If anyone lacks wisdom, he should ask God, who gives generously to all without finding fault, and it will be given to him. – James 1:5
Recently my husband Marty and I went to a potluck with the theme “Are You Smarter Than a Fifth Grader?” Around our table were people who were both intelligent and educated, so we figured we had a good chance of winning.
Alas, it turned out it had been way too long since we were in fifth grade. Even the questions about grammar – which I’d taught for years, for crying out loud – had some rules that I don’t remember ever learning. For math questions, we turned to Marty, the engineer, for guidance, and there was at least one question none of us would have got right without him.
“When a non-zero number is to the power of 0, what do you get?” To the power of zero? It almost sounded like a nonsense question, and everyone at the table just said “zero.” (“Duh.”) Everyone except Marty, who said the answer was 1. We trusted his expertise, and it turned out he was right! However, he was unable to explain why it was 1. One of our team members googled the question, and apparently, the “powers that be,” some committee of mathematicians, decided and decreed that that was the rule.
This brought back memories of when my tired mom would just say, “Because I said so.” It wasn’t a satisfying answer then, and it still isn’t today.
As a Christian, I’ve learned when God tells me something that doesn’t make sense to me, I can trust Him, because He knows infinitely more than I do. But math -? Isn’t math always supposed to make logical sense?
The next day, as we were kayaking across the lake, I was still pondering why a number to the 0th power would always equal 1, and I decided to try a different approach, reasoning through it backwards. At the trivia table, we were all looking at the problem from the ground up, using the example of the number 3.
3 to the 1st power is just 3. But if there are no 3’s present, where did the 1 come from? As my arms were paddling, my brain was calculating. This time instead of starting with smaller numbers and multiplying, I started from the larger numbers and divided, and I ended up with 1!
Here’s how it worked for me:
3 to the 3rd power: 3x3x3 = 27
3 to the 2nd power: 3×3 = 9 (27 divided by 3 )
3 to the 1st power is 3 (9 divided by 3)
So, to reach 3 to the 0th power, divide by 3 one more time, and you get not 0, but 1. (*lightbulb!*)
The reason our group of intelligent, educated people didn’t think the right answer made sense was that we were looking at it from the wrong direction – the wrong perspective.
When I was in college during the “Jesus Revolution,” there was a saying, “God said it. I believe it. That settles it.” But for unbelievers and many of us who want to know God better, that cliche doesn’t quite cut it, and I think that’s at least part of the reason the world accuses us of checking our brains at the door when we go to church. I don’t for a moment think that kind of willful ignorance is what God means by “faith.” After all, we are told, “You shall love the Lord your God with all your heart, with all your soul, and with all your mind.” (Matthew 22:37-38, emphasis mine)
As a believer in Jesus, I love hearing and reading all the evidence for His divinity, mainly His Resurrection. I have seen and experienced enough evidence that “makes sense” that now when I encounter something that doesn’t seem logical to me, I trust that it makes perfect sense to God, and someday it will be explained to me – if it’s important. (Something tells me that when I am with Jesus forever in my new body, in my new home, I won’t care one bit about the things that bother me today.) Meanwhile, I am “seeking divine perspective,” and when I’m given small insights into some reality that has baffled me and others, my first impulse is to share them, hence the blog name.
God may not always explain everything, but if we seek His perspective, we might be surprised at how often He’s willing to share it.
Prayer: Lord Jesus, this world doesn’t always make sense to us, and our understanding of Your unseen kingdom baffles us even more. Thank You for what You have revealed to us through Your life, Your suffering, Your death and Resurrection. Thank You for telling us to ask, to seek, and to knock, and You will answer. Open our minds and hearts to the things You want to reveal to us today and ways to share Your truth with others, in Your precious name. Amen.
Annie, first of all, thank you for explaining why any number to the 0th power is 1! I’ll ask my wife over lunch and see if she’s able to give the “why.” Second, I appreciate what you wrote about not just accepting the truth of God’s Word without really understanding it and the evidence for it. Our youth, especially, need to know there are answers out there to their questions!
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Amen, Keith! We may be at the point where “because God said so” is enough of an answer for us, but it’s not for the young people, and we need to “be ready to give an answer …”
Hey, let me know if your wife knew the answer.
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Yes, she did. She came about it in a slightly different way and had used more than one way to explain it to her students over the years. It starts with the fact that exponents imply multiplication:
10 to the second = 10 X 10 X 1 (two tens and a one; 1 here is the identity element for multiplication)
10 to the first = 10 X 1 (one ten and a one)
10 to the zeroth = 1 (no tens and a one)
And there you have it! I showed her your reasoning, coming to the same conclusion, which she enjoyed. I enjoyed both: yours because it was creative and produced the right answer; hers because of my physics and math background.
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Thanks for that other explanation. I never would have figured that out myself, and as a fifth grader I would have demanded to know where that original 1 came from!
I gave my science teacher a hard time over evolution, because as she was talking about mutations, I kept asking what caused the mutation. (First semester we learned that in science everything has a cause, so I wasn’t trying to be a smart Alec.) She just kept saying how the mutations benefitted the organism, and I kept asking what caused the mutation? She finally snapped in exasperation, “It just happened, OK?!” (As you can guess, that didn’t satisfy. 😉 )
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Good job, Annie. The other thing about mutations is that everyone knows (just from the word itself) that mutations are almost always harmful (think monster movies), not beneficial!
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EXACTLY!
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Annie, The longer I walk with the Lord and study His Word, the clearer I understand why you chose your blog name, Seeking Divine Perspective. That really sums it up! God bless you, today!
P.S. Now I know why any number to the 0 power is always 1. So, I can cross that off my list! 🤣
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Haha! I didn’t even know enough to have that on my list!
(There’s a list?)
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Nice blog post, Annie, but oh man, my brain hurts now!
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Sorry, Mark!
Just be glad you’re not in 5th grade anymore. 😉
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I found this post really interesting, both because of the question about a non-zero number raised to the power of 0, because of the answers your mom gave—and mine, too—and because of what you say about faith.
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Thanks for stopping by, Luisa. Yes, I do think God has a purpose for our minds (to search for truth) as well as for unanswerable questions (to teach us to trust Him).
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