That's All Folks

To Infinity and Beyond

Okay so THIS is the last blog of the class. I went to Kanye West’s concert last night and I just wanted to say that this class has definitely made me a “harder, better, faster, stronger” writer. Based on the title I bet you thought I was going for something more Buzz Lightyear-ish…No, Kanye whoops Buzz’s plastic butt any day.

Looking back on this class I thought I had started out as a pretty decent writer, but this class has humbled me in a lot of ways. I thought I could just spit out a prize-worthy paper by taking an hour or so to write at the last minute, but now…well I still think I can just spit out a prize-worthy writing at the last minute (i.e. this blog), but I KNOW that the quality would be much greater if I really took the time and effort write a better paper. Just look at the last 3 blogs (all by me) just imagine if I had managed to think them out and write them on time and not just spewed out whatever ideas popped into my head at the moment.

At the end of the day, or in this case, the semester, I really enjoyed the literature, the discussion, pretty much every aspect of this class and I know that it has been a value to my life in academia and in the “real” world. I never really understood that phrase. Aren’t we all living in the “real” world? That’s a topic I guess I’ll never get to cover. Well, that’s it for me. I’m off to my “Spaceship” to find a place to live the “Good Life.” We’re done, so throw ya hands up to the skyyyyy….

Pythagoras

Pythagoras was a famous and controversial Greek philosopher who lived from 570 to 490 BC. He is responsible for what’s known as the Pythagorean theorem which relates to the geometry of right triangles. The formula is a² + b² = c². Contrary to modern beliefs Pythagoras was famous during his lifetime for his philosophy on the nature of the natural world as opposed to the science and mathematics for which he is known today.

There are many post-Aristotelian ancient sources that portray Pythagoras as a semi-divine entity, leading to much future controversy. He influenced future Greek philosophers Plato and Aristotle who in turn focused their memoirs of Pythagoras on his way of life and emphasize his philosophy rather than any supernatural abilities that he was claimed to possess.

Pythagoras eventually went on to found his own school based on his teachings. The schools dictum was “All is number.” According to philosopher, mathematician, historian Bertrand Russell believed that Pythagoras works in mathematics and philosophy became the model for works of future scholars such as Plato, Descartes, and Kant. He believes that Pythagoras brought together the idea of mathematics and theology to explain the nature of the universe where thought and reason was placed over the senses and intuition as superior to observation. The concept of the explaining the world through intellect rather than through the senses is accredited to Pythagoras. The teachings of Pythagoras’s school were as religious as they were intellectual. Many students of the school went on to found as society known as the Pythagoreans.

Themes of the Class

What have we talked about in class? Well, for starters we talked about math, or better yet mathematicians. We’ve learned that many of them tend to be loony but geniuses at the same time. It seems like every mathematician and some in real life suffer from schizophrenia or they’re reclusive or orphans or just associated with something negative. I think that’s a bit unfair. Why not create a story about a rich playboy mathematician? Hmmm, maybe I’ll write it and it’ll show up in a future Lit & Math class. That brings me to my next point. We’ve definitely talked about literature. We have literary analyzed and blogged about work after work after work. It’s safe to say that if you can’t write a paper based on the characters and themes and plot and etc etc, and if you can’t back up your claims with evidence, then I don’t know what you’ve been doing for the past few months. That was a bit harsh. I apologize.

We’ve talked about patterns. I’m starting to see the most ridiculous patterns all the time now and I curse this class for it. I can walk from the tower to the classroom in about 216 seconds…think about it. We’ve talked about dystopian societies where everyone is the same. We’ve talked about eugenics where everyone is trying to build the genetically perfect man or woman (which I think will end up killing us all if that happens). We’ve researched math related themes. What else can we do? What else can I say?

The Passion of The Mathematician

I’ve noticed something about the mathematicians we’ve studied in class - D-503, John Nash, Max Cohen and others. They are just like us. They have all have the same hope to make their existence on this earth matter. D-503 writes in his journal for future generations. John Nash attended and taught at some of the most prestigious universities in the world, all while coming up with some of the world’s greatest economic theory and battling schizophrenia. Max discovered the secret number of God (at least in his own mind). There are also others such as Einstein and Pythagoras that we didn’t extensively cover in class but they too are credited with some of the most influential works created thus far. Yes, some of these characters are fictional and yes, many of them were absolutely crazy, but the difference between them and us is that they were fortunate enough to find something in life they were passionate about and dive into it with reckless abandon. I find that to be admirable.

It’s easy to distinguish ourselves from them and say “well, they were all crazy,” but I bet if were to try hard enough we could all find something that we felt so drawn to that it might drive us a little nuts too. Just think about all the crazy things people do for love. This sounds obvious but I believe that mathematicians truly LOVE math and will do almost anything to discover its secrets. What do you love? What are you so passionate enough about that it could drive you crazy? If you don’t know, that’s fine. Neither do I, but summer is coming quickly and it’d be a great time to find out.

Final Blog

It looks like, by nature of my procrastination, that I might have the final word on this course blog. We'll pretend that that's why I waited until 6:30am on the last day of class to post this.

When I signed up for this course, I didn't really know what to expect. I thought we would be reading a lot of books featuring mathematicians, and discussing both the literary and mathematical merits of the novels.

I think the course was interesting overall. We discussed a lot of interesting topics, but I can't help but feel that we didn't talk much at all about math. We spoke in depth about rationality versus emotion, and about whether a logical choice equates to a "right" choice. But I think that with a room full of math, engineering, and computer science majors, we could have covered more technical material.

In the end, I think we all found this class a lot more rewarding than your standard writing component course, and so I hope that interdisciplinary writing classes like this one continue to be offered in the future.

Universe in a Neuron

On the top is a picture cosmologists developed which shows what the universe probably looks like if you could zoom all they way out.

On the bottom is a picture of a human neuron.

I think it is pondering this kind of thing that drives mathematicians nuts and makes them want to drill their brains out.

Georg Cantor, for example, spent most of his life contemplating infinity. He developed the Continuum Hypothesis which classifies the different "levels" of infinitude. He also happened to spend the last 20 years of his life in an insane asylum.

I think that to focus one's thoughts so intently and for such a long time on a subject which is essentially completely removed from reality is to risk becoming detached from reality in general, and appearing insane to the "normal" world.

Pi

Staring at the pages of Pi posted earlier in the blog reminded me of this drawing. It is so interesting to consider where these seemingly mystical constants like pi and e derive their values from...

Last Blog..for real this time.

Wow, I'd never thought I'd get to say this but I really do think this is my last blog. Well, first I'd like to thank God and my family. And of course my classmates, because I could not have done this without you all. Thank you so much. *Cue the music.

Nah...but I would like to talk about how I've learned some interesting things on the way, such as eugenics, Einstein's lovers, Miss America, and mathematicians' psychological disorders. This class does provide for a good conversation starter with friends. And also, there are some things here and there that remind me of this class and make me laugh a little bit. For example, my last roommate was an Aerospace Engineering major and wow, that guy was weird. I think he's pretty much the weirdest guy I have ever met in my entire life. Seriously. Anyways, I thought about him when we were watching Pi and A Beautiful Mind because that's what he's like.

So in conclusion, there's a couple of things I feel I've grasped from this class, along with maintaining and hopefully improving my writing skills (at least I think so). From writing 1.1 to 3.2, Gardner to research, the semester in this class has been pretty helpful and interesting for the most part.

On a more serious note...

Isn't it ironic how geniuses are the target of both honor and ridicule?
Think about it. Geniuses get praised for their work right? Whether it be music composition, an art masterpiece, or hypothesis/theory, geniuses have their own concentration in which they are honored.
However...what they excel in one category, they often lack in another. For instance, aren't most "geniuses" socially inactive? Minus the few exceptions, ala Einstein, Warhol, Dali, etc., most geniuses live in a dark attic or cellar in which they conduct their works of art. (Just kidding about that last remark by the way. )
Point being, while they are hailed for their accomplishments, I'm sure people make fun of them behind their backs, and not because they're jealous, but because the honoree is probably a major weirdo.

Humans Are Pattern Recognition Machines

So my girlfriend is writing a thesis paper, and her research style involves writing discrete facts on post-it notes, sticking them to her desk, and referring to them as she writes. But for this paper, she has ~260 post-it notes, and so she had to plaster them all over the walls of her living room, with research papers spread across the floor, and traipse about through the room from fact to fact looking for connections. It reminded me so much of John Nash in his schizophrenic "code breaking" episodes that I had to laugh, but worry a little on the inside at the same time...

The point is, our minds are designed to recognize patterns, so you don't have to be crazy to spread all your work out and analyze it from a high level.

Pirsig, Poincare, Pi

Since we have at least 3 motorcyclists in the class, I think it's appropriate to look at a passage from the venerable Zen and the Art of Motorcycle Maintenance, in which Robert Pirsig explores Henri Poincare's views on axiomatic systems:

To solve the problem of what is mathematical truth, Poincare said, we should first ask ourselves what is the nature of geometric axioms. Are they synthetic a priori judgements, as Kant said? That is, do they exist as a fixed part of man's consciousness, independently of experience and uncreated by experience? Poincare thought not. They would then impose themselves upon us with such force that we couldn't conceive the contrary proposition, or build upon it a theoretic edifice. There would be no non-Euclidian geometry.

Poincare concluded that the axioms of geometry are conventions, our choice among all possible conventions is guided by experimental facts, but it remains free and is limited only by the necessity of avoiding all contradiction.

Max from Pi seemed to take a similar view. He regularly discarded or changed his accepted axioms according to his situation. But at the same time, he made sure to remain consistent with his axioms, and the result was huge leaps in his understanding.

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!

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