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
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 this post I’m going to attempt the impossible: I’m going to explain (at a high level) Quantum Physics using math while trying to keep it interesting. I’m basically going to use a dumbed down and somewhat modified example I’ve taken from Roger Penrose’s book called Shadows of the Mind: A Search for the Missing Science of Consciousness.
I believe people willing to persevere through this post will find themselves surprised by the end by the rather starling philosophical implications of quantum physics. I also believe that, if you take it slowly, the math is understandable to any high school graduate. I am personally very bad at math and can only handle this example because the math is so easy. If you don’t assume you can’t understand it, you’ll find that you can.
Forget What You Think You Know
Unless you are a physicist, start by emptying your mind of what you think you know about quantum physics through popular books because there is a substantial gap between what people say about Quantum Physics and the real theory. It seems to me that Quantum Physics currently gets used as the new ‘magic’. It’s become common for the fad magical (or sometimes even religious) worldview of the moment to slap a ‘quantum’ label in there somewhere to add a scientific veneer.  The reason this happens is because quantum physics has a deserved reputation for being really ‘weird’. But keep in mind what ‘weird’ means. It only means “something I’m not familiar with.” Claiming something is ‘weird’ says nothing ontological about the object/idea in question and actually serves as a statement about the speaker’s state of ignorance of the subject. (A point I often bring up when we talk about Mormons or other religions being “weird.”) Continue reading