A wheel that turns, although nothing turns along with it, is not part of the mechanism.Ludwig Wittgenstein. “Philosophical Investigations”
The Funny Wheels That Never Turn
Brain teaser: do you know what MATH stands for?
Have a think before scrolling down…
The answer: MATH = Mental Abuse To Humans!
# insert-dry-laughter 🙂 #
Now the above was just a teaser to get you smiling and in the mood for some fun stuff (that is somewhat related to – you guessed it – mathematics)! And just as a disclaimer: I think math is awesome!
Here we go, back to the topic of wheels. Take a look at this poster for a few seconds, and see if the irony shines through:
Do you get the joke? Some of you may be cracking into laughter now, others may be staring back at the screen dumbfounded (which was how I reacted when I saw this picture for the first time). As is often the case, a Reddit response enlightens us:
It wouldn’t work, they wouldn’t rotate together because 2 of them would be going in the same direction and the other one would be going in the opposite and therefore, however way you spin them it won’t work.Reddit comment
Read the Reddit comment, and then read the title of the poster again: “Education works best when all the parts are working.” Get the irony of the title? The parts will never work together! This is a perfect illustration of Wittgenstein’s quote at the start of this blog post – we have a wheel where nothing could turn with it!
And if you are interested in more hilarious examples of wheels / cogs turning (or not turning), I would highly recommend this video from Talks At Google: “The Greatest Maths Mistakes” featuring your all-time-favorite math nerd: Matt Parker. You already get a sense of how funny Matt turns out to be from the bio that Google wrote of him:
When math goes wrong, things can get expensive. Or absolutely hilarious. For this talk we invited YouTube personality (Numberphile, standupmaths), math communicator, comedian, and one third of the Festival of the Spoken Nerd, Matt Parker, to share his favorite math mistakes from his new UK #1 bestseller, “Humble Pi – A Comedy of Maths Errors“.Talks at Google
Coming back to the wheel vs. education (learning) analogy: just like we could have wheels that look perfectly-crafted but cannot turn when put together, we could also have pieces of knowledge that seem important in isolation but cannot form a coherent system of knowledge.
Just as “no man is an island,” no knowledge is useful if it is stranded on its own, without connecting the dots with other types of knowledge to form what we call “wisdom”.
On that note of knowledge vs. wisdom, let’s turn to “transmissionism”.
The Wheels That Aren’t Really Turning – “Transmissionism” is Mistaking Knowledge for Wisdom
Andy Matuschak re-interprets the quote about wheels above in the context of education: “if you’ve simply memorized a whole bunch of piece of atomic information and yet they don’t connect to each other, you are not able to combine them into anything.”
However, as students, we may fall into the trap of not knowing that we are not really knowing – or a trap called “transmissionism”:
Transmissionism is the false idea that you can come to know a thing by having that knowledge directly transmitted into you, as if you are a slate that I as the teacher can write upon.Andy Matuschak on “Econ Talk” podcast
In other words, transmissionism is the error of mistaking superficial knowledge for wisdom, which are related but different concepts:
I would have us try to focus on two things: information, and then wisdom…(wisdom is) seeing connections between things I didn’t see before; understanding that something I didn’t realize applied to something else; seeing an analogy that might help me understand how to think about something.
…The temptation to reduce everything to a multiple choice exam tends to force us toward spit-back information and move us away from wisdom is part of the challenge. It’s certainly the elementary-to-high-school educational problem.Russ Roberts on “Econ Talk” podcast
How to Turn the Wheels (and Turn Wise)?
…is a very good and very difficult question. (<= This is a filler sentence.)
In this “Econ Talk” podcast episode, Andy Matuschak shares some tips:
- Have the right “problem-solving” mindset – in math, this may mean finding the right answer; in economics, this may mean “just to understand the factors that might be the ones you want to consider”. Know what you are really solving for, or which direction the wheel is supposed to turn;
- Practice spaced repetition: space out time between repeated practice of a material (e.g., scheduled prompts or quizzes). This type of spaced repetition has been shown to improve the stickiness of memory.
For Chinese speakers, I recommend checking out this mandarin podcast episode on how to deal with information overload in the Internet age: “过载时代的信息修养（疯投圈播客）“.
I will save a discussion on learning techniques for a later blog post. If you have any good ideas, please email me at firstname.lastname@example.org. Till next time!