Arithmetic Question

You can skip all the arithmetic and still get the point about how to help your kids grow up happy and healthy. If numbers are not your thing, you can start reading this essay at the photo of the teddy bear.

For those of you who do believe that “numbers are your friends; you can count on them!” here’s a question: “What is the smallest power of 2 that has a “7” in the thousands digit?”

Let’s think this through. Go ahead, get a pencil. Heck, get a calculator if you prefer. Whatever you like. Let me help:

Two to the first power is two.

2¹ = 2

Two to the second power is four.

2² = 4

Two to the third power is eight.

2³= 8

Note that none of these numbers, 2, 4, or 8 even HAS a thousands digit never mind a 7 in the thousands digit. You have to go waaay up the line to get powers of two that have thousands digits:

2, 4, 8, 16, 32, 64, 128, 256, 512, 1024

2¹⁰ = 1024

Now we have a thousands digit, but the number in the thousands digit is a 1. So we have to keep going to get a seven in the thousands digit. Onward and upward:

2¹¹ = 2048

2¹² = 4096

2¹³ = 8192

2¹⁴ = 16,384

2¹⁵ = 32,768 (Ooh, there’s a seven. But it’s in the hundreds not the thousands place.)

2¹⁶ = 65,536

2¹⁷ = 131,072

2¹⁸ = 262,144

2¹⁹ = 524,288

2²⁰ = 1,048,576

2²¹ = 2,097,152

(For those readers who are just joining us, welcome back!)

So there you are, the first power of two that has a seven in the thousands digit is 2²¹ or 2,097,152.

Who cares? Well might you ask. Really, nobody. No mathematician cares. Neither Monte Hall nor Alec Trebek is going to ask a question that is this time-consuming to solve without a calculator. There’s nothing remotely interesting about arithmetic questions of this type. And no, there are no “short cuts,” no “tricks” that will allow this answer to appear without slogging through all those powers of two. The only way to find the first seven in the thousands digit is to go through the steps above using a pencil or a calculator.

Unless, of course, you happen to be a human calculator.

The only aspect of this question that is of interest is “What about the guy who can answer this question “What is the smallest power of 2 that has a “7” in the thousands digit?” without a pencil, without a calculator? What about the guy who answers this question as quickly as you or I could answer, “What is three times five?”

John von Neumann was said to have instantly answered this question about the powers of two. By all accounts von Neumann was indeed a human calculator and could multiply four digit numbers in his head. When he wasn’t working on the Manhattan Project or inventing game theory or driving too fast on the streets of Princeton.

Would you agree that von Neumann’s “math brain” was different from yours or mine?

Which brings us–‘finally’ you might say–to my point about raising healthy kids. Remember, the folks who are going to pick out your nursing home are the same folks to whom you may currently be saying, “Why don’t you have an ‘A’ in math?”

Doubtless your child’s math course does not involve questions similar to “What is the smallest power of 2 that has a ‘7’ in the thousands digit?” And doubtless you believe that your child could be doing better. “If only she would study harder,” you opine. “I’m sure she could get an ‘A’ if she just worked at it.”

Here’s a thought experiment: How long would you need to be locked in a sparsely furnished room under a bare light bulb before you could come up with “2,097,152” as the answer to “What is the smallest power of 2 that has a ‘7’ in the thousands digit?” You would argue that you can’t do that calculation in your head. If someone were to tell you that you’re refusing to do that arithmetic or that you “just aren’t motivated” or that “you’re just getting back at your parents and that’s why you won’t figure out “What is the smallest power of 2 that has a “7” in the thousands digit?” you would be justifiably and righteously annoyed.

You don’t have the arithmetic ability; you don’t have the memory; you don’t have the motivation. You just plain can’t figure out this problem. And if you could figure it out, you darn sure couldn’t figure it out instantaneously like von Neumann did.

Which is why you may be having trouble with your child and her math course.

Because in all likelihood she is trying the best she can. The “noise” that is destroying the “signal” is that her annoying behaviors and seeming lack of motivation have been caused by her not being able to do that which she is asked. If she could handle the curriculum, she would.

Just like if you knew “What is the smallest power of 2 that has a “7” in the thousands digit?” you would have said so.