Christmas Full Moon – Exploring God’s Creation with Math

moon-1532310You may have seen in the news that this Christmas we’re in for an infrequent sight in the sky: a full moon.

Because of the amazing consistency with which God causes planets and moons to orbit, we can use math to figure out ahead of time on what dates full moons will occur. This year, one’s falling on Christmas. According to NASA, the peak will be at 6:11 a.m. EST.

Pause and think about it for a moment. God causes the moon to orbit so predictably we can confidently figure out ahead of time when it will be full. In light of that kind of greatness, what is man that God should care for us? We’re but a tiny speck in the universe.

When I look at your heavens, the work of your fingers, the moon and the stars, which you have set in place, what is man that you are mindful of him, and the son of man that you care for him?” Psalm 8:3-4 (ESV)

Yet care God does–enough to humble Himself and become a man. At Christmas, we celebrate the incredible reality that the Creator and Sustainer of all humbled Himself, becoming one of His creation for the purpose of dying in our place.

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Math and Chocolate

Math and chocolate–since those are two of my favorite words, imagine my joy when I came across the news that a University College London (UCL) student had been exploring the math behind chocolate fountains.chocolate-fountain

Notice how the chocolate in a chocolate fountain doesn’t flow straight down–it curves slightly inward at each tier. The research–which involved lots of math!–concluded that this is due to surface tension.

“Chocolate fountains are just cool, aren’t they!” said Adam Townsend (UCL Mathematics), lead author of the paper based on his MSci project. “But it’s also nice that they’re models of some very important aspects of fluid dynamics. We’ve used some serious maths to solve a fun problem- why the chocolate ‘curtain’ on a chocolate fountain always falls inwards.” – See more at: https://www.ucl.ac.uk/news/news-articles/1115/251115-chocolate-fountain-physics#sthash.LVBoAQGl.dpuf

Want to learn more? Here’s the UCL article: “Exploring the Physics of Chocolate Fountains”

I would add that chocolate fountains are yet another example of how math helps us understand and describe the orderly way God created and sustains this universe. Until next time, have fun using math to explore God’s creation.

New Math Articles on The Creation Club

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image by freeimageslive.co.uk – creator

I’ve recently been asked to do a guest column over at The Creation Club on mathematics and God’s creation. I thought I’d post the links here so you could head over there and enjoy them as well 🙂

Math and the Creator – For many, math has become associated with a subject of number manipulation and rules. Yet math is much, much more than that…

Math, Sunflowers, and God’s Wisdom and Care – Sunflowers are one of my favorite flowers. They’re my favorite, not because of their colors or initial beauty, but because of the incredible testimony to God’s wisdom and care hidden inside—a testimony math helps us discover…

I hope you all are having a lovely fall, a giving-thanks-filled November, and a blessed time seeing God’s handiwork in math.

Until next time,

Katherine

 

Snowflake Math

snowflake1

Math might not be the first thing you think of when you see snow, but believe it or not, math helps us describe God’s handiwork in each tiny snowflake.

To start with, we can observe that the general shape of each flake is approximately the same. Snowflakes can be described by the six-sided shape we refer to as a hexagon.

Looking at the structure of water molecules and the angles (more math) there gives us a glimpse into why hexagons are formed.

Yet despite being the same shape, you’re not likely to find two identical snowflakes. What a wondrous variety God’s hid within snow!

snowflake math

We could also talk about the symmetry and patterns in snowflakes (more math concepts). And if we wanted to expand beyond the flakes themselves, we could talk about the temperature at which water freezes (which we describe using a number), at the altitudes of different types of clouds (which we use numbers to describe), etc.

Snowflakes are an example of how we use math to describe God’s creation…and in the process see His incredible design!

“Hast thou entered into the treasures of the snow? or hast thou seen the treasures of the hail, Which I have reserved against the time of trouble, against the day of battle and war?” Job 38:22-23

“Then Job answered the Lord, and said, I know that thou canst do every thing, and that no thought can be withholden from thee. Who is he that hideth counsel without knowledge? therefore have I uttered that I understood not; things too wonderful for me, which I knew not. Hear, I beseech thee, and I will speak: I will demand of thee, and declare thou unto me. I have heard of thee by the hearing of the ear: but now mine eye seeth thee. Wherefore I abhor myself, and repent in dust and ashes.” Job 42:1-6

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Thoughts on Shapes

Throughout history, men have used their knowledge of shapes to help them design buildings. Because of the consistent way God holds things together, we can predict how different shapes will hold up under pressure. One shape that supports weight well is the arch. You can easily see this by holding a piece of paper flat between your hands and having someone push down gently in the center of the paper. You should notice the paper bends easily under the pressure. But if you bend the paper to form an arch, you’ll notice the paper does not bend as easily. An arch shape holds up better under pressure than a flat shape does. [1]

Knowing this quality about arches helps us in designing buildings and bridges, many of which have an arch shape! It also gives us new appreciation for the design in our feet. If you run your finger along the bottom of your foot, you will feel multiple arches on your foot! God, the master engineer, designed the shape of our feet to support our body’s weight. Our feet are truly marvels of engineering!

If the foot were flat and rigid, fixed at right angles to the bone of the leg, walking would be difficult or impossible. The elastic arches also serve as shock absorbers to soften the jar resulting from walking on a hard surface.

The human foot is a miniature suspension bridge which is much more complicated than an ordinary bridge. Would anyone say that the Golden Gate suspension bridge just happened? Of course not, if he were truthful! But why do people assume that the even more intricate mechanism of the human foot could have just happened without intelligent cause or the workmanship of a master Engineer? [Allen L. Gillen, Body by Design (Green Forest, AZ: Master Books, 2001), pp. 43-44.]

The point? Learning about shapes doesn’t have to be confined to a textbook! As you teach your child shapes, you can be teaching him about the shapes all around us–and seeing the Creator’s wisdom and care in how He chose just the right shape for everything.


[1] This experiment is based on one given in The Art of Construction. The book offers numerous experiments and information related to building. Mario Salvadori, The Art of Construction: Projects and Principles for Beginning Engineers and Architects, 3rd ed. (Chicago: Chicago Review Press, 1990). Originally published as Building: The Fight Against Gravity.

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.

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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.