How accurate is our understanding of reality?
“We do not ask for what useful purpose the birds do sing, for song is their pleasure since they were created for singing. Similarly, we ought not to ask why the human mind troubles to fathom the secrets of the heavens…. The diversity of the phenomena of nature is so great, and the treasures hidden in the heavens so rich, precisely in order that the human mind shall never be lacking in fresh nourishment.”
- Johannes Kepler, Mysterium Cosmographicum
The innate desire to understand our existence & reality is not just a hobby of scientists, philosophers, and saints. On camping trips under a starry sky (or after having a few drinks too many), even ordinary people like you and me start discussing such esoteric topics.
Have you noticed that during such conversations, most of us tend to grasp to our individual notions tightly? Science and mysticism fight a deathmatch. I personally relished defending science to death and the act of “debunking” ideas of people who did not share my enthusiasm for science gave me a heady feeling. I was becoming a victim to the common trap of considering science as a body of knowledge, rather than a way of thinking.
Time and again have we humans committed this mistake of assuming that we have figured things out. Some of you might be rolling your eyes by now. Is this guy saying that science should not be believed? Of course not! Science works and humanity has improved its conditions of living using scientific models and inventions. But all is not well with science. Einstein (with his theory of relativity) & Heisenberg (with his uncertainty principle) threw the scientific world into a frenzy with their unintuitive theories.
However, a name which gets missed out from the list of iconoclastic thinkers is the name of the Austrian, mathematician and logician, Kurt Godel. Without going into the technical details, I will try to explain what he proved about our mathematical system of algebra, geometry calculus etc. (I promise that no convoluted maths is coming your way in this article! So, I implore you to continue reading!)
All of mathematics is built upon certain “obvious statements”, which can’t be proved. These are called axioms. You might remember certain Euclidian axioms from school days such as: A line can be extended infinitely in both directions. Assuming such axioms to be universally true, we intertwine multiple axioms (applying different rules such as addition etc.) to build convoluted theorems. The entire field of maths is developed this way.
Godel proved that if a mathematical system built using such axioms is consistent, i.e. does not allow contradictory statements (For instance, 2 + 2 will always be 4, never 5), then it must be incomplete. By incomplete he means that some mathematical or logical statements can never be proved. (pause and let that sink in!).
Goldbach Conjecture is an example of this. It says that every even number greater than 2 is a sum of two prime numbers. (4= 2+2, 6= 5 +2 and so on.). Despite considerable efforts, it hasn’t been proved since 1742! What are the implications of this on our perception of the universe and reality?
Fundamental physics which is used to build our picture of reality consists of highly mathematical propositions and thus is subject to the validity of Godel’s theorem. While drawing a connection between maths and science this way seems very intuitive, you shouldn’t trust a random person on the internet over this. Here is what Stephen Hawking has to say about this,
“Maybe it is not possible to formulate the theory of the universe in a finite number of statements. This is very reminiscent of Godel’s theorem. This says that any finite system of axioms is not sufficient to prove every result in mathematics…
What is the relation between Godel’s theorem and whether we can formulate the theory of the universe in terms of a finite number of principles? One connection is obvious. According to the positivist philosophy of science, a physical theory is a mathematical model. So, if there are mathematical results that cannot be proved, there are physical problems that cannot be predicted…
Some people will be very disappointed if there is not an ultimate theory that can be formulated as a finite number of principles. I used to belong to that camp, but I have changed my mind. I’m now glad that our search for understanding will never come to an end…”
-Stephen Hawing, Godel & the end of physics
All being said, it does not mean that mathematics & science be scrapped as subjects (how much ever some of you may relish that!). However, it does imply that our perception of reality is severely limited and there are some things which science would never be able to prove. While this does not warrant taking a deep dive into the marshy land of pseudo-science, it does encourage humility and open-mindedness. I trust that this article has left you thinking about the lens through which you see this world.
Originally published at http://meditationsofavoyager.wordpress.com on October 25, 2020.