Critical Thinking Toolkit: Ockham’s Razor

When we are in debates, very often there is more than one way to explain something. When we are presented with more than one way of explaining some aspect of reality – be it scientific, historical, religious, or anything else – these situations arise. When they do, we want to be able to differentiate betweenContinue reading “Critical Thinking Toolkit: Ockham’s Razor”

Critical Thinking Toolkit: Possible v.s Plausible

In our common experience, there are a plethora of alternative explanations of the realities we see around us. Some of these are highly likely, some fairly likely, some moderately likely, some that are reasonable but not strictly ‘likely’, and some that are extremely unlikely. There are a variety of situations that we might find ourselvesContinue reading “Critical Thinking Toolkit: Possible v.s Plausible”

The Fallacy of Equivocation

This is one of many brief articles I am writing about how to avoid fallacious patterns of thinking. Here, we briefly discuss the fallacy of equivocation. Before I try to define it, it will be helpful to see an example of the fallacy in action. (I take this example out of the Wikipedia page forContinue reading “The Fallacy of Equivocation”

Finding Patterns in the Fibonacci Sequence

This is the final post (at least for now) in a series on the Fibonacci numbers. We’ve gone through a proof of how to find an exact formula for all Fibonacci numbers, and how to find exact formulas for sequences of numbers that have a similar definition to the Fibonacci numbers. But, the fact thatContinue reading “Finding Patterns in the Fibonacci Sequence”

Finding the Fibonacci Numbers: A Similar Formula

In this series of posts about the Fibonacci sequence , a very famous sequence of numbers within mathematics, we have just concluded showing how you can take the recursive formula (which uses previous values of to compute the next values) and turn that formula into an exact formula that can skip right over the previousContinue reading “Finding the Fibonacci Numbers: A Similar Formula”

Finding the Fibonacci Numbers: The Formula

This is the third post in a series about an exact formula for the Fibonacci numbers, , which are defined by the initial values and the recurrence relation . We have made a lot of progress towards our goal. We discovered a connection between , the golden ratio , and the Fibonacci sequence by findingContinue reading “Finding the Fibonacci Numbers: The Formula”

Finding the Fibonacci Numbers: Getting Our Bearings

This is the second in a series of posts discussing a quite elegant and interesting problem in the history of mathematics. We have previously defined the Fibonacci numbers using the starting point and defining for every larger value of . This set up is often called a recursive formula, since we use the same processContinue reading “Finding the Fibonacci Numbers: Getting Our Bearings”

Finding the Fibonacci Numbers: The Problem

The 1202 mathematics textbook Liber Abaci is arguably one of the most important contributions to the development of the scientific and cultural systems we have in the world today, especially for Western society. Written by Leonardo of Pisa, known colloquially by the name Fibonacci, this text introduced to the Western world important notations and mathematicalContinue reading “Finding the Fibonacci Numbers: The Problem”

Critical Thinking Toolkit: External and Internal Contradictions

When developing critical thinking skills, learning to recognize falsehood is as important as learning to recognize truth. This is important for many reasons. Recognizing falsehood helps you realize when you are making mistakes, when others might be making mistakes or using confusing language, and can help you find out the truth by process of elimination.Continue reading “Critical Thinking Toolkit: External and Internal Contradictions”