Episode I

Who are you and why are you blogging?

My name’s Aaron Santos. I’m a geeky physicist interested in improving science education. I graduated from MIT with a bachelor’s degree in physics and got my PhD in physics from Boston University. Between undergraduate and graduate school, I worked as a Boston Public School teacher at Boston Latin Academy.

Since leaving teaching, I’ve developed a strong desire to communicate science to the general public. Toward this end, I recently wrote How Many Licks?: Or, How to Estimate Damn Near Anything, a book of (hopefully) humorous and thought-provoking Fermi approximations.

So what’s A Diary of Numbers?

It’s a blog featuring various calculations I’ve done. They’ll be similar to the types of calculations you’ll find in How Many Licks? Things like: 

• How many calories are in the Stay Puft Marshmallow Man?  
• How many times can you wash your favorite t-shirt before it turns entirely into dryer lint?
• How much would it cost to run the entire U.S. with solar energy?

Why write a blog?

Several reasons: 

• It’s quicker to write a blog than it is to publish a book (much, much quicker). 
• The capitalist in me says it’ll help sell more copies of my already published book. 
• Hopefully, people will read it, get really excited about doing math and science, and the world become a more enlightened place.

Is this really going to enlighten the world?

Probably not. I’m not even sure who’s going to read it. But even if only a few people get a kick out of reading it and learn to enjoy thinking scientifically, I’ll feel it’s been worth my time. At the very least, the blog should provide a good forum for organizing my thoughts.

So you want people to become scientists?

I think everyone should be a scientist. I don’t mean everyone should have jobs where they have to walk around wearing white lab coats. I mean everyone should use the scientific method: make hypotheses about the world, see if there’s any evidence contradicting your hypotheses, and make new hypotheses that fit that evidence. The scientific method is useful everywhere, from high tech labs to programming your VCR clock. (Yes, I still have a VCR.)

Wait a minute! You said you’re concerned about science education. Why not write a science blog instead of a number blog?

I view estimation as being more science than math. First of all, it requires a certain degree of intuition about the real world that’s not necessary in pure mathematics. More importantly, estimation has all the rudimentary parts of science: You hypothesize about how big (or small, or expensive, etc.) something is, then you gather evidence by calculating the answer in a bunch of different ways. In this respect, your hypothesis is falsifiable. In estimation, much like science, you can never say what the answer is but you can certainly show what it isn’t. You get progressively closer and closer to a correct theory by making better and better estimates. There’s even peer review. (To anyone who doubts this last point, I suggest you do an estimate and then show your friends. There’s a good chance they’ll be harsher than most referees.)

But aren’t we learning science and math in school?

No. There’s already a lot written on the problems of science and math education. The main problem is we aren’t really doing science so much as learning about the discoveries other people have made by doing science. There are a lot of good books that teach people about scientific discoveries, but very few teach people how to think scientifically. Even the books that teach “experiments” often miss the point. Usually you’re just replicating some neat experiment, and while that’s generally pretty good for demonstrating science principles, it’s very different than coming up with your own experiments (or thought experiments) and trying to figure out answers using the scientific method. These books are entertaining and certainly educational, but I don’t think they do justice to the struggles, the ups and downs, the creativity—in short, the “process” that real scientific thinking entails. For these reasons, I think estimation is a better way to teach people to think scientifically.

But scientific discoveries are important! You’re just solving goofy math problems!

True, I am just solving goofy math problems. Some might argue that I should just write about science experiments and describe the process. That’s a pretty passive way of learning, which is usually not as good as actively learning. My hope is that the goofy problems here will inspire readers to solve their own estimation problems, rather than just read the blog. In this way, people will actively be doing science rather than just reading about science that other people have done.

All right, but wouldn’t it be better to write about actual experiments? At least then people will be learning real science.

There’s a practical reason for this: not everyone can afford atomic force microscopes and big hulking lab equipment. If you want to train someone to think scientifically, estimation is a fairly cost-effective way of doing so because anyone can do it anywhere at any time. More importantly, this is a way of doing “real science.” A theoretical physicist does these sorts of calculations and thought experiments all the time (albeit with more advanced mathematical techniques). As far as using the scientific method, theoretical science is just as much a science as is chemistry, biology, or any other experimental science.

But a lot of these calculations are really just using common sense. How is this helping people become better thinkers?

I marvel at this statement because so many people think of scientists in this way. Doing science is using common sense. We’re not robot super geniuses. We’re just trained to think critically about things. It’s not like Einstein’s brain was made fundamentally different than the rest of ours, he was just doing things that made sense given what people knew about the world.

Getting back to the main point, these simple estimation problems can be a good way to develop scientific thinking skills. This is true no matter how advanced your background is. While the calculations I do here are certainly a lot less rigorous than what you’ll probably find in a published paper, this is purely a pedagogical choice: having fun goofy problems allows anyone to get involved without being intimidated by big scary equations.

All right, so tell me how to estimate.

I can’t. The main complaint I’ve gotten about How Many Licks? has been from people who wanted to learn some secret magical trick that will show them how to calculate anything. Unfortunately, there’s no magic bullet, formula, or procedure that will work every time. Estimation, like science, is something of an art. You can estimate just about anything, but doing so requires hard work and a lot of thinking. As I said earlier, estimation is a lot like science.

Well, at least give me some general guidelines.

That’s what the problems are for. The main compliment I’ve gotten about How Many Licks? was from people who enjoyed the problems, and that’s what this blog is about. By seeing a bunch of examples, hopefully you’ll be able to pick up some general tricks and methods of solving problems. Feel free to discuss, disagree with, and argue about any of the problems I present here. Ultimately, the best way to learn estimation—and scientific thinking—is to be actively engaged in it, and if you’re learning enough to disagree with my results I’ll feel like my work here is done.