Why do many math books have so much detail and so little enlightenment? (2010)
This is a general problem with textbooks. Textbooks are not written for students. They are written <i>by</i> experts in the field, and the audience is <i>other experts</i> in the field.<p>This isn&#x27;t necessarily a problem. It&#x27;s a good thing to have experts working together to codify the current state of affairs, but it isn&#x27;t necessarily the best teaching device.<p>Even when you have people writing books that are intentionally targeted at people new to a topic, it&#x27;s easy to forget how much you know and how much beginners don&#x27;t know. I&#x27;m working on a Music Theory book with an audience of total beginners, and it&#x27;s extremely difficult for me to put myself in that mindset. In doing research for that book, I&#x27;ve been going over many of my college music theory textbooks, and re-reading some of the treatises about the subject going back to Pythagorus and Plato.<p>Things that were infuriatingly opaque to me as an undergrad are now--after decades of study--just plainly obvious and practically self-evident. You forget how little you knew after a while.<p>If there were one thing I could go back in time and tell myself when I was younger, it would be to make it clear that textbooks are not there to explain it to me like I&#x27;m five. Textbooks are scholarly works intended to be as precise as possible about the current consensus of experts in the topic area. Approach a textbook the same way that you would approach a philosophical treatise. You aren&#x27;t going to get it all the first time around. And I do tell that to my violin students who are now starting to go to college.<p>Textbooks are designed to be paired with an instructor who can interpret the book and guide the students. They are not actually designed to be self-sufficient courses of study that you can simply read and learn from.<p>The reason for this is that this is the model of education that&#x27;s been pretty much generally accepted. The university model really hasn&#x27;t changed a whole lot since medieval times and arguably going back to greco-roman times. At least in the West. I don&#x27;t know enough about Asian culture or history to comment about that. You have a master and students and some texts laying out the way of things. And in order to become the master you have to jump through a certain set of hoops.<p>It&#x27;s an almost religious sort of process, in some ways. There&#x27;s a tradition of a certain type of study with anointed masters, there are holy texts that you don&#x27;t understand but must adhere to. And if you put in enough time and survive certain types of hazing rituals, you get the privilege of becoming anointed yourself, making very little money, and possibly contributing to a holy text yourself.<p>Out of the many things that get cited as disruptive with respect to the technology revolution, one thing that doesn&#x27;t get talked about a lot is the way that the internet has disrupted the education market.<p>An &quot;explain it like I&#x27;m 5&quot; post on reddit is far more practically useful than any textbook on any topic, <i>if</i> your goal is to help a person learn about a topic. I spent the vast majority of my life studying violin, and music theory. And I was a professional performer for 20 years. When I got burned out on performing and traveling and never making enough money, I got online and started learning, practically, how to code. At first just enough to get a junior job. And I kept reading, and I got better. It&#x27;s been 11 years now, and I haven&#x27;t looked back. I can write code <i>and</i> play the violin when I feel like it, and work on a book about music theory. All that as a college dropout. It&#x27;s a life I&#x27;m deeply grateful for.<p>A generation ago, changing careers would&#x27;ve meant going back to school, probably taking on some debt, finishing up a degree that I never really wanted anyway, and then going to start something else. Which is a pretty big pause in your life when you&#x27;re in your late 20s.<p>I didn&#x27;t have to do any of that.<p>At the same time, rigorous textbooks certainly have a place in the world. The same way that Plato&#x27;s <i>Timmeus</i> or Descartes <i>Compendium musicae</i> have a place. The biggest problem with textbooks is that people misunderstand their intended purpose and audience.<p>They are tools created by academics to help create more academics. Nothing more; nothing less. If you want to participate in the academic system, you have to play by its rules. That means that you deal with these textbooks and the professors who guide you through them until you yourself are a professor, and you can in turn, guide others.<p>For those of us who don&#x27;t want to do that particular type of work and would rather be educated practitioners, there&#x27;s the internet.<p>I&#x27;m glad we have both options available now.