Mathematics 100: Geometry and Logic
Final Examination
Question: What happens when you draw lines through a pre-existing entity?
Answer: If you take an object (say, an unbroken circle) and bisect it at its widest point with a straight line, you will create a new object made up of congruent halves. For our purposes, we will call these compartments. The space once taken up by the object will also be lessened, due to the presence of the straight line. Note also that the extent of this diminishment will depend on the amount of space alloted to the straight line. If you bisect this straight line with another straight line, at a right angle, you will create a cross. This cross will diminish the size of the original compartments, and through careful analysis, you will be able to prove that the compartments can now only relate to one another in terms defined by the cross. Please also observe that while the resulting compartments have similar characteristics, they cannot join until the cross is overcome and the straight lines have been erased.
- End of Proof.
Before beginning the following question, please take time to review the following definitions:
Transitive Property of Equality:
"If a = b and b = c, then a = c.
The Transitive Property is one of the equivalence properties of equality. This is a property of equality and inequalities. One must be cautious, however, when attempting to develop arguments using the transitive property in other settings."
Lemma
"A helping theorem. A lemma is proven true, just like a theorem, but is not interesting or important enough to be a theorem. It is of interest only because it is a stepping stone towards the proof of a theorem."
Postulate:
"A statement accepted as true without proof. "
Axiom
"A statement accepted as true without proof. An axiom should be so simple and direct that it is unquestionably true. "
Question: Ben likes boys. What does that make Ben?
Answer
1) Ben likes boys. Therefore, Ben is gay (see lemma “if you are a boy and you like another boy or boys you are gay” ).
2) Gay is bad ( one can infer this from the answer to the preceding question, or by using the popular "gay is bad" postulate).
3) Therefore, Ben is bad. (Transitive Property).
Bonus question – if you get this one right, you will pass the whole course, regardless of the work you have done before…
Ben is bad. Now what?
We have proven that Ben is a bad object. However objects have many definable properties and we can observe that Ben is also good in school and can play the piano and sing. He can also cook and imitate his parents in a way that makes people laugh. If Ben works at these things hard enough for a long enough period of time, it is logical that people will overlook his inherent evil characteristics.
However, there is a new concept which is really a very old concept which supposes that all objects are good. While this concept cannot be proven, per se, we find that if adopted, it becomes self-evident. It is therefore an axiom, though it is viewed by some as experimental, controversial and vulnerable. We believe it to be correct.
Therefore,
Ben,
Who likes boys,
Is good.
He will still play the piano and sing and make fun of his parents, but he will not do it so that others will overlook any other aspect of his being. In this way, we can assume that Ben, in all probabilty, will be observed in a more comprehensive way, and can therefore exist in a more cohesive manner.
- End of proof.
Wednesday, June 28, 2006
Sunday, June 25, 2006
Why you should always remember to spellcheck.....
Look what I found on a tourism website about Canada:
NATIONAL ANTHEM"Ho Canada" was proclaimed national anthem on July the 1st of 1980, a century after to be sung the first time.
NATIONAL ANTHEM"Ho Canada" was proclaimed national anthem on July the 1st of 1980, a century after to be sung the first time.
Wednesday, June 21, 2006
Alles hat ein Ende... Nur die Wurst hat zwei.
Once a year my mother and I have our tarot cards read. Not only is it great fun (we can be as self absorbed and anxious as we want to be for over an hour) but a tarot-session is about a third the price as a visit to the therapist, and the restaurant where we go serves great tempura. I ask you, does it get better than divining and fried food? Not in this life. During our most recent visit, the medium decided to forego the tarot cards as he had decided, upon reflection, that they got in the way of the psychic energy that flowed between himself and the client. This was perfectly fine by me. After all, I come from a race that has always been keen on leaving out the middle man, both in religion and retail. Besides, who needs cards when you have imagination and a wireless connection with the divine?
So then the time came when we had to decide who was to have their reading first. Of course, we each insisted that the other begin, not because we were being polite, but because we wanted to get the other's reading over with. You see, it is quite a trial to be polite and listen attentively when someone else is talking, but not talking about you. It is best to get this over with as soon as possible. Of course, my mother (being of an artistic disposition as I am) is of the same opinion. And so she smiled and looked at me with her " remember that I am your mother and I gave birth to you and I was in labour for 70 hours, indeed, it was the longest labour of 1979 at the Women's Pavilion" look. And so, my reading began.
The medium said that I was about to begin a new phase of my life, and that I must prepare myself for by "improving my attire" and "dressing the part". I took this to mean that I needed hand-tailored suits, or at the very least some off-the-rack Canali. My mother thought
that this was just a metaphor and had more to do with self-confidence. I tried to tell her that
you cannot help but feel your best when you are wearing deluxe Italian upper 200 count wool.
She adjusted the collar on her burlap cape and we moved on.
Apparently, in this time of transition, I will also be saying goodbye to many friends. This is true. As I write to you , Soula is preparing for a concert of Mozart arias at the Berlin Philharmonie,
Wade is on a plane to Quebec City where he will sleep on his friend's couch and learn French in an immersion program of his own design, and in a few weeks Randy will depart for Shanghai to set up an office for her boyfriend's engineering firm.
And then there is Arvedt, who has been recalled to Berlin to work in the protocol office, arranging travel for Chancellor Merkel.
The other night, we were sitting by the ocean, and I was eating Malaga ice cream, which is my favourite. Malaga is like rum-raisin, but the raisins are soaked in rum which for an obscenely long period of time, and then folded into a custard with an obscenely large number of egg yolks. Really, it should be banned. Eating it makes me feel like naughty and rich, like Catherine de Medici, who fit both descriptions very well. Along with the dinner fork and the corset, she is credited for having introduced three important things to France that define it to this day: gastronomy, high heels, and riots. She also introduced ice cream. I can see her now, in her bodice and stiletto heels -- Nero-like -- giving orders to carry out the St. Bartholemew's Day Massacre of Protestants while nibbling on a delicate strawberry ice.
And I am troubled, because while the Huguenot sympathizer in me hates her, the foodie in me cannot help but worship. Had it not been for vain Catherine, the French would still be eating things like goat udder stewed in hyppocras. Worse, they'd still be eating like the English.
Now, where was I? Oh yes, Arvedt. Arvedt was not eating Malaga ice cream. He was telling me about his camping trip to Saltspring Island, which is famous for being infested with mice. Arvedt hates mice, and so he told me how spent the evening lying down in his puptent wearing his bike light as a bandana and throwing morsels of cheese and trailmix to the rodents... not so that they would go away, but so that they would stop for a moment and eat. At which time Arvedt would hit them:
"Oh gott. Means like, the mices were everyvhere, and I kept hitting them with cheese and trailmixes... I said to myself, Gott, if I die now, it would be okay."
I stared laughing uncontrollably, but he looked at me with a straight face and said
"Why are you laughing? You have never had an experience such as this?"
We started to talk about the coming months, and I asked Arvedt how he felt about leaving Canada. He smiled and said
"Well, you know, in German, we have this silly expression: Alles hat ein Ende. Nur die wurst hat zwei"
Which means: Everything has an end. Only a sausage has two.
I wonder what Catherine de Medici would think about that!
So then the time came when we had to decide who was to have their reading first. Of course, we each insisted that the other begin, not because we were being polite, but because we wanted to get the other's reading over with. You see, it is quite a trial to be polite and listen attentively when someone else is talking, but not talking about you. It is best to get this over with as soon as possible. Of course, my mother (being of an artistic disposition as I am) is of the same opinion. And so she smiled and looked at me with her " remember that I am your mother and I gave birth to you and I was in labour for 70 hours, indeed, it was the longest labour of 1979 at the Women's Pavilion" look. And so, my reading began.
The medium said that I was about to begin a new phase of my life, and that I must prepare myself for by "improving my attire" and "dressing the part". I took this to mean that I needed hand-tailored suits, or at the very least some off-the-rack Canali. My mother thought
that this was just a metaphor and had more to do with self-confidence. I tried to tell her that
you cannot help but feel your best when you are wearing deluxe Italian upper 200 count wool.
She adjusted the collar on her burlap cape and we moved on.
Apparently, in this time of transition, I will also be saying goodbye to many friends. This is true. As I write to you , Soula is preparing for a concert of Mozart arias at the Berlin Philharmonie,
Wade is on a plane to Quebec City where he will sleep on his friend's couch and learn French in an immersion program of his own design, and in a few weeks Randy will depart for Shanghai to set up an office for her boyfriend's engineering firm.
And then there is Arvedt, who has been recalled to Berlin to work in the protocol office, arranging travel for Chancellor Merkel.
The other night, we were sitting by the ocean, and I was eating Malaga ice cream, which is my favourite. Malaga is like rum-raisin, but the raisins are soaked in rum which for an obscenely long period of time, and then folded into a custard with an obscenely large number of egg yolks. Really, it should be banned. Eating it makes me feel like naughty and rich, like Catherine de Medici, who fit both descriptions very well. Along with the dinner fork and the corset, she is credited for having introduced three important things to France that define it to this day: gastronomy, high heels, and riots. She also introduced ice cream. I can see her now, in her bodice and stiletto heels -- Nero-like -- giving orders to carry out the St. Bartholemew's Day Massacre of Protestants while nibbling on a delicate strawberry ice.
And I am troubled, because while the Huguenot sympathizer in me hates her, the foodie in me cannot help but worship. Had it not been for vain Catherine, the French would still be eating things like goat udder stewed in hyppocras. Worse, they'd still be eating like the English.
Now, where was I? Oh yes, Arvedt. Arvedt was not eating Malaga ice cream. He was telling me about his camping trip to Saltspring Island, which is famous for being infested with mice. Arvedt hates mice, and so he told me how spent the evening lying down in his puptent wearing his bike light as a bandana and throwing morsels of cheese and trailmix to the rodents... not so that they would go away, but so that they would stop for a moment and eat. At which time Arvedt would hit them:
"Oh gott. Means like, the mices were everyvhere, and I kept hitting them with cheese and trailmixes... I said to myself, Gott, if I die now, it would be okay."
I stared laughing uncontrollably, but he looked at me with a straight face and said
"Why are you laughing? You have never had an experience such as this?"
We started to talk about the coming months, and I asked Arvedt how he felt about leaving Canada. He smiled and said
"Well, you know, in German, we have this silly expression: Alles hat ein Ende. Nur die wurst hat zwei"
Which means: Everything has an end. Only a sausage has two.
I wonder what Catherine de Medici would think about that!
Sunday, June 18, 2006
People with Penthouses
When it came to dating, the only advice my mother (a card carrying member of the NDP) ever gave me was to "marry up". Indeed, there was a time when the only real way to improve one's social standing was to do so.... of course, you had to be talented, beautiful and determined as hell.
Like my friend Lindsay, who met the love of her life during a production of The Mikado. She was Yum-Yum (in more ways than one, apparently) and her Nanki-Poo, Larry, was smitten. They kissed and he swept her away in his arms. One morning, she awoke from a delicious slumber in 500 threadcount sheets to find that not only was Larry a tenor, but also an internationally successful businessman with a penthouse in False Creek. And they lived happily ever after.
If you are haven't yet met your Nanki-Poo, then my advice would be to get to know people with penthouses and to go to their parties. This way, you can go to the very top and you don't need a man to get you there, unless of course he is pushing the buttons in the elevator. In any event, once you have arrived, there really is no need for social climbing at all, because you can already look down on everyone.
Except for the people with penthouses higher than yours, and trust me, there is always someone.
My friend Lindsay has great style, and throws great parties. We were going to have oysters, but there was a red tide, and rather than be poisoned, we made do with butter drenched scampi -- nibbled from a lofty perch above high above the water. It was a hardship, but we managed. The conversation turned to travel, and Lindsay mentioned that she was going to London the next day. I asked her how she was going to find the time to pack. She replied that all she needed to remember was her music and her underwear. She had an American Express card, after all, and could just buy the rest when she got there. How wise, I said, as I took a bite from a perfectly grilled ribeye steak. I looked down, and saw the people running about. They looked like ants. I thought about throwing my shrimp shells over the ledge for fun, but decided against it. How wise.
As I was mixing myself a gin and tonic, I noticed that the the gin was from Scotland and was infused with cucumber and rose petals. I asked Lindsay where she procured such a delightful beverage, and she said that she didn't know, but that it came from the "good closet". I told her I did too. Ha ha.
But then I thought, I do come from a good closet. That is where I am writing you from right now. It may be small, but it is a space of my own making, and I live on the first floor, so my feet are firmly on the ground. As they should be. And when people walk by, I can look them in the eye. Which is also how it should be.
But I cannot deny that sometimes, I wish I had a penthouse too.
Like my friend Lindsay, who met the love of her life during a production of The Mikado. She was Yum-Yum (in more ways than one, apparently) and her Nanki-Poo, Larry, was smitten. They kissed and he swept her away in his arms. One morning, she awoke from a delicious slumber in 500 threadcount sheets to find that not only was Larry a tenor, but also an internationally successful businessman with a penthouse in False Creek. And they lived happily ever after.
If you are haven't yet met your Nanki-Poo, then my advice would be to get to know people with penthouses and to go to their parties. This way, you can go to the very top and you don't need a man to get you there, unless of course he is pushing the buttons in the elevator. In any event, once you have arrived, there really is no need for social climbing at all, because you can already look down on everyone.
Except for the people with penthouses higher than yours, and trust me, there is always someone.
My friend Lindsay has great style, and throws great parties. We were going to have oysters, but there was a red tide, and rather than be poisoned, we made do with butter drenched scampi -- nibbled from a lofty perch above high above the water. It was a hardship, but we managed. The conversation turned to travel, and Lindsay mentioned that she was going to London the next day. I asked her how she was going to find the time to pack. She replied that all she needed to remember was her music and her underwear. She had an American Express card, after all, and could just buy the rest when she got there. How wise, I said, as I took a bite from a perfectly grilled ribeye steak. I looked down, and saw the people running about. They looked like ants. I thought about throwing my shrimp shells over the ledge for fun, but decided against it. How wise.
As I was mixing myself a gin and tonic, I noticed that the the gin was from Scotland and was infused with cucumber and rose petals. I asked Lindsay where she procured such a delightful beverage, and she said that she didn't know, but that it came from the "good closet". I told her I did too. Ha ha.
But then I thought, I do come from a good closet. That is where I am writing you from right now. It may be small, but it is a space of my own making, and I live on the first floor, so my feet are firmly on the ground. As they should be. And when people walk by, I can look them in the eye. Which is also how it should be.
But I cannot deny that sometimes, I wish I had a penthouse too.
Wednesday, June 14, 2006
Fondling the Zeitgeist
Here is a conversation that I had with my co-worker Jonathan during a break at the Vancouver Passport Office:
"Hey Jonathan, how was your weekend"
"Oh, fine... I helped my friend Orion recover from her augmentation"
"Augmented? Is that the new way to say 'you're fired'?"
"No... she had a boob job. She's fine, but it's going to cramp her style when she does pole dancing.
"You mean she's a stripper?"
"No.. She does it for exercise.... she takes classes at that new pole dancing aerobics studio on Davie St. It's great for your abs... Orion used to be able to do sit ups on the pole... but now, with the added weight....."
"Of course...Well you know burlesque is making a huge comeback... I was listening to this piece on Out Front CBC radio about a woman who started doing the burlesque circuit to get in touch with her sexuality. It was basically about her challenge of "coming out" as a burlesque dancer to her 5 year old daughter."
"Yeah.... if I hadn't had to take care of Orion, I would have gone to this burlesque comic book convention."
"You mean...comic books about burlesque artists?"
"No... it was basically women dressing up as comic book characters and stripping to funky beats.. "
"Oh yeah....Well I hope your friend feels better soon."
"Me too.. she asked me and my girlfriend Brandy to take her bra shopping. We're going to Park Royal Mall because I don't have to pay taxes there, and they have a kickass La Senza." *
* In addition to being a connoisseur of burlesque, Jonathan is also a hereditary chief from Bella Coola, and Park Royal Mall is on land which belongs to the Musqeam Band...
Saturday, June 10, 2006
The measure of my powers
This morning it was cloudy (in Vancouver? How IS that possible?) . This is why I decided to will the sun to come out by staring out the window and playing the Hymn to the Sun from the opera Iris by Mascagni on repeat as I drank my coffee..... Here are the words:
"Son Io ! Son Io la Vita !Son la Belta infinita,La Luce ed il Calor.Amate, o Cose ! dico :Sono il Dio novo e antico,Son l'Amor!"
"I am the sun! It is I, life! I am infinite beauty, light and warmth! O loved one, speak! I am the ancient and new god. I am love!"
It worked. I mean, if you were the sun, how could you not respond to such unabashed flattery? Maybe if King Canute had played Debussy's La Mer when he was ordering the waves to retreat in 1016 things would have turned out differently. As it stands, his failing to control the sea marked the beginning of the end of absolute monarchy in England (unfortunately it is still dying). In fact, just before he died, Canute ordered his crown to be placed on his tomb to indicate that there is only one king in heaven, and that we mortals should know the limits of our powers. I, however, have alwas been keen on testing the boundariess of my powers, as has my friend Pablo who whenever faced with a problem asks his Tarot cards what to do. Like the other day when we made Paella and he was wondering if he should break his self imposed "no yeast diet" and eat some chocolate cake. The first tarot card was "the schizophrenic" which meant that he was caught between two extremes. The second card was the 10 of cups which to him meant that the solution was to act with intensity... So we had 2 pieces of cake each. Of course, Pablo said that you really shouldn't read your own tarot cards because it is hard to make decisions objectively. I told him that one can never be objective when it comes to chocolate, which he should know because he is from Mexico. Where chocolate comes from.
Perhaps this is why Mexicans seem so happy. They are the hobbits of the western hemisphere. When I was in high school I used to go over to my friend Vanessa's (she was half Mexican and Half Mennonite..oy vey... she referred to herself as an "M&M") ... Her mother would invite me over, put on music and we would eat and dance for two or three days. She would also try to set me up with Vanessa, but that's another story. What is even better about hanging out with Mexicans is that most of them are short like me, so I don't have to strain my neck while having a conversationn. Yesterday I went to ahouse-warming at Hugo's place, a friend of Pablo's. Of course, there are 4 people sharing a 1 bedroom apartment and they have no furniture, but this means that they have more room to dance and more money to spend on the important things like chipotle crusted shrimp and smoked salmon in endive leaves. Hugo also wears Armani and has 5 kinds of cologne. I guess it is all about priorities. Everyone was speaking Spanish, which I didn't understand, but I spoke back in Italian when I could and when I didn't we all resorted to the international language of "glance and gesture".... before this I went to my friend Wade's 50th birthday, which was nice, but his friends are mostly Wasps, and therefore mostly tall, and mostly angst ridden. But we had scintillating conversations about the Tony awards and Robert LePage. I am somewhere in the middle because I am Jewish: We are for the most part short (although this is changing because we don't live in Shtetls anymore and have access to protein on a regular basis) and love to eat, but are mostly angst ridden. Although this is changing too (because we don't live in shtetls anymore and have access to protein and all that that entails, on a regular basis) . And as for theTonys... well, is there anything more Jewish than that? We pretty much invented musical theatre, which is a good thing or a bad thing depending on your proclivities. I am an opera singer, so I am again somewhere in the middle: I love outward displays of emotion, but they have to be tasteful and preferably in foreign languages. Which means, gentle reader, that I can enjoy the sentiment without the burden of comprehension.
Becuase once you begin to try to comprehend something, you can get lost and may never find your way. I think Oscar Wilde said that he who tries to scratch below the surface does so at his own peril. But it is important to try and understand, peril or no.....
although sometimes I think it is easier to impose your will on the sun.
"Son Io ! Son Io la Vita !Son la Belta infinita,La Luce ed il Calor.Amate, o Cose ! dico :Sono il Dio novo e antico,Son l'Amor!"
"I am the sun! It is I, life! I am infinite beauty, light and warmth! O loved one, speak! I am the ancient and new god. I am love!"
It worked. I mean, if you were the sun, how could you not respond to such unabashed flattery? Maybe if King Canute had played Debussy's La Mer when he was ordering the waves to retreat in 1016 things would have turned out differently. As it stands, his failing to control the sea marked the beginning of the end of absolute monarchy in England (unfortunately it is still dying). In fact, just before he died, Canute ordered his crown to be placed on his tomb to indicate that there is only one king in heaven, and that we mortals should know the limits of our powers. I, however, have alwas been keen on testing the boundariess of my powers, as has my friend Pablo who whenever faced with a problem asks his Tarot cards what to do. Like the other day when we made Paella and he was wondering if he should break his self imposed "no yeast diet" and eat some chocolate cake. The first tarot card was "the schizophrenic" which meant that he was caught between two extremes. The second card was the 10 of cups which to him meant that the solution was to act with intensity... So we had 2 pieces of cake each. Of course, Pablo said that you really shouldn't read your own tarot cards because it is hard to make decisions objectively. I told him that one can never be objective when it comes to chocolate, which he should know because he is from Mexico. Where chocolate comes from.
Perhaps this is why Mexicans seem so happy. They are the hobbits of the western hemisphere. When I was in high school I used to go over to my friend Vanessa's (she was half Mexican and Half Mennonite..oy vey... she referred to herself as an "M&M") ... Her mother would invite me over, put on music and we would eat and dance for two or three days. She would also try to set me up with Vanessa, but that's another story. What is even better about hanging out with Mexicans is that most of them are short like me, so I don't have to strain my neck while having a conversationn. Yesterday I went to ahouse-warming at Hugo's place, a friend of Pablo's. Of course, there are 4 people sharing a 1 bedroom apartment and they have no furniture, but this means that they have more room to dance and more money to spend on the important things like chipotle crusted shrimp and smoked salmon in endive leaves. Hugo also wears Armani and has 5 kinds of cologne. I guess it is all about priorities. Everyone was speaking Spanish, which I didn't understand, but I spoke back in Italian when I could and when I didn't we all resorted to the international language of "glance and gesture".... before this I went to my friend Wade's 50th birthday, which was nice, but his friends are mostly Wasps, and therefore mostly tall, and mostly angst ridden. But we had scintillating conversations about the Tony awards and Robert LePage. I am somewhere in the middle because I am Jewish: We are for the most part short (although this is changing because we don't live in Shtetls anymore and have access to protein on a regular basis) and love to eat, but are mostly angst ridden. Although this is changing too (because we don't live in shtetls anymore and have access to protein and all that that entails, on a regular basis) . And as for theTonys... well, is there anything more Jewish than that? We pretty much invented musical theatre, which is a good thing or a bad thing depending on your proclivities. I am an opera singer, so I am again somewhere in the middle: I love outward displays of emotion, but they have to be tasteful and preferably in foreign languages. Which means, gentle reader, that I can enjoy the sentiment without the burden of comprehension.
Becuase once you begin to try to comprehend something, you can get lost and may never find your way. I think Oscar Wilde said that he who tries to scratch below the surface does so at his own peril. But it is important to try and understand, peril or no.....
although sometimes I think it is easier to impose your will on the sun.
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