Teacups, Tectonics, and Trembling – Shaking It Up With Logarithms

In Alice in Wonderland, during what is arguably one of the most famous tea parties in history, Alice was asked by the Mad Hatter if she knew how a raven was like a writing desk.

But we here at the Talon like to shake things up a bit. The Mad Hatter’s question can’t hold a candle to the madness of the Talon’s editor-in-chief! How about this one?

What do a Johnny Cash song, Google, dragons, frogs, ancient Chinese culture, fire, love, stars, earthquakes, a moon landing and a 17th-century math problem all have in common?

Much in every way, as you’ll soon discover! Come and follow us down the rabbit hole! Let’s dig our way to China first.

Here in the far east, past never-ending shelves of books and empty marmalade jars, we discover the ancient Chinese culture is credited with a few firsts in the invention world, among them the compass and an early seismograph. Yes indeed. Seems the culture of our international friends here at RCS is a bit more versed in the history of measuring the shaking, rattling and rolling of earth than we are here in California. Mr. Richter and his Cal Tech invention of the scale bearing his namesake (it’s not actually a device, but a type of logarithmic equation) only dates back to 1935.

The “original” seismograph, however, came about in 132 AD through the intriguingly clever genius of Chang Heng, a Chinese philosopher, cartographer, mathematician, and artist – a thoroughgoing Leonardo Da Vinci of his time – who seemed peculiarly intrigued by the movement of the ground beneath his feet and sought a way to better understand it.

This ancient device, made of bronze, was some six feet in diameter. Around the outside of the jar-like structure were eight individual dragons with their mouths open, representing eight distinct geographic positions of the Chinese compass. Below the jar, directly beneath the dragons, sat eight frogs, also with open mouths. During an earthquake, a ball inside the container governed by a simple pendulum would fall out of the dragon’s mouth closest to the direction of the epicenter of the earthquake and land in the corresponding frogs’s mouth.

Speaking of frogs and shaking, this reminds me of another favorite tea-party story from childhood where two friends, Frog and Toad, are telling one another scary stories and experiencing “the shivers.” The story concludes, “Frog and Toad sat close by the fire. They were scared. The teacups shook in their hands. They were having the shivers. It was a good, warm feeling.”

Yes. We here in California also sit near a fire, shaking.

People poised on the edges of the Pacific Ocean indeed know something about this warm, scary, shaking feeling. We’ve all got a front-row seat to what is arguably the most prolific realm of tectonic activity in the world.

The Pacific Ring of Fire.

Up from the tip of South America, right up the California coast, to Alaska, arching over to Russia and down the eastern coast of Asia to Australia, is one fiery loop of unceasing earth-shaking activity.

“Love is a burning thing,” Johnny Cash once sang, “and it makes a fiery ring.”

Indeed it does. Teacups and all.

And if we believe that God is Love (1 John 4:16) and that He is also a consuming fire (Hebrews 12:29) whose voice shakes the heavens and the earth (Haggai 2:6; Isaiah 13:13; Hebrews 12:25-29) then we can sing right along with the “Man in Black” with confidence that this catchy tune is indeed theologically sound, not only about love, but about earthquakes.

See? It’s all starting to make sense, isn’t it?

Love, like plate tectonics, is full of quaking, flames and heart-racing, earthshaking emotion which reminds us that we are mere teacups (2 Corinthians 4:7).

And God is the Author of it all.

“And it burns, burns, burns,” says Mr. Cash. Yes it does. Oh, yes it does (Hebrews 12:18-29). That “good, warm feeling” we get when we’re scared – kind of a delightfully terrifying awe.

But whether it’s the violent shaking of the ground or of the way of man’s heart smitten with love and tea, God directs them both.

And we tremble. Like the disciples “And they went out and fled from the tomb, for trembling and astonishment had seized them, and they said nothing to anyone, for they were afraid.”

There are two Hebrew words in the Old Testament which mean “shake”; raw-ash and ra-gaz (found in verses such as Haggai 2:6 and Isaiah 13:13). Each of these words can mean both a literal, physical shaking and a fear and trembling.

Here, for example are two “readouts” of some shaking. One is a seismograph reading from the 1989 quake here in the Bay Area and the other is Neil Armstrong’s heart rate as he landed the Eagle on the surface of the moon in 1969. The ’89 quake registered around a “seven” on the Richter scale. Neil Armstrong’s heart rate was near 160 Heart Quake 69 and 89beats per minute.

Which is which? Hard to tell? That’s the essence of the Hebrew words. “A” is the earthquake. “B” is Mr. Armstrong’s heart. A little shaking going on in each, is there not?

Did you know that while on the surface of the moon, Armstrong and fellow astronaut Buzz Aldrin set up the moon’s first seismometer; a device that measured moonquakes for some three weeks? Yes. It even registered the shaking of the surface as the Eagle launched back up into space.

Long before man went to the moon, however, some earth-based mathematicians were hard at work creating logarithms which would eventually provide the foundations for how we measure the shaking of ours.

One of the men credited for the invention of the log is John Napier who put together the basic framework of his calculations in the early 17th century (1600s). Napier wasn’t just a “math” guy though, he, like Chang Heng, was a man of many disciplines, having a wide array of experience as both a physicist and an astronomer.

John Napier - 1550 - 1617 - credited with the first published work on logarithms (from Wikipedia).

John Napier – 1550 – 1617 – credited with the first published work on logarithms (from Wikipedia).

Little did Mr. Napier know that his work in logarithms would lead not only to the eventual development of a system of measurement used to determine the intensity of earthquakes, but of a system which would also measure the brightness of stars.

“In the beginning, God created the heavens and the earth.” Man came along to measure their magnitudes with logarithms for both!

And in case you missed our stories from this past weekend, logarithm is a combination of two Greek words – logos and arithmos. Logos is the very same word John uses in the opening of his Gospel account when he writes, “In the beginning was the Word.”

In a very simple sense then, logarithm means “word-number.” This may perhaps serve as a wonderfully poetic and mathematical example of God’s invisible attributes (Romans 1:19-20) – word and number in the logarithm (mathematics), wave and particle in light (physics and astronomy), and God and man in Christ (theology).

The totality of the heavens and the earth and all of man’s attempts at expressing the untold riches of the vocabulary of creation – math, physics, astronomy, geology, poetry, and language – are found in the incarnate Logos, the Lord Jesus Christ.

When you see the brilliant minds of old such as Napier or Heng, you can see a bit more clearly how they truly reflect man as being created in the image of God. A Christian should be versed in a wide variety of disciplines and take time to see the interconnectedness of God and His creation. We need more folks willing to think like these men who can see the interrelationship between science, art, poetry, astronomy, music and literature and all the rest of the things which God long ago declared to be “very good.”

The Logarithm of the Heavens

Around 1910, a logarithmic-based chart was created by two astronomers, Ejnar Hertzsprung and Henry Norris Russell. In short, it uses base-ten logarithms to measure a star’s luminosity (absolute brightness) as compared to its surface temperature and subsequent color. Logarithms help to process large numbers used in measuring stellar brightness. A simple example is that a star with a magnitude of 10^3 (10 x 10 x 10 = 1,000) is ten times brighter than a star with a magnitude of 10^2 (10 x 10 = 100).

The Logarithm of the Earth

Logarithms are also used in measuring the intensity of earthquakes. Charles Richter is credited with devising this scale of shaking magnitude in 1935 at Cal Tech. It uses the same basic logarithmic principles in determining the strength of a quake as the Hertzsprung-Russell star chart uses in determining the brightness of stars. It’s important to keep in mind though, that the Richter Scale is not a device like a seismograph, but simply a mathematical, logarithmic-based formula of measurement. While Mr. Richter’s scale is a base-ten logarithm, it’s also not to be understood as a scale of 1 to 10 as some have often thought it to be.

For example, an earthquake registering 5.0 on the scale isn’t an “average” earthquake on a scale of 1 to 10, but simply one which is ten times stronger than a 4.0 and a hundred times stronger than a 3.0 quake.

So whether you’re an astronomer, a physicist, a computer programmer in Silicon Valley, a mathematician, a geologist, or just a sojourner on the Pacific Ring of Fire singing along with Johnny Cash as you search for some information on the Internet using Google, you’re going to encounter logarithms.

But this is precisely what Scripture tells us to expect. Jesus is omnipresent, omnipotent and omniscient and sustains our entire universe and everything in it by the word of His power. He is Lord of all creation. May He richly bless you with the ability to see His lordship in everything you seek and do.

As the children of Israel sang after their miraculous deliverance from the bondage of Pharaoh and the Egyptians, “Who is like you among the gods, O LORD, who is like you, glorious in holiness, awe-inspiring in praise, a wonder-worker?…Peoples listened, they trembled, anguished gripped Philista’s rulers.” (Exodus 15:11, 14).

What indeed hath God wrought? What’s He working in your life?

“Therefore, my beloved, as you have always obeyed, so now, not only as in my presence but much more in my absence, work out your own salvation with fear and trembling, for it is God who works in you, both to will and to work for his good pleasure.”

Phil 2:12-13 (ESV)