Friday, March 31, 2017

More Through Less

ROI. At Freakonomics.

Wednesday, March 29, 2017

Tuesday, March 28, 2017

Saturday, March 25, 2017

Friday, March 24, 2017

Learning How to Read Again

The reason I started taking math courses in the first place was to learn how to read so that I could learn how to learn. Which is to say, I didn't know about the stuff around me. So I tried to read about stuff. And the books and articles that talked about that stuff had more math in it than I could understand.

Every now and then between classes, I go to the library or search databases to read about that stuff and see how I'm progressing. Firstly, it's interesting that I had a hard time finding the things I originally did. A few years ago, when I was trying to read about infrastructure, energy, society, nutritional studies, and similar things, math eventually, repeatedly, became my roadblock. It's a bit harder to go the other way around. When looking for mathy journals and articles that relate to the stuff around you, it's easier to find things that fit within the designated category right away, but harder to find source material that you'd probably be able to adequately comprehend any time soon.

I guess the eventual goal then, is to funnel things down to journals and sources that cover topics I'm interested in, but still use math to explain that stuff. There are definitely some exceptions. But the math-first stuff will need to come later.

In the past couple months, I've learned a few things like:
  1. Thank God I took pre-calculus (same goes for Algebra)
  2. A lot of these fancy symbols are stand-ins for whatever the writer wants them to mean
  3. Stay away from physics journals until you really know your shit
Pre-calculus was worthwhile because it covers a good deal of the stuff you'll find in books and journals like "Mathematics of Electronics" (actually for electronics, it definitely helps to have taken some linear algebra as well), "Traffic Congestion," "Energy Basics," "Mathematics of Agriculture," (not necessarily actual titles of the books I read, but relevant to what I've skimmed through) etc. Because when I look at equations, instead of seeing some foreign language, I can see how the particular function, scenario, street corner, input-ouput, social trend, physical condition, etc. is expected to change over time based on how the equation is structured.

Something as fundamentally simple as comprehending an equation with a negative exponent used to be a challenge for me. Yes, like 8x *10-5x. Now I just see 8x * (1 / 105x),  or 8x / 105x, which is to say as x gets larger, the result gets a lot smaller very fast.

Very simple. But it was a road block for me nonetheless.

Still, those are just the books you find in the library. It's the journals that seem to have an abundance of crazy-looking symbols and figures that read like a language from some other dimension. It turns out that in a significant number of the journals, it's sometimes explained what these symbols mean. So if you know some things like (a) a subscript attached to the right of a normal looking letter (think capital Z) often represents a function (the Z) based on a parameter represented by the subscript, or (b) what a function might look like, it doesn't look nearly as intimidating.

It's not that I can understand all the stuff in these journals. It's that re-reading them at this point gives me the confidence that I'll eventually be able to get a grasp on much of what's in them.

It's when understanding of all these symbols and relationships are implied that things get more difficult. When there's a common language and understanding of mechanics that you weren't part of prior to reading what's in front you. That's physics journals. I can't even begin to know what the hell they are talking about (not that I expected to). It may take me years to get to a point where I can comprehend them. Maybe not even then. But that's not why I started anyway. Still, I'm intrigued enough to eventually want to get there.

All that brings me back to the classes I am talking now.  Calculus is the most obviously useful.  It's used a lot of places. And it reads and feels like mechanisms in motion, just the way things in the world around you do.

My calculus teacher likes to say "math is a language." And of my current classes, nothing is more representative of the saying than discrete math. It looks and feels really hard at first, because there's so much "vocabulary" to learn in the beginning. And even as you solve problems, it's not necessarily easy to tell whether you've gotten a feel for what's going on. The real learning seems to begin when you go back and read what you've already gone through (as I've learned when studying for tests). All of a sudden, all that disjointed logic and symbolism reads a bit smoother, as if the dots have been linked by lines, that eventually smooth out and curve into an image that reads like a machine or narrative of sorts.

It's not that clear to me yet. Not even close. But I can see where it's going. A lot of benefit can be gained after taking the class and just going back and reading things.

Linear Algebra feels like it's more difficult for me than it should be. But it seems so fundamental as a basis for addressing problems with a lot of moving parts, lots of data, and as a basis for visual representation. So it's something I have a pretty strong interest in learning (I also like the material even though it doesn't come natural to me).

Also, I looked ahead at higher undergrad courses, and I see that what I'm taking is really equivalent to Introduction to Linear Algebra (it may be lower than that). Beyond that is a 300-level Linear Algebra class that assumes you've taken and done well in abstract algebra and real analysis. Beyond that are things like non-linear systems, which I'm guessing are often more representative of what happens in the natural world. And if I haven't gotten the (relatively) simple linear stuff down, how will I find my way through all of the chaos that isn't made of long, straight lines.

Linear Algebra seems so fundamentally important that I think, if I don't come out of this class with a real thorough understanding of the material, then I might just take it again (even if it's the intro class at an undergrad level rather than at community college). Even if by some miracle I happen to squeak out an A (which doesn't seem remotely as likely as it once did).

Tuesday, March 21, 2017

A Basis for More to Consider

New Yorker posted an article titled "A Few Thoughts About British Actors Playing American (and African-American) Roles."

I think it has some interesting points. Though, far more often, I used to wonder to myself why African-American actors are so often playing lifelong citizens of African countries in big budget films. It's not that it happens at all. It's the frequency of it. What are we losing there?

I'm not saying the article's author is off the mark for any reason. Not seeking to make a counterpoint. Just reflecting on my own reactions over the years.

For some reason, Idris Eldra playing Stringer Bell never bothered me as much as Morgan Freeman playing Nelson Mandela. Although, to the author's point, David Oyelowo playing Dr. King does give me pause.  (Maybe it's the weight of the role?).

Regardless, when I see a well-known American star playing the starring role about a person in some country I've never gotten the chance to learn about, am I really seeing something new to me and truly of itself, or America abroad (in part because my expectations are wrapped up in the actor/actress I'm watching on screen)? If it happened every now and then I suppose it wouldn't matter as much. But if this seems to be the case in the majority (i.e., more often than not) of big-budgeted films based in Africa that I watch, then I do begin to wonder. I guess you could extrapolate this to well-known U.K. actors as well. (And I suppose you could extend this to American actors playing non-Americans in foreign countries in general).

I'm also a big fan of "diversity within the medium" in most any category of art. Which is to say, no matter what constraints you have on a particular genre, format, category, or artform, you should always be able to find a way to not have too many finished pieces look like slightly modified copies of one other. Otherwise, what's the point of seeing a new film if it's basically indistinguishable from the last film you saw?

It had it's cheezy parts (the excessive use of sappy orchestral music playing in the background was tiresome). But I think part of the reason I enjoyed the non-U.S. film Sadece Sen (I only bring it up because I just saw it this past weekend) is that, being in a situation outside of my own, but probably intimate to those involved with the film , I wasn't wrapped up in how my own expectations defined the movie, because there was little for me to expect or rest on. This includes everything from the premise, to the language, to the actors. (I say this usually also not being a huge fan of romance films. But maybe it helped that I saw it with my lady.)

It's those kinds of on-screen experiences that actually makes the likes of big budget superhero films worth watching (I use superhero movies as an extreme example). Because together, that sort of mix provides a combined experience that a few dozen movies relegated to a single, tiresome category and/or template could not. 

Friday, March 17, 2017

Thursday, March 16, 2017

Wednesday, March 15, 2017

Linear Algebra - A YouTube Redemption

I bombed my first couple of Linear Algebra in-class quizzes, but learned from my mistakes and earned an A on the first test. On the midterm, I made some early mistakes that snowballed into panic. Silly algebraic errors, redoing problems more than once, using information from one question to answer another, not being able to answer a question. All the dummy moves (I'm not sure I want to even know my grade at this point).

This brought on some second guessing about whether I was really up to speed in class, and, just as important, if whatever knowledge gaps I might have might show up or impede upon an future learning. In order to make sure I had the concepts down, I spent the next week searching YouTube for videos of problems and concepts worked out from different perspectives. I hoped to find some combination that gave me an intuitive sense of what linear algebra was all about. What resulted can be found below.

Getting through all this will probably take me longer than the duration of my current course. But that's OK. The overall goal for studying math is as a foundation that allows me to learn other things that give me more insight into how the world works. For starters, I hope to understand the basics of calculus, statistics, logic, and linear algebra well enough so that when I encounter matrices, physical rates of change, summations, integrals, and statistical regressions in journal reports regarding local economies, energy resources and consumption, nature, urban infrastructure, biological traits, or social habits, I can read the material with the same sort of fluency I do my favorite literary and popular consumer magazines. Then be able to use that information to see deeper into the world around me as I walk through it.

Certainly, getting the feeling that my midterm exam grade could be any of the first four letters in the alphabet probably means I'm not quite yet on that trajectory. Even still, getting good grades isn't the same thing as having a sort of flexible fluency that allows you to absorb and utilize the language to see the world around you with an added degree of clarity. Either way, I can tell there's a bit of a gap in comprehension for me. And, if I'm reading things right, in a world of big data, digitally animated movies, games, and simulations, and policy driven by economic models, matrices and linear algebra will become an increasingly fundamental part of how society uses facts and figures to analyze the world around us. So it doesn't hurt to really take the time to try and learn this stuff.

The goal with this list is to have a sort of cascading effect that I can rinse, repeat, and rearrange if I need to. Each step adds to a foundation. Each next step makes use of previous material learned in the previous steps. If things are too easy, one can skip ahead. If they are too difficult, one can move backward. And even after being done with the class, I can continue to build on what I've learned.

Also, I suppose anyone who is as curious (or befuddled) as me might be able to use these resources as they see fit.

POTENTIAL PRIMER - My Why U will seem to cover really simple concepts. But I think it's important to know that you really know this stuff, before you even take a linear algebra class if possible. Some of the really simple things that caught me off guard early were being able to process and apply the methods of back-substitution or the visual and conceptual meanings of inconsistent vs. dependent vs. independent at an appropriate speed. I found myself stumbling over myself thinking too hard about "why's" and "how's" early on. Videos 39 - 51 is a good place to start. If you find you need to, check out earlier videos too. Anyway, this is what I'm doing.

1.)  START HERE -  Essence of Linear Algebra focuses on making concepts intuitive through visual means rather than computation. It's an effective and time-efficient way of getting the bigger picture in a relatively short amount of time. This video series won't give you the tools to actually solve the problems. But it make things clearer so that when you do, it won't just feel like rote calculations

2.) BASIC MATRIX OPERATIONS - After getting the concepts down, videos 52-61 of My Why U, followed by videos 03-1 to 03-4 of the Mth 309 video series can provide a good basic introduction to matrix operations and high level insight.

3) FOUNDATION IN THEORY AND PRACTICE - From what I can tell (I haven't gotten through all of the videos yet), the Khan Academy linear algebra series is both relatively thorough and comprehensive, but is both long in duration and requires a certain level of commitment. The series essentially explain a concept and proceeds to work through example problems for whatever is mentioned. 

4.) PROBLEM SOLVING - Understanding broad concepts and being able to work through problems aren't necessarily the same thing. Patrick JMT and Adam Panagos lean more heavily towards computation, problem-solving, and execution. Mathway is another great tool. That is, if you are willing to pay $20 a month for it.

5.) PUTTING IT ALL TOGETHER - Videos like The Big Picture of Linear Algebra and articles such as Better Explained: An Intuitive Guide to Linear Algebra are important, because they provide a quick way to check whether your understanding has evolved beyond just being able to work through problems, and into insight regarding how all the moving parts merge into a comprehensive whole. The real fun/interesting stuff though, is watching how the things you learn tie into the world at large (you don't actually need to know linear algebra to appreciate most of these videos):

If, at the end of all this, you find yourself wanting more regarding formal theory try Stepik 's linear algebra series.  Stepik takes a similar approach to Khan Academy, but uses denser language, formal mathematical notation, and proofs. Khan Academy will probably be a better fit for most people (including me). Stepik may be better if the concepts already come to you quickly; if you find Khan Academy isn't as precise or as you'd like to be; if you are taking a more thorough, proof-based linear algebra course; or if are planning to continue with classes like discrete math, proof writing, abstract algebra, or any material that includes any of the aforementioned subjects.

Friday, March 10, 2017

When June Met Lyft

I don't watch much TV, so I guess I don't see much in the way of commercials anyway. But I can't remember the last time I liked a commercial this much for its own sake (save Flo from Progressive. That's my girl!)

Wednesday, March 8, 2017

Monday, March 6, 2017

Sport is Love

Peaks and valleys. At Dirtbag Diaries.

Friday, March 3, 2017


Living data. At Science.

Wednesday, March 1, 2017

Learning School Again

From EdX Youth talk "What do top students do?"

Top Students:
  • Don't Aim to Just Work hard
    • They work hard at doing the right things
    • Model what the top students are doing
  • Use Practice exams
    • More than memory: "An exam does not test how you remember. It tests how you use what you remember."
  • Use Study Time Tables
    • First thing is put in things related to when you are not going to study
    • Make sure to fit in things you like doing first
    • Then schedule in time for study
    • Every day you are doing something that you love doing, making the studying more effective and less likely to wear you down