From the void to all the sound of the rainbow.


What I find very problematic in many axiomatic definitions, is that there is just bunch of things that must exists, in order to formally define an object. What I mean by that, is that if we're concerned with the totality of the object, we also must consider the specification - formal description of the system, as the part of this totality.
My particular interest in this branch of mathematics, that could be more or less, described as Constructive Mathematics originates from old times, when I confronted Godel's Incompletness Theorem for the first time. It used to bother me for few years and I used to find it at the same time completely stupid and brilliantly disturbing. I'm happy to say it does not bother me anymore. I believe that my pursuit after an intuitive understanding of this weird phenomenon fundamentally changed the way I'm looking at world and mathematics. It made me ask myself questions, why can such proof even exist?, what is actually proof? Is there a way to stay formal, without proving?
Of course I'll be happy to share the answers to those questions, which I managed to come up with. However as for my breakthrough in the way I'm looking at math, I believe its' pursuit itself and not any particular knowledge what allowed for it to happen. What's the most the most important to me which I associate with that journey was gaining the feeling of freedom in Mathematics.
When purpose behind particular thinking process, does not have specific objective, but is rather driven simply by human feelings, it made me feel like in some sense it unlocks new cognitive abilities.

Making nothing

In fact, there is nothing more abstract to a human, than pure nothingness