Lessons from the Life of Johannes Kepler

Johannes KeplerKnown as the discoverer of the laws of planetary motion, Johannes Kepler was the first to propose that the planets circle the sun in elliptical shapes rather than in circular shapes as previously thought. Although often thought of as a scientist, Kepler was also a mathematician. In his study of planetary motion, Kepler used extensive math, including definitions, geometry, trigonometry, algebra, and other math concepts.

This mathematician’s life both provides an example of math in action and is resplendent with lessons! Join me in taking a brief look.

God’s Plans Are Not Always Ours
Johannes Kepler’s life illustrates the important truth that God’s plans are much better than are own–and sometimes they surprise us! Johannes Kepler did not plan on becoming a mathematician–he set out to become a minister. But toward the end of his university studies, his professors recommended him for a math position.

The young minister-to-be didn’t like the idea of giving up his divinity studies. Although he eventually agreed to take the position, Kepler still planned on becoming a minister one day. But God had something very different in mind for Kepler, as Kepler himself later recognized. [1]

Kepler had always been interested in the movement of the heavens and had admired Copernicus and his sun-centered theory. As a professor, Kepler now had more time to investigate these matters. He spent years developing a theory to explain the movements of the heavens, only to later discover his theory was insufficient. Undaunted, Kepler kept trying. His belief in the universe as an orderly creation of God made him certain the movement of the heavens could be explained by geometry. [2]

In 1600, Kepler’s teaching career at the school came to an abrupt halt. Along with others who refused to convert to Catholicism, Kepler was told to leave the country! Yet although Kepler probably could not see it at the time, God had a plan to transform persecution and exile into a tremendous blessing.

BraheExiled from his own country, Kepler soon found himself assisting (and depending on the generosity of) the famous astronomer Tycho Brahe (pictured to the left)–that is, until Brahe died in 1601. After Brahe’s death, Kepler inherited Brahe’s position and records. Because he had been exiled from his own land and forced to take shelter under Tycho Brahe, Kepler now had the records he needed to discover the laws by which God caused the planets to orbit the sun. Who would have thought God would use a persecution and forced exile to help Kepler accomplish his life work?

Perseverance in the Face of Obstacles
One of the biggest lessons we can learn from Kepler is that of perseverance. Discovering the planetary laws did not prove an easy task. From a collection of numbers Brahe had made over a period of many years chronicling where in the sky Mars had appeared, Kepler tried to find some sort of orderly law that could express the way God caused Mars to orbit the sun.

Just how hard was this task? According to Robert Wilson, “It took Kepler eight years and nearly a thousand pages of closely written calculations before he cracked the problem and discovered his first two laws of planetary motion (the third was to wait another nine years).”[3] Can you imagine spending eight years on a geometry problem you are not even sure can be solved, then another nine years to finish the task?

Confidence God Created an Orderly Universe and Math Could Describe It
Kepler’s willingness to persevere came from his deep faith that God had created an orderly universe. Kepler longed to uncover that order so he might bring glory to His Creator and know Him better.

Kepler was unwilling to accept the “close” results obtained from the prevailing Greek cosmology of the universe, in which planets circled the sun in circles. Instead, he searched for a better model.

Questioning the Greeks was a huge step. For centuries, the Greek philosophers’ teachings had been taught as fact. To question them was equivalent to questioning proven fact. Kepler could only be so daring because he believed in God as the source of truth, not the Greeks’ human reasoning. [4]

Kepler’s Beliefs – The Good and Bad
No one reading through Kepler’s Harmonies of the World can doubt Kepler’s belief in God. He often paused in the middle of an explanation to mention his Creator, and sometimes even broke off into a hymn of praise. It seems almost as if Kepler still viewed himself as a minister, trying to uncover the glory of God throughout creation. His book on planetary motion ends with this tribute to God:

Crying out with the royal Psalmist: Great is our Lord and great His virtue and of His wisdom there is no number: praise Him, ye heavens, praise Him, ye sun, moon, and planets, use every sense for perceiving, every tongue for declaring your Creator…To Him be praise, honour, and glory, wourld without end. Amen. [5]

We can learn a lot from Kepler’s use of math as a tool to uncover God’s handiwork.

At the same time, though, Kepler’s theology and outlook on math were far from perfect. He carried over a lot of Greek mysticism into his beliefs about God and the universe. Forgetting that creation and our minds are both fallen, Kepler often drew unbiblical spiritual parallels and inferences about God. Kepler also dabbled in astrology (although he admitted it held no weight) and brought a good deal of mystical thinking into his astronomy.

Lesson? We need to be on guard against falsehoods and lies from our culture that try to creep into our hearts.

Conclusion
Within Kepler’s life, we see God’s sovereignty at work, using even an exile to accomplish His purposes. We also find a challenge to persevere–and to view the universe as God’s handiwork and worship Him while using math to explore it. At the same time, we find a warning to be careful about falsehoods that threaten to rob us of living in the completeness of God’s truth.


[1] Max Casper, one of Kepler’s biographers, says, “Looking back later when, through the discovery of his planet laws, he had become aware of his ability, he recognized the voice of God in the call which had come to him. It is God who by a combination of circumstances secretly guides man to the various arts and sciences and endows him with the sure consciousness that he is not only a part of the creation but also partakes in the divine providence.” Max Caspar, Kepler, trans./ed. by C. Doris Hellman (New York: Dover Publications, 1993), p. 51.

[2] Kepler believed God was geometry’s creator. “For the Creator, who is the very source of geometry and, as Plato wrote, ‘practices eternal geometry,’ does not stray from his own archetype.” Kepler, Johannes, Harmonies of the World, in On the Shoulders of Giants: The Great Works of Physics and Astronomy ed. Stephen Hawking (Philadelphia: Running Press Book Publishers, 2002), p. 645. The Bible, however, never tells us God “practices eternal geometry.” We should not be surprised to find that parts of God’s creation are even more complex than geometry can describe. Nonetheless, Kepler was right in his general belief that God created an orderly universe, and that math records that order.

[3] Robert Wilson, Astronomy Through the Ages: The Story of the Human Attempt to Understand the Universe (Princeton, NJ: Princeton University Press,   1997), p. 69. For more details about the obstacles Kepler faced, see Max Caspar’s Kepler or Robert Wilson’s Astronomy Through the Ages: The Story of the Human Attempt to Understand the Universe.

[4] See Chapter 6 of Beyond Numbers for a basic overview of the switch from Greek thinking to biblical thinking that paved the way for the Scientific Reformation.

[5] Kepler, Johannes, Harmonies of the World, in On the Shoulders of Giants: The Great Works of Physics and Astronomy ed. Stephen Hawking (Philadelphia: Running Press Book Publishers, 2002), p. 723.

——
Resources Consulted

Caspar, Max. Kepler. Trans./ed. by C. Doris Hellman. New York: Dover Publications, 1993.

Kepler, Johannes, Harmonies of the World, in On the Shoulders of Giants: The Great Works of Physics and Astronomy. Ed. Stephen Hawking. Philadelphia: Running Press Book Publishers, 2002.

Newman, James R., ed. The World of Mathematics. Vol. 1. New York: Simon and Schuster, 1956.

Nickel, James D. Mathematics: Is God Silent? Rev. ed. Vallecito, CA: Ross House Books, 2001.

Tiner, John Hudson. Champions of Mathematics. Green Forest, AR: Master Books, 2000.

Wilson, Robert. Astronomy Through the Ages: The Story of the Human Attempt to Understand the Universe. Princeton, NJ: Princeton University Press, 1997.

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Musings on Algebra

For our first specific concept post (see the schedule), I thought I’d offer some general thoughts on a part of math that confused me for years: algebra. Hopefully, this will help you see God’s handiwork amid the xs and ys.

What is algebra?
Algebra is the process of using letters and symbols to describe general quantities and relationships.

For example, say I head into a store with $20 and come out with $5. I would have spent $15.

$20 – $5 = $15.

My starting dollars minus my ending dollars showed me how much I spent in the store.

starting dollars – ending dollars = dollars spent

Let’s use letters to represent this relationship. We’ll use z to represent the starting dollars, y for our ending dollars, and x for the dollars spent.

z – y = x

We now have represented a general relationship that holds true for more than one situation! (We could use it to see how much we’d spent in any store.)

The above is one example of using letters to describe a relationship. By recording a relationship rather than a specific situation, we’re able to solve for unknowns and discover other relationships. This process proves useful in MANY areas (electricity, interest rates, gravity, laws of motion, etc.)

Algebra is based on the idea that certain relationships consistently hold true–that objects operate in a predictable fashion. Dollars do not mysteriously multiply in our wallets. Objects fall in a predictable way. The relationship between the power and voltage and current in an outlet remains the same. Why do things operate so predictably?

Because an unchanging God holds every aspect of this universe together! If God were not keeping everything together in an amazingly predictable manner, algebra would be completely useless. But because of God’s unchanging hand over creation, we can use letters and symbols to name and describe the predictable world around us.

What about all the rules?
A large portion of algebra textbooks focus on rules and conventions. Each “rule” is one standardized convention to represent a real-life consistency.

For years men did not use our current conventions at all! The graphic shows some different ways an algebraic equation has been expressed.

Why does algebra often seem so meaningless?
So often, algebra students completely miss seeing the amazing consistency algebra records because they get lost in the mechanics. As Morris Kline points out, “The usefulness of the techniques of algebra has caused many people to mistake the means for the end and to emphasize these menial techniques to the exclusion of the larger ideas and goals of mathematics. The students who are bored by the processes of algebra are more perceptive than those who have mistakenly identified algebraic processes with mathematics.” [Morris Kline, Mathematics and the Physical World (1959; repr. and slightly corrected, Mineola, NY: Dover Publications, 1981), p. 68.]

Conclusion
As you teach algebra, beware of emphasizing the means (i.e., the rules and conventions) to the point that your student loses site of algebra’s purpose–to record consistent relationships. Remember to let your mind pause and consider the greatness, power, and consistency of the God who, day in and day out, governs all things consistently enough for us to record general relationships and expect them to hold true in various situations. His power, might, and faithfulness truly know no bounds!

“I am the LORD: that is my name: and my glory will I not give to another, neither my praise to graven images.” Isaiah 42:8 (KJV)

Note: Watch for more on algebra soon!

The Golden Ratio

The Golden Ratio – A Wonder of God’s Creation

Above is a link to a blog post one of the members of our church posted a few months back–I’m excited to be able to share it with you, as it does such a wonderful job sharing with pictures and text about this fascinating ratio. It ends with this fitting reminder:

Man is indeed without excuse, for God has put his signature on all of creation. “For since the creation of the world His invisible attributes, His eternal power and divine nature have been clearly seen, being understood through what has been made, so that they are without excuse” – Romans 1:20.

Free Digitized 1800 and 1900 Math Books

Several months ago, I felt like I’d hit a goldmine when I first discovered Google has digitized and made available for FREE numerous math books from the 1800s and 1900s, including some of my favorite ones I’d found in old collections. Written back before math was viewed as an intellectual pursuit, many of these old books team with practical word problems!

While they’re not for everyone, as the older English wording and time-period illustrations might confuse some children, these historic math books can be quite helpful! If you’re not sure how to show your child how a concept serves as a useful tool, try looking at some of the word problems offered in one of these books. I wouldn’t necessarily recommend reading through all the presentations, as they’re not easy reads, but many of the word problems are gems! A good place to start is the Table of Contents–the books are also searchable if you want to narrow in on a specific concept.

Below are links to a few of Google’s extensive collection. If you search for these books’ authors, you’ll find other books by them as well (you may want to limit your search to “Full view only” to see all those available on the site in their entirety).

Ray’s New Practical Arithmetic
Adam’s New Arithmetic
Stoddard’s Rudiments of Arithmetic

Practical Arithmetic (upper elementary/high school)

Reminder: Request Week – Next week is request week, so please leave a comment with what you’d like us to discuss!

A New Year, a New Look, a New Schedule…and a New Book!

It has been more than a year since I’ve posted anything–ouch! I think it’s high time for a long-overdo update : ).

Revealing Arithmetic: A Practical Guide to Teaching Math BiblicallyFirst of all, Revealing Arithmetic: Math Concepts from a Biblical Worldview, is finished! The final book ended up being a more-than-200-full-sized page manual offering ideas and inspiration for teaching basic arithmetic (counting through exponents) from a biblical worldview. I can’t tell you how excited and grateful I felt when it went off to the printer…it’s been a long, but blessed journey. Thank you all for your prayers and encouragement along the way! If you’d like to learn more about the book or purchase a copy, it’s now in our online store!

Now that Revealing Arithmetic is finished, it’s my intent to focus more on this blog. I would really like to make it a place where we can explore God’s hand in math together. You may have noticed the blog has a new look and feel–and I’m hoping to add new content to it regularly.

My plan is to post at least once a week, according to the following “tentative” monthly schedule.

  • Week 1: Specific Concept – Information, ideas, or musings about a specific math concept (concepts will vary each month).
  • Week 2: A Concept’s History or Applications – An exploration of a portion of math’s history or one of its many applications.
  • Week 3: Resources – A resource link or review.
  • Week 4: Requests – Topic will vary based on requests and feedback received. (This is your chance to tell me what you’d like to see us discuss!)

As I try to begin/resume this blog, know that your comments (feedback, ideas, sharing, questions, etc.) will help keep me going : ) I look forward to learning and growing with you!

Math Articles and Tips

A few weeks ago, someone shared a link to www.mathworksheetscenter.com in a comment and I wanted to pass it along to you all, as some of the free articles there looked quite helpful. The articles are located at http://www.mathworksheetscenter.com/mathtips.

I especially liked many of the high school articles, as they gave some practical ideas on math’s applications. You could use each suggestion as a launching pad to have your student explore further.

The site also offers thousands of worksheets for a small membership fee. The lessons on the worksheets basically just explain the concept by offering an example problem worked out. A search online reveals other sites with free worksheets; however, if you’re looking for a wide variety of worksheets and don’t want to hunt all around to find them, the membership might be worth it for you. Be sure to view one of the worksheets first to see if the general quality/layout would work for you.

My prayers are with you all as you gear up for a new year of school. May each day be blessed with a deeper appreciation for God’s faithfulness and power.

In Him,

Katherine

New Math Curricula Reviews

I recently reviewed two math resources—Professor B’s Power Mathematics and Maximum Math, and reorganized my math review page to hopefully make it a bit more user friendly. I always hesitate when posting a review because not every resource or curricula works for every person. We all have different learning styles and specific needs. So please keep in mind that it’s not my intent to endorse any specific resource, but rather to describe some of the options so you can better decide what will work for your family.

My prayers are with you all as you make your plans for next year. It’s easy to get overwhelmed, taking our eyes off the Lord and putting them on the many decisions that need made. Remember to let God carry the burden—He delights in leading, guiding, and teaching you each step of the way.

By His Grace,

Katherine

“Biblical Math” May Not Really Mean Biblical

I was recently reminded of the fact that many people use the term “biblical math” to mean something very different than I do when I use it. So I thought it might be beneficial to take a look at some different ways the term has been used.

Many use the term “biblical math” to refer to using math to unlock some sort of hidden code within the Bible. In fact, there have been numerous books written on this topic. Each one claims to have unraveled a mystery within the Bible’s pages.

If you’ve ever been intrigued by any sort of “biblical numerical code,” I’d encourage you to read the article linked to below by James Nickel. I found this article incredibly helpful in understanding why I felt such a caution and uneasiness in my spirit every time I read anything about these hidden codes. Mr. Nickel explains how these “hidden” codes really have Gnostic roots and are a distortion of the gospel of Christ and the Word of God.

http://www.biblicalchristianworldview.net/Mathematical-Circles/behindBibleCode.pdf

Although many people attempt to use these codes to defend the authority of the Bible or to proclaim some other truth, the whole idea of finding some sort of “hidden” revelation is not true and is actually very dangerous. God’s truth is available to all, not just those who can crack a special code. There’s a harmful elitism and mysticism in saying we need some sort of special knowledge to understand part of God’s message to us. God warns that He has hidden things from the wise and revealed them to babes (Luke 10:21). We’re to use the Bible to help us understand math, not use math to unlock the mysteries of the Bible. God has given us His Spirit, note a code, to help us understand His Word.

Other people use the term “biblical math” to refer to a curriculum that contains Bible verses and Christian morals. Yet although the student is being taught a biblical perspective on morality and learning biblical truth, he’s not necessarily being taught how to look at math itself from a biblical perspective.

I would define the term “biblical math” as an approach to math that leaves the student with an understanding of how math itself is viewed from a biblical worldview. The Bible gives us principles that impact the way we view and approach all aspects of life, including math. God is the creator and sustainer of all things and is a consistent, faithful God; hence, we can expect the universe to be consistent. Man is created in the image of God; hence, we’re able to observe the consistent way God governs all things and record that using math. Man is fallen; hence, we are prone to error and cannot place our faith in our own reason. God gave us the responsibility to work and “subdue” the earth; hence, God has given us math as a useful tool to help us with the tasks He has given us.

The above statements are just a few (and are simplified for the sake of space) of the ways the Bible’s principles should impact the way we approach math. When we take these and other principles and build our approach to math off of them, it completely transforms math from a meaningless exercise to something both meaningful and useful—and something that, above all, points us to the Creator (see Beyond Numbers).

I hope the above explorations of “biblical math” help clarify things a little for you. It’s amazing how differently a phrase can be applied, isn’t it? : )

Balancing, Measuring, and Such

A few weeks ago, I visited a local historic home with my aunt, uncle, and cousins. Something I saw there sparked a little research and has resulted in this post : ).

The chandelier hanging in the hall of the historic house was much too high to light easily using a ladder. But men had used the ingenuity God had given them to design a device whereby the chandelier’s candle COULD be easily lit—by just one person.

The chandelier was hung using a long chain, at one end of which was a cylinder that perfectly balanced out the weight of the chandelier. Since the weight balanced, the chandelier didn’t move unless a person pulled or pushed on the chain. By pulling or pushing on the chain, a single person could easily higher or lower the chandelier, light it, and return it to its former position.

As I looked at the chandelier, I realized this was math in action. Whether or not the original designers weighted the chandelier and the cylinder, I don’t know. But I do know that the weights equaled—and that math has been historically used to help design and use counterbalances for a variety of purposes.

[Photo taken at Sully Historic Site in Chantilly, Virginia.]

Merchants used to use a scale based on the counterbalance principle to weigh their products. On one side of the balance, they’d place the item to be weighed. They’d then add items of which the weight was known to the other side until the scale balanced. The whole process required quite a bit of math.

If you’re working on measurement with your child, consider having him or her build a scale! Easy instructions can be found at the website below. As you build it, thank God for creating us capable of designing devices—like balances—to help us.

http://www.campsite24.ca/balance_scale_eng.pdf

Money Fun

A recent trip reminded me of one practical way math serves as a useful tool–money conversion. On our trip, we saw prices listed in dollars, pounds, euros, forrents, and marks–and needed to use some quick math to figure out how much we were really spending : ). We employed addition, subtraction, division, and round/estimating at various times throughout the trip.

As you study different cultures in history, consider having your child learn about their money systems too. Simply search the Internet for “money” and the country’s name. You should be able to find some pictures and descriptions of the money in that country. Then search for exchange rates and see how the money compares to American money.

If your child is young and just getting used to American money and math facts, you could simply show your child the pictures of the money, explaining that different countries use different money systems just like they use different languages, and that math helps us compare prices. If your child is proficient with math, you could actually have your child pretend to go shopping in the foreign country and figure out how much something marked in that country’s currency would cost in American dollars. You could even set up a pretend shop!

Math is truly a useful tool!