In a previous post I talked about Roger Penrose’s seven (depending on how you count them) SUPERB theories of science. Now I’d like to give you an alternative view that I think is equally fascinating, though it takes a completely different path.
David Deutsch, being a Popperian Epistemologist (i.e. Epistemology is the theory of how we gain knowledge), believes that what makes a theory one of our best theories is not its range and accuracy, but instead how much it explains. Based on these criteria, Deutsch believes our four deepest theories of science are the following:
- Quantum Mechanics
- Biological Natural Selection
- Popper’s Theory of Knowledge (Epistemology)
- Computational Theory
In fact, Deutsch believes that these four strands are the start of what he calls “a theory of everything.” Continue reading →
In my last two posts on Computational Theory, I first explained the Church-Turing Thesis which can be summarized as the idea that all (full-featured) computers are equivalent. I then went on to summarize some Computational Theory principles we can study and research once we assume that the Church-Turing Thesis is true. This research is primarily based around the limits of what a Turing Machine can do or how fast it can perform.
In this post I’m going to explore some of the philosophical ramifications of the Church-Turing Thesis, if it were to actually hold true. And at least so far (with one interesting exception) it has held true. Though in the end, I suspect many readers will feel they need to ultimately reject the Turing Thesis. But even if it does ultimately prove false, the very fact that it holds true in every case we know how to currently devise still makes it an useful scientific principle, for now. Continue reading →
In my last post I started explaining the theory of computation, starting with its central principle: The Church-Turing Thesis. In this post, I’m going to explain several areas of research in computational theory that, as per the Church-Turing Thesis, are based on the realization that all (full featured) computers are equivalent.
Turing Machines as Simplified Computers
Since Turing Machines are known to be equivalent in expressive power to modern computers, it turns out this means that Turing Machines can serve as a very simplified version of a modern computer — or any conceivable computer!
This makes Turing Machines quite useful for exploration of the Theory of Computation. Mathematicians have been able to come up with ‘programs’ written for Turing machines and then – because Turing Machines are so simple – come up with consistent ways of how to measure how fast the program runs given any number of inputs. Continue reading →
One scientific/philosophical point that all three of my favourite authors loved to delve into was Computational Theory and, in particular, something called “The Church-Turing Thesis” and it’s related thesis: The Turing Principle 
I remember, back when I was working on my computer science degree, studying about Turing machines and the Church-Turing Thesis in my Intro to Computational Theory class. Back then I thought it was a big waste of time. I just wanted to program computers and I could care less about this long dead Turing-guy (or this Church-guy) nor his stupid theoretical machines.
Now that I understand the philosophical ramifications of the Church-Turing Thesis, I wish I had paid attention in class! Because the Church-Turing Thesis, if true, has some profound philosophical ramifications and it might also tell us something about the deep — and special — nature of reality.
In a series of posts I will attempt to do a short summary of Computational Theory. This serves as the basis for many other topics to come, so it will be nice to have a series of posts I can easily reference back to. (I’ll also do a summary at the end if I get that far.) I’ll do my best to make it as easy as possible and as interesting as possible. But if this just isn’t your cup of tea, you may need to move on or just skim it for general ideas or wait for the quick summary.  Continue reading →
Before I disappeared from blogging, I had finished up reposting my Wheat and Tares posts on epistemology (i.e. theory of how we gain knowledge. Good summary of my posts found here. Full series found here, in reverse order of course.) But the truth is that throughout my series, I never really had a single post that attempted to explain what epistemology really is.
Conjecture and Refutation
To summarize how epistemology works, the basic idea is that scientific progress is made through a process of conjecture, criticism, and then refutation. Essentially we see something in the world that we wish to have explained or (even more likely) a problem that we can solve if we can explain it. Continue reading →