Monday, May 29, 2017


Perspective and controversy. At

Sunday, May 28, 2017


Joy in rhythm. Booooooiiiiiiiii!

Friday, May 26, 2017

Just Ask

Open doors. At New York.

How to Look

Seeing through. At Star Talk.

Sunday, May 21, 2017

Scout's Honor

Seeking yonder. At TEDxPSU.

Sunday, May 14, 2017

Starting From Scratch

What exactly does it mean to be scientifically literate?

If I really wanted to become "scientifically literate", to have a fundamental foundation to learn, explore, and understand the physical world, and processes involved in that discovery, what basic knowledge would I need? If I were going to do some self study to acquire this foundation, and if I was building my own educational curriculum, what kind of coursework would I want to mimic in my learning?

The most concrete examples of guidelines I could find came from Drake University, University of Oregon, University of Buffalo (UB2), Loyola University of Chicago, a New Hampshire State K-12 Scientific Literacy Framework, the AAAS, the Minnesota Literacy Council, the Earth Science Literacy Initiative, and a Big Think video featuring Charles Vest.

Cumulatively, it looks like things generally add up to the following below. Any way I look at it, it seems like a lot of work.

The Big Four
Physics, chemistry, biology, and mathematics. Or, more specifically, the equivalent of physics I and II, chemistry I and II (and III depending on who you ask), organic chemistry I and II, and biology I and II. For math, at least algebra and trig. Calculus, statistics, and symbolic logic helpful.

Human health, nutrition, wellness, fitness, the science of sex. Human psychology, biological basis of social behavior, biocultural diversity. Anthropological inquiry, origins, ecological footprint.

Everyday Physics
Physics of sound and music, the internet, energy and the environment. Quantum mechanics. Foundation of physics.

Earth & Space
Astronomy, solar system, meteorology, planetary and stellar astronomy. Geology, geography.

Soils, plants, and foodways. The sea, marine science, freshwater ecosystems.  Biogeography and Biodiversity. Energy and the environment. Environmental locality, hazards, issues, sustainability. Climate, climate change, human impact on the environment.

I suppose the one big thing the combined curriculum misses, for me, is coverage of the infrastructure, utilities, and technology we use everyday. I guess this leans more towards engineering. Electricity, energy, water systems, roads, bridges, etc. Automobiles, cell phones, wi-fi, etc.

Sunday, May 7, 2017

Stair Climbing

This man cracked me up when he was like "this is a problem for eighth
graders." I'm trying to learn this for my discrete math class right now. I guess things come easier for some than for others. Original link here since posting on blogspot seems to always cut parts off of the full view.  Related links here, here, and here.

Friday, May 5, 2017

And on and on...

I sort of want people to understand all this... Whatever comes out of the Senate (and I hope it's good), if anything does at all, it would have never even been considered if Obama hadn't gotten the ball rolling. That's sort of the point. The only reason that healthcare for people at large was considered important by the current cohort in the first place is because of the previous president (it's both a shame and a good thing I suppose). More specifically, not because they wanted to actually help people, but because they wanted to oppose the previous president as a matter of... principle (can you call it that)? And, politically there's really no way out of that. It took that man and a vote by a sea of blue for the current majority to even consider what might actually be good for the people at large when it comes to healthcare. Meaning, before now, there was more concern for power and politics and "free markets" (a term that has lost its significance - leaning too heavy on the ideas of deregulation/capitalism or socialism in isolation alike will both have adverse consequences, beyond lacking context in a post-recession age of relatively heavy inequality) than there was the basic health of Americans at large. You are riding that boat. Hopefully, we are at a point where that approach has changed. Hopefully, if something is to be done about it, you'll decide to make actual improvements that benefit the people of this country at large. And hopefully, in the future, politics and power and ego won't take precedent over the people. That was the benefit having of a man in office who had before that dedicated his entire career to public service. By default, the thought of what and why things should be done is first and foremost considerate of the people. Not of image. Or wealth. Or brand. Or anger. Or Twitter. Every time this new sitting President opens his mouth, I'm reminded of all the things he isn't, never was, and probably never will be. And it's mostly by choice.

Sigh... Australia

Also also outlawed use of guns (unless you a rural farmer) with positive benefits. I suppose we could follow suit there too.

Still doesn't change what was said before. Only adds more to it.

This Whole Healthcare Thing is Funny (in a not so funny way) To Me

Basically, the motivations seem to be political. Meaning, it's not the benefits of the citizens of the U.S. that are of most concern. It's about imagery and show and sense of authority.

Yet, this essentially affirms the need for the purpose the Obama administration's legislation by proposing healthcare legislation that would have never had a chance of existing if it weren't for Obama in the first place. It's saying

"You were right. People's health is important. We're on a platform that wouldn't be possible without you. That people can tell their children's children they benefitted from. We could do some things so that would allow those same people to tell their grandkids the great things we've (not just Obama) have helped done for their health. But we're going to use this platform to screw over those people. And their children's, children's children can tell them about the time under Obama, when the government actually considered healthcare for the everyman to be something of worthy concern."

This seems... illogical to me, given the motivations involved. Like chasing your own tail. And because there's so much emphasis in trying to get this through to replace something of universal benefit (if I'm more clear something that personally benefited me) rather than taking the time to think of something most beneficial to the citizens of this county, it looks like something that's likely to create a mess down the road (more for ordinary, and especially poor, folk than politicians or for those who wealthy enough to be able to afford not to care).

But oh well. When you are driven by image and power, what makes sense, (or what's good for the people), isn't priority for you. And it kind of shows.

Not really a surprise. It's exactly the kind of thing I expect from the people in charge.

Math and Art?

So I'm trying to come up with more analogies as I learn this stuff. And some interesting thoughts occurred to me. If you paired up calculus, discrete math, and linear algebra with any of the arts, which would each best represent?

Discrete Math as Music (or, more precisely, as rhythm): So, discrete math really, to me, feels like patterns, which in turn feel like rhythms. The first thing you have to do is understand the basics of the language. Or, if you liken to music, to be able to read or play/recognize each note. Then you need to understand how they are used in certain conditions. And you need to play. You kind of learn by doing. I found, for example, that actually going through and doing breadth-first and depth-first searches helped far more than the definitions. Once you get the "rhythm" of the things, of the patterns you are creating or identifying, it all feels like less of a mystery. And I kind of get the sense that it could eventually be intuitive. Also, a concept like bipartite (which I got wrong on my last test) is probably easier to understand if you think more in patterns than in formal definitions.

Calculus as Sketching: This really came about because I might eventually be taking a physics class. And I did some basic reading here and there. There seems to be three skill sets that will help you do OK in physics: math (often calculus), concepts, and sketching out visual representations of the problems you are trying to solve. And if it becomes second nature for you to be able to sketch out what you are thinking, maybe it's easier to give workable shape to the physical body problems you are trying to solve in your head. Reading about learning basic physics kind of made me interested in taking my school's Basic Drawing class.

Linear Algebra as ?: Honestly, I don't even know. Nothing came to mind here. I guess I start thinking more about architecture, engineering, or space than any art.

Tuesday, May 2, 2017

Heroes Do Exist

Tucked away. At Monocle.

Binge-watching. At Epicstream. (they missed a lot of things though)

Flight. At Yahoo.

Fix stuff. At Repair Cafe.

Beyond tofu. At One Green Planet.

Friday, April 28, 2017

I Love Clarkesworld

True lies. At Clarkesworld.

Feeling Less Stupid-Ish

I've actually made it through most of linear algebra. I only have the final exam left and it looks like a decent grade overall is possible. Conceptually, it's been the hardest class for me. So I'm proud of myself for making it this far.

I get the impression that it can literally take me a few hours to get through and understand the same number of problems that would take my most of classmates 15 or 20 minutes. Which is OK, so long as I'm not holding back other students while in class. And it seems that by test time I catch  up enough to do OK on exams (well, sometimes anyway).

Still, being able to do the problems is one thing. It's not grasping the concepts quickly that makes me relatively slower. I think after the class is done I'm going to go over the text on my own until I really get the material down pact. I want to get a sense for this intuitively.

I might eventually even try a proof or two.

More to See

I came upon this article by way of 3QuarksDaily. One paragraph caught my eye:

I had written some short stories but they were not any good. I didn’t know how to go on with writing. The trouble with the stories was their lack of shape and their earnestness. I read stories in The New Yorker and Esquire and tried to imitate them. This imitation was a discouraging thing. My stories seemed like theirs, but somehow they could be distinguished from the genuine, or so I was convinced. Of course, in some cases they were just imitations of imitations, and no one is looking for that.

Good and bad I suppose. If you happen to be near a library that holds archived issues, you should find that good writing at the New Yorker and Esquire go way back (some of my favorite pieces, all the way back to the 1960's, from the old New Yorkers were from Talk of The Town, because they gave so much shape to the world around you as you passed through it).

Bad in that, if New Yorker and Esquire are the only two publications (or only two sorts of publications) you are trying to imitate to become a better writer (granted the author did not actually say "only"), it might suggest that that's kind of what you limit yourself to seeing as the two sole examples of exemplary writing.

There's an easy fix to this sort of thing, I think: diversity of content. If you are reading a bunch of different things you consider great writing from a bunch of different sources you consider great publications, you are constantly exposing yourself to all forms and styles and approaches in great writing. Also, there's less of a need to imitate any particular style because you are not necessarily wedded to one particular type as acceptable enough. This kind of intimate detachment may also give a young wordsmith a stronger sense of ownership in regards to what they write.

In this way, I guess there's an advantage of having grown up a minority and enthusiastic reader. My reading interest started with the Hardy Boys mostly. But as a pre-teen and early teen looking for things that reflected me really had its limits. The magazine rack had Black Men's magazine, which was more like one extended photo shoot, not exactly a bastion of great writing. And, at the big chain book stores, even the African-American fiction and non-fiction sections at the time seemed more catered to women's interests (in the fiction section), formulaic genre (fiction), and academic treatments (non-fiction). But I did find my combination of diversity of thought/experience and reflection of men that looked like me in biographies. This brought on the habit of not ever being wedded to any particular publisher or magazine or writer, because I was so accustomed to having to work to find what I wanted. Exploration was required from the get go.

And I think that habit carried on as I got into reading a wider variety of publications. I will binge on the New Yorker for months at a time at any point (I actually didn't even really start reading the publication until my mid twenties). But I generally have a tendency to rotate the publications that I read. This is how I found The Sun, Callaloo, The Literary Review (the US publication, ), Raritan, Gettysburg Review (mostly fairly well known as far as lit mags go), and a multitude of other lesser-known literary publications, along with the multitude of glossies that seemed to last for a few years before disappearing from the stands for good. It's why I love those small specialty stores in Manhattan who solely carry hundreds of magazines titles from all over the world, (I haven't seen stores like this in any other cities in the U.S. myself, but I can think of at least three that are walking distance from Penn Station, and more outside of that area), as well as the local bookstores or community centers with titles I'm less familiar with. It's in experiencing all of them, more or less at once, that I came to think of all of them as equally valid.

I honestly get bored with too much of the same. Diversity is part of the joy of reading for me. Of any art or experience really.

Thursday, April 27, 2017

Second Thoughts

An open mind. At The Sun.

Number Theory

Asking why:
Douge Clarke - (1:20): "What are you doing? Why are you doing it? How is it helping?"
Carene Umubyeyi - (0:10): "One of the most important things to do as a critical thinker is to question everything." (0:34): "The process of using what you know to be generally true in order to make an inference about something specific." (1:10): "First, you note down your givens, your observations, things you can see from the problem. Second, you reason using deductive reasoning, using general statements to infer specifics. And thirdly, you reach your evidence based conclusion." (3:52): "It is crucial to ask why. Ask the reasoning behind the concept."

Alan Dove - (2:43): "The point is that science and only science lets us find facts that are true for everybody, everywhere." (3:20): "It doesn't matter what country you're in, what language you speak, or what religion you are. You can reproduce the result. In fact (and this is a really important point), it will work even if you don't believe it will. You can deny Newton's laws until you are blue in the face. Gravity will still apply to you. Science gives us facts. Statements about the world that are true for everyone."
Steven Strogatz - (22:23): "If you are pure [mathematician], you are mathematician as poet. That is, you love your own subject and you're looking inward. You want to understand the structure of math itself with no reference to the outside world." (29:02): "All these people were simultaneously scientists and mathematicians and engineers. And it's a 20th century conceit - well, maybe because of the age of specialization - that we're only one at a time. But, to me, I'm a mathematician who's really interested in science, as well as the arts, honestly, and humanities. So I don't really like those distinctions." (29:47): "She doesn't really care what medium she's in. It could be painting, it could be sculpture, it could be charcoal. But she's interested in solving a problem. That is, she has some artistic thing in her head she wants to express. And then she thinks about what medium will help her best express it." (50:33): "Math is a language. But it's much more than a language. And it's because we don't have a word for what it is." (51:46): "So it is a language. But it's a language with an incredibly powerful machine built inside of it." (52:13): "It's not just a language. It's a language that let's you predict the future." (52:37): "It's more like math is the operating system of the universe."

Sustainability, adaptability, modern learning, and application:
Adam Bly - (1:55): "Science is butressed by it's instability. It's in fact the ability for science to be overturned and constantly proved wrong and for theories to only last as good as they are, until someone comes along and overturns them, that gives it one of its greatest sources of stability."'
Conrad Wolfram -  (4:05): "The first step is posing the right question. If you ask the wrong question about a situation, you're almost always going to get the wrong answer." (7:47): "Well one of the things they say is 'You need to get the basics first.' I think what they mean by this is you have to work stuff out on paper before you do it on a computer. But you really got to ask 'basics of what exactly?'  Are the basics of learning how to drive a car learning how to service it, or engineer it for that matter? Are the basics of photography today loading a film into your camera or coating a plate with chemicals? I don't think so. I think those are the machinery of the moment."  (9:08): "Just because paper was invented before computers, it doesn't mean it gets you closer to the basics of the subject." (9:40): "What we should be doing is problem-centric mathematics... They should be problems that the kids involved, or the adults for that matter, are keen to solve at that point, that they find interesting." (10:40): "So you can actually use the computer to experience some of the things that you're interested in." (11:28): "If you use computers correctly to do the calculation you can do much harder problems, you can go further, you can get people more experience. That's the crucial thing." (13:23): "Programming allows you to write down your understanding of the subject. And of course the great advantage is that you can then run the program and actually do things with it. So programming is a crucial part of early maths education. It should be part of primary maths education, just as a way to express oneself." (13:40): "I'm arguing for a mathematics that is both more practical and more conceptual. The thing that is exciting at the moment is that we don't have to choose. The mathematics of the real world is far more intellectual and conceptual than the mathematics we're teaching right now. By mimicking the real world, we will improve both practical use and conceptual understanding." (20:19): "There's also the ability to use real data. Actually pull in real examples from the world. Don't do statistics with five data points. Do it with 10,000 real data points that came in yesterday from the financial markets. That's the kind of thing we can do with modern computing environment."

And of Course Neil deGrasse Tyson, modern day science's PR man, came up multiple times in the search:

Neil deGrasse Tyson - (0:22): "We look up and say, I wonder what that is. Let me go find out. Let me poke it. Let me turn it around.
Neil deGrasse Tyson - (1:44): "At some point, you have to step away from the exam and say 'I have a new thought that no one has had before. And it's not a thought that you told me to regurgitate on this exam that you just wrote.' "  (3:03): "The success of those people is not measured by how they performed on the exam that you wrote as a professor. Because they are thinking in ways that you have yet to think. Because they're inventing tomorrow." (4:02): "The system of education rewards high GPA. But the system of life rewards tenacity. Rewards your urge to tackle something you've never seen before. And even if you don't succeed, in that tenacity, to have the energy to go back and try it again. Knowing how to fail."
Neil deGrasse Tyson - (3:33): "If you're an employer and two candidates come up looking for a job. And you're interviewing the two candidates. And you say 'For part of this interview I just want to ask you what's the height of the spire on this building that we're in? ' And the candidate says 'Oh, I was an architect. I majored in architecture for a while and I memorized the heights of all the buildings on campus. I know the height of that spire is 150 feet. In fact, 155 feet tall.' Turns out that's the right answer. And the person came up with it in seconds. That person goes away. The next candidate walks in. 'Do you know the height of the spire?' The candidate says 'No, but I'll be right back.' Person runs outside. Measures the length of the shadow of that spire on the ground. Measures the length of his or her own shadow. Ratios the height to the shadows. Comes up with a number. Runs back inside. 'It's about 150 feet.' Who are you gonna hire? I'm hiring the person who figured it out. Even though it took that person longer. Even though the person's answer is not as precise. I'm hiring that person. Cuz that person knows how to use the mind in a way not previously engaged. You realize when you know how to think, it empowers you far beyond those who know only what to think.

Tuesday, April 25, 2017

Health Exchange

Life and money. At FiveThirtyEight.

Thursday, April 20, 2017

The Birds

Cloud surfing. At Asymptote.

Wednesday, April 19, 2017


This lady. We just had the worse financial crises in modern U.S. history because companies were pushing mortgages that people couldn't pay. What happens when you start attaching large fines to students who haven't even started their careers, or young adults who are starting out and already owe six figures to start with?

I don't know how someone who cares more about allowing companies to gouge customers who require degrees to meet unnecessary company-mandated checklist job requirements (I still believe excessive job requirements / hiring practices - you don't need a bachelor's degree to be able to type on a computer - are probably a significant contributor to this student debt issue) gets hired to represent the needs and advancements of public education.

This lady has no clue.

Saturday, April 15, 2017

Behind the Everyday

Randomly searched YouTube for videos that covered math concepts in a relatable way. Came up with the following below. The "Googling" videos actually seem to touch on a number of things being covered in the linear algebra and discrete math classes I'm taking. The equation in the "Maths Behind Music" video and the Lorenz curve in the "Mathematics and Social Justice" video appeared in my calculus class homework assignments.



Visual Arts

Space and Time



Internet At Large

Politics, Crime, Society

Friday, April 14, 2017

Monday, April 10, 2017

Wednesday, April 5, 2017

Feynman: Mathematicians versus Physicists


Saving it. At Dirtbag Diaries.

Again. At Pacific Standard.

Joining it. at The Nonfiction Podcast.

Alone in it, feeling it. At The Urbanist.

Knowing it. At Outside.

Staying with it. At Katy Says.

Tuesday, April 4, 2017

For The Better

Clarity and focus. At Stanford Social Innovation Review.

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

Tuesday, February 28, 2017

Thursday, February 23, 2017

Wednesday, February 22, 2017

Lost in Translation

Here's what I got so far...

Calculus I: "Change happens."

Discrete Math: "How to Speak Computer: A Beginner's Guide for Humans."

Linear Algebra: "How To Solve a lot of Problems That Look Like Each Other, All at Once, in No Time."

Intro to Databases: "Create order. Prevent chaos."

Backwards, Forwards, and All At Once

I took an online Calculus MOOC course some years ago. The toughest thing about it for me wasn't necessarily the calculus. I got the concept of limits fine enough, until it required factoring polynomials in order to simplify the limit. So I learned there were some algebra basics I had forgotten after years of not using, but I managed to study on the side just enough to stick with it.

The class also introduced trigonometry in both limits and derivatives. Trig was something that drew a blank entirely. Either I had never studied it, didn't pay attention in high school, or simply had long forgotten. At that point I decided to quit, because I had enrolled in the course with the intention of getting the most out of it. Even if I somehow managed to get through it, it was clear to me that what I intended to learn wouldn't stick at this point. When I enrolled back in school and started off in Algebra years down the road, I knew could have started higher, but I also I was there because I really wanted to get a firm grasp of all the important basics that would matter in any future classes I took or self-study I pursued. And I'm glad I did it.

This attempt to learn the basics of math and science seems to very much be about studying some topic, realizing that you have a basic knowledge gap, and going back to shore up your fundamental knowledge base before or while moving forward. This theme seems to only repeat itself, even as I (slowly) move up the ladder.

After that MOOC class I read through a couple (or a few) introductory calculus books on my own over time. I'm not sure how much I absorbed. But I tested it in part by trying to look through books I was interested in reading later. Somewhere along the way, I decided that two of the books I really wanted to not only get through, but to eventually read with ease and understand intuitively, were Mathematics in Nature and A Mathematical Walk Through Nature, by John A. Adams.  It sounds pseudo hippy-dippy corny as can be, but what I wanted to do was read the book, get a really good grasp of what he was saying, then spend some times in the woods, by the beach, or wherever I see more greenery than concrete, and see all the things he wrote about (this is still an eventual goal of mine). Then, I'd follow up with Adams' X and the City: Modeling Aspects of Urban Life and take a stroll through a nearby city to see if all the same things somehow looked different. 

When I tried to read Mathematics in Nature (that must have been some two or three years ago), it was clear I wasn't yet up to the task. But that book, along with a handful of others, did reaffirm the notion that if I was going to get a basic foundation for appreciating the world around me through a basic understanding of the laws of nature that governed it, that it would be important to really get comfortable with calculus and trigonometry.

Just last week, I attempted to get through In Praise of Simple Physics. Turns out, early on, the author mentions the book is really for readers who have already gotten through a class in freshman calculus. I tried anyway, and only made it through something like one-half to two-thirds of the book. But conceptually, I understood what I knew, and got a better sense of the things that I lacked. For one, my current calculus I professor had thankfully introduced implicit differentiation early in the class. So I came to quickly see that implicit differentiation was one of the things that stopped me from understanding calculus in other books I tried to read before. I always used to wonder were that extra term came from - it always felt like it just appeared out of nowhere for no apparent reason. And now the process was somewhat intuitive.

This week, I took on The Theoretical Minimum, which I had also tried to read years before. And it is now already remarkably clearer than my first time around. I could at least understand what was going on. I also learned something new here. Whenever I used to see symbols for partial differentiation, I never knew what the heck I was looking at. Now, the author's explanation seemed straightforward and intuitive.  The book even starts off touching upon concepts related to discrete math, which I'm also currently taking.

In chapter 6, roughly midway through The Theoretical Minimum, the author introduces the concept of The Principle of Least Action. Here, he uses Euler-Langrange equations. Somehow, I can sort of mechanically follow some or most of the mathematics and sort of kind of get what was going on conceptually with out really being able to put it all together. These are equations I could not work out myself as of yet. I stopped after the next chapter, when I realized future portions of the book are built on concepts shared in chapter 6.

I learned something from reading both of these books. One, that there's been some progression for me. Secondly, how important integrals are (I have a reason to look forward to learning about them in detail). Also, while math may be the bedrock for physics, and physics may be the considered the starting point for understanding the theory behind physical science for general, at least for me, understanding the mathematics doesn't necessarily mean understanding the basics of physics. Merging the two seems more like drawing a picture in your head, filtering to through all the mathematical gadgets and gizmos you have in your toolkit to see what might fit, creating new ones if you need to, and rearranging it all together in a way that makes sense and is truly (or at least functionally) representative of.

This makes me think that deriving equations for physical phenomena aren't always intuitive as I'd assumed. Part of doing the hard work of exhaustive and detailed reasoning is making sure you are aren't overcome by faulty assumptions. I get the impression that intuition may get one started in getting from A to B, and help smooth out rough patches in between, but that the end result hardly ever exactly matches what first came to mind. More like the creators learn along the way of trying to figure it all out. Or at least it's safer to assume so.

I don't know that I'll plan to take any physics classes in school (time and money are of concern). But I do know that I plan to use what I learn while taking these math classes to study more about the physical world, starting with concepts in physics before I move onto other things. From reading around, I found that calculus and linear algebra certainly both play a role in physics. So I went looking for books that covered both, hopefully in context of physics, and at a lower level than the two previous I read over the last couple of weeks.

Based on the synopsis and table of contents, No Bullshit Guide To Math and Physics seemed to fit the criteria I was looking for. It shores up pre-calculus fundamentals before going on to basic physics and calculus, vectors, differential and integral calculus, and mechanics. It seems conceptually thorough while still catering to the beginner. Hopefully, it will prove to be a good compliment to current classes, and a decent starting point for similar books I plan to read afterward.

Onward, ho.

Friday, February 17, 2017


Counting crime. At Bloomberg.

Wednesday, February 15, 2017

Sunday, February 5, 2017

Markov Chains for Inventory, Supply Chain, Accounts

Markov Chains were originally in the syllabus for my linear algebra class. However, the teacher announced that he'd always considered it something nice to cover, but that he knew we could skip if we needed to. And so, based on his observations, we are skipping it (why do I get the feeling though, that if I weren't in the class that it would still be covered with confidence? I say this in jest. I'm still catching up to everyone else is all).

However, I'd already started reading ahead just to stay on pace with my more math savvy classmates. I had read the Markov Chains chapter and done the homework. Since we weren't covering Markov Chains in class, it wouldn't be on our first test the following week. In the middle of studying for the test, I re-read the chapter anyway, just to get a grasp of what seemed like an interesting concept whose name I had come a cross a handful of times before I started taking classes.

When I re-read it, I got one of those "ah-hah!" moments. I wish this concept was something I had known while I doing some freelance financial modeling work a year or two ago.

Essentially, I put together two financial spreadsheet models for two different clients that had some combination of physical inventory (and associated multi-faceted cost accounting associated with it), up-front payments (and therefore more complicated accounting), various product lines (more complications), and various market-based outcomes (even more complications).

Both models were monsters in size and breadth. Looking back I always wondered how I could have made them simpler.

Markov Chains essentially do that for you. A chain considers how market conditions or combinations of inputs and outputs might change or transition over the course of a given period in the form of a row-by-column matrix. Each one of these individual transitions are represented by figure between 0 and 1 (0% to 100%), adding up to between 0 and 1 in each column, in the matrix P, called the matrix of transition probabilities. This matrix represents percentage / probability of occurrence in a given period applied to an original market condition X (say X is, for example, is the number of total items sold into a market, with each market represented by a row in X). When you multiply P*X the output Y is your new market condition.

Keep multiplying the same Markov matrix / matrix of transition probabilities and you get the assumed cumulative condition of that market overtime. The one thing I wonder though, is what happens if you have new transition probabilities. I guess instead of multiplying by the same exact matrix of transition probabilities in the given time period, you multiply by a new / adjusted version instead?

Either way, potentially, 10 large tabs in an Excel spreadsheet file could have been reduced to 1-3 more compact ones. Though I'm not sure if Excel can really handle matrices to begin with.

On top of all that, being actually able to apply this method and execute it correctly is a whole other matter.

Still, this feels like adding another compartment/notch to Batman's utility belt. More math seems to give you more options to choose from.

Saturday, February 4, 2017

Free Wi-fi

I don't understand what most of this article is saying. But I now know that for someone with a little know-how or who is willing to learn, free public wi-fi is possible.

"How to get free wifi on public networks." At freeCodeCamp.

Thursday, February 2, 2017

Old Dog, New Math

Some years ago, I decided I didn't know enough about the world. Life kept getting in the way of trying to know more immediately, so I got started a good year or so after that. Reading and reading about the fundamental rules of the physical world. And I came to find one big gap. Many of these books used the language of mathematics. And I barley knew a lick of it.

It was tough trying to learn on my own to start. So I decided I wanted to take a couple classes. Life and bills got in the way. So, finally, a couple years later, I started taking courses at my local community college. Started with intermediate algebra with old folk like me and high school folk alike. Went on to precalculus. More work and catching up (I knew next to nothing about trigonometry). Made it through.

This semester is calculus I, discrete math, and linear algebra. Three weeks in, I feel on pace in some respects and nearly out of my league in others. But I do feel with a bit of hard work that I can make my way to somewhere between the lower ranks and the middle of the pack.

Calculus comes across as the most intuitive for me (but this might be because I spent some time trying to learn it on my own before, with moderate success). Discrete math feels more intuitive than it should be with some work. But that's in part because we've only had some homework so far. When it's just you, a piece of paper, and a question on the test, your mind can start racing. And I can see there is a lot there though and I can already tell that it can catch you off guard of you don't keep up.

Linear algebra is kicking my butt from early. Not in a way that I feel like I'll never be able to catch up. But starting off I'm by far the slowest one in the class.

It's not horribly bad. I came to learn. There's plenty room to do it. And the benefit of going to school for your own sake as non-exceptional adult (more specifically, as someone at least a good 10-15 years older than most of my classmates) is that you are more focused on your own improvement than any insecurities that came with youth or competition. The downside is when you get into a class where everyone moves at twice your speed, if you spend too much time trying to make all the foundational connections your classmates spent making in 6th grade through freshman year in college, by the time you look up everyone else might be miles ahead.

I like to write. Also, I use writing to explain things to myself when I don't understand. Writing is often an exercise of clarification for me.

So I've decided to spend some time using this dormant blog (I think it's been somewhere between 3-4 years since I've written anything here) to explain math to myself.

Maybe it will encourage me to write some other things as well.