Generalizing Your Experience

Timothy Blumberg
Q.E.D.
Published in
6 min readJul 6, 2018

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This article may be better served as a series of separate articles, but the ideas are so closely related and yet so very different that their juxtaposition is just darling.

Mathematical Thinking

I am currently taking Dr. Keith Devlin’s Introduction to Mathematical Thinking with my sister in high school. We are talking about a great many number of the core ideas about mathematics that make the field truly interesting.

I count myself as a recent convert to the joys of mathematics. Like many students, my first introductions to mathematics were dreadfully boring problem sets applying algorithms and numerical tricks to solve equations for hour after hour. This charade was repeated for 2 more segments of calculus in college at which point I was fully convinced scholars of math are actually masochists. I think many people never progress past this stage, because there has never been a proper presentation of what Mathematics can really be. Recently, I’ve discovered math is less about solving for a particular number or value and more about using the things you know to reason about things that you don’t know. It’s about building and applying abstractions to problems that you would have previously never considered tractable.

Now I want to issue a disclaimer that I did not earn any sort of degree in mathematics, nor do I consider myself a mathematician. However, I have learned to embrace the notation, desire for generalization, and logic that mathematics truly allows. Mathematics is a tool, like programming, that can and should be wielded by all scientifically minded individuals.

When I have found myself reading papers about Partially Observable Markov Decision Processes or Motion Planning in Autonomous Vehicles, the formal presentations of the ideas can proffer profound insights that the text never fully captures. Presently, for really the first time in my life, slowly coming to terms with the equations of a paper can offer the deepest insights. A few lines of mathematical notation can very succinctly capture the essence of a paper many pages long.

However, there still are (and will always be) many ideas that truly confound me. I have spent many hours of investigation digging into a concept from machine learning known as Rademacher Complexity. Despite my greatest efforts, I remain light-years from an intuitive understanding of the basic principles. But, I think this perpetual confusion is perfectly acceptable! We are all struggling for relative improvement!

To put things in perspective, it helps to look back over your journey as a student on a longer time-scale. The problems I struggled with so tragically as a first-year computer science student are trivial for me today. I am the same creature that struggled for hours over the most trivial sorting algorithms just a few short years ago. But I wouldn’t be the person I am today without the understanding that I gained through the hours spent trying to wrap my mind around the concepts. Understanding can only be earned through the struggle; by becoming subsumed by a problem before re-emerging with some new insight to be carried in from the borders of your understanding. These insights and lessons build on each other incrementally. Eventually, while working on a problem, you can take a step back and admire all of the complex insights, learnings, and concepts that are required to even fathom the problem statement.

It’s a marvelous moment for all of us struggling to learn new things to recognize how far you’ve come already!

Living in a New Place

After I graduated in 2017, I moved to Shanghai for 8 months to work at a Chinese 3D mapping company. My coworkers did not speak English and I was forced to put my Chinese minor to work everyday to communicate. Despite my intensive preparations before going to China, I was rather overwhelmed by the total lack of familiarity in this new place. This alienness is even more overwhelming when it includes the language you use to interface with the world around you. In general, language is tool of basic social interactions that is so fundamental that native speakers rarely have need to contemplate it. The problems we spend most of our time thinking about take place at a higher plane of abstraction. We talk about and discuss problems using language. We ask clarifying questions to eliminate ambiguity using specialized jargon. We argue, tell jokes, and discuss ideas that excite us.

But in China, I was distanced from comfort–constantly backpedalling as I struggled to make sense of the rules that govern this new place. Things took place that delighted, shocked, offended, and surprised me, and yet, seemed entirely unremarkable to the many thousands that surround me on those Shanghai streets. It required me to take a hard look at the things that I thought I knew about what a modern society ought to do. I was being shown a vibrant counter-example to my long-held belief that Western Society is the theoretically optimal form of human society. (For a great book on the subject, please read Mahbubani’s brilliant tome)

This departure from the known was a wonderful opportunity to delineate the things that I knew from the ways that I have always expressed or heard them expressed. Ideas were set free from the biases and constraints that English had implicitly placed on them. I was given a new lens to view myself and my thoughts through. At least on a weekly basis I would stumble across a new 成语 (chengyu: idiomatic phrase with a story behind it) that would blow my mind. They provided deep insight into a facet of human character that I maybe always “knew”, but rarely engaged with because I lacked the machinery to do so.

There were countless disagreements that I had with my coworkers about the way we should design or implement one of our projects. Over the course of an hour or so, we would dig down from this key disagreement into the hard details shaping our arguments. Most frequently, we would discover some fundamental misunderstanding in the way that we were communicating. The modes of miscommunication varied widely, but would frequently fall into the following categories:

  1. I would misunderstand an important word being used
  2. I would mistranslate a concept directly from English to Chinese
  3. A difference in the assumptions that we made because of the societies that we were raised in

After unearthing a seemingly trivial difference, we would realize that the majority of the energy of the argument was wasted. We were arguing two entirely different points, and agreed upon each others’ positions fully. I am most thankful for these long struggles, because they provide startling examples of how your background can mould your logical thinking.

Unsurprisingly, I learned my most profound lessons about Chinese business and society through these deep communications failures. In each, I was forced to generalize my thinking in a strange and unexpected direction.

A nice example of one of these differences is comparing Go and Chess. Both games are war-like simulations played on grid-like boards. In Go, play pieces are added incrementally to the board on the intersections of the lines, while in chess the pieces are removed during play and rest in the squares outlined by the lines on the board. These are small differences, but they offer some interesting insight into how this property of “similar, but altogether different” can play out in more nuanced discussions.

Seek New Things

If I have learned anything at all in my life, it is certainly that I know nothing. My thoughts are small, biased, and lesser presentations of the ideas of much smarter humans, but they are mine. I entreat you to always seek new things. Challenge even the most trivial assumptions that you make. Seek to understand something from a new perspective. Talk to an immigrant about their homeland! Talk to a mathematician about their favorite insight that they ever gained!

I think we all fundamentally capable of pushing the needle for humanity as a whole. Not as an isolated individual that can make all of the difference, but by taking part in the frenzy of building new technology.

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Timothy Blumberg
Q.E.D.

Eternal Learner and Programmer; Communicates poorly in Chinese; Working on Crypto.