Computability and Comprehension – Is Science About Prediction?

Posted on October 1, 2012 by Bruce Nielson

Science is the process of how we use reason to find patterns in reality and then to explain them in finite explanations of reality that allow us to represent reality via processes that are computable.

In my last post, I introduced David Deutsch’s book, The Fabric of Reality. Deutsch’s main interest is in understanding – and by that he means understanding everything. Deutsch believes that understanding something is to have an accurate explanation of it and that this, in turn, serves as a sort of algorithmic compression of all observational data.

Deutsch’s point of view falls under what we might call Scientific Realism. It’s the idea that science is not just about coming up with clever predictions about the world, but rather it’s about discovering reality’s true nature and comprehending it. Continue reading →

What Does it Mean to Comprehend Something?

Posted on September 30, 2012 by Bruce Nielson

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?

Continue reading →

Computability and Algorithmic Compression

Posted on September 30, 2012 by Bruce Nielson

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

Posted on September 28, 2012 by Bruce Nielson

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 →