You Are Math in Motion

If I asked you, “Do you like math?” would you answer that you dislike it? Would you complain that you “never use it in real life”? Would you claim that you are not a “math person”? If you would answer in those ways, consider a follow-up question: “Do you like music?”

If you are like most people, you will say that you enjoy music; it makes up a significant part of our lives…in entertainment, in relaxation, and—perhaps most importantly for Christians—in worship. The love of music is a human phenomenon that crosses all geographic and cultural boundaries. With this in mind, let me suggest that if you answered the last question about music in a positive way, but the former question about math negatively, you have just contradicted yourself.

How have you contradicted yourself? Because music is math in motion.¹

Music is Math

Music is a tangible way in which we actively experience math as it unfolds through time and space:

Music…is a play of mathematics, coherent patterns of number and shape in time and space, expressed in rhythm and timbre, tone and pitch. It is the closest most of us get to seeing and feeling the beauty of mathematics.

– Stratford Caldecott²

If you need more convincing, contemplate this:

At the creation, “the morning stars sang together” (Job 38:7). Music is universal and its structure is thoroughly mathematical.

– James Nickel³

If even that is not enough, then it might help to consider one of the most famous mathematicians of our times—a man whose name is practically synonymous with “math genius”—Albert Einstein. Einstein was an accomplished amateur musician. He once said:

If I were not a physicist, I would probably be a musician. I often think in music. I live my daydreams in music. I see my life in terms of music…⁴

The Scriptural Mandate for Math through Music

Allow me to ask you a third question, one I believe should matter to us a great deal as classical, Christian home educators: “Do you think the Scriptures speak to us about the study of mathematics?”

I think it is true to say that most of us believe our children need to learn math because we studied it. We are creatures of habit, and therefore assume our children should study math, too. We also think students should learn math because the educational standards of the governments under which we live mandate it. In addition, we may believe it is important for our students to study math because our society values careers which emphasize math, such as engineering, the sciences, or medicine. We want the best for our children, and we want them to have fulfilling, respectable, and lucrative careers. In our modern world, there is no denying that mastering mathematics is an important factor in gaining entry into those fields.

There is certainly nothing wrong with seeking such careers. However, as Christians, shouldn’t the Lord’s instructions for us matter more than what the state dictates or careers require? I think most of us would agree that it should. If so, where do we find math prescribed by Scripture?

Math certainly appears many times in the Bible (one only has to consider all the minutiae of mathematical instruction given by God for the building of Noah’s Ark or the Tabernacle), but it is in math as music that I believe Scripture speaks clearly in this regard. For one thing, look again at the quote above from James Nickel, referencing the Book of Job. It tells us that at the very beginning of all things, the heavenly bodies sang. Scripture also tells us that where the Lord’s presence is manifest, there is music:

For the LORD shall comfort Zion…and He will make her wilderness like Eden, and her desert like the garden of the LORD; joy and gladness shall be found therein, thanksgiving, and the voice of melody.

-Isaiah 51:3 (KJV, emphasis mine)

Melody—that is, orderly sound that is pleasing to the ear as opposed to “noise”—is closely tied to the character of God. Therefore it is only natural that the Scriptures should instruct us to praise God through music:

Praise the LORD with the harp; make music to him on the ten-stringed lyre.

-Psalm 33:2 (NIV, emphasis mine)

Not only are we to praise God with music, but we are to communicate with each other musically, and to make melodies to Him, not just with our voices and instruments, but “in our very hearts”:

Speak to one another with psalms, hymns, and spiritual songs. Sing and make music in your heart to the Lord.

-Ephesians 5:19 (NIV, emphasis mine)

Furthermore, Scripture suggests that there is a close relationship between praying and singing, namely that both be done with the spirit, but also with the understanding—that is, with comprehension (personal understanding) as well as comprehensibility (the ability to communicate that understanding to others):

I will pray with the spirit and I will pray with the understanding also; I will sing with the spirit, and willsing with the understanding also.

-1 Corinthians 14:15 (KJV, emphasis mine)

The Bible also reveals that making music relates to our confessing God’s name, our witness for the Lord. Again, Paul writes:

And that the Gentiles might glorify God for [His] mercy; as it is written, for this cause I will confess to thee among the Gentiles, and sing unto thy name.

-Romans 15:9 (KJV, emphasis mine)

These constitute a sampling of the occasions when music is mentioned in the Scriptures. From this selection we can see how important music is to the Lord and, therefore, how important it should be to us as people who bear His name.

Musical Instruments

“That is all well and good,” you might say. That is an argument for studying music (which, by the way, we generally also tend to neglect to study properly⁵), but why does that necessitate studying math?

That is an excellent question. To answer it, let us first examine how the Bible describes us as God’s instruments:

Neither yield ye your members [as] instruments of unrighteousness unto sin: but yield yourselves unto God, as those that are alive from the dead, and your members [as] instruments of righteousness unto God.

-Romans 6:13 (KJV)

Normally, we think of an instrument, in the sense used above, as a tool.⁶ What if we take a second step, and think of this more metaphorically? What if we think of ourselves as musical instruments? After all, this is not such an outrageous idea. Our voices are precisely that: our vocal cords vibrate when we sing just as the strings of an instrument vibrate when they are played. In addition, in terms of musical metaphors we often talk of our “heart strings,” of being in “harmony” with one another, and of ideas resonating with us.

So, what do we have to do with our musical instruments before we play them? One of the first things we traditionally have gone to great effort to do is to make sure they are finely tuned, that they are in fact “in tune”…for if they are not, we will not produce beautiful melodies. Instead, we will make discordant noises. If then we consider ourselves “instruments of righteousness unto God,” we can understand that this might mean a great deal more than simply that we are “tools.” Indeed it could imply that we are, by our very natures, in our bodies, spirits, and minds, musical beings—and therefore mathematical beings—who also need to be “in tune” with our Creator; it is thereby that we can have a presence like His, which brings with it orderly melody:

Every sound that is pleasing to the ear can be described mathematically…The order and harmony of true music will create order and harmony in those who listen to it and play it.

-James Nickel⁷

Mankind has understood this for centuries. The ancients grasped it well. For example, Plato writes in one of his most famous dialogues, The Republic:

Musical training is a more potent instrument than any other, because rhythm and harmony find their way into the inward places of the soul, on which they mightily fasten, imparting grace, and making the soul of him who is rightly educated graceful, or of him who is ill-educated ungraceful.⁸

Although Plato was of course not a Christian, through common grace he apprehended an important truth. It is through being “in tune” that we can genuinely praise the Creator in song, that we can make music in our hearts, that we can sing with the spirit as well as with comprehensibility, and that we can sing unto His name as we confess Him in a darkened world. Much of the Scriptures—I would even venture to say that all of it—has as its purpose the goal of helping us be “in tune” with our God so that we can love Him with all our hearts, souls, and minds (see Luke 10:27).

Finely Tuned Instruments: Resonating in Praise

How then can we come to be “in tune” with God? By studying His Word, in which He has revealed himself, but also by studying His creation, whose laws and mechanisms are all undeniably mathematical in nature. And we cannot fully study the creation—we cannot seek the Lord out in it—if we do not understand the language in which it is described: mathematics. We may sense it, glimpse it…but unless we are “finely tuned,” most of us will not deeply resonate with it.

This “resonating” is ultimately something we are intended, in and throughout eternity, to do—“to sing in tune,” having been made ready to join with the heavenly hosts in praising the Lord (note that the word “praise”⁹ in the following passage is the same Greek word used in Luke 2:13, describing the singing of the heavenly host announcing the birth of the Christ Child):

Then a voice came from the throne, saying: “Praise our God, all you His servants, you who fear Him, both small and great!” Then I heard what sounded like a great multitude, like the roar of rushing waters and like loud peals of thunder, shouting: “Hallelujah! For our Lord God Almighty reigns. Let us rejoice and be glad and give Him glory! For the wedding of the Lamb has come, and His bride has made herself ready.”

-Revelation 19:5-7 (NIV, emphasis mine)

If you answered negatively to the initial question about math, I hope I have helped to draw the possibility of a picture of a different reality for you, and for the children that you are homeschooling: there is no such thing as a human being, made in the image of God, who is not a “math person.” We are not only all “math people,” we are instruments who are ourselves quintessentially mathematics in motion.¹⁰

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¹ Music is described with the mathematical language of trigonometry:

Every sound that is pleasing to the ear can be described mathematically as the summation of what are called sinusoidal functions.”

-James Nickel (see note 3 below, p. 239).

Of course, the language of music itself—musical notation and the theory that governs it—has a symbolic and mathematical language all its own (notes, time signatures, symbols for dynamics, and so on).

² Caldecott, Stratford. Beauty in the Word: Rethinking the Foundations of Education. Tacoma, WA: Angelico Press, 2012. p. 58

³ Nickel, James. Mathematics: Is God Silent? Vallecito, CA: Ross House Books, 2001. p. 237

⁴ Calaprice, Alice. (Ed.) The Expanded Quotable Einstein. Princeton, NJ: Princeton University Press. p. 155

⁵ Without a doubt, we need to reclaim the study of music in a classical context. Consider this point made by Stratford Caldecott:

The word “music” has acquired a rather more restricted meaning than it once had. Today we think of a musical piece as a piece of writing, whose author is known and which is generally performed for aesthetic pleasure in a concert hall setting. Music has been mechanized and packaged in ways typical of our society. As we saw earlier, among the Greeks the “art of the muses” enfolded the whole of intellectual and literary culture…while even in its narrower meaning it included dance and poetry as well as singing and the playing of instruments. As such it was not a specialized study but a vital part of all humane learning, as well as being closely related to its companions in the Quadrivium, arithmetic, geometry, and astronomy.

– Beauty for Truth’s Sake: On the Re-enchantment of Education.

Grand Rapids, MI: Brazos Press. 2009. pp 93-94

⁶ In this passage, the word “instruments” literally means the Lord’s weapons, or “arms” in warfare, coming from the Greek word ὅπλον (hoplon). This word is also translated as “armour” in Romans 13:12, a strong implication that resonation in this manner, or “being in tune,” with the Lord thusly, also provides protection in spiritual warfare (see also 2 Corinthians 6:7):

The night is far spent, the day is at hand: let us therefore cast off the works of darkness, and let us put on the armour of light (KJV, emphasis mine).

⁷ See note 3 above, p. 239

⁸Benjamin Jowett (trans.), The Republic of Plato. Oxford Clarendon Press, 1888. p. 88.

⁹ From the Greek word αἰνέω (aineō: to sing praises in honor to God). See also Luke 2:20, Luke 19:37, Luke 24:53, Acts 2:47, Acts 3:8-9, and Romans 15:11.

¹⁰ We are this quite literally, in fact, if we begin to examine the mathematical complexities of our physical bodies, let alone our minds and spirits.