i have been waiting for the weather to break forever. between multiple snowstorms, chilling winter nights, and constant strong winds, each time i checked the weather i’ve been prepared for the worst. thankfully, the second week of march provided us with a glimpse at what is waiting for us in spring. since i had tuesday off from work and hayley did not have class, we decided to take full advantage of the sunny 60°+ day. below is a map of our day, followed by a recap of the days events (with some photos and other media).

a little after noon, we met near the brooklyn bridge – city hall stop on the 4, 5, and 6, trains in manhattan. after walking around the area and grabbing some iced coffee and a bagel, we started our trip by crossing the brooklyn bridge. along the way, we stopped to take some photos.

once we arrived in brooklyn, we strolled through brooklyn heights, stopping at a starbucks to scoop up some iced tea. we then crossed into carroll gardens, where we visited a used bookstore that proved to be a treasure trove of awesome. as we walked through park slope, en route to prospect park, we found a nice grocery store and bought some sandwiches, hummus, and watermelon. we took a brief stroll through prospect park before we stopped at the brooklyn public library to check out some art that was on display.

after grabbing some drinks we stopped at the brooklyn botanic garden to eat some lunch and toss a frisbee. even though the majority of plants have yet to accept the end of winter, the gardens were still fun to explore. after lunch we found a park bench to post up on, and we rested our legs and emerged ourselves in books that we had brought along for the day. while we were reading, two kids (probably around 6 years old) came over and announced that they were superheroes, with the ability to read. i ended up tossing a frisbee with them for around 20 minutes, until the gardens started to close. at this point, we walked through crown heights on the way to my apartment. when we arrived we hung out, saw a crazed cory fox, and watched the first half of vicky cristina barcelona before hayley had to leave to meet up with her cousin. we walked to the nostrand stop on the A train, where she departed back to manhattan.

all in all it was a great day. we saw a number of neighborhoods in brooklyn and the combination of great weather, great company, and a great borough made it a day i won’t soon forget.

Since chaos is such an interesting topic, I wanted to try to convey a basic understanding of what chaos is, and how we can see it in our everyday lives. Being the type of person that I am, I regularly see and appreciate chaos. It might be how a line of customers moves forward, how people crossing the street effect traffic, or even how facebook status updates occur.

This post isn’t meant to get into chaos, but rather to explain how the series is going to work. I plan on having the first few posts be necessary introductory information. They will probably operate in linear form, with one leading into the next. After the basics are covered though, I plan on moving in different directions all at once, branching out in ways that I haven’t even fully thought out yet. At the beginning of each article, I will be linking to all of the previous posts that I think are prerequisite for said article.

I have a decent outline for where it is heading, but its written in sand rather than stone. The introductory material is pretty solidified, but beyond that, I just have ideas of things I would like to explore. I would like to put out my ideas on how we can model our society with these principals, possibly introduce my personal definition of god (here’s a hint, it won’t be the god of abraham), and get into some interesting examples of chaos.

Lastly, I’m really hoping this concept works out. The goal is to express the scientific understanding of chaos in a way that opens the subject up to people who aren’t science oriented. That may not always work out as well as I may hope. Feedback, questions, and concerns are welcome and encouraged. If something doesn’t make sense to you, leave a comment. I may just reply to the comment, but I might edit the post or even write a new one. I’m trying to hone a skill that I (like to think I) already have, the ability to explain.

Now, onto the series (not a link yet).

This is a quick post, containing a quick (and hopefully neat) math proof. It is much easier to understand than my last math-physics post. It’s pretty well known and something that an undergrad math student would probably have seen. Most people aren’t undergrad math students though. If you haven’t seen it, read on and I hope you find them interesting.

Proof – Largest Prime?
Prime numbers are pretty sweet. There is a lot of really neat math dealing with them, particularly in Number Theory. Credit cards, cryptography, and internet security all use the properties of prime numbers. Prime numbers are even subject to nerdy/math humor, such as the always hilarious Prime Number Shitting Bear. Now onto the quick-sweet-fun proof.

As a quick reminder to those in the humanities, let’s start with what prime numbers are. A prime number is a natural number (1, 2, 3, 4, 5, etc.) that is only divisible by 1 and itself. 11 is prime as it is only divisible by 1 and 11 whereas 8 is not prime because it is divisible by 2. Also, any non-prime can be broken down into its prime factorization, a list of all of the primes that will divide it evenly. A number not divisible by other primes must be prime. Now that we know what primes are, I ask you is there a largest prime? Every now and then a math publication will announce the discovery of the ‘largest known prime number’ (unfortunately math/science publications are fucking stupid and I can’t link to one because they always require subscriptions or internet-fu to find what you want). Will we ever reach a point where we’ve found the largest of the primes though?

To tackle this question, we’re going to take advantage of a property of the natural numbers. If you take two numbers (a and b), and add 1 to their product (ab+1), the result isn’t divisible by either. Further, any product plus 1 isn’t divisible by any of the factors. For example, 2*3*5=30 and 31 isn’t divisible by 2, 3, or 5. If we divide 30 by 2, we will have 15 r0 (6 with a remainder of 0). When we add 1 to 30, the 1 will go to the remainder since 1<2. Again, this works for all natural numbers.

We'll start by assuming that there is a largest prime, which we'll call P. Since the natural numbers are ordered, we can then say that the prime numbers are finite, and write them all down. The list of all primes would be a list looking like 2, 3, 5, 7, 11, …, P. Now lets take the product of all the numbers in that list, add 1, and call it h; 2*3*5*7*11*…*P+1=h. Using the property above, we know that h isn’t divisible by any of the primes. Since h isn’t divisible by any of the primes, it must be a prime itself. However, h>P, so P must not be the largest prime. With this contradiction, we have proved that there isn’t a largest prime number! Go us!

So, I’m an atheist. I don’t believe in a god or a deity or any higher power. If you know me, its probably not a big surprise, but it’s always best not to assume. First, I’m going to talk about the single most amazing thing in science, and what it means to me personally. Then, I’ll get into opinions about religion and why I’m not religious. I’m planning on closing with problems I have with theists and atheists. If people like this kind of post, I have a bunch more thoughts both written and in my brain that I would be glad to share.

I’m an atheist, and that makes my life awesome! I believe in science, or what Neil DeGrasse Tyson calls “the best way to know about our physical world.” [link] We are at the current point (as opposed to the end) of a chaotic process that resulted in the universe that surrounds us that took place over a time period longer than any person could possibly conceptualize. From the big bang, we had atoms. Forces fused these atoms together inside of stars to form other, heavier atoms (going from hydrogen to things like iron, oxygen, and carbon). These heavier atoms were ejected from dying stars during supernovas and formed molecules, which over time began to form the most basic building blocks of life. From there, evolution took hold. The organisms that did the best were more likely to reproduce, resulting in a newer generation that was even better suited to its environment. Given another unfathomly long timescale, these organisms became all of the creatures (bacteria, fungi, plants, animals) that we see around us today, and make planet earth the best documentary ever. This process happened, and is happening! This is so completely amazing to me that I can’t even put it into words. And we FOUND THIS OUT! After all of this time, the little pieces of matter were able to understand and articulate this. We are quite literally, to steal the phrase from sammy, matter trying to understand itself. Personally, the understanding of this process allows me to be amazed every single day, and it makes my life much better.

But all of that is just about science, which I don’t think is mutually exclusive to religion. (I could talk more on this, but that could easily take up a whole post). It is completely possible to trust the scientific process and God at the same time. Given my view on and understanding of science, all of the more fundamental, take the bible literally religions are obviously not for me, but those are just a some of a huge array of belief systems. I don’t think all religious people are homophobic creationists who believe the earth is 6,000 years old. The root of my atheism has nothing to do with a small faction of crazy people. Those exist everywhere and in every group of people you would care to look at.

The reason that I am an atheist can be traced back to one word: faith. In my mind, when a claim is made, the burden of proof falls on the shoulders of the person/group/whatever making the claim. If you tell me that ‘The Flying Saucer Cafe‘ is a great place to go grab a coffee and a sandwich and do some interneting, I will probably believe you, but if I asked you why you better have a better answer than “just trust me.” (for the record, the FSC is a pretty tight spot with a good atmosphere and free wifi). The words “just trust me” completely infuriate me. They basically mean, “we have no proof, but we want you to believe what we say anyway” which is something my humble 15 pounds of grey matter just can’t do. Going further, religion doesn’t even deny that this issue of proof is there. Rather, it embraces it, claiming that having faith is an essential tenant of the dogma. Thats why I can’t hop on board the S.S. Holy Ghost.

I do understand though that people can beyond my problem of faith. And if you are one of those people, awesome. I have no problem with someone being religious or being excited about their faith. I really go back to live and let live for pretty much everything. The only people that I have problems with are those who decide to push their beliefs (or the consequences of their beliefs) onto other people. There are very obvious public examples of this (gay marriage, creationism, etc.) that I won’t get into as I’m sure you can figure out what I have to say anyway. However, what does upset me is the passing on of religious beliefs from one generation to the next. Once you have established that your opinion and perspective is right based on faith, then it becomes very difficult to incorporate new ideas into your understanding that disagree with what you believe, even when there is proof. I feel like it is detrimental to society, and does hurt us collectively. At the same time, I’m not going to tell people how to raise their children and I would never act on this opinion. It’s a grudge I’ll keep private.

Lastly, I want to take a few seconds to talk to any atheist out there. I said that I have a live and let live philosophy to life. This includes you too. If you sneeze in an elevator and someone says “God bless you.” please don’t respond with some tantrum about how God doesn’t exist. I understand you feel like a persecuted minority, and at times that may be true. However, we don’t need to be militant in fighting back. I’m an atheist, and all of the things I said in this post are true. At the end of the day though, the best part about being an atheist is not having to concern yourself with any of this mumbo jumbo. You just live your life with one less thing to be stressed about. I think its pretty silly to get rid of whatever stress comes with religion and replace it with some other stress associated with atheism.

Disagree? Want to praise me? Have an idea on what else I should talk about? As always, feedback is welcome.

i took a bunch of pictures of it and assembled them the best i could (click on the link images for a huge imgur view).

just a little bit of context, february was the hot chocolate festival and we had a different flavor of hot chocolate each day, this was drawn on the last one.

“adventurous meat –>”
guy 1: “what are you guys gonna talk about?”
guy 2: “um…art, chocolate…i didn’t get that far.”

guy 1: “wait…you’ve been trying to get her to meet you here and your gonna talk about chocolate in a place that makes chocloate? thats it? when is she coming?”
guy 2: “well…uh i don’t know…i just figured since it’s the last day for the hot chocolate specials she might show up…”

guy 1: “you could tell her about that time with the chalk.”
guy 2: “brilliant.”

i’m not quite sure what the story behind it is, but i guess this guy liked this girl and wanted to ask her out, but didn’t know how, so he drew this.

adorable.

the basic story elements are simple enough. a man is stranded on an island with a teacher and her seven female students. they deal with each other and outside issues as they arise. hilarity ensues.

there are so many reason why ‘father goose’ is a great way to spend an hour and a half. to start off, the writing is top notch. we get ‘father goose’ is an entry in a time capsule from the days of ‘mad men,’ but in the best way possible. the lines are solid enough that they represent the time period, but are still hilarious today.

on top of that, you have cary grant as the lead. the man is so awesome that they modeled james bond after him. we’re seeing him in one of his last roles, when he was in ‘kick back on an island’ mode. even then, he still does a hell of a job.

this is a great movie. you should check it out sometime.

i’m not what i would consider ‘typical ohio,’ but i have a lot of the traits. for better or worse i am marked by my 23 years in ohio. i know that i have the accent, and i can recognize it in others (‘bag’ is almost always a dead give away). when i’m at work, i have to be working or i feel like i’m cheating someone. i know what a lot of snow looks like and i know how to drive in it.

even though i’m straight up ohio, its more northeast ohio. the only thing that i know better than route 90 between cleveland and conneaut is the culture between them. its a culture that i love and miss. i bring it with me wherever i go.

cleveland knows what its not. the 216 knows that its not nyc, or boston, or chicago (at least we’re not detroit). we are a humble midwest city on the lake who has been through a lot. we were doing the recession before it was fashionable. we might not have the best skyline, or the best celebrities, and some even say we are the most miserable city in the united states.

thats not the cleveland that i know though.

the cleveland that i know is home to a great ultimate scene. there is case western reserve and their ultimate teams, which are some of the coolest people i’ve met through the sport. i’ve partied with them at their place and at mine. we’ve had some good times together. they were a decent sized portion of my college life, and i miss them as much as some of my wooster friends. it also has a culture built around the old jawbone teams that made runs at nationals, with a lot of those vets still kicking around. i’ve played so much ultimate in cle between club and college leagues as well as the always awesome groundhogs tournaments.

i love the cleveland that loves lebron james and shows unwavering loyalty towards him, even in this crazy season. he means more to that city than any one person means to any other city. other than single-handedly making the cavs relevant, he’s just a giant fun-boy who dominates, and we love him for it. across from the q, there is a giant LBJ sign. its epic. its also so close to the highway that it violates advertising laws. we love lebron so much that we got the governer to say, ‘fuck tha police. this is lebron james we’re talking about.’

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the cleveland that i know is also home to the cleveland clinic, and university hospitals, two of the best hospitals in the country. the latter being the hospital that made sure that my totally badass nephew alive when he was born a few months earlier than he should have been. at the clinic, he got world class healthcare that helped turn him into the baloo that we all know and love.

in short, cleveland and ohio rock and i’m glad i grew up there. i had a solid upbringing and i’m happy with how i turned out. i owe the majority of that to my fam, but i’ll give some credit to ohio as well. now i’ve left my home, but when people ask me where i’m from, no matter what happens, i’m going to be saying “oh, i’m from ohiah.” with a big smile on my face.

i’ll leave you with kid cudi’s thoughts on the area. (he knows it pretty well as he’s from shaker heights). “after this song’s done ain’t much i can say, except cleveland is my city.”

politics and how the internet can/should change them and why it won’t

views on religion and atheism and how they work together and not together (link)

something on euler’s identity: e^(pi*i)+1=0

something on length, area, volume

i’m in the worst shape of my life and battling out of it

the past 6 months and how they have changed me

poster wall

high tide

catch 22 or brave new world or 1984

like i said, no promises on any of these things. poster wall is already half done, but half done might be an overstatement.

This idea was first presented to me by Dr. Lowell Boone in a first year physics course at the College of Wooster. It has stuck with me since then, because I think its pretty nifty.

Imagine you are standing at point A with two ice cream cones on a hot summer day. Across a long, barren stretch of pavement, your buddy is patiently waiting for his cone. You want to get to him as quickly as possible to avoid having ice cream running down your hands. The fastest route you can take is a straight line. We could talk about path integrals to prove this, but I don’t think we need to do that for such a commonly accepted statement.

To calculate the time it takes you to get from point A to point B, we just multiply the distance times your velocity

Now let’s tweak the situation just slightly. Imagine you are going to carry the ice cream cones to your friend again, except some of the trip will happen on cement and some on sand. You still want to get to your friend as quickly as possible, but the ideal path isn’t a straight line anymore. Since you can walk faster on the pavement than on the sand, you will have to take that into account.

The two different turfs will effect your velocity. Instead of specifying your velocity on each surface, we start with your maximum velocity (which we’ll call ‘v’), and multiply it by an index (which we’ll call ‘n_i). For example, you walk at a maximum speed of 5 meters per second (so v=5m/s). On the cement, your index is 1 (so n_cement=1). Thus on the cement you will walk 5m/s (5*1). However, the index for sand is 0.5 (n_sand=0.5), so your velocity on sand is 2.5m/s (5*0.5).

Now back to the lesson at hand. To solve for the fastest path, we are going to break our route into two parts. We will walk a straight line on the pavement from point A to a point X on the boarder, and then a straight line from point X to our friend at point B. Our total time will be the time it takes us to walk the first path plus the time it takes us to walk the second path.

We can find the total time based on the speed indices and distances, since the time of each path is the velocity on the path multiplied by the distance traveled.

We will label the distance between Points A & B and the boarder as h_a and h_b. Now, the distance that we walk in both the cement and the sand is dependent on where point X is and the length of the boarder between A and B.

Using the distance formula, we can write d_a in terms of h_a and x and d_b in terms of h_b and l-x. Since the length of the boarder and the distance between the points and the boarder are defined by the problem, we now have the total time as a function of where we choose Point X to be, t[x].

We can plot t[x] for specific scenarios. For example, if your max velocity is 1m/s, the velocity indices are 1 and 0.5, Points A and B are 5 meters from the boarder, and the boarder is 20 meters long, than our graph of the total time versus the position of Point X looks like this

As you can see, there is a clear minimum on this plot, where the total time is the lowest. To find where Point X should be for the fastest path, we would want to find the x value of the minimum on this graph. If you have taken calculus, then you know that this means taking the derivative of t[x]. (The derivative of t[x], called t’[x], tells us the slope of t[x] for all values of x). We will then set t’[x]=0, meaning the slope of t[x] is a horizontal line, which only happens at minimums and maximums.

This equation represents the relationship between x and the other constants (n_a, h_a, l, etc.) for the fastest path. We can manipulate it to find some interesting properties of this route.

If we revisit the trip from A to X, we see that we have a triangle with sides h_a and x and a hypotenuse of d_a. Further, there is an angle between the hypotenuse and the boarder and its complimentary angle, which we’ll label φ_a and θ_a.

If we look at the left side of equation 7, we see a ratio between one of the sides and the hypotenuse, which indicates a trig relationship. In this case, we can replace the ratio with cos[φ_a] or sin[θ_a]. The same argument can be made for the right side of equation 7, leaving us with

We now have a relationship between the two velocity indices and the angles you will be walking at to deliver the ice cream if you want to take the fastest route to your friend. In the real world, you probably don’t care enough to do the calculations to figure out the fastest route. You probably don’t know the velocity indices, and you probably can’t do ridiculous mental math, and you already have your ice cream. However, this ice cream situation is analogous to another one, one that relates to the physics of light.

Instead of a person walking over cement and then sand, imagine light passing through water and then air. The light will pass through the water slower than through air. The light will bend, and it will bend just as predicted in equation 8. This means that light takes the fastest path when passing through different mediums.

That is pretty amazing, and we have noticed it. Sometimes, the world is just awesome.

I worked at a dumpling restaurant run by a former chinese stockbroker from Chicago. I worked for long hours on my feet with no breaks and no benefits and I loved it. Then I hated it. Then I loved it again. But I never once got tired of eating pork and beef dumplings smothered in plum sauce. I also had a fiery affair with Sriracha.

On the Fourth of July I watched a band play on the roof of their Bushwick apartment building. As the sun was setting behind them, with scenic vistas of Brooklyn in all directions, and a few early fireworks beginning to pop throughout the city, I felt like nothing could be more emblematic of my short-term post-college aspirations than this single moment. Or maybe I was just in a miracle whip commercial?

I doubted my ability to find a good job on my own so I went to a Career Counselor. When asked to imagine the specifics of my life ten years from now, I was terrified. When asked to imagine the specifics of my life thirty years from now, I left the question blank and said “I’ll fill it in for next time.” That was the last time I went.

I threw a frisbee in Prospect Park, I threw a frisbee in Central Park, I threw a frisbee in Fort Greene Park. I drank a 32 oz. beer out of a large white styrofoam cup in McCarren park and spectated a locally run softball league for hipsters.

I never once got mugged. I wondered whether I should feel bad for ever thinking I might get mugged… But thats when they get you…

I used to feel like an outsider whenever I had to check a subway map in the subway to figure out how to get where I was going. Now I just check it with a smug attitude like “fuck you, I’m from here now and I can check the map if i want to!” and feel like I belong.