In case you missed it, I have nine kids ranging in age from 23 to 7 that my wife homeschools. They’re a riot. Each of them has to find a way to be different from all of the others. This makes for some real characters. Let me introduce you to Peter.

This week, Peter, who is 11, has been working on a times table. You may remember these from when you were a kid. Say you want to know what 7 times 8 is (this was always my hardest “times” to remember). You take your finger down the rows to the seven and then go across to the 8 column and see 56.

I’ve long thought times tables were a horrible crutch. Commit these times to memory and get over it. I still remember taking timed tests in elementary school to see who could complete a bunch of times in the shortest time possible. I suspect this pedagogical practice is looked down on these days. I suspect my success at these also set me up to love math. My nearly 20-year-old son continued to use his trusty times table throughout much of his schooling. Don’t judge him (or his parents) too harshly, he has many other redeeming qualities!

Now most people find times tables in their math book or buy a glossy version with nice font. Not my kids. They write them by hand and use clear packing tape to laminate them.

Most people’s times tables go from 1 to 10 on the rows and columns. If you need to multiply 11 and 13 you can use the principles from the 1 to 10 table to multiply double-digit numbers.

Peter’s times table is different. Currently, it has 22 rows and 76 columns. I say currently, because his current passion project is making the table 100 rows by 100 columns. I pointed out that he really only needed to make it a triangle since 22 times 76 is the same as 76 times 22. He didn’t seem impressed. Committed to the bit, I think he wants to make the matrix square. If nothing else, he’ll improve his penmanship.

Peter’s younger siblings think Peter’s times table is amazing. They love trying to defend Peter’s honor. Trying to show me that Peter’s times table is “smarter” than me, they now ask me random times problems. Dutifully, I do the problem in my head. They then confirm that I got the right answer. I have succeeded in being at least as smart as Peter’s times table. Of course, I have failed by giving in to this stupid game.

Peter tells me that his times table is great because he doesn’t have to memorize these big times problems like I do. This strikes me as similar to the “new bad idea” that Google makes it so that I don’t have to remember anything. Google will answer my questions so quickly about anything. There’s no reason to read books or attend lectures! This of course is compounded by the “newer badder idea” - ChatGPT and its ilk - that is invading college courses. If you’ve followed any of my content over the years, it shouldn’t surprise you that I favor Actual Intelligence to anything artificial.

When I ask Peter why he doesn’t just memorize the 10 by 10 times table he brushes me off telling me that would be too much work. Besides, looking up 76 times 22 would be faster than actually solving the problem with a pencil. Anyway, when he gets older and doesn’t have to follow our Draconian rules, he’ll just use a calculator. I have enjoyed telling him and his 6 older brothers and sisters that I made it through an Ivy League engineering program where most of the courses - and all the math courses - did not allow us to use calculators. They then look at me the same way I look at my 80-year-old neighbor who tells me what life was like when he was a kid.

How can you have advanced math classes without calculators? Much of the math uses symbols in place of numbers. This emphasizes concepts. For example, I can do 76 times 22 by noting that 76 times 2 is 152 and so 76 times 20 is 1520. To get 76 times 22 I add those values together - 1672. The concepts involved in this problem relate to understanding how addition and multiplication relate to each other and my experience in breaking down big problems into smaller problems.

As soon as we use specific numbers we make the task too concrete to be educational. By using symbols we keep the task general and emphasize the concept. If I were to ask you the derivative of x cubed, I’d know that it was 3 times x squared. Not because I memorized that rule. But because I remember the concept of derivatives that you bring down the power and decrease the power by one. That’s a lot easier to remember than memorizing all the possible facts. Furthermore, it makes it easier to take the derivative of 1 divided by x because that is the same as x to the negative one power. The rule will work here as well.

What does this have to do with programming and reproducible research? Why do I tell you all this? Well I hope you’re at least a little more receptive to my arguments than Peter for why his impressive times table is stupid! I have two reasons.

First, using a crutch like a times table, google, or the artificial intelligence is not faster. Sure, initially, it is faster until you learn the material. I use the ggplot2 cheat sheet. Well, not really anymore, because I learned the cheat sheet and the concepts baked into the design of ggplot2. I am far faster for having learned this material than I would be if I had to use the crutch. I am even faster for putting in the effort to practice the concepts in many different contexts by making many different figures.

Second, using crutches will also limit your ability to do new cool things. It will also hinder your ability to understand why something is or isn’t working. With the growth in artificial intelligence tools, the number of people telling me they asked ChatGPT to fix their code for them has also grown. Part of me dies when I hear this. How do they know to trust ChatGPT if they don’t understand the code? Since ChatGPT is basically a big plagiarization engine, how will it ever do something new? How will we do anything new if we outsource the task of learning to a tool? If we want our work to be derivative, sure ask ChatGPT. Otherwise, develop some actual intelligence.

I recently listened to an interview where the guest commented that a downside to using R is that it has a learning curve. What tool doesn’t have a learning curve? The better comment is that R has a learning curve that it is worth the ride. Dr. Tracy Teal once shared this plot with me that immediately resonated with me. I think it nicely sums up my point.

Feel free to replace “geek” and “non-geek” with your favorite comparison. I might think of “R user” and “Prism user”. By learning R I have been able to do so many cool things. Things I never would have been able to do with other tools like Prism that have more shallow learning curves.

Looking ahead to 2025, I want to encourage you to invest in future you by taking the time to learn to code and automate your analyses. It does get easier. But not because you’ll be able to use the equivalent of a bigger times table or a calculator. No, because you’ll learn generalizable concepts that allow you to better implement your vision.

I can’t wait to see what we come up with in 2025!

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