A Mind for Numbers
Learn how to best manage your mind for optimal efficiency when problem solving.
Taran "tearing it up" Bains • July 31, 2021
Disclaimer: these are just MY key takeaways… there’s a bunch of shit I left out of the book
for a couple of coding interviews… and yes, A Mind for Numbers is the motivation for this blog post (if you haven’t guessed 😜).
Similar to my approach to Mortgages in Canada, I’m going to provide some of my key take-aways as I’ve just finished reading the material and it’s still fresh in my mind. I can’t recommend it enough, but if you’re looking for a quick reference (talking to you, Future Taran 😆), I’d suggest starting here.
Innantely, at a biological level, we know that there are certain kinds of thinking/states of being that we’re able to situationally enter. But what are these patterns of thinking? Can I tap into them at will? What are the benefits of one type of thinking over another? I’ve pondered these questions for a bit and I’ve learned, throughout my 28 years on this earth, that I’m either thinking freely and creatively about a problem or I’m thinking narrowly, or as others have referred to it, thinking in a “flow” state where I’m completely immersed in what I’m doing and the task at hand.A Mind for Numbers describes these two modes of thinking as Focus mode and Diffuse Mode respectively.
Referring to the above image, if we imagine our mind to be like a game of pinball, focus mode would be akin to a game in which there are multiple crowded bumpers in the game area (the left most diagram). A thought (the ball in our analogy) will bounce off multiple bumpers in a localized region. The closer bumpers are telling of the fact that we’re able to focus more on a precise thought and therefore concentrate on a concept that we already have down pat.
When we’re focusing on something, the prefrontal cortex sends out signals that links neural pathways along the brain that are related to what you’re currently working on. When we first approach a problem, we usually approach the problem with the focus mode switched on. We read the text, look over notes, scour Google for an answer, think back to previous problems we’ve faced in the area and attempt to utilize past experience and patterns to solve the problem. This is generally great, but for problems where changing one variable or some key details drastically changes the approach and/or solution, relying on focus mode becomes problematic.
When dealing with subject matter which employs abstract concepts, focus mode becomes more effortful. An example of an abstract concept would be the idea of love. We try our best to define it with words, display it with our actions, but it is not physically possible to point at an object and say “that is love” — there’s no real life model. Don’t come at me with some BS about how you “love” your friends and family. Bitch, I can’t point to that and say objectively that that is love 🤣. In the world of computer science the idea of a stack is also an abstract concept… there’s no real life model of a “stack” where someone is popping and pushing stuff onto it. Before you come at me with the whole stack of pancakes analogy, I’m not saying pancake stacks are not real, but a stack in computer science is an abstract data type. IT’S IN THE NAME!
Another related problem to subject matter which employs abstract concepts is the Einstellung effect (pronounced “EYE-stellung”). Basically, this means that you’ll focus on your initial thought so much, that you won’t be able to see better more elegant solutions. The difference between a master and the student is that the master will spend, on average, more time attempting to understand the context regarding a problem/issue before trying to jump into creating a solution. The student will jump right into trying to find solution without allowing themselves the time needed to truly comprehend what they’re looking at.
Don’t fuck yourself over by jumping straight into solving a problem. Think about it. Allow yourself the time to ruminate. Play around.
Sticking with the pinball analogy, then diffuse mode would be akin to a game in which there are a minimal amount of bumpers for our pinball to hit; this means that the ball can travel quite a long path before hitting the next bumper and can traverse in such a way that it can travel throughout the entire game area with minimal issue.
This is how diffuse mode operates. A thought (the pinball) is able to traverse a large portion of your neural network and make connections that aren’t necessarily straightforward. When we’re facing a brand new problem that we haven’t seen before, or an enemy that we’ve never faced in battle, there’s no existing neural pattern that we can lean on… we need to be flexible!
Diffuse mode allows for you to think in a “big picture” kind of way, grapple with new theories, and apply previous experiences from different areas of your life to the problem you’re working on or concept you’re trying to understand. This is why procrastination is such a bitch. Not only are you stressing yourself out by not doing the work but the act of putting off doing the work is robbing you of the time that you’d normally use to enter diffuse mode thinking and exploration because you just have to finish whatever the hell it is that you need to finish.
Diffuse mode is also great for another reason… it does work in the background for you! Have you ever been working through a difficult problem for hours on end to eventually hit a wall and get stumped to only arrive at the exact solution you were searching for while doing something mundane like cleaning your car or going for a walk? Well, baby, that was diffuse mode working in the background.
Moreover, diffuse mode is how we learn at deep and creative levels. When we’re hyper focused, it becomes very difficult for us to see the forest, we’re too preoccupied with the trees. How are you supposed to internalize a tree data structure when you’re too focused on how you want to go about creating the nodes and how best to link them. Before you jump into an implementation, it just makes more sense to understand the big picture and the overall goal.
In a nutshell, that’s diffuse mode and it’s fucking marvelous. Like Bruce Lee said, all knowledge is self knowledge.
It’s all well and good to know what these two modes of thinking are so that you could impress your friends and family, but I’m all about practicality. It does me little good to know about these two modes and not know how to somewhat influence my state of being.
When first approaching a problem, utilize focus mode to begin grappling with the situation at hand. After that initial struggle, you’ll want to slip into a diffuse state to allow your mind to access other areas of your neural network and explore new possibilities.
But Taran, that’s all well and good, but how the fuck do I do that? Bitch, calm down, I’ll tell you how.
The pomodoro method is a time management technique that involves breaking down your work into intervals, traditionally 25 minutes in length, separated by short breaks. You basically focus on some piece of work and then take short 5 minute breaks in between. During the 25 minutes of work, you must shut off all distractions—messaging apps, Facebook, Twitter, Netflix, etc.— and focus solely on doing the fucking work.
After that 25 minute block of work, stop… HAMMER TIME.
Okay so it’s not hammer time 🙊, but it’s break time for sure. The purpose of this break is to disengage with the thing you’re grappling with and allow yourself to enter diffuse mode. While we can’t really actively control when we enter/exit diffuse mode, we can do things that kind of nudge ourselves in the direction. For example, you could meditate, take a walk, or listen to some music without any lyrics. It’s also acceptable to engage in some idle chit chat with coworkers but make sure the chit chat isn’t too intense or heartfelt, or else you might just end up back in focus mode.
I’ve been utilizing the pomodoro method for the past two weeks and I gotta say, and this is just me talking here, I feel pretty damn good after work! I have more energy and honestly feel like I’ve done a better job than those days where I sit at the fucking screen for 4 hours trying to figure out why that fucking scrollbar won’t disappear in my React app. In fact, whilst writing this blog post, I’ve been utilizing pomodoro. How’s that for an application of our learning future Taran? Huh, Taran? What do you think? Taran loves learning. Almost as much as Terry loves love.
I know what you’re thinking… you’ve heard about the pomodoro method for year and you’ve never tried it. Maybe you think that it’s a waste of time and that you’re taking too many breaks throughout the day. Maybe you think that you won’t be able to get any real work done in 25 minute increments. Hell, that was me back in the day too. However, if you’re anything like me, knowing the why behind an idea makes you more likely to accept and implement it.
At the end of the day, we’re not being paid (if you’re employed) for the amount of hours we put in (assuming the type of work you’re doing) is not menial in nature. We get paid to work efficiently and effectively. The pomodoro allows just this. Moreover, Additionally, and this is fucking important, the pomodoro method teaches you a valuable lesson: process over product.
Have you ever struggled with starting an assignment or some sort of work? Has a task ever felt daunting as fuck and because of these negative emotions, you put off doing whatever it is that you’re supposed to be doing. As much as I hate to admit it, I too used to suffer with this shit (and still actively do). However, once you engage this interleaved working style, you’ll being to realize and truly understand the proverb: “A journey of a thousand miles starts with a single step”.
During these blocks where you’re actively just doing the work and attempting to make progress, a funny thing happens… YOU ACTUALLY MAKE PROGRESS. Sure, you might not be done your homework assignment in 2 pomodoros, but you’ll sure as hell be a lot further along than having not done anything at all. Everything in this life is done in increments. If you’re a Christian, even God himself needed 6 days to create all of creation. If you’re a Muslim, it wasn’t just one prophet that needed to be born, but thousands. My fucking point is this: the important thing is to start moving. Take the first step and the universe will lift your other foot almost magically.
If you’re learning a new concept or trying to memorize some new information (perhaps how to conjugate verbs in another language), one thing that can be really helpful is interleaving (spacing out) your practice sessions. The funny thing about the brain is that even the act of trying to remember something helps in your learning. Struggling is helping you make progress? Crazy right. Apps like Anki are great for this kinda thing. Test taking also has been proven to help with learning since you’re in a high pressure situation and have to rely on your own memory and neurons to do the heavy lifting and not Google.
Another thing that is super duper fucking important is taking breaks (I’m talking to you buddy, the one whose PS5 I used to play Bloodborne). When I say taking a break, I don’t mean stopping one task to go and do another task. If you’re working on some hard computer science problem and then as “a break” switch to studying a new language, well first of all, fuck you, and secondly, you’re taking breaks wrong. Contrary to popular belief, resting is also a part of training. If you’re working out regularly, you don’t go to the gym and do biceps every fucking day. Your muscles need time to rest. Your mind is like one giant bicep. IT NEEDS TO REST.
However, there’s a difference between resting and just flat out not doing the thing. Use it or lose it holds true for neural connections. If you’re not actively attempting to remember/utilize some new found knowledge or skill, you risk said knowledge not being moved into long-term memory and staying in short-term only. Eventually, after enough reps, whatever thing you’re trying to understand + any other related concepts will create one cohesive chunk in your brain.
Think about when you were first learning how to do addition and subtraction. You struggled with these abstract concepts and really had to work hard memorize that + meant add a thing with another thing and - meant remove a thing from another thing. 2 + 2 = 4 looks god damn scary if you’re a 4 year old. However, we all eventually were able to grasp these concepts and created a mathematical memory chunk in your brains. We only were able to do this because we grappled with addition on the regular at school.
If there’s best practices, how the hell could there not be pitfalls to avoid lol.
Simply put, don’t fool yourself into thinking that you know how a thing works without actually going through the steps to verify your understanding. Hey you, future Taran, yeah, you. Just because you watched a couple videos on the various services that AWS offers, doesn’t mean you actually know what the fuck you’re talking about or that you could even explain the why and what for every service. Human’s trick themselves into thinking they can read a chapter in a book and “just get it” and be able to pass a test. Bitch, you just read a thing and have it in short term memory. If you don’t have the textbook in front of you or some sort of prompt, you can bet your ass you won’t be able to remember the thing you just read.
Moreover, if you’re working through a problem and you just feel it in your bones that you’re right, that’s great, but you still need to verify everything. Focus mode tends to be abundantly optimistic and therefore open to issues. We need to play the Devil’s Advocate and ask… does the thing I’m actually trying to do make sense? Look for inconsistencies. Side note, I suck at this currently and am working on it (I’m naturally a positive person 😊).
If you have strong discipline and strive to achieve great things in your life, you’ll struggle with pulling yourself away from your work. I suffer from this. Whenever the timer goes off, I have to fight my knee jerk reaction to say to myself “Five more minutes… I almost got the solution…” but the the thing is… five minutes is never five minutes… it usually ends up being five hours 😱. Trust the process and do the smart thing… walk away… just walk away.
Just don’t do it. I know. It sucks working on stuff you really don’t want to but you know what, I know it’ll be difficult and that the thing you’re doing might not be as fun as watching Brooklyn 99 or hanging with your friends, but it’s fucking important.
Procrastination occurs because negative feelings rise up when we think about the effort and feelings we’ll experience when we have to do something we don’t really want to do. That’s okay. That’s normal. The important thing is what you do after these negative emotions arise. The knee jerk reaction is to do something more pleasant like jumping on Netflix or calling up a friend or gaming but these things are just distractions and hurting you more than they’re helping you. You’re slowly building up a habit of avoiding things and running from discomfort. Don’t fucking do that. At the other end of discomfort is everything that you’ve ever wanted.
You can’t always be going 100 miles per hour when you’re trying to learn something new. You also can’t be lolly gagging around since learning is an active endeavor. You need to find the balance. You need to employ both strategies.
You must be shapeless, formless, like water. When you pour water in a cup, it becomes the cup. When you pour water in a bottle, it becomes the bottle. When you pour water in a teapot, it becomes the teapot. Water can drip and it can crash. Become like water my friend.
Go hard when you need to go hard and pull back when necessary. You can’t always be sprinting through life.
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