Author: Mark

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Large Parties

And I like large parties. They’re so intimate. At small parties there isn’t any privacy.

F. Scott Fitzgerald, The Great Gatsby

A few weeks ago I read The Great Gatsby for the first time. It was a pretty good book. I don’t have much experience reading Fitzgerald, and the style of his era — as well as the upper class focus — is a bit different from what I normally read. I enjoyed the story, but the only thing that really stuck with me was the quote above. It is not central to the book, but I find it particularly profound and relevant today.

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That’s a Bad Pirson

I was on one of my favorite subreddits today, /r/learnmath (of course I sort by New), and a question came up that ultimately came down to understanding order of operations. These always frustrate me because they stem from a poor understanding of how the order of operations work; furthermore, any problem involving order of operations can be fixed and cleared up with an additional set of parentheses.

Consider this math problem below — the type I see making its way around Facebook.

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Holes in a Paper Towel Roll

At work the other day, we had a bit of a break to celebrated the month’s birthdays. During this time — my coworkers sitting around a large table, munching on pie and ice cream — a conversation broke out. How many holes are there in a paper towel roll: 1 or 2?

Of course, there is the joke that if you claim 1, then there is only one hole of consequence in the human body: that which leads from your mouth to the escape of your digestive system. At that point you’re just talking out of your ass.

But, being a company full of nerds and pedants, those of us who were sensible had to claim 1; after all, a paper towel has width to it and is thus homeomorphic to a torus (think, bagel).

Topology is a fun subject. Imagine taking geometry, and saying “I don’t really care about angles, or lengths, or these things that make geometry what it is. I mainly just care if I can stretch something to make it into something else, and how many holes there are in the shape.” That’s the base level of topology. An introductory topology course teaches you about homeomorphisms, which means you can continuously stretch, pull, push, or generally manipulate an object without cutting or tearing it.

Imagine you had a very flexible, putty-like bagel. If you mad the bagel very thin, skinny, and tall, you can imagine forming yourself a paper towel roll. This is what we mean when we say they are homeomorphic. We don’t put an extra hole anywhere, we just squish and shape things to our will.

Some people may ask why this is useful, particularly when you learn a coffee mug is also homeomorphic to a torus. The easiest explanation is math is about abstractions and patterns. Sure, a cube and a non-cubic rectangular prism have some differences, insofar as the rectangular prism doesn’t have three equal edge lengths. A cube and a triangular prism seem even further removed. Yet, any prism, or more generally polyhedron (which includes pyramids as well!), are all homeomorphic to a sphere. These three dimensional figures share certain properties, most notably that they are solid objects with no holes in them. And there’s something to be said for that!

While topology goes well beyond this idea, it gives a good grasp at what mathematicians are interested in. They noticed that we can generalize some of these properties, and map between objects using these homeomorphisms. So, instead of topology being about classes of objects which are the same in some small way, it is really about how we relate these similar objects. Topology is about showing the similarities and patterns between objects. It’s interesting that with a consistent set of rules, we can say “cube is to sphere as bagel is to paper towel roll.” We notice this pattern, and figure out how to make it rigorous and useful.

This is an under-appreciated aspect of math. It is not about rules that have no reason, or about abstraction for no reason. It is about finding a pattern, and seeing how other objects follow a similar pattern. This is what make mathematics a very fun subject, yet it is a mindset very few people are able to have. I hope this can change in the future.

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Coffee Shop Blogger

I’ve been curious how cultural trends adjust our feelings toward various habits people have. The biggest change to me has been that of the hipster blogger, sitting in a coffee shop with their MacBook, doing some personal photo-journalism for the benefit of mankind. I think the common notion of what, and who, a writer is has changed dramatically. No longer is it necessarily someone cramped up in an attic, papers everywhere, a drink at hand; it can be anyone with just about any device. I’m sure there are people out there who write posts from their phone — I know I’ve at least edited a few posts from mine.

Of course, there is still some tongue-in-cheek (and I’m sure for some people, legitimate) ridicule for such endeavors. With so many people opening themselves up to the internet in this way, they are also opening themselves up to the critical eye of the internet populace. Many people wanting to blaze their own path end up falling into a broader statistic. But this isn’t new, nor what I want to focus on. Particularly because I’m writing this post in a Panera before I go to work this morning.

I want to focus on whether this development is good. Is the ability for people to have these platforms for themselves, to bombard more and more servers with their thoughts, photos, and any other media they wish a positive change in society? My initial reaction is yes, it is good. People are writing more, sharing their ideas, helping others out, and making their experiences known for others to learn from. Not only is it good for a society to voluntarily participate in efforts to make themselves more literate, it is also beneficial to have more information available to compare and make use of.

If I attempt to remove my optimist hat, I must acknowledge some of the legitimate gripes people have with this shift. Perhaps the biggest is the lack of credibility on the internet. Due to relative anonymity, people can claim what they want about themselves, and subsequently write what they want about the world from a perceived position of authority that is entirely undeserved. This is what we see in anti-vaccine movements, issues with climate change, and many other anti-science positions that flourish in certain corners of the internet. People with very little knowledge or background in a subject dishonestly post what they believe, framing it with the intent to make it come off as fact, especially to some particularly vulnerable people who roam the internet.

This extends to relatively innocuous aspects of thought. For my little corner of the internet, these people are largely crank mathematicians. Prior to the internet, amateur mathematicians would simply mail their ideas to professors, who could pretty quickly disregard anything that said “Trisect” or “Squaring a circle“. Now, many a young student gets drawn into arguments provided by people with insufficient background, wondering how it could possibly be that 0.999… is equal to 1, or why Gödel’s Incompleteness Theorems don’t invalidate all of mathematics. I’m sure there are similar situations for just about any field of interest. For example, consider video creation and YouTube. That was quite the democratizing effort, and has provided amazing content. And some horrifying results.

I don’t wish to be so naive as to suggest that only people who “should” be talking about a particular subject can be allowed to. Ultimately the democratizing aspect of the free internet should win out. We can provide due diligence by educating people (particularly our parents who did not grow up with it) about how to properly navigate information on the internet, but beyond that I still firmly believe that having these platforms is good. Despite very few people reading this blog right now, I’m happy this opportunity exists. The same goes for podcasts. It is exciting to create the type of media you enjoy consuming. 

While I still do not identify as a coffee shop blogger, and likely will never own a MacBook, I’m happy people can do it. More power to them.

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No Keyboard for Old Men

As I come to the realization that a significant part of both my work and personal hobbies involve sitting at a computer, I have become increasingly wary of the stories I hear about things such as repetitive stress injuries (RSI), and what will likely be the impending damage to my eyes. In an effort to avoid, or at least delay, the former issue I have tentatively purchased an ergonomic keyboard. Specifically, the Surface Ergonomic Keyboard from Microsoft. I say tentatively because it’s not cheap. I may return it, but so far I’ve put a few thousand keystrokes on it and it’s feeling pretty good. This review is meant to get as in-depth as a keyboard review can be when written by someone who has never written a keyboard review. I’ll briefly explain my rough, but sufficient, testing procedure and what I found out. Then I’ll get into some details and comparisons I noted to other keyboards I’ve used.

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Why Linux? Part 1: Free As In…

During sophomore year of college, I embarked on a project to put a Linux operating system on my laptop. I had been interested ever since using a computer in one of the engineering labs which ran Ubuntu, one of the most mainstream, user-friendly distributions out there. I was intrigued both by the visual design, and the ease with which complex programs could be run. There was also the intrigue of feeling like a cool hacker, using a terminal and typing commands to get around a file system. I was hooked, and since then I’ve had a Linux distribution running on every computer I’ve owned over the past three years.
I want to spend a good chunk of time explaining my growing passion for Linux, and why I think more people should seriously consider it as an option for the computers in their lives. This first post will focus on two of the oft-repeated phrases in the Linux community, and its main inspiration: Linux is free.
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Spongebob is Back

I recently discovered that Spongebob Squarepants is available on Amazon Prime Video. Since I am still a subscriber to said service, I enjoyed a fun weekend night watching the first couple of seasons. I’ve always had such positive nostalgia for the show, in large part due to how quotable it is. Little did I realize that nearly every line in the show is quotable, and how good each episode was in the early seasons. Even today, they have a certain innocent charm to them, yet the jokes still have enough depth to be legitimately funny now.
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