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Many things have happened this week. First of all, on Friday, Luiza, claiming the ensemble's main flaw at the Ukrainian New Year celebration was a bit of sloppy footwork, taught us all a little Highland dancing to improve our precision. That rehearsal was not a good rehearsal for me; my turns were all over the map, and even straightening out my backbone did not help. However, I am now trying to practice the first step of the Highland fling in front of the mirrors. On Sunday, Kella, the director of the school, taught us new barre exercises: a Hungarian plié exercise, a French-Canadian tendu exercise, a circle warmup from the mountains of Ukraine, and a grand battement exercise in the Irish style.
She's handsome, she's pretty,
She's the belle of the whole fine city,
She's lovely, one two three,
Please, will you tell me who is she?
On Saturday's aikido class, we received our kyu certificates: a backlog of ranks that for my brother and me dates back to sixth kyu. I am now in odd aikido limbo, as officially I am certified as a fourth kyu, although I have not taken the test, and I am not at all certain I know the curriculum requirements. I keep on trying to schedule a weekly kyu workshop, but some god conspires against me.
After that, I spent the rest of Saturday afternoon watching the first five episodes of The Master and Margarita. Naughty me, I kept on thinking, "Better get to work. No, just one more episode..." I got to the fifth one before I drew the line. That is a series you can watch over and over and over again.
On Monday in Syntax class, I was struck by the sudden urge to design aliens. It started with an alien hand; I will justify my actions by saying the hand was inspired by a syntax tree. Lazily observing the review of traces and transformations - I am actually slowly beginning to agree with most of them, but I let the secret spark of syntactic rebellion smoulder - I drew alien hands and the alien skeleton, colour-labelling joints and cartilage. I need to ask the Dark Lord about graphic arts; I dearly wish to animate this alien hand and see what kind of movements it can make. Given my current crowded schedule, the spare time to animate alien hands will probably come in June. "Dark Lord, could you tell me where to download Blender?" "What do you need it for?" "Oh, I was drawing aliens in Syntax class, and I wonder how they move..."
Seriously, the more I learn about linguistics, the more it makes me wonder about the science-fiction possibilities of alien contact. Most SF stories, written by non-linguists, kind of assume that translating alien languages is going to be easy ("Death and Designation Among the Asadi" excepted), except for a few alien words for concepts in extraterrestrial culture. Perhaps the best idea I have heard for a truly alien tongue is the languages of Tlon in Jorge Luis Borges' "Tlon, Uqbar, Orbis Tertius," a story I also reread this week. In one of the languages of the imaginary world Tlon, (which is featured in all the literature of the imaginary country Uqbar, which is imagined by the imaginary society Orbis Tertius, which is imagined by the real Borges) there are no nouns; everything is expressed by verbs. In another language, everything is expressed by adjectives alone. One can also look at the list of language universals, compiled by the Linguistics Encyclopedia, and imagine a language which violates every single one of them. Well, the writers of The Empire Strikes Back were brilliant in assigning Yoda a standard word order seen in almost none of the world's languages: Object-Subject-Verb. It actually made them suitably alien.
Speaking of aliens, I now know the first thing we have to ask them upon decoding their language. In History of Math, Pestov led us for a while through the Continuum Hypothesis and the Zermelo-Fraenkel-Axiom of Choice (ZFC) axioms of set theory. Those axioms are as absolutely basic as mathematics can be; they are what the foundations of mathematics rest on. However, Godel proved, with the Incompleteness Theorem, that given any system of axioms, you cannot prove that the system does not lead to a contradiction while staying within the system itself. If that confuses you, it is the same as when I write a check, I should not be the one to also verify its creditworthiness. (Sweet, the Incompleteness Theorem in a nutshell.)
The problem with that is the Continuum Hypothesis. The number of elements in the set of natural numbers, integers, or rational numbers is aleph-naught; the number of elements in the set of real numbers and complex numbers is C (\mathfrak{C} in LaTeX-ese). We know that C is bigger than aleph-naught; the question is how much bigger? Are there any numbers between them? The CH says there are none, and it may have been the most famous problem in all of mathematics: to prove or disprove the CH. Using ZFC.
Now Godel did not rest on the laurels of the Incompleteness Theorem; he then went and proved that if ZFC is not self-contradictory, then ZFC plus CH is not self-contradictory. Great, the non-mathematicians sigh with relief; CH is true then? No, along came Paul Cohen and proved that ZFC plus the assumption that CH is false is not contradictory either! So theoretically we can do math in either world.
"Wait a sec," I raised my hand. "Either a set with cardinality less than C and greater than aleph-naught exists or it does not. We cannot have both situations in the same world, can we?"
"Ah," said Pestov, "it depends on what you mean by 'exists.' "
"If it can be imagined and does not lead to contradiction, then it exists," the wannabe mathematician and even more wannabe fantasy author maintained.
"But we cannot show that set while we work in ZFC, here."
I grunted. "I know the first thing we need to ask aliens once they land. 'How do you do set theory?' " Oddly, no one laughed.
Well, Pestov believes, and began a "proof" to convince us as well, that very soon ZFC will be replaced by a stronger axiomatic system, in which the CH will be obviously false. That appeals to me. Having only two first transfinite cardinal numbers would be simpler, but the possibility of others in between them appeals to me.
On Monday, I also babysat the 11-month-old I had mentioned before. I learned
a) Barney is better than Teletubbies, and the Wiggles are better than Barney
b) my arms are still sore from hosting that mighty five-kilo weight around as I dance, and it's been a week.
c) Adriano Celentano's "Stivali E Colbacco" is a great song to dance to, and looking up the lyrics, I find they make me smile. Ah, the Slavic soul
Mi sembra la figlia
Di un capo cosaco
Con quegli stivali
E quel nero... colbacco
Ahi, ahi,ahi
Ahi, ahi, ahi
Chiunque ti guarda
Rimane di stucco
Ed ogni ragazzo
Si sente un calmucco
Ahi ahi ahi ahi ahi
Ahi ahi ahi ahi ahi
Tutta la gente si gira
Si gira.
Quando ti vede passar
Passar.
Non sente piu che c'e freddo
C'e freddo.
E resta ferma a guardar.
Sei alta sei bionda
Sei proprio uno spacco
Con quegli stivali
E quel nero colbacco.
Ahi ahi ahi
Ahi ahi ahi
Tutta la gente si gira
Si gira.
Quando ti vede passar
Passar.
Non sente piu che c'e freddo
C'e freddo.
E resta ferma a guardar.
Sei alta sei bionda
Sei proprio uno spacco
Con quegli stivali
E quel nero colbacco.
Ahi ahi ahi
Ahi ahi ahi
Ahi ahi ahi
Ahi ahi ahi
Tutta la gente si gira
Si gira.
Quando ti vede passar
Passar.
Non sente piu che c'e freddo
C'e freddo.
E resta ferma a guardar.
Sei alta sei bionda
Sei proprio uno spacco
Con quegli stivali
E quel nero colbacco.
Ahi ahi ahi
Ahi ahi ahi
In advanced aikido classes now, we are avidly doing kick techniques. It takes an indredible amount of trust to let yourself be thrown without your feet, with nothing between you and the ground but air and nage's skill and your own, and you tucking your head in for fear, so much that your neck tendons still hurt five days later.
I will learn.
But Friday dance rehearsal was the best ever. For once, Lord Pencilturn had looked disappointed the Friday before, when I told him I will not be there for the ensemble's Winterlude show, so don't put me in "Encounter." This time, Elizaveta finally expained to me that trick of choreography in "Encounter" I never understood, and while we were practicing turns, Lord Pencilturn yelled to me to keep my arms higher and not jump so far. I finished the turn sequence and withdrew to the wall to let the men advance, grinning at Elizaveta from ear to ear: "He yelled at me! That means he acknowledges I am not beyond help!" Our first run through of "Encounter" was sketchy, but the second one, I admit freely, is the best I have yet danced "Encounter" in my life.
And then we worked on Lord Pencilturn's new choreography: it is amazingly fast, but I can do it! Just...not at speed. Yet. Afterwards, even before the rehearsal ended, I understood Robert Graves' line from "To Juan at the Winter Solstice": "All fish below the thighs." Only it should be interpreted as "All dead below the thighs"; allegro dancers of the world, stand up and agree with me! But my thighs are looking a lot better now that they did this summer, for one thing, and for another, I found myself thinking how Lord Pencilturn's choreography made a weird kind of sense. I know I first started getting aikido with exactly the same feeling: "It makes sense!" Dancing makes sense! I make sense!
Tutta la gente si gira
Si gira.
Quando ti vede passar
Passar.
Non sente piu che c'e freddo
C'e freddo.
E resta ferma a guardar.
Well, today I skipped dance completely. I had to finish a lot of homework. And clean the house for guests. And then welcome said guests. I tried to atone for my failings by dancing to Afric Simone's "Hafanana" and then "Stivali E Colbacco" again.
And there ended my high opinion of my dancing. My mother came and told me that my movements were too jerky, and I, upset when I was dancing that she was hitting at what I loved most, yelled at her "I am trying to work on it!" and fled the room. Later she called me back and explained to me that still, if I continue on like this, it is pretty evident why I am not in the core ensemble, and once my ligaments lose their elasticity at 32 or 35, I will find myself doing a turn and snapping the ligaments in my knee. She cited a yoga instructor who came to her after injuring a muscle in his shoulder two months before. He had thought he would just work it out, and ended up exacerbating it so much he could not raise his arm above his head anymore. She suggested I work on slow music instead of fast music, or do tai chi.
I went to wash the dishes, thinking about this. If I am that bad, why is the ensemble nice to me? Why do they lie about me, then? Because they are polite and well-bred? Well, indeed they are polite and well-bred, but I cannot recall the last time Taglioni criticised me. Is it because the time she did, I somehow gave her the impression it was a waste of time to give me advice; I do not follow it? And the ensemble is polite and well-bred, but I have no real friends among them; they may say hi to me, or chat in circles that include me, but no one ever invited me to any gathering outside rehearsal. And the same goes for aikido. And the same goes for school, except for those times when guys end up havign crushes on me. I must face the facts and acknowledge them: busy and active as I might be, I have no friends.
Except possibly Athaira and Concolor, but it is hard maintaining a long-distance friendship in Athaira's case. I have no friends, and I am not really good at anything. If I was good at math, would I get D's? I am no good at dance; I am going in completely the wrong direction, it seems. I may look vaguely good at aikido, to a beginner, but no one in fifth kyu is ever actually good, both martially effective and graceful, and the first brute on the street will show me how "good" at aikido I really am. And if I was good at writing, wouldn't I be published by now? And wouldn't I not avoid reading through the first chapters of my work? And if I was good at linguistics, wouldn't I...I guess I cannot find a flaw; I am good at linguistics. But I want to be great at something, indeed, great at everything, and I want to be loved as well. And it seems all around me are simply well-bred sycophants, who do not think for a second about me when I am not in front of their eyes, and I will have to acknowledge that what my parents have been telling me since I was seven was right: I have no friends except my family.
That realisation came to a little child, and it comes again and again now. Go away and let me cry.
She's handsome, she's pretty,
She's the belle of the whole fine city,
She's lovely, one two three,
Please, will you tell me who is she?
On Saturday's aikido class, we received our kyu certificates: a backlog of ranks that for my brother and me dates back to sixth kyu. I am now in odd aikido limbo, as officially I am certified as a fourth kyu, although I have not taken the test, and I am not at all certain I know the curriculum requirements. I keep on trying to schedule a weekly kyu workshop, but some god conspires against me.
After that, I spent the rest of Saturday afternoon watching the first five episodes of The Master and Margarita. Naughty me, I kept on thinking, "Better get to work. No, just one more episode..." I got to the fifth one before I drew the line. That is a series you can watch over and over and over again.
On Monday in Syntax class, I was struck by the sudden urge to design aliens. It started with an alien hand; I will justify my actions by saying the hand was inspired by a syntax tree. Lazily observing the review of traces and transformations - I am actually slowly beginning to agree with most of them, but I let the secret spark of syntactic rebellion smoulder - I drew alien hands and the alien skeleton, colour-labelling joints and cartilage. I need to ask the Dark Lord about graphic arts; I dearly wish to animate this alien hand and see what kind of movements it can make. Given my current crowded schedule, the spare time to animate alien hands will probably come in June. "Dark Lord, could you tell me where to download Blender?" "What do you need it for?" "Oh, I was drawing aliens in Syntax class, and I wonder how they move..."
Seriously, the more I learn about linguistics, the more it makes me wonder about the science-fiction possibilities of alien contact. Most SF stories, written by non-linguists, kind of assume that translating alien languages is going to be easy ("Death and Designation Among the Asadi" excepted), except for a few alien words for concepts in extraterrestrial culture. Perhaps the best idea I have heard for a truly alien tongue is the languages of Tlon in Jorge Luis Borges' "Tlon, Uqbar, Orbis Tertius," a story I also reread this week. In one of the languages of the imaginary world Tlon, (which is featured in all the literature of the imaginary country Uqbar, which is imagined by the imaginary society Orbis Tertius, which is imagined by the real Borges) there are no nouns; everything is expressed by verbs. In another language, everything is expressed by adjectives alone. One can also look at the list of language universals, compiled by the Linguistics Encyclopedia, and imagine a language which violates every single one of them. Well, the writers of The Empire Strikes Back were brilliant in assigning Yoda a standard word order seen in almost none of the world's languages: Object-Subject-Verb. It actually made them suitably alien.
Speaking of aliens, I now know the first thing we have to ask them upon decoding their language. In History of Math, Pestov led us for a while through the Continuum Hypothesis and the Zermelo-Fraenkel-Axiom of Choice (ZFC) axioms of set theory. Those axioms are as absolutely basic as mathematics can be; they are what the foundations of mathematics rest on. However, Godel proved, with the Incompleteness Theorem, that given any system of axioms, you cannot prove that the system does not lead to a contradiction while staying within the system itself. If that confuses you, it is the same as when I write a check, I should not be the one to also verify its creditworthiness. (Sweet, the Incompleteness Theorem in a nutshell.)
The problem with that is the Continuum Hypothesis. The number of elements in the set of natural numbers, integers, or rational numbers is aleph-naught; the number of elements in the set of real numbers and complex numbers is C (\mathfrak{C} in LaTeX-ese). We know that C is bigger than aleph-naught; the question is how much bigger? Are there any numbers between them? The CH says there are none, and it may have been the most famous problem in all of mathematics: to prove or disprove the CH. Using ZFC.
Now Godel did not rest on the laurels of the Incompleteness Theorem; he then went and proved that if ZFC is not self-contradictory, then ZFC plus CH is not self-contradictory. Great, the non-mathematicians sigh with relief; CH is true then? No, along came Paul Cohen and proved that ZFC plus the assumption that CH is false is not contradictory either! So theoretically we can do math in either world.
"Wait a sec," I raised my hand. "Either a set with cardinality less than C and greater than aleph-naught exists or it does not. We cannot have both situations in the same world, can we?"
"Ah," said Pestov, "it depends on what you mean by 'exists.' "
"If it can be imagined and does not lead to contradiction, then it exists," the wannabe mathematician and even more wannabe fantasy author maintained.
"But we cannot show that set while we work in ZFC, here."
I grunted. "I know the first thing we need to ask aliens once they land. 'How do you do set theory?' " Oddly, no one laughed.
Well, Pestov believes, and began a "proof" to convince us as well, that very soon ZFC will be replaced by a stronger axiomatic system, in which the CH will be obviously false. That appeals to me. Having only two first transfinite cardinal numbers would be simpler, but the possibility of others in between them appeals to me.
On Monday, I also babysat the 11-month-old I had mentioned before. I learned
a) Barney is better than Teletubbies, and the Wiggles are better than Barney
b) my arms are still sore from hosting that mighty five-kilo weight around as I dance, and it's been a week.
c) Adriano Celentano's "Stivali E Colbacco" is a great song to dance to, and looking up the lyrics, I find they make me smile. Ah, the Slavic soul
Mi sembra la figlia
Di un capo cosaco
Con quegli stivali
E quel nero... colbacco
Ahi, ahi,ahi
Ahi, ahi, ahi
Chiunque ti guarda
Rimane di stucco
Ed ogni ragazzo
Si sente un calmucco
Ahi ahi ahi ahi ahi
Ahi ahi ahi ahi ahi
Tutta la gente si gira
Si gira.
Quando ti vede passar
Passar.
Non sente piu che c'e freddo
C'e freddo.
E resta ferma a guardar.
Sei alta sei bionda
Sei proprio uno spacco
Con quegli stivali
E quel nero colbacco.
Ahi ahi ahi
Ahi ahi ahi
Tutta la gente si gira
Si gira.
Quando ti vede passar
Passar.
Non sente piu che c'e freddo
C'e freddo.
E resta ferma a guardar.
Sei alta sei bionda
Sei proprio uno spacco
Con quegli stivali
E quel nero colbacco.
Ahi ahi ahi
Ahi ahi ahi
Ahi ahi ahi
Ahi ahi ahi
Tutta la gente si gira
Si gira.
Quando ti vede passar
Passar.
Non sente piu che c'e freddo
C'e freddo.
E resta ferma a guardar.
Sei alta sei bionda
Sei proprio uno spacco
Con quegli stivali
E quel nero colbacco.
Ahi ahi ahi
Ahi ahi ahi
In advanced aikido classes now, we are avidly doing kick techniques. It takes an indredible amount of trust to let yourself be thrown without your feet, with nothing between you and the ground but air and nage's skill and your own, and you tucking your head in for fear, so much that your neck tendons still hurt five days later.
I will learn.
But Friday dance rehearsal was the best ever. For once, Lord Pencilturn had looked disappointed the Friday before, when I told him I will not be there for the ensemble's Winterlude show, so don't put me in "Encounter." This time, Elizaveta finally expained to me that trick of choreography in "Encounter" I never understood, and while we were practicing turns, Lord Pencilturn yelled to me to keep my arms higher and not jump so far. I finished the turn sequence and withdrew to the wall to let the men advance, grinning at Elizaveta from ear to ear: "He yelled at me! That means he acknowledges I am not beyond help!" Our first run through of "Encounter" was sketchy, but the second one, I admit freely, is the best I have yet danced "Encounter" in my life.
And then we worked on Lord Pencilturn's new choreography: it is amazingly fast, but I can do it! Just...not at speed. Yet. Afterwards, even before the rehearsal ended, I understood Robert Graves' line from "To Juan at the Winter Solstice": "All fish below the thighs." Only it should be interpreted as "All dead below the thighs"; allegro dancers of the world, stand up and agree with me! But my thighs are looking a lot better now that they did this summer, for one thing, and for another, I found myself thinking how Lord Pencilturn's choreography made a weird kind of sense. I know I first started getting aikido with exactly the same feeling: "It makes sense!" Dancing makes sense! I make sense!
Tutta la gente si gira
Si gira.
Quando ti vede passar
Passar.
Non sente piu che c'e freddo
C'e freddo.
E resta ferma a guardar.
Well, today I skipped dance completely. I had to finish a lot of homework. And clean the house for guests. And then welcome said guests. I tried to atone for my failings by dancing to Afric Simone's "Hafanana" and then "Stivali E Colbacco" again.
And there ended my high opinion of my dancing. My mother came and told me that my movements were too jerky, and I, upset when I was dancing that she was hitting at what I loved most, yelled at her "I am trying to work on it!" and fled the room. Later she called me back and explained to me that still, if I continue on like this, it is pretty evident why I am not in the core ensemble, and once my ligaments lose their elasticity at 32 or 35, I will find myself doing a turn and snapping the ligaments in my knee. She cited a yoga instructor who came to her after injuring a muscle in his shoulder two months before. He had thought he would just work it out, and ended up exacerbating it so much he could not raise his arm above his head anymore. She suggested I work on slow music instead of fast music, or do tai chi.
I went to wash the dishes, thinking about this. If I am that bad, why is the ensemble nice to me? Why do they lie about me, then? Because they are polite and well-bred? Well, indeed they are polite and well-bred, but I cannot recall the last time Taglioni criticised me. Is it because the time she did, I somehow gave her the impression it was a waste of time to give me advice; I do not follow it? And the ensemble is polite and well-bred, but I have no real friends among them; they may say hi to me, or chat in circles that include me, but no one ever invited me to any gathering outside rehearsal. And the same goes for aikido. And the same goes for school, except for those times when guys end up havign crushes on me. I must face the facts and acknowledge them: busy and active as I might be, I have no friends.
Except possibly Athaira and Concolor, but it is hard maintaining a long-distance friendship in Athaira's case. I have no friends, and I am not really good at anything. If I was good at math, would I get D's? I am no good at dance; I am going in completely the wrong direction, it seems. I may look vaguely good at aikido, to a beginner, but no one in fifth kyu is ever actually good, both martially effective and graceful, and the first brute on the street will show me how "good" at aikido I really am. And if I was good at writing, wouldn't I be published by now? And wouldn't I not avoid reading through the first chapters of my work? And if I was good at linguistics, wouldn't I...I guess I cannot find a flaw; I am good at linguistics. But I want to be great at something, indeed, great at everything, and I want to be loved as well. And it seems all around me are simply well-bred sycophants, who do not think for a second about me when I am not in front of their eyes, and I will have to acknowledge that what my parents have been telling me since I was seven was right: I have no friends except my family.
That realisation came to a little child, and it comes again and again now. Go away and let me cry.
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