Introduction to Computational Theory: Areas of Research

A Turing MachineIn 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

An Introduction to the Theory of Computation: The Church-Turing Thesis

A Turing MachineOne 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 [1]

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. [2] Continue reading

Morally Demanding of Others That Which We Will Not Give

I wrote a post once encouraging people to think carefully before they use deception as a way of dealing with the potential problems that arise from having reinterpreted one’s faith in the LDS Church. I gave several examples of the types of deceptions that I’ve seen. I, myself, have been personally hurt by such deceptions. For example:

  • Technically, they believe the Book of Mormon is “inspired” because “inspired” means something more nuanced than what most believers mean [e.g. "inspired just means it teaches good things."]
  • Technically they believe Joseph Smith is a prophet, because a prophet is something more broad than most believers understand [e.g. "prophet" is what we call the leader of our Church. Or maybe a "prophet" is someone that teaches at least some good moral principles..]
  • Technically they believe the church is “true” in the sense that… [e.g. The church is "true" because all religions that teach good ethics are "true" because religion is really just about teaching ethics. There isn't really a God.] Continue reading

How Did People in the 19th Century Perceive Younger Wives?

Joseph SmithIn yesterday’s discussion on Meg’s first post I started to write a comment that (as sometimes happens) became a tangent that then became a whole post.

I’m not even sure what comment originally prompted this. But I was thinking about Joseph Smith’s younger wives, particularly Helen Mar Kimball. Meg and I also got talking and she pointed to Nancy Winchester as being about the same age when they ‘married’ Joseph Smith.

The evidence is currently against either having consummated their marriages to Joseph. Continue reading

How We Gain Knowledge

Popper and KuhnBefore 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