Literature and Mathematics

I was thinking more about the portrayal of mathematicians in literature as we have discussed it this semester. I was thinking back to our original attempts to define what constituted literature. At first, we tended to include almost anything, like text books or magazines. But if I recall correctly, we finally decided that literature generally had topics of "substance" and had a lot of "depth" to it, and was perhaps concerned with "asking thoughtful questions". So Dostoevsky writes literature but J.K. Rowling does not (I know, harsh). Given this context, it might not be surprising that the mathematicians in literature would tend to be the crazy ones. For instance, We is certainly a book of substance seeking to discuss some deep questions, and is thus literature. D-503 is basically a tool for discussing these questions. But the questions being asked require D-503 to behave in these extreme ways so that the novel can illustrate its points about happiness etc. In other words, it is not just a book about mathematicians, and thus is not very focused on portraying them in a realistic manner, since that would not serve to address the questions the novel is trying to ask. Since most literature has this type of depth it wants to cover, it's not surprising that if the protagonist is a mathematician, he would not be a typical one but rather a very "deep" and extreme example of one.

Pi and Lost

Hey guys I'm back.

I had another random set of thoughts about Pi. I don't know how many people watch Lost, but there's some parallel ideas to some of the stuff in Pi. In Lost, there are these numbers that are kind of around throughout the show and no one knows what they mean. The numbers pop up in basically all aspects of the show and in really random places. It kind of touches on the same idea as max looking for the number 216, and finding it because he expects to find it. In the show, the numbers show up in so many places it would be impossible to really analyze every occurrence of them. In addition, since numbers can just show up at random, like as a character's jersey number or something, you can never really know if it's a legitimate connection to the meaning of the numbers. I thought this was similar to Max's teacher joking that it could take him 216 steps to get to his apartment. You can't tell which instances of the pattern are meaningful.

Ants in my pants!

Ants. Pants. Dance. Trance. France. Lance. Chance.
in my...make me..... to....... in............with.... if i get the.

Moving on.
So turns out Family Guy took off all of it's videos from YouTube. Damn. I think most of you know which clip I would've used for my last post regarding wheelchair sex. "Oh, oh, oh. Yes, right there. Oh. Stop, you're hurting me. Oh." Point being, I hope yall enjoyed the video I posted up instead, I thought it was hilarious.
My regards.

So what am I going to talk about in this blog? Hmmm, how about....group paper!?

Ok. So it had it's ups and downs, pros and cons, goods and bads, kicks and rips (I don't know, I made this one up).
For starters, a 6-8 page paper is a hell of a lot easier to write when you have 3-4 people writing it. I had an 8-10 pager due last semester and just let me say it took a loooong time. Having 3-4 people collaborating on a paper cuts that time in half.
However collaboration is not always a good thing, especially if you're used to working by yourself, like I'm sure most of us are. (Is "are" a preposition? Can I end the sentence in it?)
Anyways, collaboration is weird. Sometimes there's just too many ideas out there and funneling them into a single paper can be hectic. Either everyone wants the paper to be done their way or no one wants the paper a certain way, either way nothing gets done. Despite this, when it comes to crunch time any group will do pretty much whatever it takes just to finish the project and turn in something that resembles a complete paper.

Til next time...(which is in about 5 minutes( I still need like 1-3 more blogs))

Einstein is my homeboy

So while working on our group paper, I was assigned to do some research on the Stein man. It turns out this guy was a player! No joke. He had a bunch of girlfriends and eventually he got married, but that didn't stop him from having sanchas. I'm shocked. Really. Last time I checked, the connotation of Einstein was nerd, geek, etc., not gangsta, playa. I think the word "Einstein" needs a realty check. It should be associated with "Ballin'" and "Krunk". Some good examples could be "Damn, that is Einstein!" or "Yeah, I'm pimpin' it like Einstein." Anyways, back to Einstein himself. Did you know he even got it on with movie stars? Shyeah, true story. ALL the ladies were all over him, and their boyfriends were all player haters. Moral of the story: brains can equal brawn, you just gotta have more than everyone else.

Except Stephen Hawking! That guy is in a wheelchair and uses a computer to talk. I don't think many women find that attractive. Unless they're in a wheelchair using computers to talk as well. Hmmm.

Numb3rs

Does anyone watch Numb3rs? I really enjoy it, and yes, I am so cool that I watch it on Friday nights when it originally airs. I think my favorite part of the show, aside from guest appearances from Bill Nye the Science Guy, is the fact that the mathematicians and scientists in the show are mentally stable! They are slightly nerdy and a little socially awkward, but definitely not crazy. As we have seen in class, this is a rarity, and it’s a nice change to see relatively normal mathematicians in pop culture. The characters also solve crimes and do neat experiments which add to their “cool” factor. Not all of the math done on the show is entirely accurate, but I appreciate the effort and am willing to overlook the flaws. I hope everyone has a great summer, and maybe you will watch Numb3rs because it’s awesome!

Pi and A Beautiful Mind

I had never seen either Pi or A Beautiful Mind before this class, and I thought they were very appropriately paired together. There are many similarities in the lives and work of Max and the fictionalized John Nash. Most obviously, they were both crazy mathematicians. There have been many blog posts, and collaborative papers about crazy mathematicians in literature and pop culture, but personally, I don’t believe it was the math that drove either one of these men crazy. My mom always told me (and my mom is always right) that all things are okay in moderation, and that an excess of any given thing will often cause problems. Both John and Max were obsessed with their mathematical work and neglected other aspects of their lives. I believe that this sort of obsessive behavior in any field is sure to cause mental sickness. I also found it interesting that both John Nash and Max were working on mathematical problems concerning the economy. Math is relevant everywhere, but it is interesting that these two men chose to use their knowledge of math in the economy. Lastly, both men were perceived by society as geniuses for their work. Max was approached by Wall Street executives to help decipher a pattern in the stock market while John Nash received the Nobel Prize. I enjoyed watching both movies (minus the part where Max drilled a hole in his brain) and it’s always fun to see movies about a subject that you are personally interested in.

A brilliant madness

Mathematicians, across all types of fiction and non-fiction literature, tend to posses this elitist quality, which causes them to have trouble conforming in society. This quality may not actually be common to all mathematicians, but it is a popularly recurring trait among mathematical characters throughout literature. John Nash, in the documentary A Brilliant Madness, is no exception to this. "[John Nash] thought of himself as superior, intellectually, [and] mathematically superior" to his colleagues, and other mathematicians (Mel Hausner, A Brilliant Madness). He thought of himself as the best and "was only interested in people who could operate more or less on the same mental level that he was at" (Felix Browder, A Brilliant Madness). He definitely thought of himself as at the top, but he was not getting the recognition for it. Nash's elitist quality is really exaggerated when he becomes mentally ill with paranoid schizophrenia, "a severe mental illness, characterized by hallucinations, delusions or peculiar forms of thinking" (Louis Sass, A Brilliant Madness). Based on his delusions, it is clear how important he thought he was to the world. "John talked about the people from outer space who were destroying his career, [...] the international organizations that were attacking him," and he thought he was "the messenger of Allah" (Harold Kuhn, John Nash, A Brilliant Madness). In his delusion he is put in a situation where his work is very important to the world. Even in his delusions he was an elitist.

21, Counting Cards

I just recently saw the movie 21, and noticed some of the same themes we have been talking about throughout the semester. If you don't know what 21 is, it is based on a true story about M.I.T. students who counted cards as a team and took weekly trips to Las Vegas to take advantage of blackjack. In the movie, they proceed to make simpler mathematical theories appear much harder than they really are. There were many references to mathematical terms throughout, but what I thought was most interesting was how much harder the movie showed counting cards to be. The idea behind counting cards is to keep track of what cards are left in the deck and make larger bets based on the "count." There are many different strategies to use to count cards, and the one used in the movie is the simplest. You assign either a +1, -1 or a 0 to each card that is delt, with +1's given to 2, 3, 4, 5 and -1's given to 10, J, Q, K, A and 0's given to all other cards. Counting cards is as simple as adding and subtracting one based on the cards delt and keeping a running total. When the "count" gets high enough, above +12 or so, the odds in the game which are normally in favor of the house by half a percent or so is now in favor of the gambler. It is at this point that you should make bigger bets to take advantage of a hot table. The movie shows this simple adding and subtracting one from a running total to be something only the smartest mathematical students from M.I.T. can pull off. I just found this to be interesting.

geniuses

As I've been thinking of the stereotype that we have been talking about in class -- that mathematicians are kind of crazy -- i have developed a few insights that i think might be interesting to contemplate. It is not just mathematicians seen as crazy, it is geniuses in general. Though I'm sure not all geniuses have been seen as crazy, a good portion of them are. Geniuses are almost always paired w/ eccentricities or mental defects of some sort that accompany their extremely high level thinking.
Mathematics is seen as a complicated subject of study, especially the higher levels, and so for this reason many mathematicians are seen as geniuses and thus the stereotype of eccentric and abnormal mental behavior is associated with them.
And it is strange how many geniuses of all kinds live up to this stereotype. Music geniuses, art geniuses, math geniuses, science geniuses -- all of these different groups of geniuses have their share of "crazies". Sure, their are many geniuses that do not live up to the stereotype, and there are many crazy people that do not live up to the genius status so it is strange that all geniuses are seen as crazy but not all crazy people are seen as geniuses. And it is almost as if the great contributions that come from the crazy geniuses almost come from their craziness. I wonder why"?

Research and A Beautiful Mind

Hey again...

On another note about A Beautiful Mind, we did some research about the actual Nash for our paper as I suspect a lot of people did, and it is indeed interesting how they took his story and fit it into the narrative arcs that we discussed in class. In our paper we wrote some about the idea of the 'tragic hero' as part of the reason literature tends to portray mathematicians the way it does, perhaps to make them more accessible. That way everyone can identify with the character when they wouldn't otherwise probably be able to.

I thought the whole group research project was an interesting idea. I think how one divides up the work is an important part of it. I think we divided ours up along the lines of topics in our argument, and perhaps we should have done so along the lines of tasks, like research and writing or something. The problem with dividing up sections is that it's so easy to lose track of what you're trying to say. On the other hand since you have so many people writing you get a lot of material to work with and edit down, so you're left with a lot of good stuff hopefully.

Anyway I believe this is my last post. Bye everyone. Yay writing component! No but seriously it was a good class.

The ending of Pi

Yeah I know, rapid fire...

I do have another thing to talk about though. I was talking to my roommate about Pi and he had some interesting thoughts about the ending. At the end when Max is on the bench, he's looking up at the sun again. It's like he wants to get his insights back and he's still thinking about his quest for understanding. That might suggest that it wasn't just the math that was leading him to his insanity, but something more 'fundamental' inside him. I'm not exactly sure what else to say about this. Perhaps it kind of illustrates the fact that this quest for understanding is fundamental to people and independent of whatever form it takes, be it mathematical or religious in the case of the Jews in the film.

Math and Music

When we were watching A Beautiful Mind I was thinking some about the connection between music and mathematics. I've heard a bunch of times that people who are good at one are often good at the other, or at least more disposed to it. I'm definitely a math person and I've also played piano since I was seven, and I definitely can understand the connection. Music is in many ways very mathematical, as far as rhythms and pitches are concerned and what not (especially classical). I can see the similarity between the creativity in a lot of high level math as far as proofs and general problem solving and the creativity of coming up with a musical composition which is also very structured according to certain rules. I think a lot of times if people aren't familiar with this side of mathematics, they consider this connection hard to understand. At least that's how all my relatives were when I was younger and they'd tell me about this (because they knew I was somewhat mathematical).

I thought of this at the point when Nash has started taking his medication and his friend comes to visit him on his porch. He's listening to Mozart, and you can tell it's supposed to kind of suggest his state of mind as a little insane.

groups writing papers

Before starting assignment 3, i thought writing a group paper -- in which 4 people write one paper -- would be extremely difficult and would end up horrible. And though I am not particularly pleased with our final product, i was surprised to find that writing a group paper was in some aspects easier than writing a paper by yourself. I knew that some aspects of writing a group paper would be easier and better in some ways (research, amount of ideas, etc), but I thought that the actual writing of the paper would end up a mess, mainly because everyone has different writing styles. However, what I found was that once one person begins a part of the paper and the other group members have had the chance to read it, the tone becomes apparent to all and the members can pretty accurately achieve relatively the same tone and style. Still, it is sometimes hard to communicate ideas to the other group members . You know sometimes where you have an idea in the back of your mind but you don't know how to put it into words.. but then as you continue to write your paper you suddenly find a way to fit it in? When writing as a group, it is hard to develop your thoughts enough about the paper as a whole since you are so focused on the one section that you are supposed to write. Writing as a group is good in that you can see other people's ideas on paper, which is a much clearer way to communicate ideas than through verbal speaking, but the paper as a whole suffers because everyone is too intently focused on their own part. I think the ideal method would be for everyone to write the same paper with the same thesis and then one person rewrites the entire thing. This way, the writer has a chance to develop all of his thoughts and no "great" ideas are lost.

what makes mathematicians crazy

Though fiction works do exaggerate the eccentricities and overall craziness of mathematicians in order to add to the drama of their works, i do think that mathematicians do have the tendency to be somewhat off the wall --whether it's that math contributes to their eccentricities or that eccentric people are attracted to math is the question. I think it's a little of both. The ways that people's minds work make people better at certain things. Certain people have more mathematical views of the world than more and perhaps eccentricity is simply a by product of that view.
I do see how constantly performing high level mathematics all of the time could
cause abnormalities in behavior as well, though. Mathematicians are constantly looking for patterns. Perhaps after so much time spent looking for patterns cause
some mathematicians to start seeing patterns that aren't really there which could lead to forms of schizophrenia and obsessive compulsive behaviors. Also, mathematicians are required to hold a substantial amount of information in their head at one time. This, I'm sure puts a ton of stress on the mathematician which could cause mental deterioration.

cuckoo for blogs..

Because I have nothing to say and need 123904235 more blog posts, I will free write until I have something to say...
say.
say say..pay pay pay day day day may may ray ray hay hay or is it hey?
lay lay lay way way kay kay kay ky ky ky ky lye lye lye lie lie lie eye eye eye cry cry
die die die fry fry fry burger? or chicken? salad?
no.
math math bath bath wrath wrath path path path
fath..lisp
fast..no lisp
mosquito.
America.
eugenics.
booger.
would this get published in The Return of the Vas?
vas vas..nas!
Vvvrrroooooooooommmm...
mmm...hmmm...mmhmm.

einstein. copernicus. bacon
godel. newton. blaire
descartes. nash. doppler
pascal. darwin. dougall
arichmedes. da vinci. ezra
euclid. watson. ferguson
aristotle. schmidt. fibonacci
pythagoras. pell. galton
bernoulli. franklin. hubble
burgess. watt. gauss

...and my sincerest regards for those of you I forgot.
by the way which of these men were eugenicists?
All of them!

Just kidding, I have no idea, google it.
chicka chicka yeah, google.

Ok well I hope you learned a little something about freelance writing when you're stuck between a rock and a hard place. Please, if ANYONE needs another example, feel free to leave me a comment.

Kurt Godel

Since we have been talking a lot about the mental instability of mathematicians, I thought it would be interesting and rather relevant to blog about a particularly unstable mathematician that I have come across while researching for assignment 3. Kurt Godel is most famous for his two incompleteness theories, which had a profound impact on 20th century mathematics and philosophy. "The more famous incompleteness theorem states that for any self-consistent recursive axiomatic system powerful enough to describe the arithmetic of the natural numbers (Peano arithmetic), there are true propositions about the naturals that cannot be proved from the axioms. To prove this theorem, Gödel developed a technique now known as Gödel numbering, which codes formal expressions as natural numbers.He also showed that the continuum hypothesis cannot be disproved from the accepted axioms of set theory, if those axioms are consistent. He made important contributions to proof theory by clarifying the connections between classical logic, intuitionistic logic, and modal logic." (wikipedia)...... But enough with the boring stuff... as Godel got older, he became obsessed with the spread of germs and became notorious for wearing ski masks with eye holes everywhere he went in order to protect him from them. Also, he developed an obsessive fear of being poisoned. He would not eat anything without his wife eating it first (to make sure it wasn't poisoned).. what a gentleman! He died because his wife was hospitalized and could not test his food for him and so he refused to eat. His death certificate says he died due to "malnutrition and inanition caused by personality disturbance". Seriously, what's the deal with brilliant people and mental disorders.

flashing lights

so next week, Kanye West is bringing his 'Glow in the Dark' tour to Austin and since I am his number one fan and his future wife, I am incredibly excited about this. I was telling crista yesterday and she had no idea who I was talking about, so, if anyone else out there hasn't had the pleasure of discovering the amazingness of Mr. West, this is for you:

Kanye West is an American rap artist and hip hop producer. He released his debut album The College Dropout in 2004, his second album Late Registration in 2005, and his third album Graduation in 2007. His first three albums have received numerous awards (including nine Grammys), critical acclaim, and commercial success. West also runs his own record label GOOD Music. West's mascot and trademark is "Dropout Bear", a teddy bear, which has appeared on the covers of his three albums as well as the singles cover for his songs Stronger and Homecoming.

I got that info off wikipedia, and you can find out all about KanYe on there, just type in his name and his whole life story comes up. It even talks about the recent passing of his mother, who was a HUGE inspiration to him, especially in his music. He also has a website KanyeUniverseCity(dot)com where he posts blogs daily and fans get to comment back and forth with him and each other. Unfortunately, there is a $25 yearly charge to be in his fan club, and I am not about to pay $25 to post a comment on his blog.
He says he lives for fashion and loves going to all the fashion shows in Europe as well as here in the states. He loves furniture, he's always posting blogs with pictures of some random expensive architecturally innovative pieces of furniture.

anyway, here's one of his latest music videos for Flashing Lights, enjoy!

Probably the last post to go on this one

Once again i forgot to do a post, in fact this is number two that slipped my mind. so i better make this one good and very informative because i know that every person in the entire class is just itching to see what i have to say ;-). Man, i do sound arrogant sometimes.

Now, what to talk about to entertain all of John, being that you will probably be the only person to read this. Ah... i've got it. This post will be all about lions and tigers and bears... NAH.

How 'bout i just talk about something more relavant like how my group worked on our paper. Well i must say that is a fantastic idea and i thank you for suggesting it John.

My group, being Cheney, Haseeb, and I, worked together quite well if i can say so myself. There was no exact leader, although Cheney did lead the conversations. The work was split up evenly and finished to the same caliber, or i would think that it is. Our paper is basically a close reading on A Beautiful Mind and compares it to what we found about John Nash's real life. it basically goes a bit like this, there are three parts we are focusing on Nash's: student and work life, his relationships with family and friends, and his hallucinations. We then took each one of these and split it up to something like this: what actually happened, what the movie portrays, why they are different, and analysis. although looking at our work the why and analysis are pretty much squished together because we have so much info to work with. Now that you know what our basic paper will look like i hope you enjoy it on Thursday, because reading stuff that you don't enjoy just isn't fun

how did i do this???

How indeed? Somehow through all the stuff that has been going on i seem to have forgotten to do two of the blog posts, and that should just not happen. first of all i would like to apoligize for being so tardy with the work. it never should have been done this late, and i was so on top of it all earlier in the semester.

Now that is all done, what to talk about??? I know John Nash... screw that how about Ron Howard and the A Beautiful Mind movie. Since that is the basic topic of my groups paper, we are the sine waves if you didn't know. For the first time ever, for me at least, i watched the director commentary on a movie. And you know it wasn't all that bad. Ron Howards voice is definitely funny to listen to as you watch the character's mouths move. i kept trying to match up what he was saying to what they were mouthing, but it never worked. I did learn a lot of stuff though, even while being amused and distracted. For example, Ron Howard pointed out that all of the imaginary characters show up in the same way, a very formulaic way in fact, that i never noticed. It goes a bit like this: a sound is heard of screen, then the character is introduced from John's POV, then the movie can do normal movie stuff. I have seen this movie multiple times and never noticed that pattern, although it was a bit hidden behing Ron's other uses of POV which come in handy for his other situations. He also pointed out something of a dead give away that had also never occured to me, that being the seen where Marcey runs through a flock of pigeons and not one of them moves or flies away.

I think that i am going to start watching more commentaries to see why directors do certain things. i found it informative and interesting, plus it is just a way to watch the same movie over again and not be as board, because new stuff is actually happening.

God and stuff...

So we are writing about D-503 and God and stuff...for our paper...

Some thoughts I've had so far...

The Benefactor is D-503’s God. In Psalm 95 God is described as a “great King above all gods” who formed the sea and the land, and who should be knelt down to in praise. The Benefactor is the Creator of D-503’s world, the One State. D-503 describes the Benefactor as “glowing in the sun's rays” and “coming down to us from heaven” similar to the way the Bible glorifies God. Psalm 104 exclaims, “O Lord my God, thou art very great!” In the same way, D-503 praises the Benefactor throughout We as if he were God. He exclaims continually throughout the novel, “I swear by the Benefactor” and "Thanks to the Benefactor!" , showing that he glorifies the great leader of the One State. D-503 reads the “Daily Odes to the Benefactor” and seeing the Benefactor as an “icon”, longs “to compose poems and prayers” to him.

Since childhood D-503 has always loved Unanimity Day, a great holiday which he compares to “Easter”. Each number is presented with a new unif for this day, making sure that all are wearing their “Sunday best”. This day is the symbolic yearly election of the Benefactor in which all raise their hands in “majestic unison” to “place in the Benefactor’s hands the keys to the imperishable fortress of [their] happiness”. This is the day in which “the heavens declare his righteousness, and all the people see his glory” and it is meant to remind the congregation of the One State that they are “the Church, one and indivisible".

Quotes from We and the Bible...

Untitled

I have been trying for a while now to come up with some witty, math-related title for this blog post, but to no avail. Maybe it will come to me by the end of the post. But, I didn't want to be left out in including my final thoughts of the class in the blog. So here goes:

This semester, I was originally signed up for M372K, Partial Differential Equations and Applications, TTH 12:30-2. However, after no more than three class periods in the class, I realized the class was more Physics than I cared for and I dropped it. I happened to stumble apon Literature and Mathematics in the Course Schedule in the same time slot, and I needed my second writing component class, so I figured it would be an interesting course to take. To my surprise, after a couple classes, I was possibly more intimidated by this class than I was Partial Differential Equations. The thought that I would write an essay arguing my grade seemed to be a daunting task and gave me even more control over my success or failure in the class, rather than just doing homework assignments the night before they are due. Also, I had not been assigned reading from a novel since my senior year in high school, so I wasn't so sure about that one. I mean, I came to college to study Engineering, and even though I switched to Mathematics last year, I still did not expect to be persuading a teacher to give me an A in any way other than my performance on homeworks and exams.

Regardless, it has been an interesting class, to say the least, and I think I have used portions of my brain that had been dormant for a while, which is always a good feeling. The class has also caused me to think about new things and old things in a different manner. I have long been one to get lost in my head and just think about something endlessly and formulate my own opinions and theories. The class discussions we had were very similar to the conversations I have with myself often and it was fun to be able to vocalize such hypothetical thoughts with someone other than my two cats who care much less about my thoughts about mental illnesses and abortion than they do about when I am going to feed them.

As seems to be a common sentiment with several people in the class who are heading in the Pure Mathematics direction, I have no clue where I will be 5 years from now, but I hope to do Teach for America when I graduate and then would like to have the opportunity to teach in foreign countries. I feel knowing English, Math, and, with some brushing up, Spanish, I have some valuable skills that can take me anywhere I would like to go. Or at least I can hope.

Farewell E3.141592653589J

The experience of taking this class made me realize how uncomfortable I am outside of the RLM. Aside from the occasional armed robber, the RLM signifies a safe place where I can find people with my same interests, background, and most importantly, homework assignments. The first day I walked into this class, I felt intimidated and a little scared. Firstly, we sit in a rectangle. Secondly, we have discussions. Thirdly, these discussions are not technical math discussions. Lastly, I can’t see the RLM from PAR.
All kidding aside, part of our research paper will discuss the isolation and sometimes elitism of mathematicians. I have met some cool people outside of the RLM especially in this class, and I have realized that majors do not define people or my interaction with them.
I would like to end talking about something I like even more than math. I like this organization called the Campus Environmental Center. Tomorrow is Earth Day, and we are celebrating all over campus. On the West Mall, there will be free cake and Sweet Leaf Iced Tea. Also, if you bring five plastic bags, we will give you a free canvas bag! After all, if it weren’t for nature, there would be no patterns. If there were no patterns, there would be no math. If there were no math, I wouldn’t be writing my last blog for this class!
It’s been fun; I hope to see you all sometime! If you want to stop by, my address is 2515 Speedway Austin, TX 78712.

The End

The fact that this is the last blog adds a lot of pressure to make it a good one. I don't really know what to talk about... so lets see where this goes...
I read A Mathematicians Apology yesterday. It was interesting. Hardy was really depressed! I wonder if instead of thinking there's a corollary between being crazy and being a mathematician there's more of one between depression and mathematics. It makes sense. Mathematical truth is harsh, pure and explicit. It is what it is. And math is really difficult and it constantly tests how bright you are in the subject. It's really intimidating and it makes you feel so stupid sometimes. So how do you know if it's worth doing it for yourself? How do you know if you've got what it takes to make a mark in the field? How do you know that you're not just beating your head against the wall forever and for nothing?
Hardy says that mathematics is a young man's game... which is a pretty harsh statement. So those bright enough to accomplish even one great thing in life reach their peak early on and then it's all downhill from there. That's a pretty depressive thought... to know that your life work can only get worse. If that's true, I can see why mathematician's would get depressed. On the other hand, at least they know that at one point they had it... something that I can only imagine most mathematicians will never experience. Hardy was amongst the top five mathematicians in the world at his time. To be the top five in the world of anything is really cool... but to be in the top five best mathematical minds must be the greatest high...
Next year I'm taking my GREs and applying to grad school... and that's it. Then I have to wait and see what the future holds for me. That limbo between schools... I don't even know if I want to go to grad school, but I've been working towards a degree in mathematics for three years with the intent of going to grad school... so that's what I'm doing now. Looking back I don't think I ever made a choice. I was kind of going with the flow at every point. My dad's a mathematician, my mom did her bachelor's in mathematics... I'm good at it and I like it so it seemed like the reasonable thing to do. But now it's serious business... because I'm kind of committed to doing this thing for the rest of my life... and a pure math degree by itself... I don't know what that's good for... so I must get something else... and what can I do? I don't want to work at a bank, or for a company... so I guess I'll teach. I don't want to teach middle school or high school really, so I guess I'll get a PhD and teach college... but that's math for life!
How do these mathematicians know that they're passionate enough about math to do it for little pay for the rest of their lives and doing it purely for the improvement of math. It's so pure and so... pointless it feels.
"I shall ask, then, why is it really worth while to make a serious study of mathematics? What is the proper justification of a mathematician's life?" - Hardy

What They Said

After hours of gusting away a tower of gray insulation-grade dust hiding the interior organs of my P.C., it seems this was just the treatment my dear SHLOBOO required. She returned to good health despite the onset of a new strained wheezing, necessitating the contact of a moderately aggressive technical tap to set her right. Once again she gave me quite the scare. I am glad once more to be able to record my thoughts.

The reflective blogs posted before my own have put me too into a reflective mood. And I suppose this has its value in light of the impending Learning Record. I came into this class with a taste for science-fiction, dystopian novels, and an aesthetic appreciation for math. I must confess I had never really taken note of the importance of math in We. I had not anticipated the focus on mental instability and delusion, but greatly appreciate its fascinating incorporation with the consideration of math. If you enjoy the delusional passion of one who is consumed in the knowledge that they are on the edge of fantastical discovery I highly suggest Robert Charles Wilson. Every story in The Perseids and Other Stories has that same wonder of possibility shown in Pi, VAS, sort of A Beautiful Mind, and maybe We. Insanity is the strand that connects the stories.

The first story has a young, very poor boy as the soul caretaker for his schizophrenic sister. His mentor is the owner of a bookstore who exchanges chess games with the very strategically gifted boy for books. Eventually secrets of the universe and the patron are revealed that considerably change the context by which he defines his sister’s insanity. All the stories are like this, sane protagonists are shown increasingly insane with such subtly as to surprise both the reader and the protagonist himself that he has been so led on. There is also a strong theme of a love for the strange.

Perhaps a few excerpts will whet your interest: from the title story, The Perseids,
“What made Roger’s notion original was that he believed human beings had—for the first time in millennia—begun to colonize a wholly new domain, which he called the gnosophere: the first abroad, the ghosophere felt more like geology than ecology: a body of artifacts, lifeless as bricks. [….] “But the gnosophere at the end of the twentieth century had grown vast and intricate, a landscape both cerebral and electronic, born at the juncture of technology and human population, in which crude self-replicating structure (Nazism, say; Communism) had already proven their ability to grow, feed, reproduce, and die. Ideologies were like primitive DNA floating in a nutrient soup of radio waves, television images, words.”

Sound a little like VAS?
In the Afterward, Wilson reflects on each of the stories where another excerpt echoes VAS:
“People love cats. Because we love them, we surgically alter their genitalia, keep them confined in our homes, and subject them to lethal injection when they become ill or inconvenient. At work in this story is the awful suspicion that something out there loves people.” (This refers to a story titled Ulysses Sees the Moon in the Bedroom Window about aliens)

I’m done blabbing about some of my favorite books, but I hope you enjoyed the excerpts. Cheers, here's to a productive weekend.

Reflections

So I could use this valuable blog time to good use by writing on my paper topic but I'm not really in the mood for that so like those before me I guess I’ll reflect on this class. When I registered for classes I needed a writing class and I didn’t really care which one I signed up for so I picked the one with the coolest name. That class called “Midnight Sun People” turned out to be a Scandinavian studies class focusing on the native Sami people of the north. Yeah big mistake. I saw this class on the list of available writing classes and kept passing over it because I was thinking I’m already signed up for three math classes why take a fourth class relating to math when I could take a writing class on any topic. However the subject kept intriguing me so I gave in and switched into Literature and Mathematics.

I’m really glad I did. The class turned out to be a really good outlet for seeing math in a real world setting. Well the world of Max and the “utopia” of We may not exactly be real world scenarios but I was able to learn about patterns and the potential negative aspects of technology mixed with governmental control. I never really approached math in this sort of way and this class has been a sort of release from the headache of complex analysis and number theory. It’s also been good to learn that if I dive deep enough in to my studies it’s quite possible that I’ll be driven insane. Anyway it’s been fun. Good luck to everyone on finals and whatnot.

the good bye blog...

Well guys, it's been fun huh? Blogging about stuff... yep.

Anyhow, if you guys are like me and want to read literature that is about math and not necessarily made for people who do not like math, check out David Foster Wallace's Everything and More. It is about infinity but not in a cheesy way. There is a considerable history of the subject. Everything from Zeno's Paradoxes to Cantor and more modern set theory and transfinite numbers. I don't know if you guys have read much Wallace but if you haven't, do. He's a very talented and engaging writer. As a result of this blog, I intend to watch more Futurama, so thanks to all those who posted about that. Yep.

Happy Times or Good Times

I read Brian's Blog post and it reminded me of how amazing this semester really has been. I feel like a character, Ender, out of a novel called Ender's Game because I've learned so much through this class. Ender is a genius kid who gets enrolled in a school for smart kids who train to defeat the enemy. Ender is placed in lots of different scenarios and is a winner in almost all. At the end, (spoiler) it turns out he was actually orchestrating the allies and defeated the army in real life.

I feel like I've learned a lot in this class too just like Ender did at his school. From editing sentences to reorganizing papers altogether to blogging to working in a group has all been a great experience for me and my growth as a student. I don't think there is a trick ending to my semester performance like there was in Ender's Game but I hope there is a happy one.

I didn't know there was a connection between mathematics and literature but one that pops up in my head now is the question what will you do with a math degree or a literature degree or both? It's a difficult question to answer common to both fields...In my case I am just a math major and plan on going to graduate school for higher education after I work for a few years.

All's Well That Ends Well

As the semester nears it's end, I can't help but reflect on what I've learned these past few months. I registered for this course because I really enjoy math and literature, but I really had no clue as to how the class would pan out. The first few days of class were rather interesting because we discussed topics that I had really never touched on. The weeks that followed really opened my mind to just how great the world of mathematics is and the importance it has in our society.

I feel slightly intimidated sometimes because my peers in this course are extremely intelligent. I've had the pleasure of collaborating with many of them on numerous projects throughout the semester and have really learned a lot from them. With such a diverse group of personalities always giving different viewpoints, I always feel like I'm being presented with new information.

Although this is my final blog post for this class, I envision myself writing about the topics we've covered in class in the foreseeable future. Most of all, I think that this class has given me a greater appreciation for others. I really don't think it's possible to live a happy, successful life if you don't interact with others on some sort of level.

To put an end to this spiel, I've enjoyed this class and I've enjoyed working with all of y'all. Math is so intriguing to me and I hope that all of y'all continue to appreciate it as much as I do.

Don't turn into this thing!

Even PBS Makes Him Look Crazy

Thanks to Ian's suggestion, I rented the PBS Documentary "A Brilliant Madness" from I Luv Video. As one might expect from the title, it is about John Nash and his struggle with paranoid schizophrenia. This film, however, interviews Nash himself, as well as his friends, family, and colleagues from Princeton and MIT. Just like "A Beautiful Mind," the film begins by discussing his time at Princeton and his successes in Governing Dynamics with the Nash Equilibrium. During the interview of this period of his life, the pictures of Nash shown are of him young and clean cut and they are clear and intact. Though, as the film winds on, the picture of Nash in his younger years that is most often shown is one that is wrinkled and torn, severely weathered, as seen below:

Of course, the photo used in the film did not have the writing and titles on it. Consequently, this photo is also one of the first that comes up on a Google Image Search for John Nash. Also, as the film goes on, there are images of a hand placing a Go piece on the board with deep, echoing sounds, as if it were inside your head. Also, images of red sneakers and high-water plaid pants are seen later in the film, referencing Nash's return to Princeton when he was referred to as "The Ghost." Just as we saw in Pi, all these dramatic effects are used to symbolize the schizophrenia and give the viewer a sense of what being schizophrenic might feel like. When Nash is shown in current day, at times he is alone in a room, looking off camera, and only his profile is shown.

Aside from all the dramatic elements, the documentary included some interesting details that "A Beautiful Mind" did not include. For example, Nash received his Ph.D at 21 years old after only 2 years as a graduate student. He also had a son with a former love interest but refused to pay for his son's delivery or accept him as his son and the child was placed in a foster home. There are also interviews with this son in the documentary.

During his time at MIT, Nash interrupted a class and declared that he was on the cover of TIME Magazine, disguised as Pope John XXIIV, citing the fact that 23 was his favorite prime number as the reason. He also claimed he was receiving messages from space via the New York Times and that men wearing red ties at MIT were members of a secret communist organization. During sections of the documentary, the camera zooms in on a red tie. Nash also turned down a prestigious position in Chicago because he claimed he was scheduled to be the next emperor of Antarctica. Interviews with his colleagues and wife revealed that these changes took place very quickly, over the course of a week even, as Nash went from seeming simply socially awkward to severely delusional. Nash also recounts that during his time of mental instability he felt that he was the most important person alive and nobody could understand that.

I could go on and on about the details, but I won't bore you. The documentary is very interesting and insightful and I would recommend it to anyone who is interested in learning more about John Nash.

Complex Culture Revisited

I’ve just finished reading a book on immigration to the U.S., focused on undocumented immigration from Latin America to San Diego, California. It's called Shadowed Lives: Undocumented Immigrants in American Society, a case-study written by anthropologist Leo Chavez. In the epilogue the author investigates the intent of 90’s immigration reform and argues that its aim was split along production and reproduction. By denying legal and illegal immigrants social services women and children would be less likely to live and settle in the U.S., but migrant workers as well as other young single men and women would not be further deterred from finding work in the U.S.

“Proposition 187 and most of the immigration and welfare reform proposals that followed it, targeted health care, education, and other social services as the principle attractions for immigrants, both legal and undocumented. This approach to the control of immigration, however, targets women and children, or the reproduction of the immigrant family, rather than targeting the labor of the immigrant worker (both male and female). Since immigrant women and children are more likely than immigrant men to use health care, educational services, and other social services, denying immigrants these social services would, supposedly, reduce the incentives for family formation (i.e. reproduction), and thus fewer spouses and children of immigrant workers would decide to come to the United States.” “Proposition 187 did not advocate more funds for ensuring fair labor standards and practices and thus reducing the incentive for hiring immigrant, especially undocumented, labor.”

Chavez goes on to say “…the point I am trying to make is that denying immigrants social services would clearly make immigrant families’ lives more difficult. But if the families of immigrant workers decide to return to Mexico or other family members back home stay put, then we will have reduced costs associated with immigrant labor while maintaining, and even increasing, the profits of that labor.”

Such reform undoubtedly perpetuates the often unfair, unregulated treatment and wages of undocumented immigrants which benefits employers. Chavez’s point about the intention of such reform is driven home with the example that Governor Pete Wilson, “one of the most vociferous proponents of denying health care and education to undocumented immigrants, often encouraged the immigration commissioner to stop raids on California companies, arguing that sweeping up undocumented workers caused unnecessary disruptions to business.”

These reforms, whether or not intentionally, logically lead to immigrants that contribute equally (in some cases more so) than U.S. citizens to economy and culture but cannot benefit equally from the combined efforts of the society to which they contribute. Immigrants are treated as inferior citizens, sub-class. This complex, conflicted, evolved creature that is the politics of immigration in the U.S. reminds me of the passage in VAS in which a doctor contemplates euthanizing a moribund young girl with inexplicable symptoms before her father would arrive and disallow him from performing an autopsy.

Axioms and Religion

I was thinking more recently about the role of religion in some of the depictions of mathematicians that we've been looking at. They would seem to suggest that mathematicians would rather turn to a logical system for meaning than one based on faith. However, there is an interesting parallel with religion in this approach that I think is illustrated in Pi. In Max's search for meaning, the first thing he has to do is accept his initial assumptions, namely that everything can be described with mathematics and that there are patterns everywhere in nature. In all of the study of mathematics one has to accept an initial set of axioms such as these, which are not proven, and then proceed from there. This is not always similar to faith however, since they are usually simple enough to be verified adequately by everyday experience. Max's axioms, on the other hand, such as meaningful patterns existing everywhere, are deeper than most common axioms in math and thus perhaps more closely related to the idea of a faith.

What Do Trees and Math Have in Common?

After watching "A Beautiful Mind," I got to thinking about how weird it would be to not be able to discern between reality and delusion. I started thinking about certainty. This got me to thinking about trees.

You have heard the old question:
"If a tree falls in the forest, but no one is there to hear it, then does the tree make a sound?"

I'm sure you've thought about this question at some point or another. It gets at the idea that we can't have complete certainty of something's existence (in this case, sound) without perceiving it ourselves.

In one of the discussion-based philosophy courses that I took, we talked about knowledge and certainty, and this same question came up. However, the professor changed it up a bit. He and a student in the class had the following discussion in class (a paraphrase):
Professor: "If tomorrow, at noon, humanity ceased to exist, then would mathematics also cease to exist?"
Student: "Yes, because mathematics is a creation of humanity."
P: "So are you arguing that all creations cease to exist when their creators cease to exist?"
S: "Uh, yah, I guess so."
P: "Ok. Tell me something. Is your great grandmother still alive?"
S: "No."
P: "When she passed away or ceased to exist here on earth, did your grandmother (her daughter) also cease to exist?"
S: "Ok, I see your point. But humans are different from things."
P: "Alright then, lets look at the creator of this building. Do you suspect that when he or she ceases to exist, that this building will consequently cease to exist?"
S: "No, I guess not. What I was trying to say is that math only exists in peoples' thoughts. When people cease to exist, so do their thoughts. Therefore so does math."
P: "What do you mean when you say mathematics exists only in thoughts?"
S: "Well, take the number 3 for example. The word 'three' and the symbol '3' are just constructions, created by humans for the purpose of explaining certain occurences in nature. So in essence '3' means nothing without a human to give the symbol significance."
P: "Oh I see. So you are not saying that the occurence, for which the symbol '3' was created, would cease to exist as a result of humanity ceasing to exist. Just the significance of the symbol '3' would cease to exist."
S: "Thats right."
P: "Lets look at a particular mathematical truth: 1+1 = 2 . So when humans cease to exist tomorrow at noon, the symbols '1', '+', '=', '2' would lose their meaning. But would the principal that underlies the sybols cease to exist. Lets look at another example: the standard gravity constant, 'g', which is used to explain the acceleration due to gravity on earth. Once again, when humans cease to exist, so does the significance of the symbol 'g'. But does that mean that gravity itself ceases to exist? Would the old rule of 'what goes up must come down' cease to exist?"

Would love to continue discussion on these questions.

Mathematicians are Pretty Crazy

Can crazy people be successful mathematicians? This is an important question to ask because it determines whether mentally handicapped students in schools have the capability of reaching their potential, competing at high levels with students without mental disorders. I did some research and discovered that some scientists have been successful in their endeavors even though they have faced difficult mental illnesses. These scientists include Turing, Newton, Cantor, and Godel.

My mom has a mental disorder and she is a mathematician teaching 8th graders. She plays with numbers all the time. No fun. No romance in life. She has no sense of where she is driving sometimes. She knows how to cook a few foods but that's about it. But these people they also have their life.

The Art of Math

Today Ana and I were interviewed by a writer from the New York Times who is writing an article about communities. She wants to write a chapter about math communities. This is exciting because the association is not often made, as we have discussed in class, between math and socializing. However, my experience as a math major has been the opposite (most of my friends are math majors and we throw awesome math parties!), and I am glad that perhaps she will provide a more accurate account of math and the average person who studies it. And, it turns out that her last book won the Pulitzer Prize!

I checked out a really cool book from the library that analyzes how mathematicians think and the common misconceptions people have about doing math. Most people have to study algebra, geometry, and at most, Calculus. The curriculum usually emphasizes the mechanical and computational aspect of these fields rather than the conceptual part. I know that it has been a long time since I have done any arithmetic. I always dread the question, “Hey, you’re a math major, what is 12039823497255 x 9870462395734?”
In some schools, math is considered a liberal art as opposed to a natural science. What makes this subject bridge these two rather disjoint categorizations?
I would like to add a few quotes from the book that I really like:

“What is missing is the creativity of mathematics…As people about mathematics and they will talk about arithmetic, geometry, or statistics, about mathematical techniques or theorems they have learned. They may talk about the logical structure of mathematics, the nature of mathematical arguments…Rarely, however, do most people mention the “doing” of mathematics when they talk about mathematics.”

“Mathematics has something to teach us, all of us, whether or not we like mathematics or use it very much. This lesson has to do with thinking, the way we use our minds to draw conclusions about the world around us.”

Math for Kids!

There is actually some cool children’s math literature that I have read/seen.
Firstly, if you haven’t read anything by author Jon Scieszka and illustrator Lane Smith, I highly recommend The True Story of the Three Little Pigs, The Stinky Cheese Man, and Math Curse. Math Curse is a brilliant little story of a kid who is cursed by his math teacher Mrs. Fibonacci, and he starts thinking about math throughout his daily activities. I won’t give away the ending, but it is really well done, and has some cool math and logic problems.
Also, has anyone seen Donald Duck in Mathemagic Land? The protagonist, Donald Duck, is forced to discover the math in nature (Fibonacci Number, The Golden Ratio, etc.), meets Pythagoras, and learns the geometry behind music and billiards. Initially, poor Donald is frightened, but at the end he appreciates math and even wants to learn more about it.
While I wish that were everyone’s experience (wouldn’t it be cool to meet Pythagoras?), it is a good attempt at trying to get kids not to hate math. Both the book and movie involve characters that initially go crazy because they have to think too much about math. The visuals are intense and sometime frightening, reminiscent of Pi. Luckily, neither the student nor Donald end up with a hole in their heads.

the fibonacci numbers

i know this is a little different from the golden ratio, but still on the tracks of math and numbers, I read another article which talks about the fibonacci numbers and claims that much of the mystique surrounding them is misplaced. it says we ought to recognize that this sequence is simply one example of a large class of sequences with such properties. by focusing too narrowly on a specific example, we may lose sight of more general principles at work. the authors believe that it is more fascinating that an entire world of such sequence exists and should not be overlooked. there are a lot of equations and proofs and claims which i'm not going to try to interpret, but basically this papers saying that the properties that make this sequence so 'special' isn't limited or unique to the fibonacci numbers, it happens everywhere, all the time, in other number sequences as well (like the golden ratio). it's not trying to take away from the amazingness of the fibonacci numbers, but it's just saying that we should step back and look at the big picture more often. you can find the article here: use google scholar from the UT library website and you can view this article for free if they try to charge you otherwise.

autism and cognitive domains

i read an article comparing the rate of autism in two separate groups of students, one consisting of students in the fields of physics, engineering, and mathematics and the other consisting of students studying literature. autism is diagnosed on the basis of abnormalities in social development, communication, and imagination. it talks about how cognition has a domain-specific structure, cognitive domains exist in the human brain as a result of natural selection. two of these basic cognitive domains are folk psychology (social understanding) and folk physics (understanding inanimate objects). evidence shows that children with autism are impaired in the development of folk psychology (this seems to be consistent even in adults with autism who are of "average" intelligence). evidence shows that in children, folk physics is intact or even superior, which can be displayed through obsessional interests, such as systems with mathematical/spatial regularities. it goes on to compare the families of the two groups of students and it shows that autism occurs more often when family history shows that relatives were more often associated in careers of engineering, physics, and mathematics, which is true for the students who are currently studying these fields. i just thought it was interesting that there are some mental illnesses to which people who understand inanimate objects better than others, are more vulnerable to. here's the link to the article:

Another Post on Aspergers (Thanks Ian)

This is kind of a comment on Ian’s post but I got into it enough to make it my own blog post. Another attribute of Aspergers is severe depression, mood swings, anxiety, and paranoia. Also just to note many people with Aspergers will be unconscious of nervous hand movements/twitches. All of this I’ve learned through experiencing second hand my cousins at the age of 10 already battling with Aspergers. I posted a blog a month or so ago about historical people with genetic disabilities and came to find out that many prominent people in history are thought to have had Aspergers and these aren't just limited to the mathematical community. Men of science and art and even people like Lincoln made the list. What is curious to note is that predominantly Aspergers is found mostly in men.

My 10 year old cousin was diagnosed at the age of 3 with it, and various other relatives in my family display symptoms as well. In modern times they start early by putting him in some special classes to teach him how to relate with other students whereas back when it usually went unnoticed and undiagnosed until symptoms are more severe. I am very curious as to how my cousin will turn out as an adult living in modern America with Aspergers.

Getting back to A Beautiful Mind however I look at the character of Nash who had schizoid tendencies but to me he also displays almost every attribute of someone who suffers from Aspergers. I wonder if from the beginning if he had been treated for the social disorder if he wouldn’t have turned out very differently. Is it the introverted nature of Aspergers that leads to the person become consumed and obsessed with math or science or art or is it the other way around. If he had been treated from early life would he have never uncovered mathematical theorems and developed game theory of economics. The treatment in his latter life for schizophrenia made it difficult for him to work on math which would lead me to believe that, no he would not have produced theories on the same level.

Gematria

One of the coolest parts of the movie to me was when they were talking about the Torah, so I looked into it a little more. This example that I'm about to give is definitely reaching a bit, but I thought it was pretty fun, so I'll share it.

Apparently, in Jewish tradition, there is a word that appears in portions of the Books of the Prophets that is occasionally read Kri, which is differently than it is written, Ktiv. So the mystery is that the numerical value for the written word is 111 while the numerical value for the way it is read is 106! Now, the ratio 111/106= 1.047169811. Doesn't mean anything yet right? Wait! Read this!

"A plain reading of 1 Kings 7:23 suggests that its author believed that 3, rather than 3.14159..., is the value of Pi. The verse describes the molten sea that was made in the Temple as being 10 cubits from brim to brim (diameter) and as being encircled completely by a line of 30 cubits (circumference)." (Wikipedia - of course)

So it still doesn't mean much... BUT... the ratio between Pi and 3 is approximately 1.047197551. So the conclusion is that 111/106 * 3 = 3.141509434 which is 99.997% of the known value! (obviously since it got the first 5 digits right and the rest are unimportant anyway...) So it is believed that they had a better approximation of Pi than we thought.

The study is called Gematria. There are different types of Gematria but they all consist in finding patterns between the 22 letters of the Hebrew alphabet and either mathematical objects or sentences from the Torah. For example, there are 22 solids made of regular polygons, so there should be some relationship there. It's pretty neat stuff...

Also, if you count the letters of this phrase "God is ever a geometer" (ἀεὶ ὁ Θεὸς ὁ μέγας γεωμετρεῖ) you will find the first six digits of pi!

Decimal	Hebrew	Glyph
1	Aleph	א
2	Bet	ב
3	Gimel	ג
4	Daled	ד
5	He	ה
6	Waw	ו
7	Zayin	ז
8	Heth	ח
9	Teth	ט
10	Yodh	י
20	Kaph	כ, ך
30	Lamed	ל
40	Mem	מ, ם
50	Nun	נ, ן
60	Samekh	ס
70	Ayin	ע
80	Pe	פ, ף
90	Tsadi	צ, ץ
100	Qoph	ק
200	Resh	ר
300	Shin	ש
400	Taw	ת
500	Kaph	ך
600	Mem	ם
700	Nun	ן
800	Pe	ף
900	Tsadi	ץ

So if anyone's bored... try to find patterns!

40055294609039401775363356554719310001754300475047
19144899841040015867946179241610016454716551337074
07395026044276953855383439755054887109978520540117
51697475813449260794336895437832211724506873442319
89878844128542064742809735625807066983106979935260
69339213568588139121480735472846322778490808700246
77763036055512323866562951788537196730346347012229
39581606792509153217489030840886516061119011498443
41235012464692802880599613428351188471544977127847
33617662850621697787177438243625657117794500644777
18370221999106695021656757644044997940765037999954
84500271066598781360380231412683690578319046079276
52972776940436130230517870805465115424693952651271
01052927070306673024447125973939950514628404767431
36373997825918454117641332790646063658415292701903
02760173394748669603486949765417524293060407270050
59039503148522921392575594845078867977925253931765
15641619716844352436979444735596426063339105512682
60615957262170366985064732812667245219890605498802
80782881429796336696744124805982192146339565745722
10229867759974673812606936706913408155941201611596
01902377535255563006062479832612498812881929373434
76862689219239777833910733106588256813777172328315
32908252509273304785072497713944833389255208117560
84529665905539409655685417060011798572938139982583
19293679100391844099286575605993598910002969864460
97471471847010153128376263114677420914557404181590
88000649432378558393085308283054760767995243573916
31221886057549673832243195650655460852881201902363
64471270374863442172725787950342848631294491631847
53475314350413920961087960577309872013524840750576
37199253650470908582513936863463863368042891767107
60211115982887553994012007601394703366179371539630
61398636554922137415979051190835882900976566473007
33879314678913181465109316761575821351424860442292
44530411316065270097433008849903467540551864067734
26035834096086055337473627609356588531097609942383
47382222087292464497684560579562516765574088410321
73134562773585605235823638953203853402484227337163
91239732159954408284216666360232965456947035771848
73442034227706653837387506169212768015766181095420
09770836360436111059240911788954033802142652394892
96864398089261146354145715351943428507213534530183
15875628275733898268898523557799295727645229391567
47756667605108788764845349363606827805056462281359
88858792599409464460417052044700463151379754317371
87756039815962647501410906658866162180038266989961
96558058720863972117699521946678985701179833244060
18115756580742841829106151939176300591943144346051
54047710570054339000182453117733718955857603607182
86050635647997900413976180895536366960316219311325
02238517916720551806592635180362512145759262383693
48222665895576994660491938112486609099798128571823
49400661555219611220720309227764620099931524427358
94887105766238946938894464950939603304543408421024
62401048723328750081749179875543879387381439894238
01176270083719605309438394006375611645856094312951
75977139353960743227924892212670458081833137641658
18269562105872892447740035947009268662659651422050
63007859200248829186083974373235384908396432614700
05324235406470420894992102504047267810590836440074
66380020870126664209457181702946752278540074508552
37772089058168391844659282941701828823301497155423
52359117748186285929676050482038643431087795628929
25405638946621948268711042828163893975711757786915
43016505860296521745958198887868040811032843273986
71986213062055598552660364050462821523061545944744
89908839081999738747452969810776201487134000122535
52224669540931521311533791579802697955571050850747
38747507580687653764457825244326380461430428892359
34852961058269382103498000405248407084403561167817
17051281337880570564345061611933042444079826037795
11985486945591520519600930412710072778493015550388
95360338261929343797081874320949914159593396368110
62755729527800425486306005452383915106899891357882
00194117865356821491185282078521301255185184937115
03422159542244511900207393539627400208110465530207
93286725474054365271759589350071633607632161472581
54076420530200453401835723382926619153083540951202
26329165054426123619197051613839357326693760156914
42994494374485680977569630312958871916112929468188
49363386473927476012269641588489009657170861605981
47204467428664208765334799858222090619802173211614
23041947775499073873856794118982466091309169177227
42072333676350326783405863019301932429963972044451
79288122854478211953530898910125342975524727635730
22628138209180743974867145359077863353016082155991
13141442050914472935350222308171936635093468658586
56314855575862447818620108711889760652969899269328
17870557643514338206014107732926106343152533718224
33852635202177354407152818981376987551575745469397
27150488469793619500477720970561793913828989845327
42622728864710888327017372325881824465843624958059
25603381052156062061557132991560848920643403033952
62263451454283678698288074251422567451806184149564
68611163540497189768215422772247947403357152743681
94098920501136534001238467142965518673441537416150
42563256713430247655125219218035780169240326699541
74608759240920700466934039651017813485783569444076
04702325407555577647284507518268904182939661133101
60131119077398632462778219023650660374041606724962
49013743321724645409741299557052914243820807609836
48234659738866913499197840131080155813439791948528
30436739012482082444814128095443773898320059864909
15950532285791457688496257866588599917986752055455
80990045564611787552493701245532171701942828846174
02736649978475508294228020232901221630102309772151
56944642790980219082668986883426307160920791408519
76952355534886577434252775311972474308730436195113
96119080030255878387644206085044730631299277888942
72918972716989057592524467966018970748296094919064
87646937027507738664323919190422542902353189233772
93166736086996228032557185308919284403805071030064
77684786324319100022392978525537237556621364474009
67605394398382357646069924652600890906241059042154
53927904411529580345334500256244101006359530039598
86446616959562635187806068851372346270799732723313
46939714562855426154676506324656766202792452085813
47717608521691340946520307673391841147504140168924
12131982688156866456148538028753933116023229255561
89410429953356400957864953409351152664540244187759
49316930560448686420862757201172319526405023099774
56764783848897346431721598062678767183800524769688
40849891850861490034324034767426862459523958903585
82135006450998178244636087317754378859677672919526
11121385919472545140030118050343787527766440276261
89410175768726804281766238606804778852428874302591
45247073950546525135339459598789619778911041890292
94381856720507096460626354173294464957661265195349
57018600154126239622864138977967333290705673769621
56498184506842263690367849555970026079867996261019
03933126376855696876702929537116252800554310078640
87289392257145124811357786276649024251619902774710
90335933309304948380597856628844787441469841499067
12376478958226329490467981208998485716357108783119
18486302545016209298058292083348136384054217200561
21989353669371336733392464416125223196943471206417
37549121635700857369439730597970971972666664226743
11177621764030686813103518991122713397240368870009
96862922546465006385288620393800504778276912835603
37254825579391298525150682996910775425764748832534
14121328006267170940090982235296579579978030182824
28490221470748111124018607613415150387569830918652
78065889668236252393784527263453042041880250844236
31903833183845505223679923577529291069250432614469
50109861088899914658551881873582528164302520939285
25807796973762084563748211443398816271003170315133
44023095263519295886806908213558536801610002137408
51154484912685841268695899174149133820578492800698
25519574020181810564129725083607035685105533178784
08290000415525118657794539633175385320921497205266
07831260281961164858098684587525129997404092797683
17663991465538610893758795221497173172813151793290
44311218158710235187407572221001237687219447472093
49312324107065080618562372526732540733324875754482
96757345001932190219911996079798937338367324257610
39389853492787774739805080800155447640610535222023
25409443567718794565430406735896491017610775948364
54082348613025471847648518957583667439979150851285
80206078205544629917232020282229148869593997299742
97471155371858924238493855858595407438104882624648
78805330427146301194158989632879267832732245610385
21970111304665871005000832851773117764897352309266
61234588873102883515626446023671996644554727608310
11878838915114934093934475007302585581475619088139
87523578123313422798665035227253671712307568610450
04548970360079569827626392344107146584895780241408
15840522953693749971066559489445924628661996355635
06526234053394391421112718106910522900246574236041
30093691889255865784668461215679554256605416005071
27664176605687427420032957716064344860620123982169
82717231978268166282499387149954491373020518436690
76723577400053932662622760323659751718925901801104
29038427418550789488743883270306328327996300720069
80122443651163940869222207453202446241211558043545
42064215121585056896157356414313068883443185280853
97592773443365538418834030351782294625370201578215
73732655231857635540989540332363823192198921711774
49469403678296185920803403867575834111518824177439
14507736638407188048935825686854201164503135763335
55094403192367203486510105610498727264721319865434
35450409131859513145181276437310438972507004981987
05217627249406521461995923214231443977654670835171
47493679861865527917158240806510637995001842959387
99158350171580759883784962257398512129810326379376
21832245659423668537679911314010804313973233544909
08249104991433258432988210339846981417157560108297
06583065211347076803680695322971990599904451209087
27577622535104090239288877942463048328031913271049
54785991801969678353214644411892606315266181674431
93550817081875477050802654025294109218264858213857
52668815558411319856002213515888721036569608751506
31875330029421186822218937755460272272912905042922
59787710667873840000616772154638441292371193521828
49982435092089180168557279815642185819119749098573
05703326676464607287574305653726027689823732597450
84479649545648030771598153955827779139373601717422
99602735310276871944944491793978514463159731443535
18504914139415573293820485421235081739125497498193
08714396615132942045919380106231421774199184060180
34794988769105155790555480695387854006645337598186
28464199052204528033062636956264909108276271159038
56995051246529996062855443838330327638599800792922
84665950355121124528408751622906026201185777531374
79493620554964010730013488531507354873539056029089
33526400713274732621960311773433943673385759124508
14933573691166454128178817145402305475066713651825
82848980995121391939956332413365567770980030819102
72040997148687418134667006094051021462690280449159
64654533010775469541308871416531254481306119240782
11886900560277818242350226961893443525476335735364
85619363254417756613981703930632872166905722259745
20919291726219984440964615826945638023950283712168
64465617852355651641277128269186886155727162014749
34052276946595712198314943381622114006936307430444
17328478610177774383797703723179525543410722344551
25555899986461838767649039724611679590181000350989
28641204195163551108763204267612979826529425882951
14127584126273279079880755975185157684126474220947
97218433093529726652100156625145529947451276315509
17636730259462132930190402837954246323258550301096
70692272022707486341900543830265068121414213505715
41750575086399076739463351462090828889349383764393
99256900604067311422093312195936202982972351163259
38677224147791162957278075239505625158160313335938
23115005186268905306583681299881086632632719806112
71548858798093487912913707498230575929091862939195
01472119758606727009254771802575033773079939713453
95326461952699965963856549175904583335857991020127
13204583903200853878881633637685182083727885131175
22776960978796214237216254521459128183179821604411
13116714069148271709810154577819392023115638719508
05024679725792497605772625913328559726371211201905
72077140914864507409492671803581515757151405039761
09638467555692989703835473141002238025834687673501
29775413279532060971154506484212185936490997917766
87477448188287063231551586503289816422828823274686
61065927321979071623846421534898524762167890502609
98045266483929542357287343977680495774091449538391
57556548545905897649519851380100795801078375994577
52991967005476022525520344539887125387801719607181
64078124847847257912407824544361682345239570689514
27226975043187363326301110305342333582160933319121
88066082683414289104151732472160533558499932245487
30778822905252324234861531520976938461042582849714
96347534183756200301491570327968530186863157248840
15266398356895636346574353217834931998255421173084
67745297085839507616458229630324424328237737450517
02856069806788952176819815671078163340526675953942
49262807569683261074953233905362230908070814559198
37355377748742029039018142937311529334644468151212
94509759653430628421531944572711861490001765055817
70953024688752632501197052094761594167687277844720
00192789137251841622857783792284439084301181121496
36642465903363419454065718354477191244662125939265
66203068885200555991212353637182269225317814587925
93750441448933981608657900876165024635197045828895
48179375668104647461410514249887025213993687050937
23054477341126413548928068410591077166778212383328
10262185587751312721179344448201440425745083063944
73836379390628300897330624138061458941422769474793
16657176231824721683506780764875734204915576282175
83972975134478990696589532548940335615613167403276
47246921250575911625152965456854463349811431767025
72956618447754874693784642337372389819206620485118
94378868224807279352022501796545343757274163910791
97295295081294292220534771730418447791567399173841
83117103625243957161527146690058147000026330104526
43547865903290733205468338872078735444762647925297
69017091200787418373673508771337697768349634425241
99499513883150748775374338494582597655609965559543
18040920178497184685497370696212088524377013853757
68141663272241263442398215294164537800049250726276
51507890850712659970367087266927643083772296859851
69122305037462744310852934305273078865283977335246
01746352770320593817912539691562106363762588293757
13738407544064689647831007045806134467312715911946
08435935825987782835266531151065041623295329047772
17408355934972375855213804830509000964667608830154
06128243087406455944318534137552201663058121110334
53120745086824339432159043594430312431227471385842
03039010607094031523555617276799416002039397509989
76293353258555756248089966918298642226775023601932
57974726742578211119734709402357457222271212526852
38429587427350156366009318804549333898974157149054
41825597380808715652814301026704602843168192303925
35297795765862414392701549740879273131051636119137
57700892956482332364829826302460797587576774537716
01024908046243018565241617566556001608591215345562
67602192689982855377872583145144082654583484409478
46317877737479465358016996077940556870119232860804
11309046293508718271259346687127666948738998245985
27786499569165464029458935064964335809824765965165
14209098675520380830920323048734270346828875160407
15466538346196112230137594515792526967436425319273
90036038608236450762698827497618723575476762889950
75211480485252795084503395857083813047693788132112
36742813194879502280663201700224603319896719706491
63741175854851878484012054844672588851401562725019
82171906696081262778548596481836962141072171421498

67447472059985023582891833692922337323999480437108
41965947316265482574809948250999183300697656936715
96893644933488647442135008407006608835972350395323
40179582557036016936990988671132109798897070517280
75585519126993067309925070407024556850778679069476
61262980822516331363995211709845280926303759224267
42575599892892783704744452189363203489415521044597
26188380030067761793138139916205806270165102445886
92476492468919246121253102757313908404700071435613
62316992371694848132554200914530410371354532966206
39210547982439212517254013231490274058589206321758
94943454890684639931375709103463327141531622328055
22972979538018801628590735729554162788676498274186
16421878988574107164906919185116281528548679417363
89066538857642291583425006736124538491606741373401
73572779956341043326883569507814931378007362354180
07061918026732855119194267609122103598746924117283
74931261633950012395992405084543756985079570462226
64619000103500490183034153545842833764378111988556
31877779253720116671853954183598443830520376281944
07615941068207169703022851522505731260930468984234
33152732131361216582808075212631547730604423774753
50595228717440266638914881717308643611138906942027
90881431194487994171540421034121908470940802540239
32942945493878640230512927119097513536000921971105
41209668311151632870542302847007312065803262641711
61659576132723515666625366727189985341998952368848
30999302757419916463841427077988708874229277053891
22717248632202889842512528721782603050099451082478
35729056919885554678860794628053712270424665431921
45281760741482403827835829719301017888345674167811
39895475044833931468963076339665722672704339321674
54218245570625247972199786685427989779923395790575
81890622525473582205236424850783407110144980478726
69199018643882293230538231855973286978092225352959
10173414073348847610055640182423921926950620831838
14546983923664613639891012102177095976704908305081
85470419466437131229969235889538493013635657618610
60622287055994233716310212784574464639897381885667
46260879482018647487672727222062676465338099801966
88368099415907577685263986514625333631245053640261
05696055131838131742611844201890888531963569869627
95036738424313011331753305329802016688817481342988
68158557781034323175306478498321062971842518438553
44276201282345707169885305183261796411785796088881
50329602290705614476220915094739035946646916235396
80920139457817589108893199211226007392814916948161
52738427362642980982340632002440244958944561291670
49508235812487391799648641133480324757775219708932
77226234948601504665268143987705161531702669692970
49283162855042128981467061953319702695072143782304
76875280287354126166391708245925170010714180854800
63692325946201900227808740985977192180515853214739
26532515590354102092846659252999143537918253145452
90598415817637058927906909896911164381187809435371
52133226144362531449012745477269573939348154691631
16249288735747188240715039950094467319543161938554
85207665738825139639163576723151005556037263394867
20820780865373494244011579966750736071115935133195
91971209489647175530245313647709420946356969822266
73775209945168450643623824211853534887989395673187
80660610788544000550827657030558744854180577889171
92078814233511386629296671796434687600770479995378
83387870348718021842437342112273940255717690819603
09201824018842705704609262256417837526526335832424
06612533115294234579655695025068100183109004112453
79015332966156970522379210325706937051090830789479
99900499939532215362274847660361367769797856738658
46709366795885837887956259464648913766521995882869
33801836011932368578558558195556042156250883650203
32202451376215820461810670519533065306060650105488
71672453779428313388716313955969058320834168984760
65607118347136218123246227258841990286142087284956
87963932546428534307530110528571382964370999035694
88852851904029560473461311382638788975517885604249
98748316382804046848618938189590542039889872650697
62020199554841265000539442820393012748163815853039
64399254702016727593285743666616441109625663373054
09219519675148328734808957477775278344221091073111
35182804603634719818565557295714474768255285786334
93428584231187494400032296906977583159038580393535
21358860079600342097547392296733310649395601812237
81285458431760556173386112673478074585067606304822
94096530411183066710818930311088717281675195796753
47188537229309616143204006381322465841111157758358
58113501856904781536893813771847281475199835050478
12977185990847076219746058874232569958288925350419
37958260616211842368768511418316068315867994601652
05774052942305360178031335726326705479033840125730
59123396018801378254219270947673371919872873852480
57421248921183470876629667207272325650565129333126
05950577772754247124164831283298207236175057467387
01282095755443059683955556868611883971355220844528
52640081252027665557677495969626612604565245684086
13923826576858338469849977872670655519185446869846
94784957346226062942196245570853712727765230989554
50193037732166649182578154677292005212667143463209
63789185232321501897612603437368406719419303774688
09992968775824410478781232662531818459604538535438
39114496775312864260925211537673258866722604042523
49108702695809964759580579466397341906401003636190
40420331135793365424263035614570090112448008900208
01478056603710154122328891465722393145076071670643
55682743774396578906797268743847307634645167756210
30986040927170909512808630902973850445271828927496
89212106670081648583395537735919136950153162018908
88748421079870689911480466927065094076204650277252
86507289053285485614331608126930056937854178610969
69202538865034577183176686885923681488475276498468
82194973972970773718718840041432312763650481453112
28509900207424092558592529261030210673681543470152
52348786351643976235860419194129697690405264832347
00991115424260127343802208933109668636789869497799
40012601642276092608234930411806438291383473546797
25399262338791582998486459271734059225620749105308
53153718291168163721939518870095778818158685046450
76993439409874335144316263303172477474868979182092
39480833143970840673084079589358108966564775859905
56376952523265361442478023082681183103773588708924
06130313364773710116282146146616794040905186152603
60092521947218890918107335871964142144478654899528
58234394705007983038853886083103571930600277119455
80219119428999227223534587075662469261776631788551
44350218287026685610665003531050216318206017609217
98468493686316129372795187307897263735371715025637
87335797718081848784588665043358243770041477104149
34927438457587107159731559439426412570270965125108
11554824793940359768118811728247215825010949609662
53933953809221955919181885526780621499231727631632
18339896938075616855911752998450132067129392404144
59386239880938124045219148483164621014738918251010
90967738690664041589736104764365000680771056567184
86281496371118832192445663945814491486165500495676
98269030891118568798692947051352481609174324301538
36847072928989828460222373014526556798986277679680
91469798378268764311598832109043715611299766521539
63546442086919756737000573876497843768628768179249
74694384274652563163230055513041742273416464551278
12784577772457520386543754282825671412885834544435
13256205446424101103795546419058116862305964476958
70540721419852121067343324107567675758184569906930
46047522770167005684543969234041711089888993416350
58515788735343081552081177207188037910404698306957
86854739376564336319797868036718730796939242363214
48450354776315670255390065423117920153464977929066
24150832885839529054263768766896880503331722780018
58850697362324038947004718976193473443084374437599
25034178807972235859134245813144049847701732361694
71976571535319775499716278566311904691260918259124
98903676541769799036237552865263757337635269693443
54400473067198868901968147428767790866979688522501
63694985673021752313252926537589641517147955953878
42784998664563028788319620998304945198743963690706
82762657485810439112232618794059941554063270131989
89570376110532360629867480377915376751158304320849
87209202809297526498125691634250005229088726469252
84666104665392171482080130502298052637836426959733
70705392278915351056888393811324975707133102950443
03467159894487868471164383280506925077662745001220
03526203709466023414648998390252588830148678162196
77519458316771876275720050543979441245990077115205
15461993050983869825428464072555409274031325716326
40792934183342147090412542533523248021932277075355
54679587163835875018159338717423606155117101312352
56334858203651461418700492057043720182617331947157
00867578539336078622739558185797587258744102542077
10547536129404746010009409544495966288148691590389
90718659805636171376922272907641977551777201042764
96949611056220592502420217704269622154958726453989
22769766031052498085575947163107587013320886146326
64125911486338812202844406941694882615295776253250
19870359870674380469821942056381255833436421949232
27593722128905642094308235254408411086454536940496
92714940033197828613181861888111184082578659287574
26384450059944229568586460481033015388911499486935
43603022181094346676400002236255057363129462629609
61987605642599639461386923308371962659547392346241
34597795748524647837980795693198650815977675350553
91899115133525229873611277918274854200868953965835
94219633315028695611920122988898870060799927954111
88269023078913107603617634779489432032102773359416
90865007193280401716384064498787175375678118532132
84082165711075495282949749362146082155832056872321
85574065161096274874375098092230211609982633033915
46949464449100451528092508974507489676032409076898
36529406579201983152654106581368237919840906457124
68948470209357761193139980246813405200394781949866
20262400890215016616381353838151503773502296607462
79529103840686855690701575166241929872444827194293
31004854824454580718897633003232525821581280327467
96200281476243182862217105435289834820827345168018
61317195933247110746622285087106661177034653528395
77625997744672185715816126411143271794347885990892
80848669491413909771673690027775850268664654056595
03948678411107901161040085727445629384254941675946
05487117235946429105850909950214958793112196135908
31588262068233215615308683373083817327932819698387
50870834838804638847844188400318471269745437093732
98362402875197920802321878744882872843727378017827
00805878241074935751488997891173974612932035108143
27032514090304874622629423443275712600866425083331
87688650756429271605525289544921537651751492196367
18104943531785838345386525565664065725136357506435
32365089367904317025978781771903148679638408288102
09461490079715137717099061954969640070867667102330
04867263147551053723175711432231741141168062286420
63889062101923552235467116621374996932693217370431
05987225039456574924616978260970253359475020913836
67377289443869640002811034402608471289900074680776
48440887113413525033678773167977093727786821661178
65344231732264637847697875144332095340001650692130
54647689098505020301504488083426184520873053097318
94929164253229336124315143065782640702838984098416
02950309241897120971601649265613413433422298827909
92178604267981245728534580133826099587717811310216
73402565627440072968340661984806766158050216918337
23680399027931606420436812079900316264449146190219
45822969099212278855394878353830564686488165556229
43156731282743908264506116289428035016613366978240
51770155219626522725455850738640585299830379180350
43287670380925216790757120406123759632768567484507
91511473134400018325703449209097124358094479004624
94313455028900680648704293534037436032625820535790
11839564908935434510134296961754524957396062149028
87289327925206965353863964432253883275224996059869
74759882329916263545973324445163755334377492928990
58117578635555562693742691094711700216541171821975
05198317871371060510637955585889055688528879890847
50915764639074693619881507814685262133252473837651
19299015610918977792200870579339646382749068069876
91681974923656242260871541761004306089043779766785
19661891404144925270480881971498801542057787006521
59400928977760133075684796699295543365613984773806
03943688958876460549838714789684828053847017308711
17761159663505039979343869339119789887109156541709
13308260764740630571141109883938809548143782847452
88383680794188843426662220704387228874139478010177
21392281911992365405516395893474263953824829609036
90028835932774585506080131798840716244656399794827
57836501955142215513392819782269842786383916797150
91262410548725700924070045488485692950448110738087
99654748156891393538094347455697212891982717702076
66136024895814681191336141212587838955773571949863
17210844398901423948496659251731388171602663261931
06536653504147307080441493916936326237376777709585
03132559900957627319573086480424677012123270205337
42667053142448208168130306397378736642483672539837
48769098060218278578621651273856351329014890350988
32706172589325753639939790557291751600976154590447
71692265806315111028038436017374742152476085152099
01615858231257159073342173657626714239047827958728
15050956330928026684589376496497702329736413190609
82740633531089792464242134583740901169391964250459
12881340349881063540088759682005440836438651661788
05576089568967275315380819420773325979172784376256
61184319891025007491829086475149794003160703845549
46538594602745244746681231468794344161099333890899
26384118474252570445725174593257389895651857165759
61481266020310797628254165590506042479114016957900
33835657486925280074302562341949828646791447632277