Stephen Wolfram’s Principal of Computational Equivalence kind of puts everything on equal footing. The concept of “comparing the computational sophistication of systems that we study with the computational sophistication of the systems we use to study them” is a unique way of looking at issues related to observation and measurement, a mainstay of philosophy and quantum physics. His Principal of Computational Equivalence indicates that our assumption that our analytical abilities far outstrip the natural processes we study is wrong. Therefore, our predictions can not be any shorter than the actual computations that create the behavior we study – they are “computationally irreducible” (except for systems with very simple or repetitive behavior). Could this be why there is no Theory of Everything?
I often feel, when I look at the world, that I am looking at a mirror. I figure this is a function of the way the world comes in through my senses to be interpreted by my brain. The senses, the brain, that’s me. The world merely stimuli. But, if I think of myself as a computational system measuring another system of comparable complexity; then the mirror is not a function of my being cut off from the real world, but merely a function of all the things shared between me and everything outside. One of the main tenets of life is that energetic transactions are circumscribed in space. My chemistry is not unique, but it resides within my skin, that is the basic underlying requirement for life – the cell wall, the body. The ability to replicate, delineates life in time as well as in space. By replicating, life can go forward in time and be subject to natural selection.
To describe any system that exact same delineation is needed. What is the system being examined? How do I carve it out. It is fun that systems operate on multiple scales. We can pick a large-scale to examine, and ignore everything at smaller scales. Yet, according to Wolfram, those processes at smaller scales are not necessarily simpler. But, anyone who has studied cell biology already knew that! So what do we do with life, with the universe, all made up of systems within systems. We study pieces as we define them and then get frustrated that gravity doesn’t fit in with quantum mechanics. Perhaps we try to reduce too far. As Wolfram points out, there may be a simple equation that represents the Theory of Everything, but there is no way to recognize it without letting it run from the beginning. And what do you get when you do that? Everything, irreducibly everything.
