Computability and Algorithmic Compression

In a previous post I showed how to calculate PI and made the point that purely mental concepts, like PI, actually do exist.

Also, don’t miss this post where I considered how to use math to measure the earth and the moon – a power once associated with Divinity.

Now I want you to think about PI again for a moment. Back in school I was taught to use 3.14 to approximate PI. If I needed more precision I used 3.1416. But actually PI is what we call an irrational number.

Do you remember doing repeating decimals? You know, where you divide a number out and a pattern forms. For example, you take 1 and divide it by 3. The end result is 0.3333… where the 3 goes on forever repeating. The way they teach you in school to write it down is to write 0.3 and then put a bar over the 3 after the decimal to signify that it just keeps repeating forever. Continue reading

Measuring the Earth and Moon

I ran this back on 2010 as part of my W&T series. I’m including it here for completeness.

God came from Teman… He stood, and measured the earth. (Habakkuk 3:4,6)


Who hath measured the waters in the hollow of his hand, and meted out heaven with the span, and comprehended the dust of the earth in a measure, and weighed the mountains in scales, and the hills in a balance? (Isaiah 40:12)

In my first post over at Wheat and Tares (check it out if you missed it), I mentioned one of my favorite books, Mathematics for the Million. I also took an example from it on how to calculate the value of PI using reason.

This book also gives several interesting examples of other things that you can do with math. Did you know that you can mathematically calculate the size of the earth, the distance to the moon, and the size of the moon? Did you know that if you know the trick, you can form a right angle without a tool?

Measuring the Earth’s Radius and Circumference

The trick to measuring the Earth’s circumference is to find a well that the sun directly passes over so that you can see the reflection at the bottom of the well. This can only happen on the tropic of cancer, and only on June 21. At the same time that happens, also measure the angle of the shadow at some distance away but at the same longitude. The book uses the example of Syene and Alexandria.

Continue reading

Reason as a Guide to Reality

This is a reprint from Wheat and Tares. It was the first of my “reason as a guide to reality” posts.

Did you ever hear the one about the dyslexic, agnostic, insomniac? He stayed up all night wondering if there really was a dog.

Like many people, I’m curious about the nature of reality and really do sometimes stay up all night wondering about… well, just about anything.

A while back I wrote this post about the ramifications of a comprehensible God. If God and reality are comprehensible then using reason and rationality to explore reality is a worthwhile goal. But if God and reality are not fully comprehensible, then reason and rationality will only work haphazardly, and therefore are not reliable guides.

A Slice of PI

What I find so fascinating about logic and reason are that they do work. For example, what is the value of PI? Continue reading

Explaining Quantum Physics – The Nature of Reality

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. [1] 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

42: Science, Religion, Philosophy, and Everything

I have wanted to do a series of posts discussing various topics I find interesting. I love trying to find the cross section between science, religion, and philosophy. Sometimes I have to look really hard to find such a cross section. At any given moment, any two of these areas of knowledge are likely going in such opposite directions that there is no hope of them ever meeting without a major paradigm shift. But I find it fun to try all the same.

I once did a series of posts for Wheat and Tares (M* got pointers to the posts) on epistemology. Epistemology is a fancy word for “theory of knowledge” or, in other words, it’s a word for a theory on how we gain knowledge.

Karl Popper’s theory of epistemology is in the forefront of all other theories of knowledge because his theory is superior to all contenders. However, Popper’s own presentation had some flaws that I felt Thomas Kuhn filled in nicely. (Though Kuhn’s conclusions that there is no such thing as scientific realism seem patently false to me.) My posts made an attempt to integrate some of Kuhn’s better ideas into Popper’s overall framework. In addition, I threw in some of David Deutsch’s improvements on Popper plus some ideas from John Polkinghorne. For those interested, see my summary of this epistemology here. Continue reading