Tag Archives: math

The Daily View: Math Resurgence, Economic Growth, Student Loans

The Math Revolution:The number of American teens who excel at advanced math has surged.

This agree with earlier posts I have written countering the commonly held belief that America is ‘dumbing down’, when in fact it may not be. It also agrees with posts about the rise of ‘nerd culture’, and how STEM skills are increasingly valued both culturally and economically in our new economy. It’s the tyranny of the bookish, of smart people pulling ahead as everyone else struggles with a perpetually anemic labor market, stagnant home prices, and falling real wages. Math and code are the new ‘scriptures’ of modern society and economy, with mathematicians, philosophers, physicists, and economists the new ‘priesthood’. More and more young people are studying code and symbols, much like Bible readings, as a way to salvation, except not an intangible one, but one measured by higher wages and more respect.

Interestingly, on Reddit and 4chan, English, History, and Philosophy majors are also respected, too, as they sacrifice monetary gains to pursue a ‘higher’ calling. Such degrees, even though they may not pay very well or have immediate real-world applications, are a solace of intellectual purity, patience, and understanding in a society spoiled by instant gratification, ostentatious materialism, low-information pandering, and sensationalism. Both STEM and some liberal arts (not the useless ones like child development or gender studies) combine authenticity, sufficient intellectual rigor, introspection, and abstractions. For the math major such abstractions include axioms, postulates and theorems; for the literature major, it’s words and grammar; for philosophy, it’s ontology and epistemology. ‘Low-information’ means not circuitous enough, too obvious.

Related: The Writer and the Coder

However, the article notes that in certain aptitude tests America scores low compared to foreign countries:

Only 40 percent of fourth-graders and 33 percent of eighth-graders are considered at least “proficient.” On an internationally administered test in 2012, just 9 percent of 15-year-olds in the United States were rated “high scorers” in math, compared with 16 percent in Canada, 17 percent in Germany, 21 percent in Switzerland, 31 percent in South Korea, and 40 percent in Singapore.

The problem is these studies lump Americans, who are ethnically and culturally diverse group, with homogeneous countries. It would be more accurate to compare Singapore-American students to native Singaporeans, German-Americans to Germans, or Korean-Americans to native Koreans.

The Next Big Idea in Economic Growth

Yet corporate profits, stock prices, & earnings are still at or near historic highs. It would seem like the private sector has adjusted just fine to anemic GDP growth, and investors are not too concerned.

This story is going viral: Arrested for student loan debt

Believe it or not, the US Marshals Service in Houston is arresting people for not paying their outstanding federal student loans.

Paul Aker says he was arrested at his home last week for a $1500 federal student loan he received in 1987.

He says seven deputy US Marshals showed up at his home with guns and took him to federal court where he had to sign a payment plan for the 29-year-old school loan.

But fed. student loans are still at taxpayer expense and students should bear some responsibility for majoring in low-ROI subjects, taking on too much debt, or not understanding the terms and conditions of the loans. There so so many forgiveness and deferral programs that student loans are seldom paid in full, anyway. It’s often dragged out forever as in the case of Paul Aker, who had the ability to pay but refused to. Harsher penalties, including but not limited to jail time, are necessary for a system that is broken mainly against taxpayers.

Credentialism is another problem, as well as too many low-IQ and immature student being encouraged to enroll in college despite the high drop-out rate. Another problem is the perpetually anemic labor market.

Vox asks, if banks got bailed-out, why not students? The problem here is that student loan debt (at over $1 trillion) already exceeds the bank bailouts, and debt forgiveness will only add to the problem. There is no systemic risk in having some students default, but there is potential systemic risk if key financial institutions fail. As recently as 2011, TARP was paid in full and as of 2014 posted a profit of $15 billion, making it one of the most successful government programs, even if the most despised.

I support financial aid for students who have the cognitive aptitude to complete college (without dropping out), as well as majoring in a high-ROI subjects, but the system we have now just throws money out indiscriminately to students who shouldn’t be going to college, who will dropout with nothing to show for it but debt.

Related:

Some Ideas to Reform Higher Education
Improving Obama’s Community College Plan

Functional Stock Market Theory

The idea is that the stock market can be described through a functional that is constrained by endpoint conditions depending on characteristics of the stock or market, such as volume, duration, and geometric factors.

The theory borrows some concepts of relativity, but is simpler because the stock market occupies a single spatial dimension instead of three.

The results can explain why certain symmetries and patterns in the stock market exist. The modeling of discrete buy and sell orders has applications for option pricing.

General Theory

Single Solutions

The second is still a work in progress

STEM vs. Liberal Arts: Which is Harder?

The essay Who’s the alpha male now, bitches? got me thinking – not about the subject matter of angst-ridden young adults and mass shootings, but the inimitable eloquence of the writing style itself. The precision and skill of how the words were chosen and arranged to make the essay informative yet galvanizing.

So, is STEM easier or harder than the liberal arts? The online opinion seems to skew in favor of STEM being harder, but it would be nice to have an official academic study about this. Another, perhaps related, question is: which subjects are perceived to be harder? For student who found high school easy and got good grades, which subjects are they more likely to major in college, versus c-grade high school students. I imagine students who perform poorly in high school, once in college (assuming they go), will choose subjects they perceive to be easier. If c-grade high school graduates are choosing STEM in collage, and a-grade high school graduates are choosing literature, philosophy, and history, then STEM may be easier. And then you would have to look at the graduation rate and GPA. If c-grade students who major in STEM outperform c-grade students who major in liberal arts, it would further lend credence to liberal arts being harder.

Although the data shows the humanities have a higher GPA than STEM, this does not necessarily prove the humanities are easier:

Major Average GPA
Education 3.36
Foreign Language 3.34
English 3.33
Music 3.30
Religion 3.22
Biology 3.02
Psychology 2.98
Economics 2.95
Engineering 2.90
Math 2.90
Chemistry 2.78

It could be that all the a-grade students are flocking the the humanities, while the c-grade ones go to STEM. The a-grade students, possibly being smarter, get higher grades than the c-grade students.

If SAT scores are a good proxy for high school performance and IQ, we would expect low-scorers to major in ‘easier’ subjects:

Interestingly, literature, social science, and linguistic majors have as high of SAT scores as most STEM majors. Although math and physical sciences rank among the highest, the difference isn’t substantially higher than that of the literature majors. The major ‘liberal arts’ is only four points lower than biology. The study also doesn’t tell us the completion rate, only the choice of major.

It’s also been observed that the verbal sections of both the GMAT, ACT, and SAT are harder than the quantitative sections, with top verbal scores being much rarer than top math scores, although this can be attributed to the verbal sections having a higher ‘ceiling’ than the math sections.

One possibility is that the threshold to become ‘good’ at math is lower than to be ‘good’ at literature and writing. Maybe it’s easier or more attainable for your typical high school graduate to grasp advanced calculus and special relativity than, say, publish an article in the New Yorker.

Perhaps STEM is more inclusive than liberals arts. It seems there is a sort of pretentiousness in liberal arts, especially with literature and the divide between ‘low-brow’ and ‘high-brow’ tastes. Another question is, how do you define ‘hard’ and ‘complexity’; what makes a subject ‘complicated’? Is it the number of things you have to memorize, the quantity of reading, the synthesis of information? STEM may be easier because usually the only thing that matters is the correct answer or outcome, not the ‘prettiness’ of the underlying mathematics. Whether you pass or fail depends on your ability to product correct responses to technical questions, not necessarily elegant responses. The liberal arts, especially writing for publication, requires not only a unique perspective but the ability transcribe your ideas into prose that is grammatically correct and enthralling to the editor and reader. It’s like imagine in math you not only have to produce the correct answer, but are restricted to a certain set of symbols in your derivation, but, on the other hand, some STEM problems are very difficult.

The Truth? They Can’t Handle The Truth

As evidenced by the down-votes for this Quora answer to the question How Does One Become a Mathematical Genius, many people wish to live in a world where either IQ does not exist or, if it does, it doesn’t measure anything important and is of no predictive value for success at life. It’s easier, perhaps more comforting to create an alternate reality than confront our existing one. According to the biographies I have read, all mathematical geniuses displayed precocity – maybe not directly in mathematics – but all were very talented from a very young age. It’s not like you can be a dull 20-something with no outwardly obvious signs of intelligence and, then suddenly, through ‘deliberate practice’ transform into math genius, sorry. Although I’m open to the possibility of being wrong, I don’t don’t think its possible to be a math genius with less than a 120 IQ or so. Of course, the word ‘genius’ can be subjective, but if you need an IQ of around 100-115 to at least graduate from college, I imagine you would need a much higher IQ, still, to become a ‘mathematical genius’.

Ongoing Research

For the handful of people who visit this site, I try to cultivate a unique experience for the reader. You may not agree with much – if any – of it, but at least it’s unique. One assume my interests are limited to fringe ideologies, but I also have a fondness for mathematics. Last year I tried to create an option pricing formula under the assumption that the stock price is not permitted to fall below a certain level. The results are mixed in that it’s purely theoretical as such a situation will never arise in real life, and an option pricing formula is only useful if one assumes that quoted option prices can somehow be improved and or are wrong, a view that would go against some efficient market theories.

However the audience for math is even smaller than for neoreaction and rationality. It’s pretty much nonexistent. Another problem with math is that pretty much everything, no matter how obscure, has been found. You can always write something from a new angle or come up with a new top-10 list, but math concepts require considerably more research. Recently developed new infinite series for calculating the circumference of an ellipse, that is very fast and works for all eccentricities. Since James Ivory and Gauss – Kummer’s hypergeometric series and Arthur Cayley’s log series for eccentric ellipses, to the best of my knowledge no further non-trivial (non trivial I mean by not iterating the elliptic integral or truncating an existing hypergeometric series multiple times) infinite series have been recorded. I derived the first of these new formula in 2009, visiting the problem in 2015 and found some errors that I resolved: https://en.wikipedia.org/wiki/User:Ellipseformula/sandbox

I try to put the same attention to detail and accuracy in these posts as I do in math. So if what I write seems wrong to outsiders, I’m still usually right – sometimes it’s just a matter of time before I’m vindicated. The skills in mathematics can be applied indirectly to analyzing news and events by filtering out the noise from the signal and arriving at the correct conclusion – just as you would arrive at the correct answer in a math problem. But I have been patently wrong on a few occasions, and that is part of the process, too.