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I recently finished reading the book Quiet, by Susan Cain. In it, Susan Cain puts forth her concept of the “Extrovert Ideal” in western culture, and what introverts can do to help themselves in a world dominated by extroverts. In addition, she makes a case for why introverts are often exceptional leaders at all levels, although this may depend on the dynamic of the workplace itself. As a self-avowed introvert, I found much of what she said to be very appealing and helpful. Most useful to me was the idea of a restorative niche, an environment to which you naturally go whenever you’re feeling a bit down or out of place. I enjoy this part of the book in particular, as it is personality-agnostic. She makes a case for having self-awareness of your personal restorative niche, regardless of your introversion or extroversion. The reason being that we all need a place to go and revitalize ourselves. Introverts are often characterized by susceptibility to over-stimulation. As a result, it is often necessary to seek a quiet place of solitude, or perhaps one or two close friends. I know whenever I had to be in front of a large group (anything more than eight for me) I could do it, but then felt very drained. It was imperative that I find a spot to be to recover, or perhaps connect with a single person in that large group quickly so that I have something concrete to focus on. Conversely, the group situation above can often be the restorative niche of an extrovert. After a long day at work or studying, they crave a group of friends to go spend the evening with. Perhaps they work somewhere and find themselves severely under-stimulated (a common occurrence and your average campus job) and just need to unwind with a large group of friends. The key is to know where you stand, and seek out a schedule which maximizes the time spent in your restorative niche. Of course, this is not to say that every introvert should work alone from home all the time, or that extroverts should spend every waking hour at the stock exchange. There is a balance to be struck. But understanding your own mood patterns, as far as they relate to your social habits and preferences, is powerful when trying to form a schedule that suits your needs. Another point of interest is how introverts and extroverts interact with those of similar and opposing dispositions to them. There was a study in which groups of introverts talked with themselves one-on-one, as did extroverts; then the groups were mixed together so that introverts talked with extroverts. In the first part of the conversations, introverts tended to immediately delve into personal topics about each other’s lives, or about current events in the world. They often found a common topic of interest very quickly, and were able to stay focused on one or two ideas for most of the time. Extroverts required a bit of warming up, talking about the weather and more surface-level details about the other person’s lives. The dynamics were clearly quite different. Once introverts and extroverts joined together, they were able to adapt to each other. Introverts let the conversation become a bit shallower, and the extroverts reported feeling at ease, since they felt heard to a greater extent than when talking to other extroverts. Introverts reported being more at ease, since the other person would lead the conversation. They were both able to interact well, and had very good ratings of how the conversation went. What’s important here is that we can all help each other, and serve a role, whatever our social preferences are. Extroverts can often talk about many things very quickly, processing things out loud with other people, and having an introvert who will happily sit quietly just to listen, and respond when appropriate, can be very helpful for this. In addition, an average introvert may not always want to be engaged in incredibly serious discussion, or just wants a bit extra social interaction. Being carried along in a conversation (or some other situation) with an extroverted friend can help move someone out of their comfort zone. This book has some very important ideas for everybody to be aware of. While I did not touch on some of the larger ideas presented (how extroverts dominate the business world, and the ways this effects employees), even just the two things that resonated with me are worthy of significant discussion. Give it a read. It’s a very concise narrative style, easy to follow, with great ideas and advice for becoming more aware of how you operate within the wider world. I know it had a great effect on me.

Just to have this out for people to look at, here is my honors thesis from my degree. It is broadly about some of the mathematics behind a particular phenomenon in quantum mechanics. Thesis Thesis Formatted as a Book

I recently graduated from college, and while I may touch on that or write a longer post about my experience and what that means for me, all it means in the context of this post is I now have free time. While I objectively had less “scheduled” time during college, I always felt that I needed to be doing something towards my degree and my future. I only read a handful of books for fun during those four years, as I felt it imperative that I instead spend the time working on my programming skills or looking through math textbooks. I did not want to “waste time”, and this greatly affected how I spread myself out. I will be moving onto a full-time job fairly soon, and while this obviously eats up a chunk of every day, it is a consistent chunk. I know the time I have left, and all that time is spent on projects that I am invested in. I get to decide on what to do. This summer, I’ve finally gotten back into reading. I’m also hoping to record my podcast more frequently, especially now that I have taken over editing duties. I began playing baseball again (kind of) and playing music a bit more. There is a lot I can finally begin to do which I put off during my time in college. What that means for my writing here, is that I’m going to try and post consistently. My plan is to write a post every week. There is truth to the idea that making a schedule out of something takes the fun out of it, but I know I am the sort of person who needs deadlines to be productive. My goal is to post on Mondays (as I am doing now). I’ve also removed my Facebook link to this website, so I don’t have an effective way to share it. This was mainly to take pressure off of the writing process. If those who have read it in the past stumble on it again, that’s great. But this is just meant to be a place to put my normal “personal” writing, while allowing it to technically be accessible for those who care. If it obtains a following, that will happen organically. The posts are going to vary as widely as the current posts do. Sometimes it will just be a small piece of math that I find interesting. It may be an explanation of how I work, or what I do in my free time. I want to keep it open, and allow a slog of a week to have a shorter post like this (sub 500 words). For anyone who comes across this, you now have a bit of context for the posts that will (or will not) appear in the future.

I’ve been struggling a lot over the past few months in starting a new post, or a new piece of writing for myself, and faltering a few paragraphs in, not sure what to do with myself. A large part of this, as was mentioned in a previous post, is due to my habit of editing as I write. I don’t often plan my writing ideas, put them in some flow chart or other organizational structure, or summarize the points I want to make before I write. This helps keep my writing natural, and keep its place as a release valve rather than work. This also puts me in the position of sitting down with what seems to be a well-formulated idea, only to have it peter out faster than anticipated. I recently had a conversation with someone who pointed out that this isn’t necessarily bad, as it still shows that I’m thinking about these topics. I start to second-guess my own thoughts. It also means that I am still writing, even if the finished product does not get produced as prolifically as I would ideally have it. All this has led me to think about the importance of completing projects in life, and to what extent my large folder of draft documents can be justified and excused. ...

Over the past 6 months or so, the idea of pushing and pulling in education has been on my mind. What I mean by this is whether we should focus on pushing kids who are achieving in a particular subject as much as we can – advanced study in mathematics and reading, honors classes, extracurricular options – or focus on pulling kids up who have struggled in some subjects. I have been intrigued by this dichotomy in the education system precisely because I have seen both sides of it, and it makes me feel conflicted. ...

I learned an interesting fact in my Stochastic Processes class the other day, and I managed to come up with an easier way to present it than using Markov chains (which are really cool, but not conducive to making a good blog post). ...

Much of the rhetoric that has been pervasive over the past year, and especially with the election of President Trump, is related to how much value society places on qualifications when it comes to hiring and listening to people to help run the government. ...

As I have progressed through college I have found it necessary to look for and invest in the right tools for the tasks I have at hand. I think it is important to be aware of how I work, and test out ways to improve my efficiency. ...

The way that I approach a first draft is not quite the same way that other (more experienced and successful) people approach one. The general advice is to hack through it without looking back. Particularly in writing, it is important to not focus on any grammatical errors, any misspelled words or issues with flow. One needs to get all of their ideas onto the page before they can hope to begin the process of refining those ideas. I do the opposite. ...

Today we will be looking at two problems in probability: the Monty Hall problem and Gambler’s Ruin. These are two common probability “brain teasers”. For the Monty Hall problem, it feels paradoxical when you first learn about it, while the Gambler’s Ruin is instructive and important as you go forward in life. With that brief introduction, let us begin! There was a game show (so I have been told, though I am too young to have watched it) hosted by Monty Hall. One of the main elements of the show was a classic three-door setup, where behind two doors there were goats, and behind the third door there was a brand new car waiting to be won. The way this would go is that Monty Hall would ask you, the contestant, what door you wished to select. You picked door one, two or three. Then Monty Hall, bold and clever, would open up one of the two doors that you did not pick, only to reveal one of the goats! At this point in the game he would come back to you with a smirk, asking if you wished to stay with the door you picked at first, or if you wanted to switch to the other closed door. The problem is: in order to maximize the probability that you win the car, do you switch or stay (or does it even matter)? ...