Posts in Mathematics

The Marvelous Effectiveness of Mathematics

Written By | February 16, 2015 | Posted in Mathematics | 2 Comments

(Opening disclaimer: as with most of my writings on science, I have no formal training in the area. Perhaps someday, but for now I am merely a curious bystander. What I present below is my best attempt at understanding the topic, but for detailed information (and fact-checking), follow the various provided links.)

Mathematics is a language with its own grammar and syntax. Mathematicians work to see what coherent sentences can be written with that language. Many times they do not know what to do with the sentences they compose, and many times those sentences later turn out to be accurate depictions of physical phenomena. Because they form complete sentences, they can also reveal things previously unknown in physics.

Imagine you are working on a physics problem and you are able to string together a theory that looks something like, “The quick brown fox…” You are absolutely certain that this phrase is part of the solution to your problem, but you are also certain that it is incomplete. Your friend the mathematical grammarian happens to stop by for a visit and she looks at your discovery. “Well that’s funny,” she says, “that looks just like the first part of a sentence I uncovered with the language of mathematics.” You look at her sentence, “The quick brown fox jumped over the lazy dog,” and you realize her complete sentence is not only a perfect match to the fragment you already have, it helps to explain things you previously could not figure out. Your friend had no idea that her sentence corresponded to the real world. To her it was just a beautiful formulation from mathematical grammar. For you, this abstract piece of math helps to open a new window into the world.

This basic analogy points toward a broader reality: mathematics has the uncanny ability to describe the world around us.

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God Arguments: The Nature of Nothing

Written By | February 2, 2015 | Posted in Mathematics Philosophy Physics | 2 Comments

Now that we have defined some ground rules of our discussions and defined some terms that are commonly misused, it is time to start digging into some of the hard questions. In this first series, I am going to look at arguments for the existence of a supernatural creator and how to evaluate them given our previously agreed-upon rules of engagement.

Our first foray into this *very* heavy question will be into what I consider to be the best argument that believers have for the notion of gods: the Kalam Cosmological Argument, otherwise known as the argument from creation. At its most basic level, it states the following:

  1. Everything that begins to exist has a cause;
  2. The universe began to exist;
    Therefore:
  3. The universe has a cause. (Wikipedia)

We need to evaluate both the initial claims and the conclusion of this classic argument. How does it hold up to scrutiny?

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Thinking About Thinking: Evidence and Statistics

Written By | January 21, 2015 | Posted in Mathematics Philosophy Science | 3 Comments

In the first post in this series, we defined the first principle of all decision-making: the laws of logic, and specifically the Law of Noncontradiction. In the second post, we explored the concept of confirmation bias and the two tests to correct for it: treating similar evidence equally and devising tests to falsify your own beliefs. In this third post in the Thinking About Thinking series we are going to discuss how to determine if evidence actually supports your claims using statistical analysis.

For starters, let’s look at a brief overview of the science of statistics and some of its important concepts.

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