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# Math, Fireflies, Light Bulbs, and the Creator’s Design

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.

[i] Debbie Hadley, “How Do Fireflies Light Up?” ThoughtCo., https://www.thoughtco.com/how-do-fireflies-light-1968122 (accessed June 13, 2022).

[ii] Yong Xu, Plant Factory Using Artificial Light, 2019, 2.1.6.1, https://www.sciencedirect.com/topics/engineering/luminous-efficacy

[iii]National Pest Management Association, “The Science Behind Fireflies: 6 Things You Didn’t Know About Lightning Bugs,” https://www.pestworld.org/news-hub/pest-articles/the-science-behind-fireflies/ (accessed June 13, 2022) and Debbie Hadley, “10 Fascinating Facts About Fireflies,” ThoughtCo., https://www.thoughtco.com/fascinating-facts-about-fireflies-1968117  (accessed June 13, 2022).