Arbtirary thoughts on nearly everything from a modernist poet, structural mathematician and functional programmer.

Saturday, October 27, 2007

Bitch, moan, and stay up all night!

I'm having my 3rd or 4th huge existential crisis in the last year. The source eludes me, but something is sitting wrong. It's sort of been building for the past few weeks, and I think Serenity Now has finally been replaced with Insanity Now. I really don't think I'm going to sleep tonight... Which will make the 3rd night in exactly one week.

So, what's on my mind? Let's begin with the most immediate, and move backward; a psychological stack, so to speak.

I'm rather confused by the fact that I actually feel more than a crush on a girl for the first time in nigh 5 years. A large part of me is feeling a rather tempestuous aversion to the idea. It's enough to make me think "maybe I should just say I can't do this", but the moment I say that, so many voices in my mind cry out in horror. Part of it is the longing for companionship, but mostly it's that Katie is awesome, and I want to share something more than simple companionship with her. At the same time, I feel there's a gap somewhere. I think the gap is in my ability to let things into my heart, but maybe, just maybe, there's a missing plank somewhere on the bridge...

On that note, it's extremely difficult to articulate thoughts and emotions. The more I want to say, the harder it is to say anything, mostly because my brain never works in any manner that resembles coherence. I cannot communicate my conclusions, or the "overwhelming" idea, as it is ridiculous and empty without the millions of wordless mental states that my mental processor shifts through per second. Obscure tangents contribute nearly as much to my "final" state as anything that directly relates to it.

Of course, confusion because I've forgotten how to feel cannot have been bugging me until I ran into Katie 2 weeks ago, so I doubt this is the primary cause. I have recently realized how much I hate the class setting. I really love to learn, and the university setting is a brilliant for it, but I hate classes with fury and vengeance. There are so many reasons why I may hate them, but none of the classic ones seem to fit:

Calc 3 is easy, and a bit boring, yes, but the overall subject matter is interesting; Adler is an asshole, but he's a good teacher, and I really don't mind his lectures. Data Structures are interesting, the code isn't bad (except test cases), and Beckmann is brilliant and awesome-- one of the coolest professors I'll probably ever have. Shakespeare is perhaps one of the best playwrights of all time, and some of my favorite lines and characters come form his plays. Discreet math is the basis for everything I want to do with my life, and I find it interesting. Gruia is an idiot, and a terrible teacher... well, yeah, that's why I hate that class. but the other three? I have no good reason for disliking those classes, but I do.

What it comes down to is how much I vividly despise the general class structure. It doesn't work with smart people. I don't even know how well it works for normal people. "Why doesn't it work with smart people? And what kind of arrogant ass calls himself too smart for school?"

Answer to question 2: me.

Question 1 is a little more difficult. Smart people have trouble exerting mental effort until they need to. So, when (for example) you're stuck in a class where all you do is add an extra 2 variables to something you've been doing for 2 years, it's very difficult to gather the energy to give a shit. Instead, I don't do anything, then get into the test and say, "Maybe I should have spent more than an hour looking at my book... I would have aced this test." Yet, I still can't gather the energy to care, because it isn't difficult.

People are too used to being fed formulae, so when they have to think (which isn't difficult), they get confused and don't know what to do. Too much focus is put on detail, and not enough on concept. The method of solving ∫ xln(x)dx is trivial if you understand what you're doing when you integrate by parts, but all the formulae in the world won't help you do that problem if you don't understand what an integral really means. You won't be able to write a strong essay if you can't hear the way a sentence falls together, no matter how much grammar you know.

And lectures don't teach you anything about literature. Sure, you can have all the historical context there is, but people bouncing ideas off each other, reacting to statements from others will teach everyone more about a work than any amount of historical research, or detailed analysis.

I'm sick of the importance everyone puts on economic success, and it's relation to college education. There are so many people who would be some much happier, so much more successful, so much more effective without having gone to college. I also hate parents that push their children into a "useful" degree: The purpose of college is to learn, not to get you more money. I don't care a damn if engineering will get me more money than literature, I don't care a damn if it's "hard to make money multiplying infinite cardinals", if that's what I want to learn, that's what I'll study. There are enough people in the world that if everyone found their own niche, we'd all do pretty well (comparatively), but no one seems to realize that.

What it comes down to is that I'm sick of academia being about self-importance. It should be about being interested, about being curious, about learning more about yourself or life or God or anything else by finding something interesting and studying it, watching its beauty radiate as you begin to grok it.

More importantly than all of this is that I can't feel God the way I want to. The same steel lock that's holding Katie out has been holding God out for as long as I've been able to try to let him in. Every time God finds that key, I steal it out of his hands and walk away. By the time he pulls me back to him, the lock's been changed, and it starts all over again.

I'm pretty sure I want to be a rogue scholar. Academia needs to stop taking itself so seriously and realize how crucial it is. It is not that difficult to try to communicate your ideas to someone who wants to learn them, so why the elitist atmosphere in anything written by the intelligentsia?

Basically, I'm sick of myself: I don't want to feel such ennui toward everyone; I want to care about classes; I want to love God; I want to open myself up to Katie...
but I can't: I care too much, or I care too little, or both at once and neither one... I don't want to be tired, but I don't want to sleep.

I'm spiteful, I'm rude, I'm ridiculous. And no one realizes how fucking crazy I am but me. Everyone thinks I'm a sociable, intelligent, empathetic, well-balanced individual, but none of this is quite true: I'm just barely smart enough to realize what an idiot I am (Or just barely stupid enough to think I'm an idiot...); I'm just social enough to realize how few people I really consider my friends; I understand people just well enough to not know a damn thing about any of them; and I'm just rational enough to realize how ridiculous and absurd everything I say or think is. I'm also just close enough to God to realize just how impossibly far from him I am, and will always be. "And it breaks my heart, and it breaks my heart."

So: Tonight, I'm gonna actually study the material for the class I never go to; I'm going to start learning the calc 2 that I never learned; I'll actually do my calc 3 homework for the first time ever; I'll clean my kitchen till I get bored with it; and I'll still have time to study enough algebra for a few weeks of the math class I'm going to be bored in when I take it in the next year or 2, not to mention the thousands of hypothetical social situations that will never happen, and the hundreds of responses to this rant that will never be written or even thought by anyone but me... And I'll spend the gaps laughing at myself for being so ridiculous, or wondering what I should do about the subluxation in my back.

Monday, October 15, 2007

On .(9); that is: On 1

I was driving today (That is, when I originally wrote this) and I realized a flaw in a contradiction of a specific proof that 0.999...=1

A whole argument came flashing back to me. I was part of an argument on an online forum on the topic. There were actually mathematicians trying to argue that .99... does not equal 1, which, to me, sounds kind of like a biologist claiming that dolphins are not mammals because they live under water.
I assure you: they are.

The claim that the number in question is actually two numbers generally comes from a misunderstanding of infinity. Firstly, (.9...thly?) we must make sure we make a clarification. This argument is happening in the real number system. Hyperreal, superreal, surreal, and any other class/field of numbers have no place in this argument, because they different systems.

Next: infinity is not "the largest numebr ever." It is NOT a member of the real numbers. When invoking infinity within the reals, it is a concept: "greater than any real number". This is not to be mistaken for "the greatest number". Infinity+1=infinity. Period. Infinity-1=infinity.
It does not equal some number less than infinity, because infinity cannot relate to other numbers: it is like trying to walk from Hawaii to the Continent. As further explanation, infinity is not actually included in the set we shall call R (the set of all reals); it is, however, included in the affinitely extended real number line. That is {negative infinity, {R}, positive infinity} Arithmetic with infinity (which will be w) is defined in this (which I will call R, if I reference it again in this post) as follows:

x + w = w
- x = w
x*w = w Unless x = 0, in which case.. things go funny.
x/w = 0 Unless x=0, in which case, see above.
There are a few more, and these all work with -w as well, but, well... you get the point.

So, one last attempt to concretely define a purely abstract concept. Infinity never ends. There is no "last term" in an infinite sequence.

So... on to proofs:
.99... can be thought of as the sum of an infinite series:
9*(.1^n). So, there is a number with an INFINITE number of 9's. Now, the difference between 1 and this series can be thought of as a complementary sequence: 1*(.1^n). Notice, not the sum (that would be a series), but a sequence. So, when there is one 9 in the sequence (.9), the difference has no 0s followed by a one(1-.9=.1), when there are two 9s, there is one 0 followed by a 1 (1-.99=.01). So, logically, when there are infinite 9s, there are how many 0s? w-1, which we've stated earlier is infinity.
Now, we have here a problem. An infinite sequence is non-terminal, so the 1 at the end cannot be there: there IS NO end. thus, the difference between 1 and .99... is 0.0000 or, 0. If there is 0 difference between two numbers they are equal, thus 1=.99...

Next, a quicker proof:

An objection to this argument was made: when you make this argument, you invoke the "w +1"-th term in the series. There is no number after infinity, so the resulting ".99..." actually ends.

This is not true: w +1=infinity. Also, the length of the new series of 9s is w-1, which is infinity.
So, either way, we have an infinite series of 9s, which means the argument still stands.

Or we could go straight back to the series, and do the math to find what number it converges to. 9*(10^n) converges to 1. I don't feel like doing the math. If you are determined to try to prove me wrong, you can do the math... and see I'm right.

One more objection is "but in the real world there is no .99... It HAS to end."

True. In the real world .999... does not exist. In fact, in the real world, one does not exist. It is an abstract concept. There is no Platonic one that all real-world ones strive toward. There is no perfect, actual one. It is a concept used to understand the world around us. Numbers are abstract. You cannot go into nature to find an object called "one" or "two." There are only things. which can be counted. Using numbers. Which are concepts. The fact that they so accurately represent the world around us is a testament to the beautiful design of nature, and the the ingenuity of the human mind.

What this note is showing is that .99...=1. I don't mean "They are equal for all practical purposes". They are equal. For ALL purposes, practical or impractical. The pronoun "they" does not make sense, because there is no "they" there is it. It is one number. Not two. Not .9...; One.

Making Up for Lost Time (Part V) OR: Sorry for the Super-Long Post

[Story Removed]

Bah... posted an old version. I may replace it sometime soon...

Making Up for Lost Time (Part IV)

A poem... Ironically, I feel it sounds like a bland version of Theme for English B

This isn't me.
Why, oh, why
Do I feel the need to follow the line in the sand
Of footprints left by a greater man?

Borges, Eliot, Milton, Danielewski.
They aren't me, but when I look back, it's what I see.
Suddenly, I find myself quoting
obscure lyrics to an unknown harmony!

And yet this is me.
I am skilled with words,
I can construct a "trope" with the greatest of ease,
And the trite little rhymes burst forth naturally.
Yet, when the dust clears, and my memory clouds,
I am Lewis, Dickinson, Hughes and Marquez.

Frustration sets in when I see what I've become.
How do we escape the shadow of those who we love?
Do you abandon it all, and say "Fuck it, I'm done!"
Or do you write and write, until you overcome.
And does it matter, when it's over and done?
Will you still look back and think "I've really done nothing
But at least it was fun"?

Making Up for Lost Time (Part III)

Below is a nearly finished section from a barely started literary pastiche/philosophical critique of Blake's The Marriage of Heaven and Hell.

In planting listen, in harvest ask, in winter think.
The wise man reaps before he sows.
The grass is greener above the casket.
Generate little; generate much.
David dances in only an Ephod.
He who desires but acts not, breeds pestilence.
The cut worm forgives the plow.
Drink once from the river, and you will ever thirst.
The tree of knowledge is the tree of life.
An unlit candle is a wasted flame.
Eternity is instantaneous.
Sorrow alone begets joy.
Wisdom is folly; folly, wisdom.
Even the spider can master a trap, but the rabbit needs none.
There is not an eagle who should not dip lower.
There is not a serpent who should not soar higher.
Only the dead can harm the living.
If a wise man persists in his wisdom he becomes foolish.
The knave and the saint both lay claim truth.
Prudence is arrogance.

Can your beauty compare to the peacock's?
Can your stealth compare to the serpent's?
Can your power compare to the lion's?
Can your sculpture compare to the human form?
The found are formed from by displays of faith, the lost with words of hate.
Excess of sorrow speaks. Excess of joy hears.
The watchful fox is ensnared.
The bird a nest, the spider a web, man friendship; each has an end.
Even the selfish smiling fool and the sullen frowning fool are understood by the wise.
What was once proved is now only imagined.
Always watching and never acting achieves nothing.
The cistern dries: the fountain is forever.
An ancient truth outlives a timeless mystery.
Always be ready to speak your mind, and even the base will listen.
Even a mountain cannot block the truth.
Though the eagle lost time with the crow, he gained an eternity.

The fox provides for himself, but he is still caught.
Think in the night. Act in the evening. Eat in the noon. Prepare in the morning.
The rabbits of love are stronger than the tigers of wrath.
Tepid water does not refresh, nor can it be made into tea.
You always know more than you need. You never know more than you want.
The fool's reproach is still a reproach.
The weak in courage is strong in pride.
The thankful receiver bears a plentiful harvest.
If others had not been foolish, we should be so.
True joy comes only from satisfaction.
As the truth is like a graceful antelope, so the priest is like a lion.
To find a fish is the effect of wisdom.
Pain braces. Health relaxes.
The best wine is the oldest, the best water the newest.
Prayers plow. Praises reap.
Joy rests not! Sorrow sleeps not!

As the air to a bird or the sea to a fish, so is love to the wise.
All creatures seek refuge. From what?
Exuberance is Beauty. Contemplation, sublimity.
If the lion were advised by the fox, he would lose his glory.
Improvement makes strait roads, but the crooked roads without Improvement lead to better places.
Apostasy before deceit.
Where man is not, nature is barren. Where man is, revolting.
Truth can never be told so as to be understood, and not be believed.
Enough! Yet too little.

Making Up for Lost Time (Part II)

Is it clear what we're to do?
Walking around, we hear always a sound
beneath the orange glow of city streets.
The faint dim starlight exiled to lonely nights
far from home.

Is it just for me and you?
Dodging, hiding, fleeing to cafes,
while children talk and laugh and play,
and life and love and loneliness,
sit and simply wait.

When Esther danced, did her heart shine through?
Did she know her heart, her self, her life would be
yet here today for you and me:
shall we look and think and pray,
Or sit and simply wait?

Making Up for Lost Time (Part I)

A Borgesian Pastiche.

As the 20th anniversary of Borges's death draws near, I see essays of praise for the works of the prolific writer, and I hear discussion of his life. I have yet to see anything about his most personal work: The Dream of Jacques Bonhomme. As with a manifold of his other short stories, Borges transcribes an essay on, or an explanation of, an author whose existence consists of naught but the words of Borges. Many of the readers will not have recognized the title of this story. The academia has hidden it well, as its style is incongruous with Borges other works. Therefore, I will divulge the essence of the story.

Borges writes of his correspondences with the Swiss author, Jacques Bonhomme. This name has ample symbolism: Jacques Bonhomme is both the popular name for a French revolutionary, and a reference to a common, simple French peasant. Borges provides only excerpts, yet through them he reveals much. Jacques to the disagreement of his contemporaries feels his best work is the surreal novella, Echo. The story takes place in Geneva, where the protagonist (whose name is inexplicably removed from the epistles) is a watchmaker. As his life progresses, he gains notoriety, yet his actions are exactly identical from one day to the next. At precisely 6:47 every morning (I am convinced that this moment has significance, but I am presently bedeviled by the choice) he awakes; at 7:00 he eats breakfast, stops by a cafe 25 minutes later and arrives at his shop at 10 minutes before 8. He makes the exact same watch, by the exact same process every day. His responses to inquiry and his conversations are no different, in inflection, diction, or gesture from the previous days'. As Borges describes the work to the reader "anyone who has studied Echo will agree that Jacques' ability to create a dynamic world with an utterly static protagonist has no parallel in literary work, past or present." Borges compares the style to that of numerous medieval and ancient writings, none of which are described as equal to Echo, and all of which are fictitious.

Before I continue with The Dream of Jacques Bonhomme, I feel obligated briefly to analyze the exiguous details of Echo, as they are central to the piece. Hardly subsurface, Echo is an expression of dissatisfaction towards the tediousness of life. Quite clearly, the simple, obvious redundancy is analogous to everyday life in the eyes of Bonhomme. What is less obvious, however, is the grain of optimism. More subtly important than the protagonists actions is the knowledge that not every day is actually the same. While the protagonist repeats the same actions, the world moves forward. Although the noticeable parts of life remain the same, the world is ever changing; Jacques places the non-repetitive parts of life among the few aspects of life we should try to remember.

While there are components of The Dream of Jacques Bonhomme that are, from an analytical perspective, more important than Echo, the novella is the literary focal point of The Dream of Jacques Bonhomme. As such it deserves recognition. As with most stories invented by Borges, he pretends they exist so that he can argue the same thesis in far less space. However, with the Dream, Borges ridicules the entirety of Bonhomme's argument.[1]In all of the excerpts from their letters, Borges is condescending Bonhomme. For example, in an excerpt from Borgess third letter, he elucidates his position on Echo: "The novella is extremely well written, with an original approach; however, the subtext of Echo is hardly hidden and Kafka and Sinclair drip from your words like milk from the lips of a nursing calf." This simile, overdone and wordy for Borges, is a not so subtle attack at the literary maturity of Echo. The fourth letter shows a similar attitude, which Bonhomme notices.

The purpose of the letters, which many of my readers still will not know, is a recurring dream Bonhomme had for the first time three years after publishing his novella. After the critics began to silence, Bonhomme had a dream that he was the protagonist in his novella. After six months, he went to Borges hoping for help. To his dismay, Borges could do and say nothing that helped. Luckily, about 1 month after the first letter, the dream became less frequent; however Borges does not declare an end to the dreams. Bonhomme was distraught, because the dreams affected his everyday life. He began to respond to similar sentences the same way every time; he couldnt concentrate on any work because he felt doomed to repeat what he had just done.

What may come as a surprise is Jacques Bonhomme is Jorge Luis Borges. Borges finds himself simple and immature (hence the milk and calf analogy and the name, Jacques Bonhomme), yet slightly revolutionary. Borges uses this story to attack every argument he has ever made in any story, to contradict itself, and finally to say that his work is immature, yet revolutionary and alone.

This essay may seem to have gotten off task, yet I feel everything I have said is necessary. This essay was designed to examine why Borges wrote The Dream of Jacques Bonhomme, so there will be no further suspense. All of Borges's author characters have two things in common: They have one defining work, amidst an amalgam of substandard or modest literature and these works are all semi-autobiographical. The two qualities can be considered the same. Borges has one defining work, one that is relatively hidden. The Dream of Jacques Bonhomme is his ultimate revelation of self: He feels that life is cyclical and repetitive, yet he finds himself ridiculous and immature because of it.

[1]This point can be said of Pierre Menard, Author of Don Quixote and An examination of the Works of Herbert Quain, but the argument can be countered. In The Dream, any counter-argument to this statement is wholly unsupported.

Post Script: As has been relayed to me by all readers with whom I have conversed, the exact nature of the preceding essay remains unclear; please allow me to clarify:

This essay is both a pastische and analysis of the works of acclaimed Argentinian author and librarian, Jorge Luis Borges. I resolved to compose a work which not only attempted to analyze the style of Borge, but also to repeat it; thus, I resolved to analyze a hypothetical short story written by Borges. In order to invent this story, I determined the elements which epitomize Borges: An author is the central character, the story involves time, and the protagonist can be related to Borges himself. I quickly conceived the dream, which was originally central to the piece. As time progressed, this became a mere foundation. Although a foundation is of utmost importance, it can hardly be comsidered central.

Through a conversation with Mr. Peter Hokanson, I established a firmer foundation, which immediately led me to the plot (if it can so be considered) of the story. This became the content of the epistles and Borges's commentary thereon. As my brain is generally not suited for elaborate planning (and I am often too impatient), I began writing, achieve many of the symbols (such as Jacques Bonhomme) and key elements during my first draft. As I wrote the essay, Borges's story took flight in my head. (I may endeavor to transcribe the work. However, even my best attempt at immitating Borges would be shallow in comparison.) As this story invented itself, I began actually to analyze the story I was imagining. This led to a far deeper and more realistic analysis than I could have ever hoped for. Everything which succeeds the fifth paragraph was written entirely as an analysis of the story which I had read and annotated for hours in my mind.

This essay, which I can only hope is convincing, exceeded even my greatest expectations. Only through the unorthodox process of creation could this esay have turn out as it did. I hope I have clarified it through these last few paragraphs. I also hope the essay can now be more fully appreciated for the work of literature it is, and not merely a dry analysis of an obscure story.

I know... I know.

I've finally broken down and created a blag. Here go writings, rants, and fun things I find through the intar-tubes and elsewhere.

First, allow me to apologize: I know; it's a blog. I'm sorry.
And more apology (although using a slightly more obscure definition): I decided I should consolidate all my (illustrious in neither scope nor scale) writings into one place, and one which is accessible from anywhere. Namely, the internet. I also occasionally decide to rant about something that really doesn't matter. Also, I like to rave about fun things... Like math.

On that note:
1) I recently stumbled across It's got some rather interesting sci-fi. Mostly, I'm impressed by the great homages to Borges and Assimov.
2) I've decided to start naming my computers after mathematicians, starting with Pythagoras, and working toward present day. I kind of want to skip Aristotle, because he was an idiot, but I guess he did contribute in his own way...
Creative Commons License Cory Knapp.