Fragility and Antifragility in Knowledge

Shivam Gandhi
Jul 23, 2017 · 5 min read

Introduction

Recently I read the book Antifragile by Nassim Nicholas Taleb. While I have a variety of criticisms of the book, ranging from Taleb’s arrogant tone to many poorly reasoned claims he makes, the book got me thinking about systems that benefit from chaos and uncertainty as opposed to weaken from them. I wanted to apply the concepts of antifragile systems to my daily life so that instead of getting pissed off by random events that stop me from getting to my daily goals, I could use them to get closer to my goals.

A good way to summarize the concept (source 1)

This morning, I was reading Surely You Must be Joking Mr. Feynman and came across a line that got me thinking about Antifragile again:

I don’t know what’s the matter with people; they don’t learn by understanding; they learn by some other way-by rote, or something. Their knowledge is so fragile!

Some context is warranted. Feynman was talking about how he pranked students at MIT when it came to a certain tool that allows you to draw curves. What was special about the tool was that at the bottom of the curve the tool lets you draw, the tangent was completely horizontal.

The students at MIT were completely dumbfounded by this fact, but the truth is that this fact is obvious if you think about it mathematically. At the minimum of any curve, the tangent will be horizontal (this is the result of the derivative of a function hitting 0 at minima and maxima). Feynman was complaining that the MIT students’ knowledge was fragile since this elementary mathematical concept was lost upon them, and he was able to use that to trick the them.

I want to explain how I think fragility and antifragility can be connected to knowledge from this anecdote and talk about my thoughts on what makes knowledge fragile or antifragile.

Fragile Knowledge

Let’s start by examining the word fragile in that quote above. We defined fragile as a system or object that is harmed by volatility and stress. In the context of an individual person’s knowledge, the primary harm to knowledge comes from time. Unfortunately, we’re all well aware that anything we cram into our minds (like cramming for a test) will most likely be gone within a week. Even for knowledge that we spent a more extended period of time studying, it’s unlikely to remain as clear in your mind months after, unless you’re using it on a regular basis.

In Feynman’s anecdote, he calls the knowledge of the MIT students fragile since the students memorized the facts and didn’t really understand the material. As a result, their knowledge of the material is week, and will not withstand time since it was crammed.

If we’ve decided that fragile knowledge is knowledge that doesn’t persist in your mind over time, defining antifragile knowledge becomes much easier.

Antifragile Knowledge

Simply put, antifragile knowledge is knowledge that persists over time and even becomes more ingrained. The question is, how do we make knowledge become stronger over time? The answer would lie in making connections between piece of knowledge.

By making connections between pieces of knowledge, there are more avenues in a person’s daily life for them to be reminded of a certain concept. It allows them to see how different ideas are fundamentally similar or can use each other as metaphors. I’ll provide a simple example.

Suppose I’m trying to understand what the mathematical concept of isomorphism is. An isomorphism is a relation between two sets A and B so that every element in A is paired uniquely with an element in B, and every element in B also gets paired uniquely. I understood isomorphism by making an analogy to married couples and how two people are paired uniquely. In this analogy, a day to day example grounds my knowledge of the abstract concept of isomorphism and isomorphic sets, and I haven’t forgotten the concept to this day.

When going deeper into mathematics, I can use concepts that I already understand well and connect a more complicated idea to said concept. For example, I had already made an analogy of rotation matrices to a globe, so it was easier for me to connect the concepts of angular momentum in quantum mechanics to rotation matrices. In this way, I’m building an indirect analogy where there is some intermediate concept that I get through before arriving at the tangible real world example.

However, there are times where I don’t attempt to draw analogies between mathematics or physics to the real world, and I’ve found that my understanding becomes weaker. When learning about tensors for the first time, I didn’t try to make the analogy between tensors and companies, which I do now. (The analogy here is that a tensor is a company, where there are managers which correspond to the elements in the dual space, and there are employees, which correspond to vectors. The tensor as the company builds a product, which is like a real number in my mind). Without trying to build a good analogy, I didn’t understand the material properly and ended up having to relearn the concept.

There isn’t really any method to how I make these relations between concepts outside of what is immediately memorable for me. Sometimes, I make analogies between absolutely nonsensical ideas to a concept. For example, I’ve made the analogy of the Spanish word “caber”, which means to fit, to the image of trying to fit a bear in a cab. So when I’m trying to recall the spanish word for “fit”, I get a bizarre picture of a bear trying to fit into a cab and caber comes to mind. You have to use whatever works for you.

My caber analogy wasn’t made by me, I got it from this absurd picture…

What I Plan to Do With This Information

Now that I have a better understanding of what kind of information sticks in my mind and what doesn’t, I’m going to try spending more time constructing analogies between concepts and other concepts/real world situations more often so that the things I learn don’t just disappear from my mind. Of course this means that I can’t cram to study anymore, but I was trying to build better study habits anyways, so I’d consider this a win.

Let me know what you think about the idea of using analogies to better understand information and if you think my analysis on fragile/antifragile knowledge is satisfactory.

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