two-year course of mathematics in a year. "But you won’t be able to attend all the courses, you don’t have enough room in your timetable ," he protests. He’s so persuasive that I begin to believe that the feat I am proposing is indeed impossible. Then I remember that I went to a mathematical school. Explaining this to him is no easy task. You can hardly blame a teacher for doubting a student from a foreign country – and a girl at that! – when she says that she’ll finish a two-year course ( a course that English students often have troubles with) in a year.

Eventually, I managed to persuade him. Nineteen exams in a year was a bit tough, but boy am I glad that I didn’t give up and attend first year courses like he wanted me to – trying not to fall asleep would have been much tougher.

As for the test on that first day of school, I never did find out my results and it seems it was not such an important exam after all.

"unfinished"

From Witley Court, the ruins of a Jacobean palace, complete with an impressive fountain and a stunning Baroque chapel.

1

Water and light

One... two – the bells announce the hour. Still nothing. Hell, it’s hot here. I’m not sure now if I’m standing in the best place – yeah, I’m facing the front of the fountain, but more crucially, I’m also facing the sun, and judging by the glaring look it’s giving me, it doesn’t like being stared at. A few more agonizing minutes, and the cupids on either side of the fountain, having decided they’ve kept us waiting long enough, lazily shoot some water from their bows.

The long moments in which nothing happens were probably intended to increase the tension to an unbearable level; I stifle a yawn and contemplate my over-heavy mountain boots. One by one, the fountains surrounding the central sculpture shoot into the air. They don’t change direction, the figures don’t move, and yet it all suddenly springs to life. The graceful arcs of water emphasize the curves of the centerpiece, they glitter and dance in the sun. Their delicate watercolor draws my attention to different parts of the scene. In the center there, with a mighty, but still only metaphysical sweep, Perseus swings his sword and pierces the sea monster’s jaw. Its teeth, like those from a T-rex fossil, look surprisingly sharp – but its eyes have already been dulled by Death’s scythe. It’s very artistic, the way the creature’s watered down blood squirts into the air. All the tension of the story is concentrated in that fountain, and it shoots higher and higher, a man-made cloud. It’s not quite the fountain in Geneva, but it’s got the same monumentality; and it’s tall enough for me to doubt whether even the largest sea monster could have as much blood as all that.

“I won’t be stared at if I hide well,” the sun reflects as it looks down into the clear fountain pool. And it wraps its face in a cloudy veil, and I know I have chosen the best place to stand. Droplets of water fall on my face and arms. The battle has been won; I persisted in watching the spectacle despite all obstacles and was duly rewarded by the retreat of my sunny enemy.

2

Problems with perspective

On the spectrum of audio guide makers, the ones from Witley Court should occupy the opposite end to “practical” people, somewhere towards the “poetic” section. But of course they wouldn’t know what I mean, as they don’t understand the meaning of the words “opposite end” – when they used this expression to denote the position of the next point on the tour, it didn’t mean, as some might have supposed while standing with their back against a wall, the part of the room in front of them, but a different room altogether, located not in front of them, but behind.

This wasn’t the only time on this trip we had doubts about geometry. In the Baroque chapel, we debated whether the painting on the ceiling was “upside-down” or not. With the character’s feet closer to us and the sky away from us, it did look uncomfortable, especially when compared with a second wall-painting, orientated the other way around. But then it’s only natural to draw the sky further away than the ground, isn’t it? The matter was further complicated by the fact that the artist realized that the painting was going to be hung on the ceiling, so he foreshortened the figures a bit to suggest that they are actually above us. Above us and at the same time having their own private ground and sky? Makes my head spin.

But neither this painterly drawback nor the broken CD player in the corner emitting cho-cho-cho-choral music of a slightly more mi-mi-mi-minimalistic nature than intended by the composer prevented us from appreciating the place.

The amazement we feel at seeing a thing is unfortunately a function of how common it is (this function is probably different for everyone and depends on many other variables; but on average it’s an inverse proportionality). In Poland I couldn’t stand Baroque architecture – argh, the overflowing gold, the kitsch angels... – while Gothic churches were a source of constant awe. But this year I’ve come to feel that flying buttresses are the same everywhere, and though gems such as Winchester or Yorkminster still squeeze a gasp out of me, your average Gothic or Neogothic minsters will only warrant a polite nod. Baroque churches of the type found on the Continent, on the other hand, are almost unheard of here, and so the chapel in Witley Court caused the intended widened eyes and increased heartbeat. There were no chubby angels here, and the gold leaf adorning a relaxingly white wall was overdone with much more style than is found in a typical Polish Baroque church.

No witty ending for this article.

Cantor's Seductive Sets

This article has absolutely nothing to do with travelling, it's something I wrote for a competition for a math article (actually for a "maths" article, as it was a British contest). The results have just been out, and no, I haven't won it. I actually didn't stand a chance, because there was a word limit, and I accidentally sent them the version with a couple hundred extra words. Arghhhh...

PS Sorry 'bout the varying sizes of the pictures; I still haven't quite got the hang of inserting pictures here.

A Beautiful Concept: Cantor’s Seductive Sets

“There are just as many even numbers as there are natural ones.”

“What…? But how…?” you might be thinking…

See for yourself: let’s pair ’em up:

Generally, every number n in the set of natural numbers is paired with 2n in the set of even numbers, and so in the land of numbers there are no bachelors. As this land can be quite conservative, bigamy isn’t allowed, and so there must indeed be as many even numbers as natural ones.

But how can a set have as many elements as a subset that isn’t that set? There can’t be as many women as people if there exists at least one man…

Welcome to the world of infinity, where these strange things do indeed happen! Your passport is an open mind, and the most important law goes like this:

If and only if there exists a one-to-one correspondence between two sets, both sets have the same number of elements (so-called cardinality).

Working under this law, we soon discover that there are just as many rational numbers (fractions), as integers (natural plus negative numbers), as natural numbers, as even numbers. This infinity, the infinity of the natural numbers, is called ‘countable infinity’. Is it the only one?

Nope. In fact, there are more points on any line segment, no matter how small, than there are fractions in the vast expanse of Numberland.

And, as if this weren’t enough, there’s an infinite (at least countably infinite, that is) number of infinities – every set of subsets of a set has more elements (a larger cardinality) than that given set. I’ll try to outline the proof for your benefit and amusement.

Imagine you are in a room with infinitely many children. Perhaps uncountably many yelling, screaming brats... You give each kid a piece of paper (so much for saving trees...) and ask them to make a list of all their friends present in the room. Could it happen that each possible list of children was written down by one of the kids?

Given the sheet of paper, each child is faced with a problem. Is he his own friend? Consider all the kids with a low self-esteem, who decided they don’t like themselves. Make a list of them. Could this list have been written by any of the children? Suppose a child had indeed made this list. Is this child, then, her own friend? If she is, she should be on her list – but her list names only the children who aren’t their own friends. Suppose then that she’s not her own friend. Then we should include her on the list of kids that aren’t their own friends – but that’s the list of her friends, and she isn’t her own friend!

Clearly, the list of children that aren’t their own friends can’t be matched up with any child, so not every possible list can be written down by some child.

The conclusion? The set of all subsets of a given set always has a larger cardinality than the set itself. (Don’t quite see it? Disregarding all children’s rights, throw the yelling and screaming brats, the whole infinity of them, into a nearby dump, replace them with elements of any set, and look at what’s left of our story.) The second conclusion? Low self esteem doesn’t pay off...

***

“Do any of you love set theory?” asked my maths teacher once upon a calculus lesson. Undaunted by the jeering silence that followed, he continued. “Because, you know, you’re at the age in which young people are often under the negative influence of that theory.”

Setting aside my teacher’s charming cluelessness about the level of teenagers’ vulnerability to beautiful mathematical concepts, what could he have meant by that foreboding “negative influence”?

At the time Georg Cantor (though I owe the topic of this article to him, I still haven’t introduced him, so... everyone, meet Cantor, the brilliant 19^th century German mathematician, father to all the different infinities!) created set theory, it was truly revolutionary. Up till then, the only acceptable type of infinity was a potential one – numbers could be as large as one wanted, but they never actually reached infinity. Cantor changed all this – he wrote about infinity as if it was as much of an existent being as any of our little number friends.

But how can infinity exist? When we talk about 0’s and 25’s, we can pretend that we are just talking about abstract properties of ‘the real world’. But when we start talking about the infinity of real numbers, where in the universe can we find anything that even resembles it? This is one of the reasons many of Cantor’s contemporaries rejected his theory. Another objection they had was Cantor’s use of the so-called reductio ad absurdum proof. This is the sort of proof the ‘brat story’ is – we assumed that the children could have made all these lists, and then showed that this assumption leads to a contradiction, so its negation must be true.

Kurt Gödel, a brilliant 20^th century logician, once proved that God exists. His proof was strictly logical, starting with a carefully blended mixture of axioms, and ending in the elegant filet mignon of the conclusion; the same type of proof used in mathematics. Our belief in points, numbers and infinity is no more or less justified than that in God. Mathematics proves that certain numbers and points exist – but what that existence means no one has much of an idea. At best, mathematics seems to be an impossibly nerdy religion.

Cantor’s set theory, even when clad in the unladylike rags of infinitely many brats, is too elegant to be thrown into the dump. Perhaps my maths teacher knew more about young men’s nature than he let on... After all, it’s not all that difficult to capture a young man’s heart, and set theory is the perfect seductress. She might not be true, but she sure is beautiful.