What do Mark Zuckerberg, Jeff Bezos, and Larry Page all have in common?
Yes, they’ve founded multi-billion dollar businesses with virtually no formal business training, with combined revenues of over $80 billion. But they are also former software engineers and hackers, an experience that undoubtedly taught them skills in critical thinking and problem solving. Making savvy business decisions is not only about engineering, but also sales and marketing, business development, recruiting, and all the other functions of business. (Bezos had experience working as a quant investor at hedge fund DE Shaw prior to founding Amazon, but his duties had little to do with entrepreneurship or operations). I argue that their programming backgrounds was critical to their success in these other areas as well.
I haven’t been an active coder since I was in my late 20s, but there’s no question that my experience learning how to code when I was 12 and teaching children and adults how to program has changed the way I think about every aspect of my life. I developed an obsession with research and formal process documentation in investing, entrepreneurship, education, and even in my personal life, which all derive from that formative intellectual training.
Justin James, lead architect for Conigent, notes that great programmers understand not only what their code does, but also how and why. Programming is effectively high-level problem solving.
Writing code, however, is no easy feat. Compilers (which are responsible for translating the programmer’s code into machine language) don’t tolerate the ambiguity and imprecision of everyday speech. The challenge for programmers, then, is specifying requests in such a way that the compiler, and ultimately the central processing unit, will understand them. If a programmer can explain problems in a way that a computer can understand them, those problems are already effectively solved, because the programmer has figured out how to do it. Problems may not always appear computational, but a skilled programmer nevertheless finds ways to solve them computationally.
Programmers formalize, quantify, and solve problems (primarily with the aid of a computer) using algorithms, or finite sets of well-defined instructions which, when followed exactly and applied to a relevant problem, produce guaranteed results. With the exception of a small number of well-documented problems in computability theory (e.g., the halting problem), algorithms are theoretically capable of solving any computational problem. Not all algorithms can be carried out in a reasonable amount of time, but a great many can.
It should be no surprise, then, that leaders who bring their programming experience and algorithmic thinking to business have reshaped the playing field. After all, in the eyes of an algorithmic thinker, solving problems based on intuition, opinions, and unsystematic analysis of data is not an option. The algorithmic thinker will find a better solution and eat his or her less savvy competitor’s lunch.
A skeptical reader might be thinking that algorithmic problem solving is abstract and unnecessary—that such an approach is “overthinking it.” I definitely heard that response when I applied algorithmic thinking to finding a spouse. But they would be missing the point. Failing to use the right algorithm is far more costly than taking the time to come up with the optimal solution.
Consider a task in which students are asked to sort a list of 100 integers with no specified range of values. Many would undoubtedly start by finding the smallest number and putting it at the front, then finding the next smallest number out of the remaining 99 integers, and so on. This method is called selection sort. A clever student, however, might realize that she could divide the list into 100 single-integer lists, then compare each adjacent list to create 50 sorted two-integer lists, and so on. By the time the student has merged up to a single 100-integer list, it would be fully sorted. This method is called merge sort.
The first algorithm requires both a maximum and minimum of 4,950 comparisons, while the second requires a maximum of about 450 comparisons and a minimum of about 275. To put the difference in practical terms, if each comparison took one minute, merge sort could accomplish in 7.5 hours what it would take selection sort over 3.4 days to do. Good algorithms make a big difference, and merge sort isn’t even necessarily the best or most sophisticated sorting algorithm. Algorithms may sound abstract, but they are used to solve problems we face on a daily basis (sorting the mail, scheduling, and deciding on the most efficient path from point A to point B, for example).
Put simply, algorithmic thinking is breaking down a problem and constructing a set of well-defined steps to solve it. In practice, this involves rigorous testing, documentation, analysis, and procedures. The problem of solving problems is not itself well enough specified to be solved with a formal algorithm, but I’ve listed the basic steps that an algorithmic thinker takes in tackling a problem:
1. Analyze the problem and define it tightly. What are you trying to find or optimize? What information is available to do so? Are there any constraints? Elegant code is simple code, and simple code removes anything not conducive to meeting the why of the user. E.g., what concrete tools should I use to recruit great technical talent? How do I find a great startup idea? How do stay fit while working an office job? On the ff VC website, we have developed a suite of standardized processes for many of the typical processes that a startup goes through.
2. Break the problem down into components (also necessary for finding the brute force solution). What specific set of steps is required to comprehensively solve the problem? Solving a simplified example can be a useful exercise at this point.
3. Refine your basic solution. Are there any patterns in the brute force algorithm? Are some steps reformulations of other steps or already-solved problems?
4. Recurse these initial steps to the subproblems. Apply steps 1-3 to the steps/subproblems identified in step 3.
5. Implement each subproblem solution. Along the way, it’s important you design your process for repeatability. In a coding context, that means using standard best practices like defining terms (naming variables in a way that makes sense to another reader), adding explanatory notes (commenting), and formatting properly (spacing). More on that below.
6. Test each subproblem solution. Be sure to check boundary cases. Separating code into modules and rigorously testing each allows the programmer to localize errors so that instead of having to search the entire program, he or she need only search one small section. This general principle applies to pretty much any complex system.
7. Critically assess inefficiencies and iteratively improve solutions. Programming often involves returning to one’s work to make further optimizations or adjustments—ie, never being satisfied. , for example, the name of one of the most famous and elegant algorithms in computer science, was the product of decades of iterative improvements by multiple academics. The Lean Startup movement draws from this same philosophy.
8. Once all subproblem solutions have been implemented, tested, and refined, do the same for the overall solution.
How would you modify this rough pseudo-algorithm for solving problems?
While not discrete steps, two best practices are also critical for effective algorithmic problem solving:
1. Document process and results. An example of documentation is the use of metadata, defined by Frank Dilorio’s guide as “data about data and the processes that support the creation of data and related output.” Dilorio notes that designing metadata is “part fine art” and “part black art,” meaning that programmers need both an aesthetic sense and programmer intuition. To be sure, inserting metadata is extra work in the short run, but in the long run it’s a Quadrant II activity which makes your work much more useable.
2. Set up the process for long-term, unmanned use. A final characteristic of great programmers is the ability to sacrifice short-term convenience for the sake of sustainable longevity. Programming that takes easy shortcuts for the sake of expediency (e.g. non-intuitive variable naming or inefficient use of libraries) leads to unscalable, problem-ridden code. First-class programmers create with an eye for the long-term consequences of what they develop. The ability to control impulses and delay gratification is a relatively stable and important trait.
A well-known study found that children who are able to resist the temptation to eat a marshmallow for 20 minutes in order to receive a second marshmallow turn out to be better psychologically adjusted, more dependable, and to score higher on the SAT years later than children who eat the marshmallow right away. Fortunately, it is possible to improve self-control simply by thinking about the world in a more global, abstract, and high-level way.
Given the efficacy and broad applicability of algorithmic thinking, I think it should have a place in the standard academic curriculum. Here’s a proof: it’s common for employers and VCs in some of the industries with the highest recruiting standards (software, strategy consulting, finance) to hire/back people who have degrees in disciplines like philosophy, physics, and electrical engineering. This is surprising since those professions have virtually nothing to do with those intellectual disciplines.
The reason employers do this is that certain disciplines like those listed provide training in algorithmic thinking, and employers/VCs assume that if you can master those disciplines you’ll be able to master the skills to work in the specific functions for which they’re recruiting. The four highest-paying degrees in 2012 are engineering, computer science, physics, and mathematics. The marketplace clearly values them, even though relatively few students with degrees in physics or math actually work in a job that requires only those skills.
As Prof. Cathy Davidson of Duke points out, our current gold standard for large-scale testing, multiple-choice tests, was invented in 1914 on the model of the assembly line. Its creator characterized it as a way of assessing lower-order thinking. Indeed, multiple-choice tests reward rote learning.
Why not ask algorithms questions instead wherever possible? An algorithm is right if it works and wrong if it doesn’t, with better algorithms having shorter run times. Algorithmic thinking is process-oriented and exhaustive. It forces students to think meaningfully about problems: they must deconstruct the logical structure of the problem, consider every contingency, and come up with a solution. Because there is rarely a single right answer, students are always creatively engaged in finding more and better solutions. Best of all, algorithms are easy to teach. Michelle Levesque of the Mozilla Foundation, has even started testing out a few strategies to do this.
What else in your life is computable?
Thanks to Matt Joyce for help researching and drafting this, and Joan Xie for initial research. Posted this morning at Xconomy. Graphic: Sudhee.