By the very nature of the article, the reader may well be smarter than I am! The only real qualification I have on this matter is hindsight. So here’s the advice I’d give to my own ninth grade self, what I wish somebody had told me, the message that would have benefited me whether the messenger was Einstein himself or just another dumb teach.

School > Book-learning

Somehow this flew right over my head when I was a kid, and I suffered a lot because of it. I thought school was supposed to be a place of real scholarship. The truth is, there’s a certain basic skillset you need to navigate the world, and that’s about as far as the education part of school matters. Since you’re reading this, you’ve probably already got it. So focus on what’s really important: friendship, networking, and having fun.

If you’re an autodidact like me and want to teach yourself advanced quantum mechanics on the side, or write your own novel on the side, that’s awesome. But disentangle it from school. Video games aren’t really part of school; neither is teaching yourself Japanese or running your own business on the ‘net. School is about learning those fundamental basics (check) and about socializing with your peers.

People skills are a science of their own. When I was in high school, I could compute advanced integrals, but I couldn’t get a girlfriend. Looking back now, I wish I’d spent more time figuring out the latter! Trust me, when you go to college, there are a lot more integrals and you’ll meet them more easily, there’s no rush to get your first integral in high school.

Part of my problem was that I had built “being smart” into my personality, and I was scared to try hosting a party or asking a girl out or anything like that, because it was a totally different type of skillset and if I failed, I’d feel un-smart. That’s a big danger for smart people: fear of doing difficult new things, lest the “perfect record” be broken.

Teachers Are Human

Sure, some of them have become more machine now than man, twisted and evil, but somewhere beneath that dark shell of corrupt chalk-dust, there’s a human being. At one time, maybe they too were Smarter Than Their Teacher.

In the people skills game, the dumb and unreasonable teacher is a final boss, one of the most difficult challenges for you to test your skills against. Can you break through the cold jaded barrier and befriend the human within? Who knows, you might even be able to turn her from the dark side, get her to lighten up a bit and stop being such a prick.

You have nothing to prove

Of course I didn’t realize it at the time, but I was always struggling to beat people over the head with How Smart I Am. Again, all part of the Smart Personality™. Looking back now, that was kind of dickish of me. Just because I knew calculus and the math teacher didn’t, that was no reason to rub it in her face. No wonder we didn’t get along!

Intelligence isn’t something you need to prove to anybody, at least not ’til grad school. If you’re really a saint, you could go so far as to pretend to be impressed by your teacher. It would make their day like crazy, and if you kept it up, you could even influence them to become a better educator permanently.

Here’s an interesting psychological experiment. A teacher, with an ordinary class, pretended that the class was gifted. Sure enough, the class excelled, all the students performing as if it really were the gifted class. When the teacher began treating students like they were intelligent, the students somehow performed better accordingly! Thing is, though, this goes both ways. Even if your teacher is dumb, try your best to do the experiment, act like they’re the greatest teacher in the world. Watch as a more gifted instructor emerges, as if by magic!

FURTHER READING

Red Pills and Blue Pills
Become More Intelligent by Doing New Things
My Home School Story

An adulthood phase is when something new enters your reality and begins to dominate it for awhile. It’s not quite the same thing as a hobby, though they are similar. A hobby is like glowing embers which smolder on for years and years. A phase, on the other hand, is a shining flame which burns brightly for one or two years at the most, sometimes no more than a month or a week. But while you’re in the phase, it is a lifestyle. You think about it before bed at night and it enters into your very dreams.

When I was a senior undergrad, I went through an Urban Exploration phase. More recently, I’ve had a burning interest in technology, futurism, transhumanism, and that sort of stuff. When I was in the Air Force, I went through a Silmarillion phase, and that illustrates an important principle: nothing is too obscure for you to phase through

One of the differences between the childhood phase and the adulthood phase is that, as an adult, you have a lot more power to pursue your interest. You’ve got money to spend. You can finally stay up past your bedtime whenever you want. You’ve got stronger muscles to apply toward the physical or practical aspects of your fixation. Your mind is enhanced by decades of life experience and you can learn and master theoretical knowledge much faster than you could as a kid.

As you go through more phases, not only do you pick up knowledge about each individual area. In the background, you practice the abstract meta-skill of going through phases in general. You get better at navigating the world through the eyes of a newbie– and everyone should strive to be in newbie mode, because when you’re not in newbie mode, you’re not learning.

Maybe we were really onto something when we were kids. Phasing is a very efficient way to maximize total learning. In any field, there’s a lot of rapid growth when you first get into it. Later on, when you’ve mastered the field and when you become an expert, the learning process levels out a lot. You get less and less ROI, having to study for months and even then you’re never surprised by anything any more. Unless you’re paid to be a mega-super-expert, it’s probably best to move on to the next phase.

There’s a word for being out-of-phase: “Bored.” If you ever find yourself wandering aimlessly around the house, boredly browsing YouTube, staring into the fridge for minutes at a time without eating anything… then you my friend, need to go through another adulthood phase. Need some ideas? Try the List of Reality Escapes. There’s bound to be something on that list you can get yourself obsessed with for the next couple months

FURTHER READING

Arbitrary Leadership
Emotional Knowledge
Reinventing the Wheel

Before even cracking the first chapter, I was already surprised by the author’s name. See, most elementary math books are written by people nobody’s ever heard of. But Serge Lang is a household name– at least when “household” means “household of mathematicians”. He’s among the most famous and prolific and talented authors of math textbooks, but the surprising thing is, his books are usually about ridiculous advanced topics you have to go to grad school to even know they exist. That’s why I was shocked to see he wrote about basic mathematics. It’s like if you went to a 6th grade science lab and saw Einstein at the chalkboard.

The most amazing thing about Lang’s venture into high school mathematics: he discusses basic algebra and geometry using the same crisp and precise language that mathematicians use for higher mathematics. It’s a beautiful language and it’s a tragedy that most people will never encounter it, despite years of compulsory education. That would change right away if high schools adopted Lang’s masterpiece.

Just reading through Serge’s exposition of multiplication and addition somehow makes me feel smarter– and I’m a guy who’s been studying math for almost fifteen years now. Most authors seem to find it impossible to talk about solving linear equations without assuming a condescending, downright insulting tone. But not this guy. He makes me think I’m sitting with him talking about math, like we’re peers working together to discover the theorems and laws from scratch.

I began searching for good books on elementary math because I’m always getting email from people asking: “What’s a good book to learn math on my own?” It seems to be a common quandary. There’s so much trash out there, what with universities and public school boards creating an unnatural market where material is churned out to maximize profit with little concern for giving the unfortunate students a good deal. You can’t really even blame the big publishing houses in this: they know that their target audience is only buying the book because they have no choice. But people like me and the readers of my blog, we want to learn this stuff, and learn it well, and we deserve a lot better.

Serge Lang doesn’t BS the reader. Here’s an example passage from the book:

It is a tradition in elementary schools to transform a quotient like

into another one in which the square root sign does not appear in the denominator. As far as we are concerned, doing this is not particularly useful in general. It may be useful in special cases, but neither more nor less than other manipulations with quotients, to be determined ad hoc as the need arises. Actually, in many cases it is useful to have the square root in the denominator. We shall give two examples…

This is a polite slam against the ridiculous “rationalize every denominator” policy pervading high-school math courses. I love you Mr. Lang! The whole book is chock full of goodies like this. For anyone who left the high-school math room a little confused, this is like taking the “red pill” and seeing The Matrix for what it is. And I do mean that literally– Chapter 17 is all about Matrix Algebra

What Not To Expect From This Book

Definitely avoid this tome if you’re a fan of modern Textbook Art. You’ll find no picture of a motorcycle on the cover. No human pyramid of grinning old people in suits will introduce the next chapter. No gimmicky “Explore and Discuss” exercises– if you have to differentiate discussion-worthy exercises from non-discussion-worthy ones, it’s time to throw away the latter!

Avoid this textbook if you like books written by ten different coauthors. In defense of standard textbook writers, I’m sure every particular one of them has very good intentions. It’s not any single author’s fault when the book goes to committee. When you take ten different visions of perfection and mix them together, you end up with a brownish muck. Mediocre works are churned out by committees, but it takes a lone man to pen a magnum opus.

Don’t read “Basic Mathematics” if you’re hunting for lots of tedious busywork. The exercises focus more on proving things logically rather than computing and crunching numbers. I love the beauty of true mathematical proof, and I’ve always wanted to share it with the whole world. When I read a particularly beautiful proof I want to grab people on the street and say, “Have you heard this!” If only public schools employed a little less Prentice Hall and a little more Serge Lang Hall, a lot more people would get to share this joy of mine!

Buy Serge Lang’s “Basic Mathematics” Now

FURTHER READING

Five Ways to be Better at Math
“Problems” in Mathematics
James Heisig’s “Remembering The Kanji”
How To Train Your Mathematical Maturity

In the past year, I finally rented a web-server and started teaching myself web programming. My first endeavor, I didn’t even know what a database was– I spent hours carefully programming a C program to generate romaji dictionary files, only to discover that servers aren’t usually happy about people uploading hundreds of thousands of text files The point is, I didn’t know squat about programming for the web. I could’ve grabbed a textbook, but that would go against the whole point: I write and develop things for fun, and last time I checked, elementary coding manuals were anything but! So I did some wheel re-inventorating. I coded my own forums from scratch, and even the wiki-like Connections Project. It would’ve been ten thousand times easier to download phpBB and wikimedia. But I wouldn’t have learned nearly as much.

By doing those projects from scratch– reinventing the wheel– I learned so much about how the internet functions! And the knowledge which I gained is emotional, not just intellectual. If I read some textbooks, even took a class in PHP or SQL, I’d gain the knowledge intellectually, but it wouldn’t have been etched into my very intuition like it has since become.

One thing about reinventing wheels is, your wheel is gonna really suck. It probably won’t roll straight, if it even rolls at all. Until today, my forums were an eyesore. I’m great at coding now, but I’m not great at web design, the art of rearranging and resizing things so they’re all purrty-looking. Maybe I’ll master that next The forums are still a long way from being as advanced as the common forum engines out there… they still suck, just not quite as much as yesterday! It might take years ’til I catch up. But when I finally do, I’ll have enough momentum, I’ll whoosh right past all the open-source forums

That’s ok, though. Once you’ve developed the skills, you can easily refine your wheel and make it better. Today, for example, I completely renovated the forums, so they use the same layout as the blog. (Now that I look back on it, that seems so obvious it’s painful. Isn’t that always the way with good ideas?) Tomorrow I’ll do the same to my Connections Project. In the process of marrying forums and blog, I made dozens and dozens of modifications to WordPress to make it more efficient and better-performing. Most of these, I never would’ve spotted if I didn’t have the on-your-feet intuitive programming skill I got from building some projects from scratch.

One of the surprising things about mathematics curriculum at the university level, is that “History of Math” is usually a senior-level course, or even early graduate level. If you think about it, this class could be renamed, “Reinventing the Math”. It isn’t so “advanced” because it necessarily requires mathematical maturity. If they wanted, they could adjust the course to be doable by freshman or high school students. The thing is, most people who aren’t majoring in mathematics, just want to pass their math requirements and that’s it. In order to study and really benefit from the history of math, you have to be really interested in mastering math. Otherwise, it just looks like algebra except the notation is even worse! Thus the requirement for “History of Math” shouldn’t be so many years as a math major– it should be so much desire to learn the subject. The benefit of learning it is, you gain a much deeper understanding and appreciation for those theorems that come from the magic hat.

Chiseling your first project from stone isn’t always the best strategy. If you need to do something under a deadline, go with whatever you can get your hands on. If you have a long-term interest in solidly understanding something, your roots established deep in a profound understanding, then start from the beginning: start chipping!

FURTHER READING

Autotidact: Be A Self-Teacher
Autodidact PhD
You might be an autodidact if…
Announcing: Forums!

I won’t try to BS you. The Esperanto itself will be useless. As soon as I got the benefits from studying it, I data dumped it. The only time I ever encountered it in “real life” was when the King Of All Cosmos spoke it once in We Love Katamari However, the same thing goes for weights at the gym. Lifting a particular dumbbell is useless. You don’t do it because there’s an urgent need to rearrange dumbbells, you do it because it trains your muscles. Esperanto trains the multilingual part of you, the multilingual muscles of your brain. And it doesn’t take years to accomplish that. You could get the benefit within weeks, if you really devoted yourself.

Within a few weeks of learning my first leksiko vorto, I was able to shift my brain out of English Mode. As a native English speaker, my mind had been frozen in perpetual English Mode for the past couple decades. Even when I was studying freshman Spanish in community college, I was thinking about Spanish in English, the inner dialogue inside my head was Anglo. Suddenly, I was set free of all that, and I could shift my mind into “Esperanto Mode”, as though I was a native speaker. And I can’t explain how happy that made me. You just have to experience it for yourself. You could experience it with “Japanese Mode” or “Russian Mode”, but it would take years of difficult study. Zamenhof’s artificial tongue will put your mind “in orbit” very quickly, because it’s such a logical, regular, easy language.

When you switch your inner dialogue to another language– and it doesn’t really matter which language that is– it’s almost like going into a mystical trance. I believe that merely spending time in this altered state of mind will flex your linguistic muscles and prepare you for harder languages. It annihilates psychological barriers, self-beliefs like “I can only speak English” or “Adults can’t learn a second language”. It alters your very self-image from “I am monolingual” to “I am bilingual”, which new self-image gives you an incredible confidence boost when you go on to study Polish, Farsi, Korean, or whatever else your heart desires.

How do you teach yourself Esperanto? There isn’t really all that much to teach. The grammar is extremely easy and intuitive, and you can master it in a week, easily. After that it’s just vocabulary, and you’ll notice that almost all of the vocabulary “makes sense”. That’s because all the root words were carefully chosen to be cognates with as many languages as possible. In a certain sense, the Esperanto vocabulary is actually very small. It’s not that there aren’t many words– there are plenty. It’s that words are built up from root words, in a similar way to English root words but much more systematically, logically, and consistently. There’s something like 2,000 basic roots, from which the entire lexicon is generated by agglutination. Most real-world languages, 2,000 vocabulary items is a drop in the bucket!

There are lessons available for free, and a whole Esperanto language-learning community, over at lernu.net. The community is so intense about trying to spread their language, when you register there, they’ll actually assign you a human, volunteer guide, who will correspond with you over email. All for absolutely free… it’s amazing. If you have money to spend, buy yourself an Esperanto textbook, such as Teach Yourself Esperanto. Even if, like me, you go on to data dump it all when you advance to a “real” language, it’s still quite worth the investment for the huge benefits of having one foreign language under your belt.

Esperantists dream of a world with a common language which everyone can speak. A world where you could go to China, Korea, Russia, Japan, or anywhere in Europe, and communicate effortlessly with the International Language. Is this realistic? Will it ever really occur? It seems like something of a pipe dream, but it would certainly be awesome.

FURTHER READING

Spaced Repetition Systems
Sentence Mining
Five Reasons to Study a Foreign Language
Autodidact: Be A Self-Teacher
Six Reasons to Learn a Language Together
Progressive Training
Will the Languages Of The World ever Merge?

There’s a natural urge to feel disappointed when you run into the plateau, but in fact it’s a sign that you’re on the right track. Plateauing should actually be encouraging, not discouraging. This is an area where our instinctive feelings are a bit obsolete. Throughout the millions of years while mankind evolved, there were no gyms or diet plans. Our apish ancestors didn’t play chess, they didn’t do karate, there were no sports or Olympic games. There wasn’t any need at all to specialize, and what skills were needed, were trained naturally without conscious effort or intent. Therefore our brains were never programmed to deal with the flat stretch of the development curve. That’s why we get discouraged, sometimes giving up completely when it feels like no further progress will come. Fortunately, we aren’t totally constrained by our basest instincts, and we can learn to associate those barriers with progress rather than stagnation.

So now you embrace the plateau as an indicator that you’re on the right track, but what can you do to get yourself over the bump? Besides just sticking to it and faithfully putting in the hours, time, and sweat, there’s a better way to invest your effort when you recognize you’re plateauing: mix things up. If it’s your bench-press which seems stagnant, then go do dumbbell bench instead. Diet running into a wall? Try switching to a different one. Not making any progress at chess? I’ve heard good things about that exotic Chinese board game Go. Not only will you make a lot of progress in these related areas, which will contribute toward the frozen area anyway, you’ll also feel a lot better about the process. When your dumbbell benching also hits a wall, then return to the regular bench press and you’ll be pleasantly surprised to find you can suddenly push through the old obstacles

In a certain sense, our primitive ancestors were really onto something. It isn’t all that natural for human beings to focus too narrowly on any one thing. You wouldn’t want to eat the same meal every day, so why do the same exercise routine, or study the same books? The long flat plateaus are kind of like nature’s way of pushing you to try new things. Switching from treadmill to yoga, you’ll meet new people and discover new things in life. A little casual boxing might be exactly what the karate redbelt needs to go black. Absolute worst case scenario, even if the new goals and activities don’t pan out, you’ll still strengthen your body and mind, making it that much easier to kick open the gates to greater mastery in the original area.

The coolest thing about the plateau effect is that once you do manage to push past the blockage, you’ll suddenly find yourself moving forward and progressing very fast. You can catch up with and even overtake the plans you made based on how things were going pre-plateau. It’s like your brain and your body were resting, and suddenly they wake up energized and ready to stride.

This effect is one I’ve experienced time and again in my mathematical studies. For the longest time, I couldn’t understand quadratic equations. I read lots of other math, even skipping ahead and studying things I wasn’t “ready” for, according to traditional ordering. Soon, the process of completing the square “clicked”. I got it, and after pushing through that limit, my mathematical maturity had grown enough that I was able to blast forward at full speed, quickly mastering all of single-variable calculus before splattering into the next wall

You’ve heard the phrase “learn at your own pace” a thousand times over, I’m sure. The reason it’s such great advice is exactly these speed-bumps on the road to expertise. People in general would be a lot better at math and science if they had the freedom that I had when I was self-teaching myself. The big trap in traditional education is, you hit a plateau but the course must go on. People get left behind. Worst part is, they think there must be something wrong with them, like they’re no good at physics or whatever, when the truth is they’re doing just fine. When you teach yourself and you have the patience and flexibility to clear the hurdles, you’ll be amazed how far you can go. Through gradual, persistent improvements, you’ll discover the deepest genius within yourself, your body will be transformed, your very life will flow with mastery.

FURTHER READING

Progressive Training
Mathematical Maturity
How To Take Control Of Life
Boot Camp

Mathematical Maturity is what allows maths to make sense. It’s a kind of inner spirit or muse which smolders within every one of us. Some peoples’ mathematical maturity is stronger than others. The way you train it is simple: you do math. Like weight training, to train your mathematurity you need to struggle with concepts and exercises which really challenge you. Material which might have been just right for you a year ago, might today be routine and you won’t grow much from it. Again like weight training, it doesn’t matter how strong you are today, all that matters is that you hit the gym and lift what you can. When I first went to pump iron, I could barely lift the naked bar (45 lbs) with no plates on it; when I first got interested in geometry and algebra, I could barely solve linear equations. Like I could have thrown down that bar and resigned myself to a life as a wimp, likewise I could’ve thrown down the mathbook and consigned myself to innumeracy. The latter course would have been just as silly as the former. Because I pushed through and slugged it out with those equations through thick and thin, today I’m a raging trigonometric Hulk, and difficult exercises tremble at the sight of my shadow

“But, but, my major requires I take Advanced (fill in the blank) to graduate!” It’s not relevant. Trying to take a specific mathcourse is futile if you don’t have the matheturity you need for it. It would be like a newbie powerlifter saying, “I need to benchpress 250lbs to win the competition for my weight class, I can’t waste time benching these puny 135lb plates!”

How do you tell which mathematics is best to study, to train yourself for bigger things? Fortunately, we have the natural ability to distinguish that material best suited for our perusal. Namely: when you’re ready for a particular area of math, it’ll be fun and interesting and exciting to you. If you’re not ready, it’ll seem like the most excruciating, boring, and/or difficult thing in the world. Therefore, regardless of what your ultimate motive is to learn, you should start with whatever excites your passions. Don’t worry: as you mature in your mathematical sophistication, a figurative blindfold will fall from your eyes, and you’ll see the sublimest beauty and feel the most profound excitement in subjects that were once an opaque soup of gibberish.

The ideal path varies from person to person, and it almost never correlates very closely with the “traditional” ordering of the subjects. Take the branches of game theory and chaos theory, for instance. At a university, these will be senior level courses at least, and yet I’ve known people who were struggling with basic algebra who were absolutely fascinated by these theories. To those people, I say: burn the algebra books and devour the pagan doctrines of chaos! As long as it’s what sparks your interest and keeps you turning the pages long after bedtime. Before I officially got into mathematics, I read books for laymen about theoretical physics. Wormholes, higher dimensions, cosmology, relativity… these things were lightyears ahead of me in the traditional sense, but they’re exactly what I was meant to read about at the time (of course, this is where the weight-lifting analogy fails: weights have a natural order which doesn’t vary from person to person, but one man might be best-suited to begin his studies with fractals while another should begin his with computer programming).

The cool thing is that when you’ve got the appropriate level of mathematical maturity trained up for a subject, it becomes incredibly easy. If you’ve done your training and you’re ready for the literature, you’ll find yourself guessing what the author’s going to say before you even read the words. It’s almost like knowing some close-held secret of the universe, like you and God are winking at each other about your private little in-joke while the rest of the lecture hall sweats bullets over a midterm.

Another important thing is that to attain the desired levels of pure sophistication, you must have a deep, emotional-level belief that you’re good at math. Forget about what any teachers have told you in the past, it doesn’t matter. Past reality is irrelevant to present moment beliefs. Repeat: “I am good at math” until it’s hypnotized into your very subconscious. If you’re busy doing ten things at once and suddenly you see an equation somewhere, your automatic, knee-jerk reaction should be: “Oh, equations, I’m good at those”. That’s how deep you should program the belief in yourself. It doesn’t matter if you have to write it a hundred times a day on paper, it’s worth the effort a thousandfold. Neither does it matter what the objective truth was in the past— the past is history, and in the present, you’re muthaf’ing Good Will Hunting!

FURTHER READING

“Problems” in Mathematics
Five Ways to be Better At Math
Rote Memorization vs. Understanding
Teaching Myself Calculus

The first step was to find a tutorial. Since I’m already a master coder (primary language C), I’m looking for a no-nonsense one which gets right to the point. A quick glance through the tutorials from google shows about half of them are aimed at people who have never written a line of code before (“Java script tutorial for the total non-programmer”) and the other half are trying to sell me an online certification (w3schools). I settled on Webmonkey’s JavaScript Tutorial, which looks like about what I’m looking for. Maybe a little on the beginner side still, but I guess I can’t expect too many guides written specifically for someone with over a decade of programming experience already. Webmonkey’s walkthrough seems to get to the point ok, with just a handful of lessons, and they have an “advanced” tutorial as well as an introductory one.

Since I’m still using neighbors’ wifi right now and it’s not the most reliable connection, I went ahead and opened all the pages in separate tabs, loading them now while I do have a connection. Now I don’t have to worry about the whole project getting interrupted if the connection goes down.

9:45 PM: Began reading the first lesson of the basic introduction. I’m listening to DJ Project- an excellent dance group from Romania- while I work.

10:01 PM: Done. Ok, it looks like the syntax is very similar to C, so this should be a piece of cake. (Since I already taught myself C years ago.) I spent more time switching songs in Youtube than reading… I skipped the exercise because this is pretty easy stuff so far. On to Lesson 2!

10:34 PM: And, the similar to C begins to fade as we get into strings. I think I’m the last person on earth who actually loves the nitty gritty null-terminated stringery of C. But hey, life’s all about adapting to new situations. Of course a web-language like JScript can’t have the omnipotent power of arbitrary pointers, or people could use it to steal our credit card numbers.

Ahh, now I’m starting to see some of the magic of this language. Apparently, you can name different elements on your page (links, images, etc.) and then use that name to manipulate them in realtime. Brilliant

As before, I’m skipping the exercises. Thanks, Webmonkey– it’s the thought that counts! On to leccion 3.

11:10 PM: It’s a little annoying that Webmonkey is going into a lot of detail about launching and manipulating new windows. The guide was evidently written before tabbed browsing. No one launches new windows nowadays, and even if it weren’t for everyone having tabs, why would I want to harass my awesome readers with popups? But the main point is obviously just to illustrate the Document Object Model. On to Lesson 4…

11:44 PM: Functions, loops, and arrays were covered in this chapter. Pretty basic stuff, but it’s interesting seeing how they’re done here. Or I should say, how they’re integrated into HTML. The actual code itself is basically just C++ with built-in web-related machinery and without pointers. In otherwords, basically Java… On to Lesson 5, the last part of the “basic” material!

12:17 AM: All finished with the “basic” stuff. That last section was just pointless bells and whistles. Nothing I’m really interested in for Xamuel.com. The main thing is, now I understand what I need: I just need the names and documentation for the machinery for checking how a reader got to my website. So I can suppress ads for regular readers and just display them for people coming from search engines.

One way to get this info would be to look up a reference of all the built-in tools that come with JScript. But a possibly faster way would be to just look at some code which I know uses that machinery. The most obvious example is the Google Analytics script which a lot of websites (including GFM) have. So, I opened a new tab, cruised on over to Xamuel.com, and went to “View Source”. I searched “javascript” and started looking through the scripts on my own page. Suddenly they make a lot more sense than they did before. They’re doing lots of stuff Webmonkey didn’t talk about, but with the basics I got over the last three hours, I’m easily able to figure out what’s going on. I also didn’t realize how many scripts FeedBurner inserts. Why are those all necessary? I’ll have to look into it later.

Anyway, I found the code for Google Analytics. It looks pretty obfuscated. But after unravelling it, I figured out the main GA script is downloaded from “http://www.google-analytics.com/ga.js” (unless you were viewing the page over an encrypted connection, in which case the main GA script comes from “https://ssl.google-analytics.com/ga.js”).

Without further ado, I manually downloaded the main GA scriptfile to peruse it. Geez, it’s a real mess! At first I thought it was intentionally run through a code obfuscator, but then at further glance, I found the various search engine names unencrypted. Thus, it seems it’s not intentionally obfuscated, it’s just not written by a human. The ga.js file is most likely “compiled” into JScript from a source in some higher level language. That’s actually similar to what I do for metadata here at GFM (metadata is data only meant for the search engines, and includes things like keywords and descriptions). In Blogger, the only way to give an individual article unique meta-data is to hardcode it into the template, but that’s a ton of work, so I made a list of URLs and metadata’s and then wrote a quick C program to “compile” my list into Blogger template format. The drawback is that my metadata only updates when I get around to recompiling the list, so the most recent articles lack metadata.

After staring at the Analytics code for ten minutes, it looks like you can simply use “window.referrer” to get the referring site to see who sent a reader to your blog. I tested this in a “sandbox” blog and got “undefined”, so that’s a no-go. Well, I saw “a.referrer” at one point and “a=window” at another, so I assumed that meant we were looking at “window.referrer”, but it turns out the variable “a” is overused a million times in this crazy script, and after another twenty minutes of straining my eyes, I couldn’t figure out what exactly the “a” in “a.referrer” was! Enough of this, I’ll just go to google and do a search. I searched for “how to check referrer in javascript”. Hey, at least the Analytics script gave me the right field to search for! The very first result, “Fun With The Referrer Property”, will do fine. And, glancing at that, I was pretty close: the correct answer is document.referrer.

With that, I now should know all I need to know to kill ads for regular readers. If you’re a regular reader, look forward to those ads disappearing!

FURTHER READING

Read my article How I Taught Myself Calculus, and I’ll guide you along the journey that took me from a flunking math student in junior high to a math PhD student and teacher.

For some computer programming analogies applied to real life time management, check out Defragmentation For Your Life.

For a much longer (about 30x longer) liveblog of me self-teaching myself, check out the liveblogging I did of my French In 30 Days challenge.

The problem back in sixth grade wasn’t that I was naturally bad at maths. As a matter of fact, no-one is. It’s just that I thought of myself as terrible at it. So what made the change? That’s an interesting story, actually.

One day I saw a very interesting-looking paperback in my best friend’s parents’ room. “Develop Your Psychic Abilities”, by Litany Burns. To a young preteen, that book may as well have been titled “The Coolest Thing Ever Written In The Whole History Of The Universe”. My friend’s dad was a professional psychic hotline operator, lending an air of credibility to the literature he read. I was too embarrassed to ask about it, so, being a little shit, I snatched the book while nobody was watching.

I could write a whole separate article about the adventures which followed, but to make a long story short, it opened my eyes to the idea that I can teach myself things, and that it’s awesome. The autodidact within me was born. (I had already taught myself some things before, like the BASIC programming language when I was no taller than your waist, but it had never been about reading books!)

At the same time, I was also interested in Dungeons and Dragons. Psionicists show up in this game, with the stereotype that they’re brainy and that their psychic powers are directly correlated with their intellectual powers. Consequently, a D&D psionicist will always be studying things like abstract math and logic. Think “Vulcans” from Star Trek. This further stirred up the sudden love of knowledge in me which, a mere year ago, had lain dormant.

I started studying anything that seemed particularly abstract or arcane. That quickly lead me to Euclid’s Elements. The Elements is the second most widely read and widely sold piece of literature in the world, second only to The Bible. It is the original geometry textbook, written thousands of years ago and still read today. Unlike modern public school mathbooks, written with the assumption that the reader is stupid, Elements is written with the assumption that the reader is intelligent. Unlike modern texts which fail utterly in their pathetic attempts to be “relevant” or “hip”, the Elements is timeless. I took one glance through the almost mystical-looking illustrations, and I was hooked.

While it’s tempting to reap the praise of being a child genius or something, the fact is, I really didn’t understand the Elements at all. The first proposition– instructions for how to draw an equilateral triangle– made sense (after reading it a million times), and that’s about it. But that one proposition blew my mind, the way the instructions were laid out so logically and beautifully, and then how the guy proved that the construction worked. It was my first taste of the Olympian-Nectar which is formal proof, the real heart and soul of mathematics.

I didn’t understand Euclid’s works, but I sure loved flipping through the pages and looking at the pictures. It was like a game, trying to find just how amazing an illustration could be. I took a ruler and a compass and some paper and I started making geometric figures of my own. I couldn’t understand what Euclid was doing, so I was doing it myself! Of course, I failed to discover anything, but what happened there was magical: my self-image metamorphosized from that of someone who sucked at math, into that of someone who was good at it.

I wasn’t born a mathematical genius. It’s just that when we get a self-image in our heads, we tend to make it real by any means necessary. This has proven true in my life so many times, I’m convinced if I could just solidify a real, genuine “multibillionaire” self-image, and really believe it, it would materialize. Once I was drawing those geometric figures and emulating Euclid, people started seeing me as a kid who was good at mathematics. It was an illusion, but over the next few years, it was set to become real.

My parents bought me some math books for my birthday that year. I got a precalculus textbook and a couple calculus ones. I devoured them, along with an ancient algebra textbook we had lying around in the house. In the precalc book, I didn’t understand everything. I didn’t understand trigonometry hardly at all. If I had to take a midterm on the stuff, I’d've failed it, but what was important was that I was “learning the language”. Most people who take precalculus in college, they don’t read the textbook at all, besides doing assigned exercises. Reading it made me feel really smart and intelligent. And even if I didn’t understand something, I was picking up the general “style” of mathematical texts. Symbols which once looked like alien writing, were transformed, if not into symbols I understood fully, at least into symbols I’d seen before. Symbols I could at least pronounce.

Conventional wisdom in mathematics says, you have to always build on what comes before. I found this to only partly true, and more than half the time, false. It’s an example of ideology, which pollutes knowledge. But since I was self-teaching, I escaped the misleading ideology. There is certain truth to the ideology, but, in mathspeak, it’s a “local truth”, which means that it generally holds true within a section or a chapter. But often you can skim one chapter and jump right to the next and you’re fine. (You can go back and pick up the hard stuff later, when your mathemuscles are bigger)

When my parents took me to interview for a radical fundamentalist private Christian highschool, we sat down with the lady who would become my ninth grade algebra teacher. She asked me if I had any questions about algebra. At the time, I was really struggling with the how the quadratic equation works. I was good at solving linear equations, it’s just a matter of “keeping the scales balanced”, but there was a certain “trick” to quadratics (completing the square), and I didn’t have the mathematical maturity to grapple with it. I asked her about it. She showed it to me, but having a person explain it in person no longer added any new light that the books did not. I was sufficiently liberated from the crutch of teachers, that I would never again need them to translate texts for me. (At least not until I started getting into real journal articles in grad school!)

Literally days after the interview, I suddenly “got” it. The process of completing the square suddenly made sense. And once I “got” it, it was so simple I was amazed that I had been stumped for so long. Suddenly, I didn’t even need the quadratic formula to solve quadratic equations, I could do it manually. But it wasn’t because of some natural born talent or anything. Completing the square was a big ol’ dumbbell that I’d been straining at forever with no progress. But meanwhile, I was also training with smaller dumbbells– reading ahead, I mean. Then one day, with muscles enhanced by the smaller weights, I returned to my old nemesis and suddenly found I could lift it with ease.

I can’t emphasize enough the importance of getting a textbook which treats you like an intelligent person. Anything in the undergrad section of a college bookstore will be trash, because it’s written for people who are only studying it because they have to. Also, this might sound a little shallow, but I think it’s important the text should have a professional look and feel to it. That rules out most textbooks with their cheesy covers, always making some futile attempt at “relevance” or “hipness”. Look, it doesn’t matter what’s on the cover of a calc book, people are gonna think it’s an arcane tome of mystic spells– so you may as well make it look like an arcane tome of mystic spells! At least then it’s impressive and cool, and I even think you learn more from it, just because you somehow take it more seriously. Mom and dad did a great job with my birthday gift, because one of the calculus books they got me was Swokowski’s Calculus, the Classic edition.

I didn’t know it at the time, but Swokowski is actually one of the most well-respected calculus texts around. Compared to some of the trash I’ve seen undergrads forced to buy here at OSU, it’s like heavenly script.

That interview with the future algebra teacher took place a while before the school season would actually start. The next time I saw her, I was well beyond the quadratic equation. Once my mathematical maturity was good enough to swallow completing the square, it was good enough for me to rocket through most of basic calculus almost nonstop. Not much in calculus is actually fundamentally harder than solving quadratic equations manually, it’s just more intimidating. By being a self-teacher, I was able to pierce right through the illusionary intimidation factor.

It didn’t take very long before I knew more mathematics than anyone in that cheap crappy private highschool. Rather than praise me for teaching myself the rudiments of analysis, it actually became a sore spot in my already very poor relations with the teachers. In my article “You might be an autodidact if…“, I jokingly wrote that you might be one if you tuned out your highschool algebra teacher to study calculus. But actually, that line was based on my real life experience! I’m one of a very select few who can boast that their ninth grade principal confiscated a textbook from them.

The Summer after ninth grade, my math autodidact days came to an end as I started taking calc classes at Mira Mesa Community College (in California, the state will pay your tuition if you take college classes as a high schooler). It was a temporary end, as I would start teaching myself far more advanced mathematics years later while I was in the Air Force. But that’s a story for another day

FURTHER READING

I wrote an article with some hints about being better at mathematics. Five Ways To Be Better At Math.

Read about self-teaching in general at my article, Autodidact: Be A Self-Teacher. There are many lifelong advantages to becoming a self-teacher. Everything suddenly becomes a whole lot easier.

Should rote memorization be used in mathematics? The knee-jerk response these days among math educators is a resounding “NO”, and I used to agree, but lately I’ve been really questioning that. Sometimes, some rote memorization is good. Read more in Rote Memorization In Mathematics.

You Might Be An Auto-didact If…

…Your dad insisted you go to med school, but you kept testing out of it.

…You didn’t just teach yourself how to whistle, but how to whistle Beethoven’s Complete Works.

…You’ve used google so often, the search bar is burnt into your monitor.

…You put an apple on your *own* desk in the morning.

…As a baby, you surprised your parents with a first word in Latin.

…You had to expand your closet space to fit more flashcards.

…You keep hoping they’ll invent waterproof books for when you have to shower.

…Congress enacted anti-”self-taught driving” legislation after the mess you made of your hometown.

…You interpret Pink Floyd’s “Another Brick In The Wall Part 2″ as a call for wider-spread self-teaching.

…You devour the biography of every politician before going to cast your ballot.

…You hit “random article” in Wikipedia and it says “Error: No unread articles remain”.

…Instead of using fashion or music, you rebel against your parents by studying philosophies and disciplines they disagree with.

…You’re ticked off that there just aren’t enough Chinese characters to learn!

…In high school, you tuned out your algebra teacher and used her class as time to brush up on calculus.

…You taught yourself Law and passed the bar exam, just to contest a jaywalking citation.

…You designed and programmed a lifelike robot to take your “Computer Science 101″ class for you.

…You took the phrase “reinvent the wheel” too literally and spent months chiseling one out of stone.

…You snuck into the neighborhood pool after hours so no pesky “lifeguards” would stop your self-teaching there.

…When you ran out of languages to learn, you started making new ones up from scratch.

…You’ve been gorging on pure lard so you can practice some self-taught open-heart surgery.

…Tired of web browsers, you taught yourself to read and write the HTTP protocol manually.

…You couldn’t find a local weather forecast, so instead you used an advanced meteorology textbook.

…On a long road trip, you listened to “Euclid’s Elements: The Book-On-Tape”

Here are some more serious articles on the subject of autodidacticism:
Autodidact: Be A Self-Teacher
Autodidact, PhD.
Short Story: The Juggling Balls of Destiny