Calculus vs. Statistics

If you have more than a passing interest in the future – be it yours, your venture’s, or humanity’s writ large - Peter Thiel’s CS183 lecture #13, “You Are Not A Lottery Ticket” is a feast for thought.  Thiel interrogates the underpinnings and consequences of determinate and indeterminate worldviews in numerous contexts, including as they apply to startups. 

For the aspiring tech entrepreneur, one of the most useful frameworks Thiel invokes is that of calculus (determinate) vs. statistics (indeterminate).  In calculus, you make precise determinations, often concerning discrete futures.  You can figure out exactly how long it will take to drain even the most irregularly shaped swimming pool.  And this enables you to do things of vital importance.  As Thiel notes, when you send a rocket to the moon, you need to know where it is at all times – you can’t just figure it out as you go.  In statistics, on the other hand, there are no certainties.  It’s about bell curves, random walks, and drawing an often uncomfortable line of best fit between limited data points.  Thiel furthermore notes a powerful societal shift towards the belief that statistical thinking ways of thinking will (and should) drive the future.   

The example of landing a rocket on the moon is probably no accident. The 1950s and 1960s (coincidentally the first golden age of Silicon Valley) were a time of widespread American optimism.  The moon landing was a fundamentally optimistic venture that captured the American imagination (and quite literally would not have happened without calculus).  It only makes sense, then, that statistics would be the dominant modality of the cynical world we now inhabit.  If you look at the natural disasters, economic collapses, terrorist attacks, and disease outbreaks of the 21st century, some might seem more or less predictable by conventional wisdom, but the popular perception is that humanity was caught napping, apart from a few obscure Cassandras.  Especially in light of the truism that we’re usually planning for the crisis that just happened, it’s easy to see the appeal of the indeterminate/statistical model.  Statistics couldn’t have predicted exactly which bad things would happen, only that some bad things would happen.  

It’s enough to make you throw up your hands, yet this is exactly what Thiel is not arguing for.  This should come as no surprise. Thiel is a renowned contrarian, and many of his greatest interests reflect a healthy disregard for statistical/indeterminate thinking, life extension being a prime example.  The conclusion of the lecture begins with an acknowledgment that as we embrace the statistical worldview, society is sliding into pessimism, and without indulging in too much pop psychology, it’s easy to see how such thinking becomes self-fulfilling.  The lecture ends with an appeal to “definite optimism”, and posits that computer science offers the best hope.  CS is not only a great way to solve problems, but as Thiel observes, its fundamental determinism may have something to teach startup culture, which is widely presumed to be governed by indeterminacy.

Of course, software itself is greatly misunderstood, and this is one of the primary challenges computer scientists face as entrepreneurs. People who don’t understand software assume that its value is statistical by nature, and fundamentally unknowable (in contrast to hardware, for example).  If you’re a math phobic, single-variable calculus and E = mc2 are just two things you don’t understand, and the differences and relative complexities are immaterial.  To make matters worse, people who truly understand software are relatively rare, especially among those with purchasing authority, and this unknowable fallacy leads to a sort of permanent agnosticism in principle as applied to software.  Within the statistical frame, it’s assumed that two competing software packages lie in the same general area of the bell curve, and therefore the differences are negligible or at least unknowable.  You know that the value of software follows power laws and the differences between good and great are logarithmic, not linear, but the statistical frame ignores all of this.

One consequence is extreme risk aversion: if you believe that the relative merit of one kind of software isn’t calculable, you stick with what you already have, and this has plagued many otherwise forward-thinking institutions.  There is also the simple matter of what’s tangible.  To the layman, hardware seems straightforward, whereas software doesn’t (even if hardware may owe much of its performance to superior software).  As a result, hardware is often seen as a reasonable expenditure, whereas software isn’t.  No one blinks at a $50 million aircraft, even if that aircraft is agreed to be 1980s technology, whereas $50 million for software is not only unthinkable to many, but being newer and better may very well work against you, due to the unknowable fallacy.  

For the aspiring software entrepreneur, there are a few takeaways.  It’s a fact of life that software is misunderstood and undervalued.  However, that doesn’t mean quality doesn’t matter.  In fact, it matters more than ever.  The challenge is that when you are up against a heavy incumbent, it’s not enough to be 10% better – you have to be 10X better, because ultimately your success is dependent on enough people feeling strongly enough about your product to risk rocking the boat.  Earlier we discussed that the idea of any complex product being great enough to sell itself is a myth, and again, concluding that being great is unimportant is absolutely the wrong lesson.  Put another way, if you want to bring people around to viewing software through a calculus frame, you have to make their daily existence demonstrably better.  But wasn’t this always the goal?

This brings up a final point about determinacy: some things are worth doing regardless.  In the last CS 183 class, “Stagnation or Singularity?”, Thiel is joined by several guests, including Dr. Aubrey de Grey, gerontology expert and Chief Science Officer at the SENS Foundation.  De Grey makes the point that while we may have a fair idea what technologies will be developed, the timeline for development is much more tenuous and subject to various externalities.  However, he concludes (paraphrased), “In a sense, none of this matters. The uncertainty of the timeline should not affect prioritization. We should be doing the same things regardless.”

Once again, it all comes down to doing important things, and when this is the stated goal, the inherent pessimism of the statistical approach becomes apparent.  This applies to your own life as well as it does when building a company.  If you wanted to take the statistical view to its logical extreme and hedge against all possible uncertainties, you’d become a jack of all trades/master of none, and consciously choose not to go long on any particular superpower or world-changing problem. If the goal is to live an inoffensive, comfortable life, this might makes sense.  If you want to do anything of lasting value, this is crazy.  In some ways, it’s easier to grasp this concept when designing new technology or building a company – although it’s easy to suffer from too many features or too many business models, most entrepreneurs accept that trying to be all things to all people is a recipe for failure (as software development illustrates so neatly).  Technology needs a problem to solve.  You, on the other hand, are not a problem to be solved – yet what to do with your time and gifts is perhaps the most worthwhile problem of all.