What Does it Mean to Comprehend Something?

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?

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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.

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The Mormon Transhumanist Association

A while back I reviewed a book called Parallels and Convergences: Mormon Thought and Engineering Vision. I enjoyed the book and was curious about the fact that several authors in the book were members of the Mormon Transhumanist Organization.

I had just learned about so-called “Transhumanists” a year or two earlier because I read a book called The Physics of Immortality. Essentially a “Transhumanism” is (from Wikipedia) “…an international intellectual and cultural movement that affirms the possibility and desirability of fundamentally transforming the human condition by developing and making widely available technologies to eliminate aging and to greatly enhance human intellectual, physical, and psychological capacities.”

I had noticed that of all the Christian religions (and probably all religions, though I’m hardly qualified to judge) Mormonism had the most touch points with Transhumanism. (Though some significant differences as well.) So I’m shouldn’t be surprised to find that there was Mormon Transhumanist Association. 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