I remember curious conversation about ghosts with my little cousin, a few years ago. I was telling her that ghosts are not real. So she asked me, “why is there the word ‘ghost’, if there are none?” That was a smart question from a seven year old kid. I didn’t want to discredit her intellectual curiosity by giving a silly/funny answer; I wanted to give an actual answer. So I tried to articulate what I knew in a simple way so that she could understand. I do not remember what I said, but I think I didn’t succeed in communicating it to her.
In hind sight, I can think of one way I could have answered that question. In Sanskrit, there is a word called Bhūta. This word has been adapted in many Indian languages. It has two meanings: ghost and past. So I could have said, some people have had fearful experiences in the past, and when they recollect the terror from the past, they represent it by a scary Bhūta. I am not aware of an etymological connection between the two meanings of the term, but it is at least a convenient coincidence. In hind-hind sight, I can think of a better way :D. I could have said, in a majority of the stories and movies that feature a ghost, the ghost is a person who is dead, and had suffered injustice in the past. The ghost appears in order to avenge the suffering; it is a personification of terror.
This question is in fact a very broad one. The vocabulary of human languages are much bigger than what is necessary to talk and think about objects and events that are real. Why do we want to talk and think about objects and events that are not real, and further treat them as if they were real? An offshoot of this question is the one concerning god, which was a topic for a different blog post.
A quick answer is that imaginary situations are a necessary part of thinking, in general. Events or situations that are not real, often appear in logical arguments. For instance, “If X was alive today, Y would have happened” is a common example of what is known as a counterfactual proposition. Such propositions attempt to analyze our understanding of reality, based on an admittedly counterfactual premise. The conclusions are often unverifiable — there is no objective way to test if Y would have really happened if X was alive today. This makes such arguments vulnerable to abuse; for instance, in a political discourse, such arguments are merely another form of rhetoric. However, from a more philosophical perspective, the thinking that goes behind every decision making process does involve a counter factual proposition of some form. Indeed, the process of thinking, fundamentally involves considering events that may not be real. While this argument validates the need for considering such counterfactual propositions, it does not fully answer the question at hand, for it leaves out another kind of counterfactual propositions — those with a surreal premise.
This is a stronger version of the kind of counterfactual propositions that I discussed above. The example I gave in the previous paragraph started with a premise that is not factually accurate, while respecting all the laws of thought and all the natural laws— it could have been real. However, one can start with a premise that violates certain natural laws; for instance, assuming that fairies or demons or something supernatural exists, and carrying out an analysis while still respecting the laws of thought. While such arguments can be logical, their conclusions can not be real. They can not be connected to elements of reality. Indeed, one can build a theory that disregards the laws of physics, but nevertheless it is perfectly logical, i.e., it respects the laws of thought. Most of mathematics is constructed this way — with no regards for natural laws and a good part of theoretical physics is also constructed this way exploring possibilities that are not realities. We may term situations that are illogical , i.e., that violate the laws of thought as impossible; those that violate the laws of physics, but respect the laws of thought as possible and those that respect the laws of thought and the laws of physics as real.
I want to point out that it may appear unreasonable that we want to call those situations that disregard the laws of physics but respect the laws of thought as possible. Shouldn’t we call them impossible simply because they disregard the laws of physics? This is the perspective taken commonly in experimental physics. Mathematics and experimental physics, in general, do not agree on the definition of the possible. In mathematics, possible is anything that can be conceived without logical contradictions. In experimental physics, possible is anything that can be conceived without logical contradictions, and conforming to the known laws of physics. The classic example, that puts this conflict of definitions in the spotlight is the notion of virtual displacement in Lagrangian dynamics, in classical mechanics. It has the reputation of being an elusive concept among students, for reasons that are perhaps related to the conflict of the two perspectives mentioned above. The Lagrangian is a functional defined over the phase space coordinates and its integral along a path in the phase space is known as the action corresponding to the path. The notion of virtual displacement appears when we minimize the action among all paths connecting two fixed endpoints in the phase space. In mathematics, this is done by the stationary conditions — the path that minimizes the action has the property that when it is perturbed, keeping the Lagrangian the same, it results in no first order correction to the action. This perturbation, in physics, is known as a virtual displacement. It is a mathematical possibility, however, under no circumstance can it be a physical reality — the path of a physical system in the phase space can not be changed without changing the Lagrangian. In other words, because this perturbed path violates Newton’s laws it can not be real. The name ‘virtual displacement’ is perhaps a representation of this problem, and possibly a consequence of a debate when the term was coined. There is no physical interpretation for the concept of virtual displacement, which is often a characteristic of ideas from mathematics. Mathematics studies the possibilities; experimental physics studies the reality.
What is the value of thinking about possibilities that have no relation to physical reality? Well, that is the definition of abstraction. For instance, in mathematics, a set is sometimes defined by collecting together different possibilities, most of which are not real. Abstraction is the precursor of creation; anything that is created existed in the creators’ mind in an abstract form well before it was created. An abstract idea that has no representative a physical object, can guide us to create one. This is perhaps a vague statement, but I will give one simple example. mathematics often has a general solution to a class of problems. The class of problems is an abstract set of problems that belong to the same family. The general solution is an algorithm that works on any member of the class of problems it purports to solve. This general solution, albeit abstract, is indeed a machine; at least the ghost of a machine. Charles Babbage, who was also a mathematician, came up with the idea of the analytical engine, which was a mechanical representation of an abstract algorithmic solution to a class of problems.
The relation between abstraction and creation, I think, is very broad. In this regard, I want to end by remarking that every human creation has an abstract ghost, to be elaborated in a possible future blog post.
Thought Flow 