…the chameleonic nature of numbers [is] so rich and complex that numerical patterns have the flexibility to mirror any other kind of pattern. (Douglas Hoftsadter in I am a Strange Loop, p. 159)
In my last post, I discussed the point of view known as ‘reductionism’ and the problems with that point of view. In summary, reductionism is the false belief that sciences that work with the smallest units of nature – atoms and below – are somehow more fundamental explanations of reality than emergent ones, such as thought or computation.
A few posts ago, I discussed computability and comprehension. My final conclusion was that while algorithms and explanations aren’t the same thing, you can’t have an explanation without having an algorithm. Continue reading
A while back I did a post about my three favorite non-fiction authors: David Deustch, Roger Penrose, and Douglas Hofstadter (Gesundheit!). This post is about Roger Penrose.
Roger Penrose has an interesting categorization system for scientific theories that I’d like to share. (Later on, I’ll give David Deutsch’s alternative approach.) Penrose believes there are three categories of theories. They are:
He goes on to say that say he’s considered making a fourth category called MISGUIDED but then thought better of it because he didn’t want to lose half of his friends.
In this post I want to talk about the seven scientific theories Penrose considers to be in the SUPERB category. These are the theories that, as Penrose puts it, have been phenomenal in their range and accuracy. Continue reading
In my last post I started to discuss the differences between Positivism and Scientific Realism. To over simplify it, Positivism cares only about the predictive abilities of science and does not care about whether or not science is getting ever closer to some underlying truth. Scientific Realism takes all scientific theories seriously as approximations of an underlying truth.
Actually, despite what Deutsch says (in my last post), I feel Positivism has value. Though I generally agree with Deutsch, sometimes you just want to predict an outcome and you don’t really care about why it works. In fact, I think most people would be shocked to realize that this is how most science and engineering are done. Scientists rarely become philosophical about what their equations mean for reality.
However, Deutsch is right about one thing. Positivism ultimately fails to grasp the value of believing your explanations. It is only through believing your explanations that you can comprehend them. And only by comprehending them can you refine them into something even more useful. Continue reading
Science is the process of how we use reason to find patterns in reality and then to explain them in finite explanations of reality that allow us to represent reality via processes that are computable.
In my last post, I introduced David Deutsch’s book, The Fabric of Reality. Deutsch’s main interest is in understanding – and by that he means understanding everything. Deutsch believes that understanding something is to have an accurate explanation of it and that this, in turn, serves as a sort of algorithmic compression of all observational data.
Deutsch’s point of view falls under what we might call Scientific Realism. It’s the idea that science is not just about coming up with clever predictions about the world, but rather it’s about discovering reality’s true nature and comprehending it. Continue reading
In my last post I considered Physicist John Barrow’s view of what science is:
So we find that Barrow’s view of science is that it is the process of how we use reason to find patterns in reality and then to algorithmically compress them into finite steps and formula that allow us to represent reality via processes that are computable.
I am going to suggest this as our starting theory of reality, but there is much that can be challenged about this view and therefore refined.
But first, I want to consider the idea of comprehending something. What does it mean to “comprehend” something? The problem with a word like this is that it’s a single word that maps to multiple possible meanings. Harkening back to my first post, if I ask you if you comprehend PI, what would that mean? Is it even possible to “comprehend PI” at all? It’s an infinitely large number, after all. It is therefore beyond comprehension isn’t it?