The internet's knowledge problem

Easy access to information is making it more difficult to learn hard sciences at home.

Ever since my early teens, I knew I wasn’t cut out for formal learning. When a topic excited me, I set my own pace and stayed well ahead of the class; this frustrated my teachers more than it impressed them. And when I lacked passion for a particular subject, the faculty never cared to help. In fact, most seemed to hate their jobs: they just wanted to finish grading papers and go home.

In the end, I can credit school for teaching me social skills, but almost everything else came from decades of self-study. Having gotten online around 1997, I also had a chance to observe how the internet transformed independent learning. My conclusion is that the web made it much easier to explore humanities or learn crafts — but markedly harder to progress in areas such as electronics, physics, or math.

To explain, let me offer an anecdote. I frequent /r/AskElectronics, a prominent Reddit forum where novices can post questions about circuit design. Earlier this week, a visibly confused newcomer asked if someone could explain to them the concept of impedance. An early answer came from a recent EE graduate; it amounted to an unnecessary and confusing segue into calculus:

“If you want the real and correct answer: impedance is the Fourier transform of the underlying differential equation.”

Not only is this reductio ad Fourierum an unsatisfying explanation of a fairly intuitive physical phenomenon, but it sends the reader on a wild goose chase. Their next stop is probably Wikipedia, which explains the Fourier transform the following way:

“The Fourier transform can be formally defined as an improper Riemann integral …

It is easy to see, assuming the hypothesis of rapid decreasing, that the integral Eq.1 converges for all real 𝜉, and (using the Riemann–Lebesgue lemma) that the transformed function f̂, is also rapidly decreasing …

Until now, we have been dealing with Schwartz functions, which decay rapidly at infinity, with all derivatives. This excludes many functions of practical importance from the definition, such as the rect function. A measurable function 𝑓:ℝ→ℂ is called (Lebesgue) integrable if the Lebesgue integral of its absolute value is finite.”

I’m not cherry-picking; this is the introductory definition near the beginning of a novel-length article; it only gets worse from there.

The article is not an isolated problem. Let’s say you want to learn about quaternions — a fairly accessible math concept used in 3D computer graphics. Wikipedia offers the following passage:

“In modern terms, quaternions form a four-dimensional associative normed division algebra over the real numbers, and therefore a ring, also a division ring and a domain. It is a special case of a Clifford algebra, classified as Cl_0,2⁡(ℝ)≅Cl_3,0+⁡(ℝ).”

In the pre-internet days, if you wanted to learn about impedance or quaternions, you’d probably reach for a book written by an educator — that is, a person who had the process of learning in mind. Today, we search the internet instead, and we’re regularly subjected to this sensory onslaught from students who are paraphrasing the final chapters of their coursework without any regard for how others can get to the same level — or if it’s necessary to go there in the first place.

This is not necessarily a Wikipedia problem, but it’s a problem of defaulting to Wikipedia if the accessibility of knowledge is not their editorial goal. To be fair, the internet is also providing a platform for talented educators — but their content usually ends up below the fold. Plus, in the era of short attention spans and gamified monetization, few authors are determined enough to develop a coherent curriculum that could turn proselytes into pros.

The quaternion example courtesy of @tj on Mastodon. For more articles on this blog — including a common-sense introduction to impedance, the Fourier transform, and more — click here.