Of Symbols and their Manipulation

My dear Abhishek,

You are a sentient human being who is capable of using symbols.

There is one fact that distinguishes us from the rest of creation: our ability to use language. Or to put it another way, our ability to do abstract symbol manipulation. That ability, more than anything else, allows us to call ourselves members of the species homo sapiens sapiens. All our best attributes flow from that unique faculty. How did our brains diverge from the brains of our pre-human ancestors? What were the evolutionary forces which molded our neocortex? These are questions that are fascinating to explore. Even the capacity to ask these questions and answer them in some fashion requires the ability to manipulate symbols. You will notice that there is a certain circularity involved in this process: we use the faculty to explore the same faculty.

We are part of that larger creation we call the Universe. We are also that part of the Universe which seeks to comprehend the Universe. So through us the Universe comprehends itself. Isn’t that the most astoundingly astonishing thing about creation? Through us, the Universe is self-aware. We make the Universe self-reflective. Our thinking about our ability to do symbol manipulation involves symbol manipulation and this is what makes the process recursive and ultimately makes it a recursive Universe. All recursive processes have a terminating condition. We are that terminating condition for the recursive Universe. We, through our ability to comprehend the Universe, bring the Universe into existence. That is what the ancients in India many millennia ago meant when they declared “Ahum Bramha” which means “I am the Creator of the Universe.” Lots of interesting implications arise from this realization. In modern day terminology, thinkers have called it “The Anthropic Principle” which basically states that the Universe exists because sentient beings exist within it which are aware of the existence of the Universe.

We will discuss more about the self-reflexive recursive Universe later in these letters. But for now, we will move on to the ability that allows us to comprehend the Universe: symbol manipulation. More specifically, we will concentrate on the symbols alone and leave the discussion on the manipulation of symbols for a later date. So what are symbols, you may ask. Well, the first answer is that they are abstractions. What is an abstraction? One way would be to call them “representations in the brain.” Another word for “abstractions represented within the brain” is “word.” See I have used the word “word” twice in this and the previous sentence. When you use words to discuss words, self-reference is unavoidable.

The word is primary. And all that the thinker does is to manipulate symbols — words. We are symbol manipulating entities. Through our senses we get impressions of the world outside our brains. These are stored as memory. Some of these inputs are mapped on to words and the higher functions of the brain manipulate these symbols. Without the words we will continue to sense the universe but we will not be able to do the symbolic manipulation which is thinking.

Here is my claim: that unless you know the word, you cannot think. Conversely, to think effectively, you have to have a very large collection of words. The collection of words that you “own” is your vocabulary. That last sentence illustrates an amazing concept — that of hierarchy. Words exist in an hierarchical structure and that is what gives them power.

Words, as we keep saying, are abstractions. They represent something but they themselves are not the thing. The word “cow” is not the thing that exists out there with four legs, gives us milk, and goes moo. Distinguishing the symbol and the thing is very important. When people fail to make that distinction, they confuse the symbol for the thing, and work themselves up into a rage and all sorts of nasty things happen. But I digress.

OK, so things exist out there in the world. Those things are what I call “atomic” things. A cow is an atomic object or thing that exists out there in the world outside our brain and we use the symbol “cow” in English to correspond to that. Atomic objects are not limited to material things. Without getting too academic about it, let’s recognize that the number “1” is also a thing and we label it and call the label the word “one.” Given our collection of atomic objects for which we have words, we then construct higher level abstractions of things that are not atomic but are what I call “compound”. So the word “cattle” stands for the abstract entity which is “the class to which cows belong”. In actuality, cows exist in the real world but cattle don’t. We just refer to the abstraction “collection of cows” as “cattle.” The word “cow” is an atomic word, and the word “cattle” is a compound word by my definition.

Now you see what I mean that words exist in a hierarchical structure? The words you own is represented by another word we call “vocabulary.” That is, “vocabulary” stands in for “the words that you own.” In a sense, the higher level word is more economical, or compact. The magical thing about words is that we can build higher and higher level words based on how we manipulate the words at the next lower level.

It is easy to see that even if the world out there has a limited number of atomic objects — which implies a limited number of atomic words — the compound words that we can form is unlimited. And as time has gone on, our collection of words have increased. Or we can say that our vocabulary has increased. The consequence of this increase? We can think more effectively. And after all this, I want to come to the advice that I would like to give you today. To learn how to think, you have to learn vocabulary. By that I don’t mean that you open up the dictionary and memorize it.

Learning vocabulary means to understand what the word means, not just its dictionary definition. When you understand a word, it means you know the connection between the word and what it represents and all that it implies and how it is connected with other words at the lower levels. All education is ultimately an attempt to acquire a vocabulary and the skill to manipulate the vocabulary to build higher level words. Think about that for a bit.

You may object and say that perhaps learning languages is about vocabulary but surely engineering or physics is not about vocabulary. But it is indeed all about vocabulary. A physicist knows physics vocabulary which he has patiently learnt over years. When he finally adds “quantum mechanics” to his vocabulary after years of studying all the component words that make up the compound word “quantum mechanics”, he can then use that word without having to think about all the bits that go into making that word. Note that he did not actually add the word “quantum mechanics” to his vocabulary the first time he heard it or read the word on the page. It became part of the vocabulary after a long time was spent in manipulating the lower level words which ultimately define quantum mechanics.

Here is one analogy that you may find useful. A compound word is like a theorem in mathematics. A theorem is a true statement in the system under study. Once a theorem is proved, then you can use the theorem to create more theorem. So also, when you collect (under certain rules) a number of words to create a higher level word, you then have the luxury of using the higher level words and it helps you to think more effectively.

So where am I going with all this? A large vocabulary is important if you want to be able to think effectively and clearly. As I noted before, education is about vocabulary (symbols) and thinking (manipulation of symbols.) The fact is that while thinking requires words as the objects upon which it operates, thinking itself creates more words. As more people think in the world, the collective vocabulary of the world goes up and this is what increases our ability to think more clearly.

So what is the point of all this thinking clearly, you may ask. I leave you with a thought that Blaise Pascal recorded: “Working hard to think clearly is the beginning of moral conduct.”

All evil in the world arises from faulty thinking. To become a truly moral person, we have to learn how to think correctly. To the ancients in India, ignorance was the root cause of misery and sorrow. We will go into that one of these days.

With a deep bow to the wordless wisdom in all sentient beings,

Atanu

Author: Atanu Dey

Economist. View all posts by Atanu Dey