Reading Update:










Chapter 4
Chapter 4 is more exciting than the past three and, though it covers a few principals found in most elementary statistics classes, it brings in new characters to the story like Galileo and Pascal! Here goes:

  • The simple space technique (using a space or coordinates to denote potential outcomes) can only be used when the outcomes are equally probable
  • The chances of an event depend on the number of ways in which it can occur. This is important, so how do you calculate it?
  • Pascal's Triangle
  • Mathematical expectation = probability of each outcome * payoff of each respective outcome, i.e. the cost of something, say a parking meter, is the probability of each outcome ($40.00 ticket 1 out of 20 times I use one and $0.25 on the rest of the time [19 out of 20]) so $40*1/20 + $0.25 each time I use it = $2.25. So the real cost of paying a parking meter is about $2.25 each time I use one if I average it out.
  • This idea has been helpful for winning lottery tickets. For example, if you calculate the expectation of buying all of the different combinations of six numbers from 1 to 44, and compare that with the payoff of about 27 million, you will find something quite interesting! There are 7,059,052 ways to choose those six numbers with a pot of that size, each ticket is worth almost $4. Now remember that it is possible for other people to win at the same time. Appropriate the probabilities of winning alone or with other people and add them all up to come to a grand total worth of $3.31. The price to buy one is $1. What is the appropriate course of action here? Hire a whole bunch of investors, fill out 1.4 million slips by hand (each with 5 games) and coordinate a massive ticket purchasing campaign. The result? 27 million dollars! 


Reading Update:

 The Drunkards Walk by Leonard Mlodinow

 







Chpater 3

Chapter three covers quite a bit of history and a few specific examples. Here it is in summary:

 

  • Gerolamo Cardano existed and, more importantly, pioneered the idea that possible outcomes of a situation could be thought of as points in space (or coordinates)
  • This chapter covers three probability problems:
  1. You flip two coins, what is the probability that at both will heads? The answer is 25%. There are four possible outcomes of the flip: (heads, heads), (heads, tails), (tails, heads), and (tails, tails). There is a 25% chance that both or neither coins will be heads and a 50% chance that just one will be heads. The other question addressed is this: Assuming one coin will be heads, what is the probability of both coins being heads? Is it 50%? No. The condition that one of the coins will be heads only removes one of our four possible results (tails, tails). The statement does not state explicitly which coin is heads, so it could either be (heads, tails), (tails, heads), or (heads, heads). Therefore, the chances that both will be heads, knowing one of them will for sure be heads, will be 1 in 3, or about 33%.
  2. The next problem is a joke I read last week involving some college students that missed an exam due to returning late from a road trip. They appealed to their professor claiming they had a flat tire. The professor issued the exams in different rooms and, in an attempt to catch the students lying, wrote the question, “which tire was flat?" on the second page of the exam. What is the probability that they answer the same tire? The correct answer is one in four. This is because there are four tires for them to choose. Check out the table. The chance that they choose the same tire is 4 in 16, or 1 in 4.
  3. Now for the most fun one, the Monty Hall problem. This one has been around for some time and has caused quite a bit of humiliation for many many Ph.D.s as you will see later. Here is the problem as submitted by Craig Whitaker to Marilyn von Savant's column in PARADE magazine: 

Suppose you're on a game show, and you're given the choice of three doors. Behind one door is a car, behind the others, goats. You pick a door, say #1, and the host, who knows what's behind the doors, opens another door, say #3, which has a goat. He says to you, "Do you want to pick door #2?" Is it to your advantage to switch your choice of doors?

The answer is yes! I will not take the space to explain why, but you can see this -- and the humiliation of numerous mathematicians-- on Marylin's website here

And that is about it for chapter 3. I will keep you up to date with what else I learn in this book




Oh I love it! Great work GLSEN!

Movie Aftereffect*: Valkarie


I left Valkarie feeling confident that I would do whatever it takes to get done whatever needs to get done. I was very sure. Very deliberate. I was dedicated. I remembered the aftereffect for Milk and saw how they connected. It lasted for about 40 minutes before it started to fade. It was mildly diluted by an hour and a half. As usual, the television did a fantastic job of distracting me from everything and contributed to the dilution. It was still there when I went to sleep and was gone in the morning.

Cognitively, I was curious about what actually happened and who the people in the plot really were.

*Movie Aftereffects: After seeing a movie, I am always left with an aftereffect, a change in my perception and interaction of and with the world. I may leave the cinema feeling ready to inflitrate MI6, save the world, or solve a mystery. These changes in cognition vary in intensity and last for varying amounts of time.

I am officially announcing my move from Firefox to Chrome. I am trying to move toward improved efficiency and fewer distractions. While I love Firefox and its many add-ons dearly, I don't have the RAM or time to spend on my glutenous usage of Firefox (I typically have at least eight tabs open at a time, one of which is a stumble upon dedicated tab). My next post will be from Chrome.

NOW USING CHROME

Reading Update:
The Drunkards Walk by Leonard Mlodinow









I am up to chapter three and I have learned very little and read a twenty page review of the first quarter of a statistics class I took. Here are the first two chapters in summary.

Chapter 1:
  • The right side of your brain is 'intuitive' and always tries to find heuristics
  • The left side of your brain is 'logical' and always tries to find patterns
  • If two events are occuring randomly and event 1 occurs thrice as much as event 2, in guessing which event will occur next, you will be correct more often if you simply choose the event that occurs more often everytime.
  • Praising a person for good behavior is more effective than punishing people for bad behavior
  • This can seem counter intuitive due to regression toward the mean; that is, after someone does much better than they usually do, it is natural for them to do about as well as they had been doing before that accidental success, the same goes for accidental mistakes.
Chapter 2:
  • This is a review of probability rules
  • The probability that two events will occur can never be greater than the probability that each event will occur individually
  • You can predict the probability that two events will occur by taking the product of the probabilities of the two events ONLY IF the two events are completely independent of each other.
  • The probability that, given an event with multiple different and possible outcomes, the probability that one outcome or another outcome will be the result is the sum of the probabilities of two potential outcomes (assuming that the sum of all of the possible outcomes is 1 [100%])
  • When making a point about the potential outcomes of an event, make sure you are looking at the correct proability.

Things it is not:

Saying "Merry Christmas" instead of "Happy Holidays"
Giving gifts
Giving to charity
Being Christian


Things it is:

Only assuming that all white people that do not 'look Jewish' celebrate christmas
Only saying 'happy holidays' around the 25 of December
[obvious] Having the 25 be a national holiday and not have ANY OTHER RELIGION recognized
Thinking about others only at this time of year
Thinking about 'the poor' as if they are not human
Millions of people excluded from identifying with our consumerist culture who's advertisements focus on christmas celebrators

I have chosen to minor in Peace and Social Justice, a minor that was created last year. I have now taken two classes that count toward it, one is Nonviolence in Action and the other is Intergroup Dialogue* Facilitator Training. I am most interested in talking about the prior. As a class, we noticed the lack of support or importance placed on us by the university considering we did not have a room for the 50 of us to occupy. We ended up having class in large lounge of the residence hall attached to the union.

...I have a paper to write, so I am cutting this short. Really short. All I wanted to say was that there is not a wikipedia article on it and I am in a bit of a wikipedia editing craze. I am trying to revamp the article Nonviolence, which means I also need to edit Nonviolent Resistance (Don't even get me started on this one), Pacifism, and several other articles with similar ideas. I also want to fix Social Justice and make an article for Intergroup Dialogue. Anyone want to help?

paper time.....less than a week left


*P once said the 'dialogue' sounded pretentious. Maybe it is, but there is a definite distinction to be made between debate, discussion, and dialogue. Dialogue is a particular kind of communication that is supposed to be the ideal learning conversation. When a group of people are in dialogue, members of the group are open with each other, take personal risks, share their social identities, seek understanding, etc. The term dialogue is used to convey a very specific kind of interaction. See "Intergroup Dialogue in Higher Education : meaningful learning about social justice" by Ximena Zuʹñiga, et al. I will loan it to you if you want it.

I had a thought:

A good way to get word out about a cause is to be innovative for the sake of being innovative. Be the best at something: design, use of color, whatever. That way, the message will be spread not only for the sake of spreading the message, but also because it is amazing at whatever it is the best at. Problem I foresee is that the message will be lost in the hype of things. Example of this working. AIDS slogans at baseball games: visuals to come

Time to tutor more.

Update (12/27/08): Here are those pictures I promised:







A Revolutionary Primer

There is never enough time.

And as many people are eager to advise use, time is the thing we have the least of. I decided that it would be more beneficial to write my initial thoughts on student movements and national movements before I did any more work.

I finished reading an article about the Black Panther Party that discussed the history, goals, effects, and downfall of the party. Intrigued and edified, I did a little bit of research on another group that was mentioned in the article: The Students for a Democratic Society (SDS). At first, I was rather excited as I expected to find a strong student movement that was making significant progress towards change. One that had a large membership of student activists who worked as a nationally cohesive team towards progressive ideals. One that I just happened to miss these past twenty years.
What I found instead was disheartening to say the least. The SDS has fallen from the position it once had as an affiliate of the Black Panther Party. No longer does it carry a voice that can be heared on college campuses around the country. To me, it looks like almost every other student movement and organization I have seen. A short burst of activity and membership that withers as younger members lose interest and older members graduate.

Perhaps I am exaggerating a little. Apparently, in January of 2006, the movement to revive the SDS began. It looks to me that it lasted about a year. While it hasn't been around for very long and I can already see it start to fade, I am impressed with how far it has come.

ow that I have procrastinated enough on this by getting distracted doing other things I must retire from writing this miniscule primer.

Goodnight.

Because I have never remembered this poem:

The Hollow Men

I

We are the hollow men
We are the stuffed men
Leaning together
Headpiece filled with straw. Alas!
Our dried voices, when
We whisper together
Are quiet and meaningless
As wind in dry grass
Or rats’ feet over broken glass
In our dry cellar

Shape without form, shade without colour,
Paralysed force, gesture without motion;

Those who have crossed
With direct eyes, to death’s other Kingdom
Remember us — if at all — not as lost
Violent souls, but only
As the hollow men
The stuffed men.

II

Eyes I dare not meet in dreams
In death’s dream kingdom
These do not appear:
There, the eyes are
Sunlight on a broken column
There, is a tree swinging
And voices are
In the wind’s singing
More distant and more solemn
Than a fading star.

Let me be no nearer
In death’s dream kingdom
Let me also wear
Such deliberate disguises
Rat’s coat, crowskin, crossed staves
In a field
Behaving as the wind behaves
No nearer –

Not that final meeting
In the twilight kingdom

III

This is the dead land
This is cactus land
Here the stone images
Are raised, here they receive
The supplication of a dead man’s hand
Under the twinkle of a fading star.

Is it like this
In death’s other kingdom
Waking alone
At the hour when we are
Trembling with tenderness
Lips that would kiss
Form prayers to broken stone.

IV

The eyes are not here
There are no eyes here
In this valley of dying stars
In this hollow valley
This broken jaw of our lost kingdoms

In this last of meeting places
We grope together
And avoid speech
Gathered on this beach of the tumid river

Sightless, unless
The eyes reappear
As the perpetual star
Multifoliate rose
Of death’s twilight kingdom
The hope only
Of empty men.

V

Here we go round the prickly pear
Prickly pear prickly pear
Here we go round the prickly pear
At five o’clock in the morning.


Between the idea
And the reality
Between the motion
And the act
Falls the Shadow

For Thine is the Kingdom

Between the conception
And the creation
Between the emotion
And the response
Falls the Shadow

Life is very long

Between the desire
And the spasm
Between the potency
And the existence
Between the essence
And the descent
Falls the Shadow
For Thine is the Kingdom

For Thine is
Life is
For Thine is the

This is the way the world ends
This is the way the world ends
This is the way the world ends
Not with a bang but a whimper.

-
T.S. Eliot

‘The Stone Age didn’t end because of a shortage of stones.’

My Problem with 'avian' and 'swine' Flu

I really dislike the term "Swine Flu". Let's do a quick review on Influenza. There are many different types and strains of the virus, but the type that we are always referring to is Influenza A (They strains vary by the make up of certain proteins eg H1N1, H2N5, etc.) . Some of them are specific to different animals including birds, pigs, and humans. The virus can mutate one of two ways. It can have random error in its replication, or more than one strain of the virus can infect the same individual and they can mix together (reassortment). So let's say there is a pig specific flu going around in the pig community, but it isn't too bad--little piglet ts only need to stay home from school for a day before they get better. There is also a human specific flu going around in the human community that has a similar effect on little kids. These two flus aren't too bad because each population has their respective immunities. One day, a human with human flu sneezes on a pig and the pig is able to catch it. Then, her piglet comes home from school and gives her pig flu. The two flus undergo reassortment and make a new hybrid that can be spread to humans. Farmers Jane and John both die because they have no immunity. Now that you know how influenza works, please realize that the 1957 flu could have been called "duck flu" and the 1968 could have been remembered as "swine flu". My point is that one cannot label a flu by the animal it originated from because it is misleading. When you say "swine flu" one thinks you mean that a pig has the flu.

My Trip into the World of Calculus

For a long time, Calc has been a mystery to me. It has been referred to and talked about all around me; I feel like I have been missing out. For years, I have wondered what it is all about. The time to learn is now as I am taking Calc I at Eastern; although, I am beginning to wish I learned it on my own due to the disjointed and illogical nature of my lecturer. In an attempt to help study for what may very well be extremely easy quizzes (and to help me rationalize paying for and spending my entire mornings getting to and from this class) I am going to re-explain what we have done.

After 6 hours of class, this is what I have come up with:

First thing is first: Limits

Day 1: Say we had a function f(x)=x^2 (please note I am pretending by using the picture I found on google. Just pretend it is a parabola). At any point, we could say that as you approach any given value of x (lets say 2) you also approach the corresponding value of f(x) (in our case, 4!) That number is said to be the limit of a particular function as x approaches ___ (for us it was 2).
This is important because you need to use it when you want to find the equation for a tangent to a curve. Great. (The only practical example was when it is applied to mechanical physics in which they use the word 'velocity' to mean instantaneous velocity which bugs the senial-grandma-hell out of me.)

We are first going to find the slope then use the point-slope equation of a line to find the equation of the tangent. To find the slope of this tangent, we are going to find the slope of a secant whose pair of points includes the point from which we are drawing the tangent (P) . Slope is the change in values along the vertical axis divided by the change in values along the horizontal axis. rise/run (rise over run). Lets write that again replacing the words with variables corresponding to the two items we have. What do we have?
We have:
A curve
A tangent line
A secant line

The difference along the x axis is delta [x] and the difference along the y axis is [f(x+delta[x])-f(x)].
Therefore, rise/run is:





This equation gives the slope of any secant line; all one needs to do is fill in the variables with numbers.

Finally, we apply that thar limit thing to this. What we are trying to do is make the delta [x] as small as possible. In other words, we are going to make the point that is NOT the one we are finding a tangent on (Q) infinitesimally close to the one we are using (P). We do this by using a limit to say that as the difference between the x values of those two points gets closer to zero, our output of the equation will get closer to the slope of the tangent. Equationally, it looks like this:



Problems will consist of a given function, lets say x^2, and the point to which we would like to make a tangent, (2,4) for us because it's easy. So let's plug stuff in:





here, Xo was replaced with the x value of point P (2,4). Easy enough.







Now we know that f(x)=x^2 is the rule used to create the curve in the picture. In the equation, we choose another point by saying we are going to apply the function to the 'number' Xo plus some variable distance (written as Xo+Delta[x]). In this step, we plug that 'number' into the function to get (Xo+Delta[x])^2. We also replaced f(2) by what we know is the answer...4!

Now we simplify! We are going to end up with a squared Delta[x] plus four delta[x]s, no 4's all over a delta[x]. Extract a delta[x] from the numerator and cancel to get this:




Now that everything is super simple, we can directly substitute the number that delta[x] is approaching (ZERO!) for delta x and what are we left with? The slope of the tangent line, which is 4!

Plug that slope into the point-slope form of a line along with point P to get



simplify to get the equation of the tangent line:



That was day 1. Yay.

Day 2: A few additions on yesterday's material about limits.
*A function may jump around (graphically) allowing it to have several limits that may seem counterintuitive at first. A function can have a limit on a part of the curve that approaches a number that it does not reach. For example, a curve may approach 3 as the x value approaches 1, but not include it. In fact, the value that is being approached does not have anything to do with the actual value at that point (in our example function, 1 may correspond to 4,321.7).

*Limits can be viewed as approaching from the right or from the left. If the limit of a function approaching from the left is different than the limit approaching from the right, the limit (not from a particular direction) is said not to exist.

*These are things you can do to limits:




















*It is possible for limits to approach infinity in either direction

Thats it for day 2...I had a half page of notes >.<

Day 3: Repeat Day One.

Ok, I bet you are all wondering how we did everything on day one! Well, we didn't. We used a different equation to do it...or something rather. Also, I did not feel like moving everything after I typed it, so it is going to stay where it is.

That's all for today. After all of that, I am going to be mad if I don't do well on this quiz. Also, please leave a comment and correct me if I screwed anything up...thanks.

Happy 20th Birthday to Me

I bought a bike!!!!


My Emo Heart is Crying at My Inability to Perform as a Real Person
current mood: Like Stephen Colbert blogging after not being invited to the Bush child's wedding


I have decided that it is time for me to become a real person and do real person things. I was partially inspired by this recent encounter I had with a friend of a friend that works at the Espresso Royal on State St.
I walked into Espresso Royal looking for cream, sugar, and cups. I was going to brew coffee the next day for my co-workers as one of them was giving me a ride and we were leaving at an absurdly early hour in the morning. The hour reserved only for people who workout before work and high schoolers involved in almost any extra curricular activity. My friend was working; she introduced me to her friend an co-worker by the same name. I hate to mooch off of my friends by using their employee status to give me discounts or free things; however, in this case the friend of a friend insisted. She had graduated and was getting a job in New York. She put it like this: "I am leaving to become a real person."

To begin my own quest on becoming a real person, I am making what seem like significant life choices , I am pretty frustrated at what is going on with my summer plans. I was planning to take online math and physics courses at EMU. Well, after an excruciatingly long and embarrassing phone advising appointment--phone advising appointments were created for people living out of state...I am just exploiting the system-- I have found out that I did not do enough research. As it turns out, there are no math and physics online courses and I will be commuting if I want to take them. As it turns out, I am a guest student, not a transfer student (that was the most embarrassing of my lack of research). (**I am sure that I have some form of ADD. This is not one of the things, I just wanted to excuse myself for what I really wanted to say which is that I just noticed that I push the space bar predominantly on the right side, judging from the wear of the coating on the key itself. Now that I am cognizant of it, it appears that I push it mostly with my right pointer finger. I feel to constrained if I leave my hands in one place, I like to move them around a little when I type...plus, my hands get sweaty if I rest my palms on the laptop.**) As it turns out, both the physics department and the math department require absurd prerequisites before I can take the classes I want: Calculus requires a college level Trig class (despite the fact I have taken an all encompassing pre-calc class at UofM). And as it turns out, I have to file at least three forms before I can even begin to enroll for summer semester as I gave up on Spring semester and I do not want any more fees. Oh yeah, and as it turns out, I don't like being wrong so you can imagine how I taste about all of this. Bitter, Salty with a hint of parsley...paltry I mean.
I do believe I made the right decision in dealing with this problem, I pushed my plan of action several weeks into the future. This gives me a little time to sort things out and not look like a fool. Along the lines of looking like a fool, I acted on what some would consider a foolish whim and bought a 1940 Royal typewriter for $26.50. It is in pretty good condition and everything works but the ribbon, of which only a fraction is usable. I have already used it to write on two page letter that I finally sent today to the Finlandian. At this point, I must make it known that as I write I lose energy and stop caring about what I am writing. This entry is just about done anyway; I have one final thought.

Manual automobiles, rather the drivers of manual automobiles, get automatic bonus points on my sexy scale. As much as I dislike the use of petrol, and most cars do still run on petrol, I can not deny the attraction I have to a man that can drive well. One that will have an engaging and interesting conversation with you in his luxury vehicle while driving back from the modern, upscale, yet eco-friendly vegetarian restaurant you just had dinner. He flawlessly shifts the well insulated car from gear to gear and while all you hear is the light jazz from the radio and the words coming out of his mouth occasionally accompanied by a muffled roar from the engine. HOT.

Now I should go do something to further my life as a real person. I may go to the bike shop and look at some bikes.

Summary
-----------
I am working on becoming a real person
I dislike being wrong
Typewriters are fantastic
The drivers of manual vehicles are way sexy

"We are not supposed to have a dominion. If we have anything, we have the responsibility." - Morgan Freeman

On a completely unrelated note, I have decided that I have trouble doing things regularly. It seems that events in my life haphazardly place themselves into some sort of order without anything but my suggestions as to where they might fit best.

Over this summer I plan to try and accomplish several things at once by improving in a to be decided skill (hand writing, literature, studying, etc.) at a specific time everyday. As of now I operate completely without routine... this will be an experiment in will power. Soon I will make a time line of the plan; I will also have to choose a skill to improve. If I am completely indecisive I can change skills every month or so, or choose 4 and rotate every week, or I could choose a few and rotate daily, or I could choose a few and devote a majority of the alloted time to one while still finding a way to practice a smaller amount of the others (eg if the alloted time is 2 hours, spend 1.5 hours on the major component of that day and 15 on the other two). The last option could have many different variations to it.

In any case, I need to ensure that I have enough will power to initiate this.

since feeling is first
who pays any attention
to the syntax of things
will never wholly kiss you;
wholly to be a fool
while Spring is in the world

my blood approves,
and kisses are a better fate
than wisdom
lady i swear by all flowers. Don't cry
--the best gesture of my brain is less than
your eyelids' flutter which says

we are for each other: then
laugh, leaning back in my arms
for life's not a paragraph

And death i think is no parenthesis


e.e. cummings

When I speak to people who are steadfast in their beliefs and points of view, I have mixed feelings. I refuse to hold a belief so dearly, to have a position so unmovable that few things are capable of making me change my mind. That is just ignorance to me. There are few instances in which one can know absolutely everything about a given topic. Every detail, every person involved, every circumstance. One should certainly have reason for their belief, but in very few cases is that reason thorough enough to warrant sureness.

A problem inevitably arises when putting beliefs into action. If one is completely sure of a certain belief, putting it into action is easy as there are not any other things they must take into account. For rational things, however, it is harder as there will always be things that one has missed one way or another. The solution? Be able to either modify actions and policies or make up for mistakes.

I want to edit this and write more...I will if I find the time

It's been a month....that was fast.

I get so excited with new things, but I'm afraid I get bored to quickly. This has been most prominent with jobs, jobs that I really enjoy, but I feel like its the same thing over and over and it isn't fun. Should it be? Is that what work is for? Can it be? I try to find ways to make it new and exciting to me. New variations, new attitudes, new people.
Thoughts?