New Year’s Resolutions

1. Discipline… need to finish things that I start. This includes programming projects, assignments, blog posts, photos, etc.

2. Research… get some. Whether by URAP, by contacting professors/GSI’s, or by some other means, this is essential.

3. Maintain/Raise Current GPA… a high GPA will open the doors for many more opportunities in the future. Including getting a job in a tough economic environment, or getting into a good graduate school.

Will add more as necessary.

Idealized Unemployment

Unemployment sucks, let’s face it. We need the cash, so we need the work.

So let’s say you are going out and looking for jobs. What I am going to do is derive a limiting probability on how likely you are getting a job in this economic environment. This will be a heavily simplified idealization, but hopefully it will shed some insights. (This can also be generalized to applications of all nature.)

We assume that you apply to p positions/firms. For each firm, there are n applicants, each of equal merit and status, including yours. Each firm is going to only hire one person. For this setup the probability of not getting any positions is

(The probability of not getting any one position is n-1/n, and this is multiplied by itself p times since you apply for p positions – multiplication rule for probabilities. We assume that the number of applicants is the same for all firms, and that since everyone is equally qualified, the firm draws straws to choose who gets the job, so it’s completely random.)

Now let’s say you are desperate, and so you apply to many many many jobs. So is everyone else, so each firm gets many many many applications from everyone. Again we assume each application is equivalent. At this point, when both n and p become very large, their difference becomes negligible, so pn. Substituting n for p and taking the limit of the first equation as n becomes very very large yields the following expression:

This should be a familiar limit to anyone with calculus experience, and its value is 1/e, or around 0.368. In other words, you have about a 63% chance of landing a job. Not bad for if the chance of landing a single job was nearly zero.

The upshot is pretty interesting. Let’s say we have a country where nobody is employed. At once many entrepreneurs decide to build up businesses, each of which will hire k people (the generalized case, not just one), but since the population is huge in this country and nobody is educated or has work experience, the aforementioned idealizations still hold. If k = 1 then it is understood that each person has about 37% chance of not getting a job if everyone applies for every job. Put it in other terms, at the end of the day when decisions are made, 63% of the people have a job and the unemployment rate, people who don’t have a job, is 37%*. But now we look at the general case, and the probability becomes as follows:

This is striking in many ways. The unemployment rate goes markedly down if businesses hire more than one person. If k = 3 the rate drops down to 5%. When it is 6, the unemployment rate goes down to 0.24%.

According to the U.S. Bureau of Labor, the umemployment rate in November was nearly 10%. Broken down demographically, the statistics are as follows:

Among the major worker groups, the unemployment rates for adult men (10.0 percent), adult women (8.4 percent), whites (8.9 percent), and Hispanics (13.2 percent) edged up in November. The jobless rate for blacks (16.0 percent) showed little change over the month, while the rate for teenagers declined to 24.6 percent. The jobless rate for Asians was 7.6 percent, not seasonally adjusted. (See tables A-1, A-2, and A-3.)

So the question is why aren’t we reaching our idealized unemployment rate?

Well, first off, this is idealized, and the real data shows it. Not all applicants are equal. Some applicants are clearly more qualified, so they take the job; the less qualified candidate who had an equal chance in a random scenario sees his probability decreased in the real scenario. Some jobs are specialized so the unqualified candidate doesn’t have a rat’s ass chance of getting the job.

Second, some people are lazy and give up looking for a job after about 100 tries. The idealization requires everyone to try a very very very large amount of times.

There are other reasons I could expound upon but will not for the sake of brevity.

Still a nice theoretical result though, especially since we see the infamous e here again (which was the driving force for this post). I would argue that the idealized result is the best possible unemployment rate that can be achieved, which entails that unemployment, and all its evilness, can never be completely eradicated.

***NOTE: We ignore the possibility of one person getting two jobs. Let’s just say if one person gets a job from Company A and Company B both, he will reject one of the two offers wherehence the rejected company picks another candidate. In our scenario, the number of applicants is so large that the subtraction of one candidate has negligible effect. Later postscript: also note that this would be surely true if each person applies for a different set of jobs, which may be a more accurate model of what’s going on.
***EDIT #2: It might be hard to imagine unemployment issues when there are more companies/firms than people. It is also hard to imagine a “limiting unemployment rate” when an x number of firms can hire y amount of people and there are z people in the population. So with these stipulations let’s assume that
1) These ratios are ill-defined when the number of firms and number of people are truly infinite.
2) All probabilities are independent; each person applies to different firms where a large amount of people, let’s say of a different country, are also applying.
This should reduce some of the confusion. Many of my original points still stand, although I see some fault in my original country analogy now.

Jack of All Trades

A long time ago, I decided to look over my blog posts, and I realized that I am somewhat a jack-of-all-trades, but master of none. Kairos guys discussed this a while back and I was going to post on my blog about it, but it was delayed for a semester. I have basic knowledge in a lot of things – philosophy, economics, programming, football, a lot of the sciences; and I have more technical knowledge in a few other things – weather/tornado forecasting, photography, the roads and geographical layout of CA, chemistry, calculus, among others. But specialization? F that, even if economics argues that it is favorable for society.

But really, a lot of it… football, weather, photography, roads, and much of programming (which extends to stuff APCS could never teach me) is self-taught. And you know what: nothing short of amnesia can take that knowledge away from me. Which I think is pretty cool. I acknowledge that I am pretty dumb in many things, and I know many more who know a lot more, but I am thankful in the things I am knowledgeable in. I am reminded of people like Leibniz, Euler, Aristotle, among others, who excelled in mathematics AND philosophized ad infinitum. And then there was one guy who was basically good at everything – forgot his name just now. Plus that Chemical Engineering professor at Berkeley who contributed much in economic theory (featured in a Pimentel poster). They’re cool ppls.

On the flip side of course, I really do need to figure out what I need to do, regardless of what I said earlier. And as many do know, my Myers-Briggs indicates, and might I add very accurately, that I am afraid of the Opportunity Cost. And then specializing entails special struggles (whether it be not finding a job, failing at labs, not having research experience, bad GPA down the road, etc.). Gosh darnit, if money and GPA didn’t matter I’d just study atmospheric physics and theoretical chemistry with a side of fine art photography as my main college dishes!

Lol so where was I going with this post? Guess nowhere. Enjoy one of my few pseudo-succinct non-purposeful posts!

Semester-ly Review

As always, right on time. 😉 Well… close enough right?

I took four classes, all technical: Chem 3B, E45, BioE 10, and Physics 7B.

This semester was tough. I mean it was crazy. Immediately the semester starts and I run into relationship trouble with Vicki and depression due to lack of research experience. So I try for URAP, and get three interviews offered, but no positions in the end. Others who get only one interview snatch the job. I need to work on my interviewing skills… fml. But unrelated, I got a position as a yearbook photographer!

Things with Vicki got better but then I was struck with a sick illness on the day of the Grignard lab. This incapacitated me, and the coughing persisted for a month afterward.

Then the workload began. Work, work, work, work, work. I’m estimating that for every hour of a non-physics lab, I worked 1.5 hours on the associated lab report during the following week. On the worst weeks I would have a 3 hour E45 lab and a 4 hour chem lab = 14 hours of lab writeups. The E45 labs were the worst and a struggle for a mediocre grade; NMR in chem labs can just go die. On top of that, I had Mastering Physics, which took 2-3 hours a week (sometimes more depending on the amount of evil contained in an assignment), and BioE HW, which required me to stay up to 4 AM every other week.

So at this time I’m beginning to be thankful I didn’t get a URAP spot because I decided to start SPA work for minimum wage pay. Oh well, I need the money. And it was my first REAL job experience. But man getting up for work on Fridays at 8 AM – which was followed by lecture, lab, and Kairos Bible Study, reduced me to rubble. Especially after rough lab report weeks. Saturdays regularly featured 2 PM wake ups.

Subsequently I started failing the midterms (as in, below average scores) because I started taking shortcuts, i.e. neglecting physics, relaxing at Sierra Lodge and NOT studying the day prior to an E45 MT…

My social life was dead. I had no energy to talk and no time to hang out. My exciting weekends went away as I couldn’t muster a waking up prior to lunchtime.

But I wasn’t depressed anymore; I just didn’t have time for that. For that I owe thanks to my classes, as bone-breaking as they were.

I am also thankful for Pastor Ed’s “Thank You'” series of messages which for now have turned my life around.

November came and my workload died down a bit. I had time to relax for two weeks. But then it was crunch time. The last week of classes pinched me tighter than ever before. And then, FINALS. I studied like hell for them. It’s a beautiful thing how a few bad midterm scores can motivate you like nothing else. I tend to do best in those scenarios – like the Chargers. On the other hand, whenever I have A’s on my midterms, I let my guard down, and I get owned (MATH 54 GRRRR). The net result is an A-/B+ net average. Whatever.

So of course, I ended up neglecting one class I felt good with – chem, after starting out strong in studying and switching my mindset completely to physics. That was a mistake. I haven’t checked my grades for that class, but I don’t think they will be pleasing to me.

The pace of this piece feels fast, as it was a fast semester. But I certainly learned a lot. I learned how to allocate my time efficiently. Compared to prior semesters, I feel like mastered finals (maybe not grade-wise, but in other ways)… with the exception of chem. I learned to be thankful of treasures and not to be bitter about the misfortunes, and I learned how to coexist with roommates. 😀 I sank to rock bottom, picked myself up, and received forgiveness. And in the process, found myself. And surprisingly on the last day I was surprised with another gift, which I will not divulge for now, but I can owe it all to Nina’s drunkenness (if she even reads this blog).

So as usual, I conclude with notable quotes from professors:

VOLLHARDT (CHEM 3B): “The whole melange”; “it’s like the Battle of Hastings”; “x reagent is HOT”

ZETTL (PHYSICS 7B): “They told me not to do this but” … subsequently does it

GRONSKY (E45): “For all you engineers…”; “you might want to consider x in your engineering profession” (alas, I am not an engineer though)

KUMAR (BIOE 10): I fell asleep in this class.

Future posts: traffic lights (?), probability, studying equation pt. 2, jack of all trades

What to Study? In the Final Exam Mood…

It seems all too often that we get tangled up in a myriad of potential subjects to study, and in the process, spend more time deciding than actually studying. At least, I know for myself, the concept of the opportunity cost scares me.

So tonight, Vicki was asking me what she should study. And though I was reluctant to answer at first, I eventually formulated a solution. A mathematical solution. (This following formula will be slightly different from the one I gave her, but the general idea will be the same.)

Let’s define a calmness C, inversely proportional to urgency U, which will determine what you should study and what you can hold off. In other words

Now what could calmness, expressed as inverse of the importance of studying for a certain class, be parameterized by? So let’s brainstorm:

-Amount of knowledge you have now. Let’s called this K.

-Amount of studying you have already done. Let’s call this S. This may not matter much if K is small, but you’ll feel more calm and that may make an impact on exam day.

-Time between a set time t0 and time of exam te. Let’s just allow t0 to be 0 (“now”), and te to be t.

The probability that you will study a given subject when you say you will study it. Let’s call this P(S). Let’s face it. If you hate the subject you will spend half of your time “studying” on Facebook. For now, I will ignore this term because this has a sort of time dependence. We’ll assume that this factor is included in dK/dS, described below; in other words, studying will be done no matter what, but it will be done slower. (Actually, I’m ignoring it because I forgot to put this factor in my original equations.)

Rate of knowledge acquired per unit time studying. In other words: dK/dS. Some stuff is just hard to learn. Other stuff is just boring to learn. If you know you won’t learn much in 4 hours of studying, you will likely not spend those 4 hours studying! So this factor is INVERSELY proportional to the “calmness”, or proportional to urgency.

-Grade increase per unit knowledge gained, dG/dK. In some classes, the final is so ridiculously easy that you can know almost nothing and still get a decent grade. In others, the final is so ridiculously hard that you can know almost everything and still bomb the test. So this factor is also INVERSELY proportional to the the “calmness”, or proportional to urgency.

So then, how can we express U? There are two ways. I will express both.

1) As the product of the parameters:

or, alternatively and more conveniently,

The advantage to this is you can see some interesting trends. For instance, the knowledge now matters, but possible knowledge to be acquired during the study process (i.e. dK) does not show up in the formula. Rather, the grade increment per unit studying takes precedence. Which begs the question… do students really care about what they learn, or do the ends of a good GPA justify the means?

2) As a weighted sum (linear combination) of the parameters:

(Note that to be inversely proportional, the last two weights will have to be negative. Alternatively, one can write the last two variables as (dK/dS)^-1, etc, but I’m too lazy to update equations. We’ll assume we can have negative numbers in this formula.)

No way to reduce this into an elegant, self-explanatory form, but the advantage here is any individual can choose to put different weights into the different parameters, weighing them more heavily relative to other parameters. This may be the more practical formula for the confused individual deciding what to studying. And, it’s linear, so that’s kinda nice.

So now, off to more finals studying!