BY JIM SAWYER – CHIEF SCIENTIST
For as long as I can remember, I’ve been into math puzzles. You see, numbers and I have enjoyed an exceptionally close, deeply meaningful relationship for a very long time. I dig them all: the really big ones, the really small ones, the ones that exist only as theoretical concepts, and even the normal everyday ones we use all the time. I even dig the meta-level stuff like the fact that I just used the word “ones” in the last sentence to represent the entire spectrum of possible numbers. It’s all fun to me.
In fact, I started off my college life as a proud Mathematics major. From day one of my freshman year, I was going to be a Math professor, and that was simply that. I mean, every one of us started off college knowing exactly what we wanted to do with our lives on the very first day and nothing ever changed along the way, right?
Well, that fantasy lasted until I took a course on Set Theory, an esoteric branch of mathematics that deals with properties of number systems themselves and symbol manipulation and a bunch of other really challenging conceptual stuff that I’m sure really, really, uber-smart math people get, but I found was just a little out of my grasp. Case in point was the question that appeared on the closed-book mid-term exam:
I remember staring blankly at the question. Is this for real? How have I managed to arrive at this point in my life? Has my academic journey really just been a series of naïve, inelegant stumbles, culminating in this glaring, unfortunate misstep into oblivion? What am I even doing here – what is the meaning of space and time and all things good in humanity?
Needless to say, the professor was not exactly pleased with my response of: “It just is.” And that was the beginning of the end of my brief and misguided foray into Pure Math. But I digress.
So apparently, this fun little math puzzle has been making its way around the interwebz. Take a look and then come back here. Can you figure out the answer? No cheating by reading ahead! Come on, you can do it!
What I particularly liked about this article was that its main point mirrors something our Data Science team has heard me challenge on many occasions:
What’s the simplest way to approach this problem?
I’ve long held the belief that you don’t need to have the best math or the fanciest model in the world in order to make a meaningful difference in a business context. Sometimes a “good enough” model will do. In fact, adding too much complexity can at times be detrimental, obfuscating the solution under unnecessary layers of technical sophistication that are hard for you to explain, or even worse, hard for your audience to understand. In business, confusion is the enemy of progress.
This concept is generally referred to as Ockham’s Razor, and it isn’t new. It goes all the way back to Pythagoras, Aristotle, and Ptolemy, who artfully quipped: “We consider it a good principle to explain the phenomena by the simplest hypothesis possible.” William of Ockham himself was a medieval English friar and philosopher, and while he didn’t invent the term – that didn’t come until the 19th century – his “razor” refers to “shaving away” unnecessary assumptions when differentiating between two competing hypotheses. We talk about it today as a matter of everyday common sense: the simplest explanation is probably the right one.
But “simple” doesn’t feel like the usual realm of Data Science. Complexity can be tempting to us, and indeed, it’s often warranted by the nature of the data and the business question being asked of it. What I’m saying is that it shouldn’t be our default starting point. We may get excited about the latest article from our favorite academic journal or blog, or the latest and greatest modeling technique just released in an R package, and immediately seek out places where we can deploy our newfound knowledge. But this is the proverbial hammer looking for a nail. Give me a razor any day.
Can you explain your model or method in an easy-to-comprehend way? Can you clearly articulate your assumptions, the alternatives you considered, and the reasons you chose your preferred approach? Can you craft a story about your results that leads your audience to see the business value inherent in your conclusions, and drives them to act in a meaningful way based on the insights you’ve learned?
If so, your approach is probably “good enough.” Go with it.
Ockham’s Razor
BY JIM SAWYER – CHIEF SCIENTIST
For as long as I can remember, I’ve been into math puzzles. You see, numbers and I have enjoyed an exceptionally close, deeply meaningful relationship for a very long time. I dig them all: the really big ones, the really small ones, the ones that exist only as theoretical concepts, and even the normal everyday ones we use all the time. I even dig the meta-level stuff like the fact that I just used the word “ones” in the last sentence to represent the entire spectrum of possible numbers[1]Did you catch that? I’m so proud of you. And of myself.. It’s all fun to me.
In fact, I started off my college life as a proud Mathematics major. From day one of my freshman year, I was going to be a Math professor, and that was simply that. I mean, every one of us started off college knowing exactly what we wanted to do with our lives on the very first day and nothing ever changed along the way, right?
Well, that fantasy lasted until I took a course on Set Theory, an esoteric branch of mathematics that deals with properties of number systems themselves and symbol manipulation and a bunch of other really challenging conceptual stuff that I’m sure really, really, uber-smart math people get, but I found was just a little out of my grasp. Case in point was the question that appeared on the closed-book mid-term exam:
I remember staring blankly at the question. Is this for real? How have I managed to arrive at this point in my life? Has my academic journey really just been a series of naïve, inelegant stumbles, culminating in this glaring, unfortunate misstep into oblivion? What am I even doing here – what is the meaning of space and time and all things good in humanity?
Needless to say, the professor was not exactly pleased with my response of: “It just is.”[2]This was the same course where, after one of my exams, the professor met with me to discuss my test results and opened his conversation with “Well, Jim, let me start by saying that at least your score wasn’t the worst…” True story. And that was the beginning of the end of my brief and misguided foray into Pure Math. But I digress.
So apparently, this fun little math puzzle has been making its way around the interwebz. Take a look and then come back here. Can you figure out the answer? No cheating by reading ahead! Come on, you can do it!
What I particularly liked about this article was that its main point mirrors something our Data Science team has heard me challenge on many occasions:
What’s the simplest way to approach this problem?
I’ve long held the belief that you don’t need to have the best math or the fanciest model in the world in order to make a meaningful difference in a business context. Sometimes a “good enough” model will do. In fact, adding too much complexity can at times be detrimental, obfuscating the solution under unnecessary layers of technical sophistication that are hard for you to explain, or even worse, hard for your audience to understand. In business, confusion is the enemy of progress.
This concept is generally referred to as Ockham’s Razor, and it isn’t new. It goes all the way back to Pythagoras, Aristotle, and Ptolemy, who artfully quipped: “We consider it a good principle to explain the phenomena by the simplest hypothesis possible.”[3]That Ptolemy was one sharp dude. Ahead of his time, really. William of Ockham himself was a medieval English friar and philosopher, and while he didn’t invent the term – that didn’t come until the 19th century – his “razor” refers to “shaving away” unnecessary assumptions when differentiating between two competing hypotheses. We talk about it today as a matter of everyday common sense: the simplest explanation is probably the right one.
But “simple” doesn’t feel like the usual realm of Data Science. Complexity can be tempting to us, and indeed, it’s often warranted by the nature of the data and the business question being asked of it. What I’m saying is that it shouldn’t be our default starting point. We may get excited about the latest article from our favorite academic journal or blog, or the latest and greatest modeling technique just released in an R package, and immediately seek out places where we can deploy our newfound knowledge. But this is the proverbial hammer looking for a nail. Give me a razor any day.
Can you explain your model or method in an easy-to-comprehend way? Can you clearly articulate your assumptions, the alternatives you considered[4]There had better be at least two other options, or I’m going to be pretty disappointed in you., and the reasons you chose your preferred approach? Can you craft a story about your results that leads your audience to see the business value inherent in your conclusions, and drives them to act in a meaningful way based on the insights you’ve learned?
If so, your approach is probably “good enough.” Go with it.
Footnotes [ + ]
Tags: