Author: joshwilkerson

2 + 2 = 5 (For Extremely Large Values of 2)

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In keeping with the t-shirt-themed-previous-posting, I thought I would begin this entry with a snapshot of a shirt that I received for Christmas. Pretty awesome huh? Jealous? Well if you are, you can click on the picture and you will be whisked away to the website that sells them (I suppose even if you aren’t jealous, that last statement still holds). They will be happy to take your money and in exchange provide you with a shirt of your very own.

You’ll notice when you go to the website (thinkgeek.com) that they make a reference to a quote from Bishop George Berkeley. In fact, this reference is what initially sparked my interest in the shirt. Berkeley was an Irish philosopher practicing during the early 1700’s (following on the heels of his quite famous British predecessor John Locke). What’s more, Berkeley was a committed Christian, holding the position of Bishop of Cloyne.

I was introduced to the Bishop during a History of Philosophy class. In fact, I wrote a paper on his philosophy of mathematics. One of his most well known works is entitled: The Analyst, subtitled: “A Discourse Addressed to an Infidel Mathematician,” sub-subtitled (?), “Wherein it is Examined whether the Objects, Principles, and Inferences of the modern analysis are more distinctly conceived, or more evidently deduced, than Religious Mysteries and Points of Faith.”

Wow. And I thought the title for my paper on mathematics and process theology was impressive.

You can read The Analyst here.

This work is essentially a critique of the foundations and principles that Sir Isaac Newton (and Gottfried Leibniz) used to develop Calculus. Berkeley thought Newton’s reasoning was as sound as saying 2 + 2 = 5 for extremely large values of 2, hence the t-shirt. And you know what? Berkeley’s critique was a correct one. That’s not just my opinion, it was the consensus of mathematical community. The Analyst was a vital text in driving the revision and development of Calculus that we use and teach today.

The sad part is that while the importance of this work is known to most mathematicians and historians (at least the serious ones), on a popular level The Analyst is largely ignored. I’m quite sure that even those students who loathed math class remember the name Isaac Newton and can generally credit him with developing the concepts of Calculus. I’m also quite certain that, if polled, the same people would attribute Berkeley with the founding of a city in California. (Side note: the city in California is indeed named for the same George Berkeley, but he had nothing to do with its founding… what with being an Irishman who died in 1753).

All Berkeley’s endeavors, according Genevieve Brykman, were directed to the defense of what he saw as the most important truth – that we are in a constant and immediate relationship of dependence on God. Berkeley’s philosophy… was a provisional instrument in the service of his overriding apologetic aim.[1]

George Berkeley was the embodiment of what it means to think about mathematics Christianly and I think that it is important for us (those Christians who want apply their faith to the serious contemplation of mathematics) to give a more careful consideration of his work than we have previously given it.

I hope to provide some snippets from my paper in future posts.

[1] Gerald Hanratty, Philosophers of the Enlightenment: Locke, Hume and Berkeley Revisited. (Dublin: Four Courts Press, 1995), 72. See Genevieve Brykman, Berkeley: Philosophie et Apologetique (Paris, 1984).

The Enduring Uniqueness of Mathematics

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Why is mathematics different (in a good way) from every other subject you learned in school?

Two words: Pythagorean Theorem.

Let me explain. The Pythagorean Theorem in itself isn’t really the reason math is unique; it is merely an example I wish to use to illustrate my point. I chose this Theorem for an example because it has been my experience that it is one of the few things everyone remembers from math class, regardless of how much they enjoyed math or how well they did in the course. But just in case the P.T. slipped your mind, here is a recap:

For any right triangle, the square of the hypotenuse (side opposite the right (90 degree) angle), is equal to the sum of the square of the other two sides.

This result is attributed to the Greek mathematician and philosopher Pythagoras (hence the creative name for the theorem). Pythagoras lived between the 5th and 6th century B.C. and while he is ultimately the one credited with proving the theorem, there is evidence that the result of the theorem was known to the Babylonians 1000 years before Pythagoras was born. Notice this old tablet:

Wow, that is old. Here you can read more about the Babylonians and the Pythagorean Theorem.

My point is that in what other class are you performing the same operations as people were performing 3000 years ago? Certainly in history class you learn about earlier civilizations, but you are not being taught how to do history in the same manner as those civilizations. The precision that modern history requires was largely unknown to those ancient people. Perhaps in literature you read Homer’s Iliad and Odyssey, but again, you aren’t being taught to write in the same style of epic poetry.

So then why is it that in math class, while advancements have been made and technology certainly has come a long way, we still find it beneficial to perform calculations the way they were performed thousands of years ago?

My answer: there is nothing to perfect, nothing ot improve upon, when you come across truth. Real truth.

To all of us who hold the Christian belief that God is truth, anything that is true is a fact about God, and mathematics is a branch of theology.

~Hilda Phoebe Hudson