Science behind learning & creativity + other things

(This post covers Chapter 2 & 3 from the book)

(Previous post here)

Quick review – Brain operates in two modes, focused and diffused. Both modes are necessary for proper learning to happen. In focused mode our thoughts are limited to a very narrow field at excellent depth on the other hand in diffused mode the brain is much more free and the thoughts travel much broader area but in reduced depth. The focused mode is our conscious brain whereas the diffused mode is the sub-conscious.

Why two modes of thinking?

One of the possible origins of this can be illustrated by a simple example. When birds are pecking, once in while they stop to scan the horizon for predators. Their main focus is eating but they need to keep an “open eye” for predators. From this example we can see that we require two modes so that we can work more efficiently while staying alive. (NOTE : This has nothing to do with left/right brain dominance. In fact there is nothing like left or right brain dominant, read this research)

Why is Science and Math more challenging compared to say language or painting?

“Befuddlement is a healthy part of the learning process” – Kenneth R. Leopold

Simple answer lies in the amount of time the human beings have been doing either of those. The human brain has evolved over millennia of language use, in contrast we have been at math/science for about 400 years or so (at least the science/math in current form, thank you Sir Isaac Newton!). Also usually the statements in science/math are convoluted and less obvious, i.e. more abstract. Usually, one or more levels of abstractions involved (“the ratio of circumference over diameter” is a bit more complicated than bluntly stating the humble constant π = 3.14159265359). Plus sometimes we are victimized by “Einstellung” effect, our inability to think outside the box because we think all problems can be solved in a similar fashion (while solving a problem if you are stuck at something, probably it is best to stop before you smash the coffee mug…). People with strong self-control are usually bit harder by this einstellung issue.

When solving problems, avoid the temptation to stick with the first solution that pops into your mind, this blocks possibility of finding a better solution. Weirdly, blinking is vital! it provides the momentary distraction that your brain requires to start thinking in another direction. Warning, closing eyes does exactly opposite—it focuses your thoughts on the problem more intently. Another warning! Do not give up on a problem easily! struggle with it, wrestle with it and when after you have spent a reasonable amount of time and still cannot solve it, only then ask for help, because if you asked for help in first place your brain would never have done the hard work that the subject demanded. (Wow! too much weird stuff and warnings!)

What is creativity?

“But creativity is different. It paradoxically involves studying how someone pulls out of their brain something that was never put into it!” – Gabora, Ranjan

Creativity is the ability of your brain to form new neural connections in the pre-existing knowledge and pull something out of it that was never put there in first place. Creativity is not about the mastery of any particular field alone. Now how to define expertise? Expertise is the ability to shift mental gears (relaying between focused and diffused modes), and this comes from regular and repeated practice. Tip: Walking helps creativity. In fact, any form of physical activity helps boost creativity!

Mastering the material

For mastering the material we require proper practice. This proper practice involves spaced repetition, rote-learning and enough time to allow the brain to properly assimilate it, until it becomes second nature to you (ACHTUNG! All those who prefer reading the night before the exam and tease people who actually read entire semester, don’t, just don’t). This last “enough time” thing is important because just like with brick and mortar, formation of proper and usable memory traces takes time. If enough time is allocated to a problem, it slowly moves to long-term memory where it resides permanently. When we learn something for the first time or few more subsequent turns it resides in the working memory (a sub-set of short term memory where things are not actively rehearsed), where the brain does its magic thing and tries to reduce it and make the sense of it. Even in mathematics and science sometimes it is necessary to memorize material.

“One of the greatest problems I see with students is that they do not have the definitions and the theorems memorized. Well, of course, if you do not know the definitions and theorems you won’t be able to use them.” – Joseph Gallian

Tips for mastering the material:

  • Start assignments early
  • Keep working sessions short, work as long as you are not getting frustrated. And when you do, try doing another focused mode task or simply relaxing. Caveat: if the new task you are doing uses the same regions in your brain as the previous ones, everything will get mixed up and messy! My suggestion: STOP! and relax.
  • Do not let new material go untouched for more than a day
  • Be regular. Consistency over time is key.
  • Sleep! (proper resting of brain is very important when you are trying to master new material. A proper sleep allows cleaning of brain, flushing out the toxic material. Read this, this, and this. Have trouble falling asleep? trying taking deep breaths and counting backwards, or this)
  • Go over the material right before sleep, try dreaming about it (no, seriously!). Also keep a notebook handy in case you suddenly wake up with some insight into the problem.

Pomodoro (tomato) to the rescue!

Pomodoro technique is a method to organize your working time into short sessions. Set your timer for 25 minutes, turn-off all the distractions and focus on work. Done!? Now take a break for 3-4 minutes and start next session and then break and so on. 4-5 such sessions daily will surely bring you to your A game!


  1. An Evaluation of the Left-Brain vs. Right-Brain Hypothesis with Resting State Functional Connectivity Magnetic Resonance Imaging
  2. How Insight Emerges in a Distributed, Content-addressable Memory
  3. Advice for students learning abstract algebra
  4. Sleep drives metabolite clearance from the adult brain
  5. Scientists Finally Know Why Sleep Deprivation Leads to Mental Sluggishness
  6. ‘Sleep should be prescribed’: what those late nights out could be costing you
  7. How to sleep

What are you looking for? There is nothing down below… STOP! Don’t go reading through my personal business!

(kidding! read if you want to watch some boring (well if I liked them, they must be boring for you) videos and sleep-inducing/mind numbing articles).

Stuff I read this week

  1. Maker vs. Manager: How Your Schedule Can Make or Break You (18-22 min) – Loved this article. I have read numerous articles on productivity, scheduling tasks and time-tables/routines, none of them raised this important fundamental question. This article forced me rethink about my own schedule (or lack of it?). This article is inspired by this article by Paul Graham (6-8 min).
  2. To infinity and beyond, with fractals – Finding The Inspiration Factor (8-10 min) – Find fractals interesting, but need a kind of primer? Here you go, just don’t expect anything stellar just basic stuff written down plain and simple – interesting read.
  3. Prof, no one is reading you (6-7 min) – (I wish a few of my teachers read this!) This one raises an important question regarding today’s scientific publishing scenario. Is it really worth it? What is the point of publishing your work if neither anyone really reads it, nor does it having any impact (however minute) on society in any way? Is it not against the ethical conduct of the researcher to blindly publish anything just so he gets to list it in his resume? MUST READ.
  4. My Incredibly Simple Guide To Stoicism — Learn Wisdom You Can Practically Use (13-17 min) – Stoicism! The constant guest in my thoughts ever since I read this article. The more I think about it, more sense it makes. A simple solution to utterly distracted lifestyle we all lead today can be found in this ancient school of philosophy. I find the concept of stoicism incredibly appealing. If you want a quick introduction to the concept of Stoicism watch this video – The philosophy of Stoicism – Massimo Pigliucci (6 min)
  5. Globalisation: the rise and fall of an idea that swept the world (33-42 min)- One of really nice critiques I have read in some time. After reading this article, first thing you will learn is there is just so much more to the term “globalisation” than you think (I have no clue about economics, so…). Secondly, it will make you question the fact that is globalisation really that great an idea? After all, everyone (except a few) said it was the best thing for everyone involved (the few opposed and eventually both sides made a big faff about it), but it did not turn out that way. Finally, it also shows the hypocritical nature of the pundits who think they can press their opinions upon a commoner just because they sit in a position of influence. I have re-read it 3 times, that is enough to say about it don’t you think?

Videos I watched

  1. Rectangle Area Problem (mindyourdecisions) – Simple problem, but I never approached the problem in the way explained (4/5).
  2. Chaos Game (Numberphile) – This one blew my head off, clean! If you are a fan of fractals and chaos theory, WHAT ARE YOU DOING HERE!? WATCH IT!! (∞/5) (trivia: ∞ is called a lemniscate)
  3. Moving sofa problem (Numberphile) – Seriously! either mathematicians are over paid or have lot of free time; who even thinks what is the optimal shape of sofa so that it moves nicely around the corner? (so cool that it no longer matters/5)
  4. Tuning a piano (minutephysics) – Henry doing best what he does best, explaining physics in simplest way possible. Caveat – this might be a little cryptic if you don’t remember the theory of waves. (4/5)
  5. Detecting gravitational waves (Veritasium) – I heard about it, a lot! & finally I though maybe I should take time to understand this phenomenon. Needless to say, this video explained what gravitational waves are and why detecting them is a big deal (4/5).
  6. Dominoes (smartereveryday) – I never really thought there is so much happening behind the simple act of falling dominoes. MUST SEE! (4/5)
  7. Math jokes explained (Numberphile) – Because, why not, if infinite mathematicians can walk into a bar…(3/5)
  8. How volvo is eliminating turbo lag (engineeringexplained) – Simple and elegant answer to turbo lag problem. Simply use an electric motor to provide additional boost.. clever stuff! (4/5)

What did Dr. Oakley teach me?

Things I learned from the book “A Mind for Numbers”

Answer: A lot! She taught me a lot!

Whatever follows is the result of me reading the book, “A Mind for Numbers” by Dr. Barbara Oakley. If you haven’t already read it, then go read it! It is packed with stuff that you’ll want to pack into your brain.

Our brain is an excellent computer, but it has to cope up with a whopping 11 million bits of data per second (our eyes alone generate data at a rate of 10 million bits/sec). But there is often a lot of useless information to filter out—this severely limits the capacity of the brain. According to an estimate our brain can consciously process about 40-50 bits of data per second—ever had trouble doing a simple addition while your friend was constantly whispering in your ear? While most of us are okay with their habits and how they use their mental resources, I tell you it is not. Our brain is infinitely more powerful than any computer ever made, (or all computers ever made put together for that matter, don’t trust me? Then read this lengthy description by Randall Munroe here!)

The Two Modes of Operation

Our brain operates in two modes

  • Focused mode (FM) &,
  • Diffused mode (DM).

Learning involves a complex relaying between both.

The “Aha! moment” is result of proper focused attention followed by diffused mode thinking

In FM (just as it sounds) all your conscious attention is towards the task at hand—its precise. The DM is bit different (and not exactly what it sounds like). This is like a daemon running in the background; it works when you are not consciously thinking about it. For instance, you were trying to solve a problem that was very hard. At some point you threw up your arms, cursed the problem and left for movies, while you are watching Bruce Wayne say, “I’m rich”, your brain silently starts the DM engine and tries to figure out the solution. Next morning when you start working on the problem again and solve it in a matter of minutes, it is not a miracle or “fresh mood” (as people often say, I honestly have no clue what that is), it is the result of your DM trying to put things together to figure out the solution. Not all the credit goes to the DM though, the DM gives FM the right direction, but it is FM that actually decides the path and takes you to the destination.

Great! Now you say brain is actually a 2-in-1 system

Well.. em.. not precisely.. maybe 1.2 or 1.3

Both the modes of operation are dependent on each other, plus there is the thing that you cannot actually force your brain into DM on your will (although you can trick it, more on that later!). The way this system works is, you put all your mental resources into a particular problem, and after enough pondering you stop—FM, done! Now, when you have stopped thinking about the problem, the DM picks up those half-cooked bits and then processes them into something “better”. Well I say “better” and not “finished” product because sometimes it takes a few rounds between the FM & DM to completely process it all.

Care to Elaborate this Difference?

FM and DM are like two sides of the same coin

The FM is concentrated. In FM, the brain searches for the solution in a very particular area but in excessive depth. DM on the other hand searched for solution over a much wider region, but in much less detail. FM is like seeing through a microscope or binoculars in bright daylight whereas DM is like seeing with naked eyes on a full moon night (you can discern figures but cannot tell colors, texture or anything more). The FM drains your mental resources maddeningly fast whereas the DM consumes almost nothing. And for reasonable reasons FM & DM don’t work simultaneously on the same problem, they just don’t (you cannot change the tire of motorcycle while it is running, although if you try to prove me wrong, its on you). Bottom line is one is a syringe and other is a fire hose, neither you can say one is better than other nor can one replace the other (if you trying to put out fire using a syringe, you might have bigger issues).

To summarize all this (TL;DR version):

  1. Brain handles a lot of data
  2. The brain works in two different modes, Focused  & Diffused
  3. Focused mode is the conscious brain trying to solve problems.
  4. Diffused mode is the sub-conscious brain doing whatever it does best
  5. Both modes are dependent (one works on the result of another)
  6. Proper learning involves a complex switching between both modes.

Next time we will see why learning can be paradoxical and what creativity is all about.

Watch this video by Derek if you were too lazy