What is knowledge? [Letter]

Dear [redacted],

You asked me a very fascinating question earlier. You asked me how to learn -- learning is something I deeply care about and it gave me incredible pleasure to give you an answer, to the best of my ability.

I love numbers, sets of things, their ennumerability and so I like to think in numbers. Hence, it is no surprise to me that my answer took the form, in earnest, of a set of ideas. I told you four aspects of learning, as they came to mind -- curiosity, universality of knowledge, importance of internalization and the existence of the optimal learning function.

I was rather delighted, dangerously somewhat, at my accomplishment in elucidating the idea in such a manner. I write this, however, because I missed out on one the arguably most important facet of learning, which I shall shed light on in due course.

For the sake of elaboration and preservation of ideas, I feel that it is my duty to extend an explanation of each one of the ideas above. Before I do that, however, I must, I think, share a word of caution regarding the nature of human beings when it comes to learning.

It is common knowledge that man is not perfect. On many occasions people have attempted to construct the "ideal" man, in mythologies, epics, films, superhero universes and so on. What's really interesting to me is not the characteristics these constructions share but the fact that such attempts are inherently futile. The ideal man does not exist and will never do. The real man does exist and he has fundamental biases.

I speak of the existence of cognitive biases in the human brain. We are a product of biological evolution and as wonderful a process it may be, evolved creatures share a rather inescapable feature, by construction, of containing both the successes and mistakes of its evolutionary heritage. Hence, all humans have what we call cognitive biases that affect our observations and so, in effect, all our deductions -- the confirmation and disconfirmation biases, the baby face bias and the congruence bias to name a few.

In fact, by construction again, all anthropological elements viz. networks and hierarchies also contain biases. One social bias that will come up in this letter is the ad hominem-ness of networks.

It is important to note that these biases are truly inescapable. We cannot undo their effects on our thinking nor can we, strictly speaking, work around them and so the word of caution against them. But that doesn't mean we are completely hopeless. It is very interesting that even though we cannot notice our own personal biases, we are not that bad at noticing others' biases. So as a corollary, when in doubt, it is useful to bounce ideas off people smarter than you and I encourage you to undertake a deep study of all human biases at some point.

Now that the pleasantries are out of the way, let's begin with Curiosity.

Curiosity is the single most important feature of the human brain in the genesis of knowledge. The forbidden fruit and the so called devil, embodies that notion. We are most different than the rest of species that inhabit this planet in this very regard -- we are innately curious beings, we question and we seek answers to those questions. As I write this on my iPad listening to a Bach piece, I can't help but chuckle on the fact that it was only us that could become sophisticated enough to be able to invent language, technology, music and the myriad of things we often take for granted. All because we were curious to seek knowledge -- knowledge of communication, automata, beauty.

So, I posit that the man who has learnt the most, is not the man who has read the most but the one who asked the most questions. So, question everything and I mean everything with just one exception to the rule. I'll come back to that exception in the latter part of this letter.

Secondly, knowledge is universal. What that means is that there's no difference between knowledge about the same thing whether it's in my brain or yours or Einstein's or in Principia Mathematica or on a hard drive. Take a moment to appreciate that, it is a most wonderful property of the universe and it is what establishes true intellectual indiscrimination. Once, one individual understands something about this universe and shares it, the moment it is shared it becomes pure, independent of the mind containing it.

Why is that the case? Because the universe is everything that is the case, or in other words it is simply Cest la vie. All knowledge is an attempt to understand it and hence all knowledge is axiomatic in nature. Deep down, the question "Why?" breaks down. It is a very curious property of this universe.

Thirdly, the importance of internalization of knowledge. Humans invented language to share thoughts and knowledge with each other more effectively. It is a consensus-based model, we both agree on what the word apple (the fruit) means or what blue (the color) means and so do the rest of humanity. It is contextual (and so the qualifications) but we do largely agree on the thing referenced.

It is very fascinating, however, that due to the limitations of spoken and written language this consensus breaks down when it comes to the inexpressible. Love, happiness, beauty -- we all have an inkling to what those terms mean but we cannot really express the actual experience. They are relative to each individual and so are aspects of a lot of knowledge. Sharing knowledge is a very difficult lexical semantics problem, which is why teaching is so difficult.

What that means for you and your quest to learn is that it is extremely important to internalize what you learn, to intuitively "feel" it. Forgive the hand-waviness but to better understand it, think of this -- I've met only two kinds of "well-read" people, ones who understood almost all of what they read and the ones that understood almost nothing. In other words, it is rather easy to learn to talk like Nietzsche but extremely difficult to think like him.

Most people, including very often us, tend to jump to the converse conclusion that learning is reading and remembering words. This is what gives rise to the ad hominem nature of the society we live in -- the fallacy of people to make arguments appealing to emotion over logic or reasoning. If you don't "sound" like an expert (or lack the credentials of one), it is unlikely that you'd be taken seriously. Don't ever fall for that.

The fourth one and the one that was formerly the last is the existence of the optimal learning curve. If you model knowledge as a graph in three-dimensional space then to reach a specific node or piece of knowledge, you'd have to navigate the graph, jumping from one node to another, or in other words modulating between bread-first scans and depth-first scans. By that definition, there also exists a most optimal function or path to getting to that knowledge.

What that means for you is two things:

  1. Always have a goal of learning and make that goal as atomic (or concrete) as possible.
  1. Find the optimal path of jumping between breadth and depth. How you do that? Ask someone who has learnt the same thing how they did it, then mercilessly employ the good things they did while rejecting the stupid things they did.

The notion of asking people brings me finally to the one facet that drove me to writing this letter in the first place -- apprenticeship.

It is an inescapable truth of our existence that all humans are not the same. With respect to each dimension or field of learning, there exists a distribution of depth of understanding and mastery in people. In other words, there is always someone who is better than you and someone who is worse. We humans learn most effectively by apprenticing under superiors.

If there's a single most important thing you take away from this letter, it is this -- find yourself a master. And here comes the exception to the rule of questioning I laid out in the section about curiosity, question everything ruthlessly except your master, once you have chosen him.

In light of the previous statement, it is clear that it is very important to be cautious in finding your master and I don't mean to use the term frivolously. When I say master, I mean the word in the most absolute sense possible, your teacher is not your master. It must be the one you pick. The relationship between a master and his apprentice is one of the most joyous experiences either can have.

The master must be a single person, otherwise the apprentice will run into confusion regarding the rule of complete submission to the master. Also, don't let my words confound you, when I said "find" a master, I don't mean to send you off on a long arduous journey looking for the "right one", that would be futile. Rather, surround yourself with intelligent people (which you have already) and pick one who you respect in the absolute sense. Now, you may not have someone like that around you now but you will if you don't already, be on the lookout.

So, to summarize:

Be curious, question everything.
Be vary of people, your knowledge is correct because it is correct not because someone says it is.
Internalize everything you learn.
Find the quickest path to learning what you want.
And find yourself a master and obey him, completely.

Fare forward,