Is Knowledge Finite?

(the above image is taken from the internet.)

The brain is sometimes modeled as a computer. It is for most purposes, an apt model. So assuming this model holds, it follows necessarily that our memory capability is somewhat limited. This is found in experience also, we do not remember everything(and most thankfully at that). Also we do not choose what we remember. Memory is somewhat selective in what it retains. However, we can increase the probability of remembering something, by repeatedly memorizing it. All this is not new, this is just background for the kind of point I want to make.

Now there is such a thing as Knowledge, that is somewhat hard to quantify. I refer to it in the common layman term, “things that we can know”.  There are two facts about knowledge that are immediately apparent. First, that some pieces of knowledge can encompass other pieces, if you know relativity, you do not need to know the Newtonian equations, because they are a special case of relativity and relativistic equations transform into Newtonian equations when speeds are slow enough. Secondly there is trivia, that there are almost an infinite pieces of, it can theoretically cover all interactions that all human beings have had with each other and its a many many function. So the total number of pieces of trivia can safely be assumed to diverge. In what follows, I will not talk about trivia at all.

One major component of knowledge is scientific knowledge. While it not the only or even the most important kind of knowledge, it has its own significance in explaining our place in the universe and our relationship with all the things that exist in the universe. Science does this by a set of succinct laws that explain the relationships between various entities, this field of science is normally called physics and I would only talk about this field.

Physics is a vast field, from correlations governing fluid flow to the laws explaining high energy particles. No one, it can safely be said, knows all of it. And it is expanding, new relations are being discovered daily and new theories are being derived that offer new insight into the physical universe we inhabit.The question naturally arises, is physics finite? Or does it diverge?

One feature of physics and indeed of all science is called Reductionism. It basically posits that a complex system can be reduced to the interaction of its parts. What it means in principle is that the universe has been reduced to a number of isolated systems and these systems are described and solved in isolation from other phenomena that is not covered by the system in question. Now the very idea of reductionism is that it must converge, meaning there must a finite set of explanations(or equations) that must describe all physical knowledge. There has been as far as I know, no studies into whether physics or any disciplines of science are convergent are not.

There is a very real chance that knowledge doesn’t converge at all. The day when all scientific enquiry is exhausted is never going to come, our consciences would not allow for that. Why am I sure? Firstly because reductionism doesn’t guarantee convergence. Let us for the moment suppose that all the equations are known, that situation is indeed not very far from where we are today. We can very accurately describe what happened to the universe onwards from 10^-42 seconds after the Big Bang, we have almost perfect knowledge of systems that can be assumed to be linear, where we do not have theoretical constructs, we have obtained experimental correlations. Thus we have a broad idea of how the universe works. Now if we were approaching a situation where all knowledge would soon be known to us, it should be accepted that the number of open questions that we could ask about the universe would decrease(in very crude terms). That a situation would be approaching where, since most things are known and there are not a lot of unknowns left.

How would such a situation manifest itself? Well one way to look at this would be to look at how many publications are being made. It is well known that publications in refereed journals is how scientific knowledge is communicated by the discoverer to the community at large. Thus if we were approaching a situation where we were exhausting all knowledge then the number of publications should be going down.

Such a situation alas seems to be very far, if anything, there has been an increase in the number of refereed publications, over the past few decades. This prolific rate of increase can be attributed to the fact that there are simply a lot more researchers than there were a few decades ago. The research funding has increased, driving demand for more research, leading to more research being supplied(I’ll talk about the Economics of research at some other time). The ease of numerical simulations, the development of new exotic theories like the String Theories are all responsible for this growth. There simply are more questions to be asked today.

In this situation, it is high time we realize that Reductionism has simply not served us as well as was hoped. No one took the burden of collating the knowledge obtained by this reductionist methodology onto themselves, and as far as I know, not much has been done about it. Also reductionism is sort of like a divide and conquer problem, where you break up your problem domain into subparts and solve those subparts individually and then collate these into a single solution. However, what reductionists don’t consider is that new vistas of research often open up, research into an exotic sub-case of one domain can lead to a totally new domain where completely different laws apply(think turbulence, chaos).

In such a situation convergence is no longer guaranteed. It is my frank opinion that we need to think of alternative routes for the furtherance of scientific knowledge, before it dissolves into an unimaginable chaos of disciplines and sub-disciplines, specialties and sub-specialties and sub-sub-specialties and even further down. A situation could very well arise where all the mass of physics would atomize, leaving us empty handed, with faces covered in the soot of knowledge.

A future of accessible scientific knowledge on the other hand, sounds pretty interesting to me.