As we celebrated our nation’s 250th birthday last week, many went out to see fireworks. Now’s a great time to stop and think about all the math that goes into planning a firework display, along with the wonder of how God governs creation consistently enough that fireworks are even possible (which math helps us see).
Let’s start with planning the display. Here are a few examples of some math involved!
Costs – Say a city has a $100,000 budget for a firework display. That cost might need to include paying a band, bringing in police officers, and other general costs in addition to the costs of the fireworks themselves. Basic math would help compare different options. For example, say they’re selecting different fireworks for a certain 30 seconds of the show.
How much would ten $50 fireworks cost (Answer: 10 x $50 = $500)?
How much more would it be to get 8 of $75 larger fireworks? (Answer: 8 x $75 = $600; $600 – $500 = $100)
Comparing – If one firework show shot off 100,000 fireworks altogether and another did 25,000, how much more did the one do than the other? (Answer: 100,000 – 25,000 = 75,000)
Buying Fireworks on Clearance – If you buy a $50 firework on a 40% off clearance, how much would you spend? (Answer: 40% of $50 is $20, or 0.40 x $50 = $20. Thus the final price is $50 – $20 = $30.)
Math is indeed a useful tool that helps with real-life tasks. Now let’s stop and think about the fireworks themselves, as fireworks not only require lots of math in their development and deployment, butour ability to put on firework displays points to our amazing Creator.
Fireworks contain carefully measured mixtures of chemicals. Different compounds containing metal produce different colors when heated, and manufacturers must mix them in just the right proportions (which we study in math!) to create bright, reliable colors. Manufacturers can only declare with confidence that a firework is red, blue, etc., because the same combinations of chemicals consistently produce the same reactions. And why do they do that? Because God created and sustains a consistent world!
Fireworks also include a fuse—a material that burns while the firework travels up so that the shell bursts safely high in the air and not near the ground. Manufacturers have to observe how quickly different materials they could use as a fuse burn up, and then select the right material and length to make the explosion at the desired point. Designing a fuse involves math, and again relies on materials burning in a consistent fashion.
Example: Suppose a fuse burns at 24 seconds per foot. How many feet of fuse are needed for it to burn for 6 seconds? (Answer:24 sec. was divided by 4 to get 6 sec.; 1 ft. divided by 4 is 0.25 ft. Answer is 0.25 ft., or 3 in.)
How do we know what angle to launch a firework? Or how high it will travel before bursting? Again, we observe the consistencies God created and sustains in creation, such as gravity and the predictable path of a projectile. These consistencies can be described algebraically. Computers use lots of advanced math to calculate when to launch each firework and at what angle so the burst occurs at the desired place and exactly the right moment in the music. This is only possible because of the consistent way God governs creation! If He were not holding this world together in a consistent fashion, we’d have no reason to expect fireworks to go off in a consistent way.
There’s much, much more we could talk about with fireworks, such as the lift charge needed to get the firework off the ground or the arrangement of stars in a shell, but hopefully that gives you a glimpse into how math helps us with fireworks…and how our ability to use math like this relies on God’s faithfulness in holding all things together. As you think back on the Fourth of July with your children, remember to praise the great Creator and Sustainer of all. And know that the math you learn applies outside of a textbook!
Looking for next year’s math curriculum? Check out our middle and high school courses that show students the purpose to math and how it points to the Creator at every turn! And don’t miss our supplemental resources that you can use with younger ones to bring math to life for them.
As I released my new Consumer Math course, I kept hearing how excited moms were for a high school math that was actually practical. While Consumer Math certainly is that, other high school math should be too!
In all of my math courses, I’ve striven to show students why they’re learning what they’re learning. Granted, algebra might not be something students incorporate into their daily life. However, they use technology based on it daily. For example, how fast will a metal pan heat up? We can use an algebra equation to figure that out.
where
We can write formulas like the one above because of the consistent way heat transfers into pans based on their heat capacity. And why is creation so consistent? Because a faithful God governs creation in a predictable way! Algebra should be something students finish up with a deeper wow at our amazing Creator.
Now, high school math problems can get challenging and involved. Some multi-step problems can make your head spin. These problems not only prepare students for real-life math problems, but they also teach them to look at a situation where they don’t know what to do and think of different ways they could potentially approach it. That’s a skill we need with real-life non-mathematical problems too!
And then there’s logical thinking skills. If a > b and b > c, we can conclude that a must also be greater than c…but we couldn’t conclude that it’s greater than h, for instance. Why do we care? Learning how to draw logical conclusions helps us think through real-life scenarios.
I’ve put below a video Answers in Genesis recently released that shows an AI, when prompted to answer “according to strict math, logic, and mathematical probability” agreed a biblical Creator makes sense and evolution is foolish. Logic matters…and algebra and geometry help students develop it.
Looking to Help Your Students See Math’s Purpose This Year? Check out these high school and junior high school programs, complete with optional eCourses that will walk students through the lessons. Also check out the Big Book of Math timeline, usable to add in math’s application and purpose to any curriculum. It is possible for students to see God in math while developing skills that will last a lifetime.
VIDEO TRANSCRIPT: Our bodies are remarkable. We can eat, see, move, smell, and so much more. We’re clearly incredibly designed! But when we use math to see how our bodies work, we get a deeper appreciation for how amazingly God knit us together.
Notice that a child’s head is bigger in comparison to the rest of its body than the adult’s head. A big head helps protect a child when they fall. However, if we kept growing with that same ratio between our head and body, we wouldn’t be able to walk as adults! God gave us just the body proportions we needed for each stage of life.
While we’re talking about our heads, let’s zoom in on our ears. It takes advanced math, including trigonometry, to record sounds digitally so hat we can listen to them. But our bodies constantly collect and interpret sounds for us…all without us thinking about it!
Now take a look at these cells from a human body. Notice that the cells are approximately spheres. Using math, we can explore the surface area and volume of cells as they grow. Here are the formulas for the surface area and volume of a sphere. The ratio between them would be the division of one over the other, which we can show using a fraction line and which simplifies to 3/r, where r is standing for the radius of the sphere. The radius, or r, is going to get bigger as the cell gets bigger. What happens to the surface area? Well, let’s say this cell has a radius of 1 and this one of 3.
Notice that if we plug those values into 3/r, the ratio gets smaller as the radius gets bigger. That means that in comparison to the volume, there’s less surface area. This would be problematic if our cells just kept growing, as the cell absorbs nutrients through its surface area. If the cell gets too big, it will die, as it won’t be able to get enough nutrients. But don’t worry–our great Creator designed cells to divide into smaller cells before they get too big. Once again, math helps us see His design.
Next, let’s talk about the viscosity of our blood. I know viscosity is a big word, but it basically describes the thickness of a liquid. Water has a lower viscosity than the orange liquid shown here.
Here’s the formula for viscosity. God put special proteins in your blood that makes these values just right for your blood to flow around your body…and to change when you get a cut so the blood becomes thicker and we don’t bleed to death. God sure thought of everything, didn’t He?
Now there’s a lot more we could say about our bodies, but hopefully that gives you a glimpse into how incredibly designed you are. God knit you together in your mother’s womb. He knew all that would take place in your life before you took your first breath. You can trust Him and cast your cares on Him, because He cares for you.
I’m excited to have just finished the draft of a full-color, 8.5 in by 14 in by 15 ft math timeline, on which students will be able to watch math in action throughout history—and see how math points us to the Creator in the process. Below is a sneak peek into just a few of the facts students will learn. Stay tuned for publication information!
Electricity—we take it for granted and use it countless times a day. Turning on lights, using a computer, microwaving those leftovers, looking at a digital clock, cranking down the AC, opening the refrigerator, doing a tub of wash—the list of daily uses of electricity or electrical devices could go on and on.
But did you know it’s math that helps us explore electricity and design devices like lights and computers? A glance back at history reveals a lot of math—and points us to the Creator.
Back in 1785, A man named Charles-Augustin de Coulomb discovered a mathematical relationship between the force and distance between electric charged particles by doing experiments. His result can be expressed algebraically like shown below.
In other words, the force produced by electricity can be described mathematically!
Michael Faraday
Later, many other men would do experiments and discover more of the ways electricity works. One key discoverer was a man named Michael Faraday, who realized that magnets can generate electricity and invented the first electric generator. Once again, math was used in this design. In fact, the relationship between the electrical voltage, the number of coils of wire, the change in something called magnetic flux, and the time can be described like shown below.
Faraday, like many other great scientists/inventors, saw creation (which math helped them explore) as pointing to God. Faraday wrote,
“The book of nature which we have to read is written by the finger of God.”
Sit back and think about it for a minute. Even at the microscopic level, electricity (which later scientists would realize is the flow of electrons) operates in a consistent enough fashion to describe it with formulas that we can rely on to work to such a degree that devices like light bulbs and computers can be built around it. Why is creation that consistent? Because a faithful, consistent Creator governs all things.
Watching Christmas light shows has become a holiday tradition for many. But few stop to think of all the math that goes into these spectacular displays.
Strands per Outlet or Lights per Circuit
When hanging a lot of lights, you want to make sure you don’t blow a circuit! Bonfe offers this formula to help you figure out how many strands can go in each outlet: # of strands = circuit amperage ÷ strand amperage. We could also use algebra to write this same thing like this: n = c/s or y = z/x. We’re just using letters to stand for the different values, and a fraction to stand for division. Another site says to only use up to 80% of what your circuit can handle as a safety factor. Notice the percents!
Timing
Some light shows include timing with music. Syncing music with a light show requires precision that can be accomplished through various software programs that use math to determine when different effects and lights turn on and off at different moments in the show. In this case, programming the time in seconds that the lights sync with the music includes math!
Cost & Number
The financial cost of Christmas decorations can add up fast! Setting a budget and keeping track of how much money is spent uses addition and subtraction…as well as some rounding skills to keep an approximate total in the store. And how many lights do you need to decorate that garage anyway? Math can help you answer that!
Remember…
As you drive by light displays this year, remember that math applies outside of a textbook. It even aids with Christmas lights.
More importantly, think about why math applies. Why can we even know how many amps a string of light will require? It’s because electricity operates in a consistent fashion. Why? Because God created and sustains an orderly universe.
And that same Creator and Sustainer became a man to make a way for us to know Him by paying for our sin Himself.
Now that’s something to remember this Christmas and always.
Many of us have been fascinated at one time or another by tiny lights dotting the backyard on summer nights. Fireflies, lightning bugs, or whatever you call them are fascinating to watch…and perhaps try to catch. What many don’t stop to think about, however, is how amazingly designed these creatures are.
Light Bulbs
To better understand the marvels of fireflies, let’s pause and take a look at light bulbs for a minute. If you’ve ever put your hand near a light bulb while it’s on, you know that in addition to light, light bulbs produce heat (most of which is infrared radiation). We can use math to measure what’s called the efficacy of the light bulb—that is, how much light they produce compared to how much power they use. The higher the efficacy, the less power is being wasted in heat.
To find the efficacy, divide the lumens produced (a lumen is a unit of measure for light) by the watts (a watt is a unit of measure for power). We could write that as a formula like this:
Or if we wanted to save our hands and use letters, we could write it like this:
We could even use a fraction to represent the division:
Note that we just used algebra! We’re simply using letters as symbols to stand for the efficacy, lumens, and watts of any light bulb. We can write formulas like this because God created and sustains a consistent universe.
If you run to your closet and pull out a package of light bulbs, you can measure the efficacy by inserting the lumens and watts listed on the bulb into the formula. For example, let’s consider a bulb I have in a lamp in my office. It says it is a 53 W (W is an abbreviation for watt) bulb that produces 850 lumens. Leaving units off for simplicity and inserting these numbers into the formula, we’d get this:
Fun assignment: Find the efficacy of the light bulbs listed in the table on step 6 of this page. Notice that some bulbs are more efficient than others! Then take a look at this chart showing the efficacy of different bulbs.
The higher the efficacy, the more the power is going into making light and less into making heat/non-visible radiation. Some bulbs produce more light with less power than others, but they all end up wasting a good deal of power. According to what I could find, an ideal green light that doesn’t waste power in heat would have an efficacy of about 683. That’s a much greater number than the 16.04 efficacy of the light bulb in my office!
What percent of the power is actually used to product light? To find that, we need to find the efficiency, which we’ll define “as the ratio of the total light power to the total power.”[i] The efficiency can be rather tricky to figure out, as light bulbs don’t come labeled with how much power goes towards light, but one way to approximate it is to divide the efficacy (in lumens per watt) of the bulb by 683 (the efficacy of ideal green light, which is the highest efficacy possible and thus can be used to approximate the total power while we use the efficacy to approximate the power used to produce the light).
Plugging in the efficacy we found for my office light bulb would give us the following:
If we express this as a percent by multiplying by 100 and adding a % sign, we’d get approximately 2.35%. That means only about 2.35% of the power this bulb uses goes towards making a light; in other words, the other 97.65% goes toward making heat/non-visible radiation. We would say this light bulb is about 2.35% efficient.
Fun assignment: Check out this table to view the efficiency of various lights…and calculate the efficiency of some lightbulbs in your closet by first finding the efficacy, then dividing that by 683, and finally expressing that result as a percent. Notice all the math you’re using!
Fireflies
Now, fireflies don’t plug into an electrical outlet or battery to produce light. Instead, a firefly produces light using chemicals. Yes, that’s right: God created these little bugs to have a mini chemical factory on board! These chemicals prove useful to man as well—one of the chemicals used has been useful in “biomedical research.”[ii]
The chemical reaction in the firefly produces energy…which is what powers their lights. When we talk about the efficiency of the lights fireflies produce, we’ll talk in terms of energy. Note, though, that power and energy are related–power is the rate of use of energy. We could say that efficient bulbs use less power and less energy.
Unlike man-made light bulbs, the firefly produces light without wasting much energy at all—sources indicate almost 100% of the energy turns into light[iii]—in other words, it’s almost 100% efficient. Compared to the 2.35% efficiency we found for the light bulb in my office, that’s amazing! Yet if the firefly didn’t produce light efficiently, they’d heat up and burn to death.[iv] Instead, God designed them to produce “the most efficient light in the world.”[v]
Conclusion
Next time you head outside and see the light from fireflies, ponder God’s magnificent design. Think about the wisdom and care God took with His creation, even giving us light displays at night made from tiny living chemical factories. And remember that math helps us explore, describe, and better appreciate His amazing world…as well as to improve inventions (like light bulbs). We’re able to explore and design because God made us in His image. That same God wants each of us to know Him and live in His presence forever.
March 14, or 3/14, was both Einstein’s birthday and is also known as Pi Day, as the irrational number Pi (π) starts 3.14.
There are a lot of different ways you can use the day to build a biblical worldview of math in your upper elementary (or students who’ve learned about decimals) through high school students.
Ideas for Pi Day
Make a circular pie and talk about how π is the ratio between the circumference (distance around the pie) and the diameter (the distance across), or π = C/d . (Note that this is just rearranging the formula for the circumference you may be more familiar with of C = πd to solve for π.) This ratio is one we can’t even calculate all the digits of! There are parts of God’s creation we can’t even fully describe. You could also explore more applications of π and discuss it further; see the ideas and links in this previous Pi Day post.
Ideas for Albert Einstein’s Birthday
Explore (or have your students explore and give you a report on) the life and work of Albert Einstein and talk about his view of God. Here are a few fascinating highlights from his life and work:
Einstein flunked some things in school[1] and actually dropped out[2] at one point. We are all gifted differently—fearfully and wonderfully made (Psalm 139:14) for a purpose.
Einstein is famous for his Theory of Relativity, which explores the speed of light and its relationship to time and space. We’re still studying and learning about something God simply spoke into existence (Genesis 1:3)!
Einstein also derived the relationship between energy, mass, and the speed of light, or E = mc2. Consistent relationships like this remind us that this universe is consistent, held together by a consistent God.
Some of Einstein’s work was used in developing the atomic bomb. As we learn more about God’s creation, we need to make sure we use that knowledge in ways that honor the Creator. An atomic bomb was used to stop a war…but also to kill many lives. This reminds us that we need to seek God and His Word for wisdom as we apply math.
Sadly, Einstein was not a Christian, although he acknowledged that there had to be a God.[3]
I’m not an atheist and I don’t think I can call myself a pantheist. We are in the position of a little child entering a huge library filled with books in many different languages.…The child dimly suspects a mysterious order in the arrangement of the books but doesn’t know what it is. That, it seems to me, is the attitude of even the most intelligent human being toward God.[4]
Einstein realized that creation proclaims that there has to be a Creator, or at least, according to the quote below, something miraculous. He recognized an order throughout creation and acknowledged that it doesn’t make sense why men can develop theories that end up tying so beautifully with that order—something that makes perfect sense if the same God created both us and creation.
You find it surprising that I think of the comprehensibility of the world . . . as a miracle or an eternal mystery. But surely, a priori, one should expect the world to be chaotic, not to be grasped by thought in any way. One might (indeed one should) expect that the world evidence itself as lawful only so far as we grasp it in an orderly fashion. This would be a sort of order like the alphabetical order of words in a language. On the other hand, the kind of order created, for example, by Newton’s gravitational theory is a very different character. Even if the axioms of the theory are posited by man, the success of such a procedure supposes in the objective world a high degree of order which we are in no special way entitled to expect a priori. Therein lies the “miracle” which becomes more and more evident as our knowledge develops. . . . And here is the weak point of positivists and of professional atheists, who feel happy because they think that they have not only pre-empted the world of the divine, but also of the miraculous. Curiously, we have to be resigned to recognize the “miracle” without having any legitimate way of getting any further. I have to add the past point explicitly, lest you think that, weakened by age, I have fallen into the hands of priests.[5]
We know from Romans 1 that deep down, we all know there’s a God. Creation, as Einstein recognized, proclaims God’s existence.
For his invisible attributes, namely, his eternal power and divine nature, have been clearly perceived, ever since the creation of the world, in the things that have been made. So they are without excuse. For although they knew God, they did not honor him as God or give thanks to him, but they became futile in their thinking, and their foolish hearts were darkened. Claiming to be wise, they became fools, and exchanged the glory of the immortal God for images resembling mortal man and birds and animals and creeping things. Romans 1:20-23 (ESV)
But while Einstein’s exact views varied some throughout his life,[6] rather than heading God’s revelation to us in the Bible,[7] Einstein made up a god he was comfortable with, essentially worshiping the creation (his own intellect) instead of the Creator. Einstein didn’t want a God who would hold him responsible. He recognized something miraculous about creation, just like Romans 1 says we all do, but decided to worship a god of his own shaping instead.
The God Spinoza revered is my God, too: I meet Him everyday in the harmonious laws which govern the universe. My religion is cosmic, and my God is too universal to concern himself with the intentions of every human being. I do not accept a religion of fear; My God will not hold me responsible for the actions that necessity imposes. My God speaks to me through laws.[8]
Einstein’s birthday provides a great opportunity to point out to your students how creation declares God’s praises. There is a God—and we need to acknowledge Him and recognize that we’ve all broken His holy Law and need a Savior, Jesus Christ. Otherwise, no matter how smart we may be, we’ve become foolish in what matters most.
Key Reminder
As you remember both Pi Day and Einstein’s birthday, remind your students to lift their eyes from God’s amazing Creation to the Creator of it all. Encourage them that creation’s very complexity/order and our ability to explore it scream out His existence.
Please share!
If you enjoyed these ideas, please share with others so they can too.
[1] Kaku, M.. “Albert Einstein.” Encyclopedia Britannica, Invalid Date. https://www.britannica.com/biography/Albert-Einstein and “Albert Einstein,” Star Child Team, https://starchild.gsfc.nasa.gov/docs/StarChild/whos_who_level2/einstein.html
[2] “Albert Einstein,” History.com, May 16, 2019 update, https://www.history.com/topics/inventions/albert-einstein
[3] You can view some more quotes about his view of God here: https://libquotes.com/albert-einstein/quotes/god
[4] Kaku, M.. “Albert Einstein.” Encyclopedia Britannica, Invalid Date. https://www.britannica.com/biography/Albert-Einstein.
[5] Albert Einstein, Lettres À Maurice Solovine (Paris: Gauthier-Villars, 1956), pp. 114-115; quoted in Nickel, p. 210, quoted on http://www.christianciv.com/Atheists_Confess.htm.
[6] John Brooke, referenced in “Einstein Letters Show Views on the Bible and Christianity,” Answers in Genesis, May 17, 2008, https://answersingenesis.org/theistic-evolution/einstein-letters-show-views-on-bible-and-christianity/.
[7] “Einstein Letters Show Views on the Bible and Christianity,” Answers in Genesis, May 17, 2008, https://answersingenesis.org/theistic-evolution/einstein-letters-show-views-on-bible-and-christianity/.
[8] Einstein and the Poet (1983), p. 89. Found on https://libquotes.com/albert-einstein/quote/lbs0n1m
With the Major League Baseball World Series well under way, I thought it would be a good time to take a look at the math involved in baseball. We’ll also see how all of it reminds us to praise the Creator.
Basic Numbers
Some of math’s applications to baseball are both obvious and basic. How many pitches a pitcher has pitched (called the “pitch count”), the strike and ball counts, the scores (called number of “runs”), the number of innings, the number of players, the numbers on the players’ jerseys—all these and more are examples of basic counting and numbers in action. How many innings are left after the 3rd finishes (assuming the game is not tied at the end)? That can be found using subtraction; taking 9 (the total innings with no tie game) – 3 (the innings completed) leaves the answer of 6 left. Do that same math after the top of the 3rd instead (meaning only half an inning has completed), and you get 9 – 2 ½ = 6 ½. Notice the fractional amount.
Basic Geometry
Baseball also has lots of examples of basic geometry in action. The shapes of the bases (squares), home plate (an irregular pentagon), ball (sphere), and infield (square or diamond) are all basic shapes familiar to many students. The perimeter of the infield would let us know how far a runner runs when he hits a home run; the volume of the ball could be useful if we needed to find the density of the ball (which would require basic algebra—the formula is listed below, where m is the mass and V the volume.
Statistics
When watching a baseball game, lots of statistics appear on screen. These statistics are calculated using math!
For example, batting averages are the result of taking the total hits divided by the total at bats, or total hits ÷ total at bats. (Note that total at bats “does not include walks, hits by pitch, or sacrifices” https://www.wikihow.com/Calculate-a-Batting-Average.) Notice this requires both counting up the total hits and total at bats, and then uses division!
Here’s a site that explains the math behind various other statistics used: https://www.mlb.com/glossary/standard-stats/earned-run-average. If you’re teaching elementary math, you might want to check it out and make up some problems for your child to use. For example, knowing that batting averages are found using the formula total hits ÷ total at bats, make up some numbers for total hits and total at bats. (Note that the total hits will typically be less than at bats…unless a player hits the ball every time!) Say a player hit the ball 5 times and had 25 at bats; a student can calculate then that his batting average is 5 divided by 25, or 0.2, by plugging 5 in for total hits and 25 for total at bats.
You might want to point out that whenever statistics are used, it’s important to ask questions about them, as they can easily be presented in a misleading way. While this isn’t really an issue in baseball (unless someone misunderstands the stat), baseball can be used to illustrate how statistics can be twisted to help students learn to discern through the bombardment of statistics we encounter in the news, advertisements, etc., where they ae often twisted.
For example, say it’s a player’s first time at bat ever in the major leagues. He hits the ball during that at bat. His batting average the next time he steps up to the plate is 1 (he’s had 1 hit and 1 at bat), which equals 1. If you just see a batting average of 1 you might think he’s an amazing player…but we don’t really know that yet. This illustrates a general rule in statistics that the more data you have to calculate an average off, a better reflection of reality is the average is. We need a lot more at bats than 1 to really know how good a player is based on their batting average. In a similar vein, batting averages can be calculated over a player’s lifetime, for a series, or for a game. The point is that it’s always important to understand how a stat is calculated and what it’s really saying.
Algebra and Calculus
We can use algebra in calculating perimeter, area, and volume (the formulas are often written algebraically). We can also use algebra to figure out different facts from various stats. For example, if we know the formula for a batting average and one of the other values in the formula, we can use algebra to find the other value. Say we know a batting average over 100 at bats is 0.2. That means this:
Since we typically use letters to stand for unknowns in algebra, let’s replace total hits with an x. We’ll also replace the with a fraction line, as that’s the typical way to show division in algebra.
Now, because of the faithful, consistent way God governs creation, we can multiply both sides by 100 to solve for , thereby seeing that this player must have had a total of 20 hits.
Algebra (and calculus too) can also help us explore the physics behind baseball. For example, the speed of a pitch is cited throughout a game. While that speed is measured using a radar gun (a device built by using math to both understand and then design around the consistent way God governs creation), you could explain to your student how we could use algebra to calculate the approximate time the ball was in the air given that speed.
We know from physics that distance = speed • time, or d = st. If we solve this equation for time (t) by dividing both sides by s, we get d/s = t. According to the MLB, the distance from the pitcher’s mound and home base is 60 ft 6 in (approximately 0.011458 mi). Let’s say a pitcher pitches a ball that goes 90 miles per hour (mi/hr). Approximately how long was the ball in the air before it crossed home plate? Let’s plug in 0.011458 mi for distance (d) and 90 for the speed (s).
Formula solved for time (t):
Plugging in the values and simplifying:
Converting that to seconds using the knowledge that there are 60 seconds in a minute and 60 minutes in an hour, we’d get approximately 0.45832 seconds for the time the ball was in the air, so not quite half a second. That’s not long!
While I won’t go into it in this post, there’s much more that we could use algebra and calculus to explore in baseball, including exploring the force the batter has to apply to the bat in different situations. Check out Chegg’s “Baseball and Calculus” if you’d like to explore calculus (plus really a lot of algebra too) and baseball further.
Pausing to Praise
Think about the fact that in less than half a second (see the Algebra and Calculus section above), a batter is able to process a pitch and decide if and how to swing.
When I was going through a concussion recovery, I remember reading an article in the Answers magazine about how our brain is designed to learn. God has wired us so that if we practice a skill over and over again, our brain will actually change in response, allowing batters to train their brains to respond to pitches. Pause for just one minute to ponder that—and praise the God that made your incredible brain.
“I praise you, for I am fearfully and wonderfully made. Wonderful are your works; my soul knows it very well.” Psalm 139:14 (ESV)
Also think about all the math that is used in simply setting up a baseball field where the bases are the right distance from each other…and in analyzing a game (let alone a season). We tend to treat statistics as commonplace, but they’re really shouting out at us that we live in a consistent universe held together by a consistent God. After all, they’re found by using division and other math operations…which hold true because day after day, century after century, millennium after millennium, God holds creation together consistently.
Indeed, we need to take a moment to pause to praise—and to reflect on the fact that knowing our amazing Creator is the greatest goal we could ever run after. We achieve salvation from sin and a relationship with God by receiving “the righteousness from God that depends on faith” (Philippians 3:9 ESV), but the Christian life doesn’t end there. Like athletes chase after goals, we’re called to chase after living more and more like we will be one day in Heaven—Christ’s completely.
“But one thing I do: forgetting what lies behind and straining forward to what lies ahead, I press on toward the goal for the prize of the upward call of God in Christ Jesus.” Philippians 3:13b-14 (ESV)
Baseball is one of countless examples of math in action students explore in the Principles series. If you’re looking for a curriculum that both shows math’s usefulness and points math to the Creator, be sure to check out the biblical math materials we’ve put together.
The course, which is now available as part of the Master Book’s Academy, brings in the biblical worldview of math, presents the concepts, walks through examples, and more, offering an easy transition from Principles into high school math.
P.S. I’m sorry I’ve not blogged much recently–it’s been a busy time! My husband and I just moved into our first home. We’re also still working on Algebra 2 (we expect it to be finished within a few months)…along with other math projects (stay tuned for more details in the upcoming months).
My heart was recently touched to hear of the viral video posted by a teen wondering about the why behind math expressed in such statements as “Who came up with this concept?” and “How would you even start on the concept of algebra?”
The questions are ones I wondered for years too. I mean, why are there letters like x and y in math books? And what was the purpose?
While the why behind math is one that many mathematicians and philosophers have devoted their entire lives to explore in vain, I believe there are very simple answers. Below is an open letter to Gracie—and anyone else asking these questions.
Dear Gracie,
First, thank you for voicing the questions so many have asked but not spoken. They’re important questions.
I know your questions related to algebra, but bear with me for a minute, as I want to start with arithmetic and work my way up there.
Math is all based on describing the real-life consistencies we find around us. 1 + 1 consistently equals 2. If you take 1 apple and grab another, you’ll end up with 2. Throughout the years, men have used different symbols to describe that, but addition remains the same because that’s what actually happens in real life.
Now you might be asking, but why? And that’s another great question! The answer to that depends on how you look at the world. Many would try to tell you that the world operates consistently as the result of an accident (the Big Bang)—but that doesn’t really make any sense at all. If we’re just the result of an explosion, why is there such consistency?
There is no real naturalistic explanation for math. Many brilliant philosophers have tried to answer it, but failed.[1] Even Albert Einstein admitted that there was something miraculous in math.[2]
But if we look at the world from a different starting point, there is an explanation. Now, this next statement might sound a bit shocking to you, but I believe the Bible has answers to your questions. You might be thinking “The Bible, isn’t that just an old book of fairy tales!?”, or maybe you haven’t even ever thought about it, but bear with me and let’s assume what it says is true even if you don’t think it is. The Bible claims to be a revelation from our Creator; if this is true, we’d expect it to tie with what we see and explain the world in which we live. And it does.[3] It says that a faithful, consistent God created all things—including the consistencies of creation. In fact, God talks about establishing His covenant with the “fixed order of heaven and earth” (Jeremiah 33:25 ESV).
Math works because creation is consistent, created and held together by a consistent God. Thus, we can memorize multiplication facts and rely on them to always work.
The Bible also tells us that God made man in His image, which is why we, unlike the animals, can think through how to express these consistencies around us. It’s why men, like Pythagoras, have been able to attempt to explain creation.
So why algebra? Well, it’s history is long and complicated, and I’m not going to attempt to summarize it all. The Greeks developed some pieces of it, including while trying to explain the relationships within shapes (Pythagoras is known for figuring out how the sides of a triangle relate together). The Arabs developed it further (the name comes from an Arab work). And it took off during the scientific reformation, when many needed it to describe the real-life consistencies they encountered.
For example, say you did experiment after experiment measuring the net force of different sized balls when traveling at the same acceleration of 10 meters per second squared. You found these measurements.
Mass
Net Force
10 kilograms
100 Newtons
9 kilograms
90 Newtons
8 kilograms
80 Newtons
7 kilograms
70 Newtons
You might want to see if you could predict how the mass of the ball will affect its net force without having to try every possible mass. So you look for a pattern.
Such a question presupposes a consistent universe…which was a presupposition many men in the scientific reformation had. They looked at their experiments and data and figured out how it related together. In the case of the balls, you notice that in each case, the force could be found by multiplying the mass by 10—which was the exact amount of the acceleration of the balls! You could write that like this:
Force = mass x acceleration
And rather than using words, why not save time and use a symbol to stand for the words?
F = ma
Now, a lot of algebra then deals with rearranging letters on paper. All we’re doing is applying what we can observe about arithmetic to these letters we’ve used as placeholders to stand for values, such as the F, m, and a. For example, we can see that adding the same poundage to a scale that has 2 pounds on each side leaves the sides equal.
2 = 2
2 + 1 = 2 + 1
Because we’re relying on the created world around us to stay consistent this way, we can also add the same quantity to both sides even if we don’t know it’s value (we’ll just use a letter to stand for that amount, whatever it is). In the case of weights on a scale, the x is standing for some unknown weight being added to both sides.
2 + x = 2 + x
And we can use that knowledge to solve problems. Note again our presupposition that creation is consistent…which I would argue is shouting out at us that there’s design and order around us, put there by a Creator.
You might find it interesting to note that, apart from acknowledging a Creator who also created our minds, the most brilliant minds have been left baffled as to why what they develop on paper actually applies—and how they can really know it to be true. After all, do we know truth based on experimentation? But we can’t possibly test every value! Or do we know it independently from experimentation? Why then does it actually work?[3] Acknowledging a God answers that, giving us reason to presuppose order around us that will be consistent and that ties with our findings on paper because God has, in a limited way, given us the ability to think “God’s thoughts after him” (a quote attributed to mathematician/scientist Johannes Kepler, who was one famous man from the scientific reformation who saw math as a way of describing God’s creation).
Ultimately, I believe math’s existence and ability to work outside of a textbook is shouting out at us that there is a God to whom we must give an account one day. Just as we can’t change how math works because that’s how He governs creation, so we can’t change how He operates in other areas too.
So it’s important to know what God has said. As I said earlier, I’m starting from the standpoint that the Bible is God’s Word to us. There are many reasons why I believe it is–we could talk about how it was written over more than 1,000 years by several different authors yet has a unified message implying one inspiring author behind it, how Jesus perfectly fulfilled hundreds of prophecies written hundreds of years earlier, and more. But, as one editor for the Chicago Tribune who set out to prove Christianity false discovered, the Bible’s message centers on Jesus’ resurrection–and the historical evidence for that is overwhelming (see The Case for Christ movie or the book by the same title). There is compelling evidence that Jesus was this Creator God who really did rise from the dead, proving His power over death.
This same Jesus claimed that whoever would believe in Him, though he died, would live (John 11:15 ESV). The Bible’s core message is this: God made us, we’ve rebelled against Him and stand under His righteous judgment, but He’s made a way for us to escape the punishment we deserve, know Him, and have eternal life in Heaven through Jesus Christ when we repent of our rebellious ways and put our trust in Him alone. To quote a well-known verse: “For God so loved the world, that he gave his only Son, that whoever believes in him should not perish but have eternal life” (John 3:16 ESV).
Please watch this video to learn in a nutshell what I’m trying to say:
I hope that helps answer your questions. And again, I’m really glad you asked them—they’re important questions to grapple with and understand.
Sincerely,
Kate Hannon
****
For Additional Reading…
And to learn more about the Bible’s answers to life’s tough questions, please check out BiblicalPerspective.net.
For a more technical explanation of why math works, please see this article titled “Evolutionary Math” by Dr. Jason Lisle.
You can also find some answers to common questions about the Bible and Christianity on Josh McDowell’s website–he also set out to prove Christianity a hoax and discovered the opposite. His findings are summarized in his short book, More Than a Carpenter.
Please also see the footnotes below for additional resources.
[1] See James Nickel, Mathematics: Is God Silent? (Ross House Books: Vallecito, CA: 2001). This book walks through the history of math in depth, showing how men have tried unsuccessfully to explain math apart from the biblical God.
[2] “Even if the axioms of the theory are posited by man, the success of such a procedure supposes in the objective world a high degree of order which we are in no way entitled to expect a priori. Therein lies the “miracle” which becomes more and more evident as our knowledge develops…And here is the weak point of positivists and of professional atheists, who feel happy because they think that they have not only pre-empted the world of the divine, but also of the miraculous. Curiously, we have to be resigned to recognizing the “miracle” without having any legitimate way of getting any further.” Albert Einstein (quoted in Mathematics: Is God Silent?, p. 210).
About the Author: Katherine [Loop] Hannon is the author of various resources, including Principles of Mathematics, a biblical worldview junior high math program (with Algebra 2 coming in 2020!) published by Master Books. Understanding the biblical worldview in math made a tremendous difference in her life, and she’s been researching, writing, and speaking on math, as well as other topics for over a decade now. Her heart is to point people to “seek the Lord, and His strength” (Psalm 104:4) in everything.
Meet the Author
I’m a sinner saved by grace through Jesus Christ. I’m also a writer—I’ve been writing ever since I could hold a pen. I… Meet Katherine [Loop] Hannon.
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24 sec. was divided by 4 to get 6 sec.; 1 ft. divided by 4 is 0.25 ft. Answer is 0.25 ft., or 3 in.)
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I’m a sinner saved by grace through Jesus Christ. I’m also a writer—I’ve been writing ever since I could hold a pen. I… 
