## Should stats trump calc?

Harvey Mudd College math professor, and self-proclaimed mathemagician, Arthur Benjamin thinks so. He explains his reasoning in this fairly convincing three-minute talk.

P.S. Let the record show that I took calculus in college, got an A, used it a bit in microeconomics, and have rarely thought about it again. But nearly every day I encounter an issue involving statistics or probability. I’m just saying.

I agree with Professor Benjamin. This is just one way we can line up curruculum with the real world!

Really thought provoking…and correct. Thanks for this post!

Completely agree. I sent an e-mail to my previous high school curriculum supervisor about this recently. Both my brother and I had been encouraged to take the “higher track” pre-calculus (and had heard stats was a joke). Now in grad school we both have to play catch up and take quantitative methods.

I also agree that knowledge of statistics is more useful to the average citizen and would be a great way to ensure your average citizen couldn’t be duped with impressive numbers.

Very interesting…I never took calculus and have never missed knowing this subject. However as an education major in college I took statistics which I have found very valuable.

Just thinking about math gives me the hives…

I majored in history and had to take college algebra and either trig or stats. I took trig. Stats just made my skin crawl…

Wasn’t it Mark Twain who said, “there are lies, there are damn lies and then there are statistics?” 🙂

Looking back, I’m quite sure statistics would have been more valuable for me to take than trig…

Ignorance of statistics is even more common than ignorance of goegraphy. I recently talked with a 30 year veteran of the financial industry who said that you could tell who the most talented fund managers were by track records. I told him that if you you had 8000 people flipping coins you tell who were the best coin flippers by looking at those that flipped heads 10 times in a row. The funny thing is that if you had as many people flipping coins as you have fund managers, you probably would have about ten people who could flip 10 heads in a row. Using my friends logic, those people would be the most skilled at flipping heads. To identify skill you must understand statistics or you can come to the same erroneous conclusion as my friend.

Be careful what we wish for. When I envision a country of people educated on statistics track it may look like a bunch of people sitting around a poker table on ESPN.

Every step taken, every decision made without first weighing the stats, cautious and deliberate.

“There are lies, damned lies, and statistics.” – Mark Twain

Given the role that statistics played in the recent economic meltdown of the world economy I don’t think that Twain would change his opinion much.

As an old math major I know that mathematics is the science for lazy people who want to appear smarter than they actually are. That’s what I always liked about math; it’s all about finding the shortcut or taking the easier route.

Calculus and statistics are both shortcuts to avoid work. Calculus is a kind of fancy addition and you can use one quick little equation to get the same answer you would get by doing thousands of little arithmetic problems. Statistics does something similar with data collection. Why poll everybody when a small sample of people gets you a good enough answer? But therein lies the difference: Calculus can get you the correct answer where statistics gets you the likely to be correct answer.

In our everyday lives we operate within a certain level of proof; call it “proof beyond the usual doubts”. A more rigorous level of proof that is a notch above that everyday proof level is legal proof; proof beyond a reasonable doubt. Above that level is scientific proof. And above them all is mathematical proof.

With Calculus you learn how to find an answer that is provably correct beyond any doubt. With statistics you learn how to find an answer that fits within the lowest levels of proof, often times below what would be considered acceptable in legal proof.

In the end, in regards to education, calculus will be dropped and replaced with statistics but the world won’t be better off. The world is just willing to settle for lies, damned lies, and statistics.

But once upon a time there was truth, absolute truth, and Calculus.

Well Steve G. If the general public understood the lies that are cloaked in a shroud of truth that is statistics. WE might make better decisions.

That is if the general public could understand that sometimes when politician A says so and so wants a 50% tax increase, while politician B says he is only asking for a .25% increase and they are both right.

We might have fewer people attempting to make cheap talking points through deception.

According to statistics, most politicians are very bad at math.

Brendan,

Calculus and statistics are useful, powerful mathematical tools. And if people learned a lot more math it would be a plus. But signing people up for more statistics classes isn’t going to help the general public make better decisions or reduce deception.

There’s a difference between throwing dice and playing poker. With dice it’s the pure statistics of random chance. With poker it’s the pure statistics of random chance combined with the art of deception, the art of perception and a search for the underlying truth. With poker, possible deception is a part of the game and players try to figure out what that guy really has in his hand, but statistics alone can’t tell you the truth. Is that other guy bluffing, what cards does he actually have, is his hand better than yours? Statistics doesn’t get you the answers.

When we encounter statistics in our everyday lives we aren’t looking at a game of dice, we are looking at a poker game being played and we are there among the players. Possible deception is a part of the game. But how do we find out the truth?

Let’s turn this situation into a metaphorical mathematical card game and let’s pretend that Arthur Benjamin is a part of our little game. He has played his hand well, he has convinced many of the other players that statistics should trump Calculus.

My turn to see his bet and then raise.

“Mr. Benjamin, your argumets seem quite convincing to the general public. But how do we know that you are not pulling one of your mathemagical tricks? After all, you are a self-proclaimed mathemagician and, as such, you would be quite good at fooling people with your deceptive mathemagical slight of hand. How do we know that your arguments are truly valid? How can we be certain that a month or a year from now, after you have the whole country convinced, that you won’t say, ‘Fooled you all! It was a trick. Now you can see that I am the nation’s greatest mathemagician!’”

Uh oh. Mr. Benjamin might be in trouble, all his best arguments could be a part of a clever deception. Time to raise the bet.

“Mr. Benjamin, it seems to me that statistics involves lots of number crunching and analysis stuff. Isn’t that a very left-brain sort of thing? Haven’t a lot of those left-brain things been outsourced overseas or taken over by machines? One of the other players in this game of ours wrote a book about that stuff and lots of people seem to think that the right-brain stuff is the wave of the future. Should we be teaching people math skills that might soon be done by machines or outsourced? Shouldn’t we be trying to teach people how to do more of the right-brain math stuff?”

Okay, enough with that game.

Our society has been ruled by left-brain thinkers for a long time so words, numbers and symbols have been the rage. This L-directed society has its true/false, multiple choice, grade on the bell curve way of thinking and statistics fits in well with that. And most of what people learn in math is how to deal with the left-brain stuff; use words, numbers and symbols in mathematical ways.

You can see left-brain domination here in this discussion. People often encounter words, numbers and symbols related to statistics and they assume from that that statistics is therefore more useful in the real world than some other branch of mathematics. There is a common left-brain self-deception going on there but statistics doesn’t help you detect it. Statistics doesn’t help you see that the definition of the word “mathemagician” can be combined with ideas from “A Whole New Mind” in a surprising way to counter Arthur Benjamin’s ideas.

Math isn’t all about words, numbers and symbols. There is a creative side to mathematics; a right-brain side that can involve things like mathematical proof. But the right-brain isn’t the “word, number and symbol” side of the brain; it’s the big picture, pattern and metaphor side of the brain.

Part of mathematics is a thought process, a pattern of thinking. You don’t look for that part of math in the words, numbers or symbols you encounter.

Once upon a time, in the sector of the galaxy inhabited by the ell-speakers of the know-seekers, among the creatures of the herds of the math-words, there were the cats of the stats.

The stat-cats were sample folk, they just loved to sample everything and chat about their stats. Their herd of the math-word had a history linked to gambling and predicted outcomes were all the rage among the stat-cats.

Then one day something terrible was discovered by one of the stat-cats. On that day the stat-cats discovered “day” and “once upon a time”.

Now, to you and me the idea of time is something that we all know about and take for granted, but to the cats of the stats this “time” thing messed up everything. Time marches on; it waits for no one; it has a past, present and future. It was just awful!

The worst part about this time thing was that the stat-cats couldn’t sample from all of it. The closest they could come to sampling from the future was to sample from the present. But the present was so fleeting, and the present turned into the past so quickly, that it was like all of their sampling had been taken from the past. This time thing was like two jars that were separated by the divider of the fleeting present. The cats of the stats had taken all of their samples from only one of the jars; the “past” jar, and they had never taken a sample from the “future” jar.

They were in a tizzy; horrified, terrified by this unexpected change in their world. And then suddenly, that hit them too; the concept of “change”. What if there was a change; what if something changed in the future? What if the future turned out to be different from the past? What if the contents of the future jar were in some way different from the past jar? What if there was a “change that occurred over time”?

The cats of the stats were shocked and stunned when they discovered that they had been studying, analyzing and predicting the past. If the future turned out to be the same as the past then their predictions of the past would hold for the future. But if the future was different…all bets were off!

The stat-cats needed to solve this problem; they needed answers about this “change over time” thing. So they went out to the other herds of the math-words and even to the general population of the ell-speakers of the know-seekers.

But alas, the knowing that they were seeking was gone.

Generations ago, there had been a herd of the math-word that dealt with the concept of “change over time”. Unfortunately, in the ultimate of ironies, it had been the cats of the stats who had convinced all of the inhabitants of their sector of the galaxy to abandon that herd of the math-word. The stat-cats of the distant past had convinced all of the inhabitants that it was the knowing of the stats that was the most useful; that the knowing of the stats had the greatest pay-off in the real world.

Once upon a time, in that sector of the galaxy, there had been a knowing of time, a knowing of change and a knowing of changes that occurred over time. But that herd of the math-word and all of it’s knowing were gone. And so all of the ell-speakers of the know-seekers, and all of the cats of the stats were left with sampling and predicting the past.

And they all hoped upon hope that a change over time would never, ever occur and that they would never, ever have to deal with it.

Now it just so happens, that some people in our sector of the galaxy think that learning statistics is a more useful way to spend your time in math class; that learning statistics is the gamble with the greatest return on investment. Perhaps they are correct. Only time will tell.

But we should always remember that statisticians and the people at the bank drive-thru share the same preference.

No change, please.

92.8% of statistics are made up on the spot.

Calculus is the math of engineering, medicine, economics, physics, etc. Just because stats has become ‘en vogue’ doesn’t mean we should embrace its arrival by kicking calc out the door.

I think it’s a matter of ensuring that we add a healthy dose of stat/prob to the curriculum. As an ed major, like Mimi, I too studied stats and have found it to be very valuable, especially in this age of data-driven decision making in our schools.

The most surprising thing I learned long ago in elem. methods class, was that in addition to stats, most undergrads (not just ed majors) have a very vague sense of discrete mathematics, especially graph theory, combinatorics, and probability. And it is a huge problem now as many teachers will skim the surface of these concepts, mostly because their own mathematical foundations are at best shaky. (It’s not just about rolling ‘number generators’ and making predictions about coin tosses.)

In the end, I believe that the art and science of math is more than just numbers… It is through rich, mathematical experiences that we develop mental discipline, gain insight in how to further interpret our world, and thoughtfully implement creative problem solving strategies.

To imply that one branch of math is more relevant than another is dangerous… We run the risk of denying ourselves valid solutions in a problematic world.