Problem Solving with Good Explanations
David Deutsch is, as Tyler Cowen calls him "world’s first true philosopher of freedom, ever [...] with no rival". David’s books Beginning of Infinity (BoI) and Fabric of Reality (FoR) are the rare ones that only come once in a century.
David has a truly optimistic view of human existence and their role in making progress. He thinks that there is an enormous difference between human intelligence and what is sometimes referred to as animal intelligence (i.e. dogs/chimps are intelligent).
David ascribes progress made by humans to their unique ability to be creative and to come up with good explanations. Specifically, he credits good explanations to be an essential part of all progress; or to quote directly from The Beginning of Infinity:
"In this book, I argue that all progress, both theoretical and practical, has resulted from a single human activity: the quest for what I call good explanations."
- David Deutsch, The Beginning of Infinity
Good Explanations
So, what are these "good explanations" anyway? Here are three specific criteria that are usually given:
Good explanations are testable and falsifiable with these tests - i.e. testable to be true or false. This criterion is required to be a good explanation but is not sufficient. A good example is given in the Fabric of Reality about “eating 1kg grass to cure common cold”. This theory is testable, it is also falsifiable - [i.e. someone can actually eat 1kg of grass and see if it works or not.]But it's not hard to vary - hence is not a good explanation.
Good explanations are hard to vary - the “eating grass to cure common cold" theory fails here; as someone can just adjust the theory to prescribe eating 1.5kg of grass, or eating 1kg of one specific type of grass, and so on.
Make narrow, precise predictions - Bad explanations have more "moving parts", good explanations are precise. Good explanations engage the the reality; they interrogate the reality; whereas bad ones never do.
Reach of Explanations
Once we have a good explanation of some phenomenon, it possesses an automatic property of reach. The reach of these explanations then creates a self-propelled loop of generating new knowledge. Another property of this reach is that, once the explanation is out of the human mind, i.e. is described to other humans, the original explainer does not have any control over how this explanation could be used. Moreover, even if the explainer wants to have control, it is not possible.
For example, once Einstein published his relativity papers and the community accepted them after the observations corroborated the theory; even if Einstein wanted to negate his already published theory; he couldn't! At least not just by saying “I was wrong, guys”; he would have to come up with another set of good explanations of why he now thinks he was wrong, otherwise the proverbial cat is out of the bag.
In the Beginning, we had Kings and Prophets
In the beginning (hundreds of years ago) everyone used to follow the authority, and no one dared defy the kings. A theory used to be justified by the fact about where the theory comes from rather than the content of the theory itself. Worse yet were beliefs that involved the supernatural.
Next came doubting the authority; some brave people started thinking why should they obey the kings? They argued that if they can see something to be true, why do they need the king to tell them what is true? This “movement” slowly evolved into empiricism.
Empiricism is defined as a theory that states that knowledge comes primarily from sensory experience. That is, by observing a phenomenon with your senses, one can form a theory about the world around us. This theory was great for moving humanity forward from the blind reliance on the so-called experts and kings.
To describe empiricism more specifically, it is thought that one observes a phenomenon in the world, draws conclusions about the world, generalizes the observations, and a theory is born. This process of forming theory from observations is also called Induction (Inductive reasoning).
Although induction was great for humanity to get out of the clutches of the kings and their authoritative views; it is not the right way to approach forming a theory - and solving problems, as it turns out.
Then we had observations
So, what is wrong with basing your theories purely on observations?
Well, firstly, the observations we make with our sensory organs seldom represent reality. For example, we see the 3D world around us in 2D. I.e. the observations that are made by our eyes are actually 2D. But our brain and eyes have evolved over billions of years to make sense of the 3D world from the stream of 2D images. But there are errors made in this system. (e.g. those trippy gif images !).
Secondly, when you are observing something, inherently you are assuming certain things to be true before any sense could be made of those observations. In other words, we make observations in some context - some theoretical context. In addition, we also bring some expectations (some guesses) before we observe something.
To see how amazingly counterintuitive this is in our culture, watch this clip of Fyenmen trying to explain to his audience “how do we look for a new law”.
He begins by saying, “In general we look for a new law by following this process, first we guess it”, and then as he is writing “Guess” on the blackboard, the audience laughs as if he has just said something funny. He admonishes the audience by following up with “Well don’t laugh, because this is really true!”
Knowledge Creation - A uniquely human endeavor
Okay, so what do we know about how good explanations come about? Well, in reality, the human mind is the only entity that can come up with good explanations. All living things actually contain genetic information as a starting point to live on this planet, however, humans are the only species that are able to go leaps and bounds beyond this starting point.
What has made this possible? A multitude of things. First and foremost, the uniqueness of the human mind, in its ability to come up with good explanations and its creativity. But just this uniqueness is not enough, that is, it is necessary but not sufficient. At the beginning of humanity, the human mind was present, but what was missing was the tradition of conjecture and criticism.
This tradition allows anyone to criticize any theory or anyone’s conjectures. There are no exceptions. If the criticism holds after testing it against the prevailing theory, the new explanation replaces the old one. But that too is temporary.
Why? Well, the “real” reality is out there which is not exactly knowable. We are making conjectures about what reality is, but at the end of the day, they are conjectures, approximations of the “real” reality. In other words, knowledge and good explanations bring us closer to reality, but not exactly to reality.
In fact, it is suggested that a scientific theory should be called a scientific “misconception”. This way there is no confusion about what the “theory” is supposed to carry, and allows the theory to be understood free of any authority.
Everything begins with a problem
I would conclude this short essay with an example of how problem-solving could be approached more effectively with good explanations.
Can I tell conclusively, if a coin is a fair coin, if we flip the coin 100 times, and all 100 times it comes up Heads?
Can we conclude, that we have shown that this is not a fair coin? Well, statisticians say, no, because there is a non-zero chance that the coin is still fair and we get 100 Heads in the first 100 coin tosses.
But is that irrelevant? Well, initially I was trying to solve a problem; given a coin, I am to determine its fairness. I began with a problem, and I started experimenting with the coin to test my hypothesis. Now, I have observed in my first 100 tries the coin has turned up Heads. Do I stop here and consult a statistician? No!, I examine the coin further, maybe it feels a little heavier on one side than the other?, but now my problem has changed, and now I conjecture that this coin may be unfair, and I have a feeling it is heavier on one edge.
What do I do, I now set up a new experiment, I call a friend who can cut the coin in half and see if they roughly weigh the same?!. and on and on I go, somewhat similar to what this guy did!
How to create an unfair coin and prove it with math
The point is, it doesn't matter what the statistics tell me, what matters is how I address the problem, and adapt my definitions and experiments to resolve the problem. Defining a problem is the first task, then one comes up with a conjecture for solving the problem; then proceeds with testing the hypothesis (criticism) to validate or invalidate the conjecture. Science is this adaptive game of problem-solving.