The “Convergent” theory of finding truth in darkness
29th June 2012 · 0 Comments
How do you know if your startup idea is a good one? Even after twenty customer interviews?
How do you know when to hang up the towel and try another idea?
The usual answers: It’s a balance. Trust your gut. But your gut is wrong so trust data. But you don’t have enough data so trust your gut. Don’t give up just because it’s hard. Don’t push if it’s too hard.
Follow this formula. The formula says there’s no one formula. The formula is to ask “the right” questions. The formula doesn’t know what to do with the answers. It’s different for everyone.
Until recently I haven’t had a good way to explain my idea of the answer. But recently I was rereading Feynman’s Lectures on Physics and, in one of those brief flashes of comprehension that comes when your mind is wandering yet active, I stumbled across the explanation.
The fun way to explain the answer is to paraphrase Feynman himself, because the point he makes is in itself fascinating and deep. And as you’ll see by example, it turns out to directly answer to the questions above.
It is an astounding fact that the force of drag on an airplane is proportional to the square of its velocity in air. That is:
Fdrag = Cv2
It’s amazing because it’s such a simple formula for such a fantastically complex environment. Not just the curving surfaces, but every bump on the wing splits and twists the air which then interacts with itself. The drag-inducing chaos of swirling fluid is so convoluted that even modern simulators can’t model it precisely.
It is almost unbelievable that an airplane in a wind tunnel reveals a characteristic constant
C in such a simple law.
Humans love this sort of thing — emergent simplicity from multivariate chaos. There’s beauty in its brevity and power in its utility. We love it so much, the urge is in constant overdrive, and we see patterns and meaning even when there’s none.
We’re tempted, therefore, to call
Fdrag = Cv2 a “law” — a rule by which a mere human brain can get a handle on a phenomomon too complex for the fastest supercomputers.
But it turns out it’s not a law at all. It’s not power, it’s a tenuous coincidence, and not one of great utility.
How do we know this?
Because as soon as we try to understand similar situations using this law, we run into its limitations. If the airplane is flying slowly, it becomes completely inaccurate. If the airplane flies very fast it’s wrong again. If we make small perturbations on the wing the constant can change dramatically.
Perhaps most surprising is that if you physically remove one of the wings, that changes the drag on the remaining wing. There are forces inside and outside the aircraft, hidden to a casual observer, uncaptured by simple formulas.
Where is all this in our “law?” Nowhere. If we step outside our little cocoon, the law crumbles. It’s not a fundamental law, because it does not predict what happens in novel situations.
Contrast this to another so-called law — the Conservation of Energy — which states that the total energy of a system is constant. So if a ball falls in a gravitational field, as it loses potential energy it gains kinetic energy such that the total energy never changes.
Is this a true “law?” How can we tell?
We can make a complex series of ramps inside a vacuum, starting a ball at different heights and positions and letting it roll down and up and around, measuring the velocity the whole time. We find that the ball’s speed everywhere exactly ensures the two energies remain equal, regardless of the configuration of the ramp. This feels powerful — even in an arbitrary configuration, the law still accurately predicts the result.
With a real ball and a real ramp, friction slows the ball, thereby reducing total energy and therefore a violation of law! Ah, but we realize that “heat” is also energy — something we can measure and convert into other forms of energy — and when we measure the increase in heat in our experiment (in the ball and in the ramp) we find that the energy due to heat exactly replaces the energy lost as the ball slows, and again our law is correct. In fact, our law predicts how much heat, and we find exactly that amount, so now the law has just predicted the existence of new kinds of energy, and did it accurately, which is even more impressive!
Then from other experiments we have evidence that matter is in fact composed of gargantuan quantities of tiny objects, moving and colliding and vibrating. That suggests a different definition of heat itself — that it’s not a “new” form of energy at all, but rather the total kinetic energy from jiggling particles! Under this hypothesis we can make definite predictions about how much energy heat contains, how heat and particle density and pressure would have to change in a gas under various conditions, and so on, all on the sole basis that energy must be conserved, and in fact those predictions all prove accurate!
Even in the modern era with relativity bending and weaving time and space and quantum mechanics so strange that Feynman himself said that no one really understands it, still the conservation of energy has always been found to be perfectly correct.
With the drag-force equation, the deeper we dug the more we discovered that the “law” doesn’t encompass much truth; with the Conservation of Energy we found that the closer we look and the more we stretch ourselves the more powerful and simple the law becomes, the more applications we have for it, the more predictions it makes, and that is the characteristic of a bona fide fundamental law of the universe.
Truth in startups emerges or crumbles in the same way.
Specifically, before I validated the ideas behind WP Engine, I validated another idea for a startup. The key thing to notice is that during my customer development, everyone said “That’s a great idea, you should do it!”
Except, as I dug in with each person, the “truth” started diverging. One said I should target enterprises, charging $1000/mo and selling through consultants. One said I should make it freemium and figure out how to make money converting 5% to $5/mo. Another said charge a minimum of $50/mo to cut out the moochers who email support but don’t pay for stuff. Another said the small-to-mid-sized business market is the untapped niche. One said I should use it to measure online ads and forget about measuring leads; the next said I should use it to feed leads to salesforce.com and forget about measuring marketing efforts; the next said I should use it to reveal marketing efficacy and not try to close leads.
Like the airplane law, I had discovered something intriguing, even exciting, but not something fundamental, not something with clear steps forward, not a Venn Diagram of ideas creating a large, dark area scintillating with lumps of variation, but rather a blotchy Venn Diagram with twenty lobes of dissonance.
But my experience vetting WP Engine was convergent. The more people I spoke with, the more agreement there was over the pain they had, whether my solution was an acceptable, and the the amount they were willing to spend. $50/mo to make a site fast, scalable, secure, and someone who knows WordPress to answer the phone. Kick in a staging area and backups and it’s a done deal. Thirty of forty people agreed to sign up during their interview. (Twenty of the thirty later did.)
I had found the startup equivalent of a fundamental law — not an immutable physical law of course but something that behaves like truth — where multiple areas of inquisition lead to a common destination instead of leading to different planets. Whereas before I had an idea with the behavior of a curiosity with no power behind it.
Of course there’ll be no rubric to determine whether an idea is tenable or whether the situation is so bleak that you should give up. But in my experience this feeling of convergence or divergence is very strong if you’re being introspective and honest with yourself.
Your hardest battle is in fact with yourself, as you’re constantly tempted to bias the evidence in the most convenient direction (validation), and your fear of figuring out that your pet idea, while undeniably cool, is not a business, in the sense that other people don’t agree enough to give you money for it.
Just remember how expensive it is to blind yourself. Your project will meet the same end, only after a significantly larger investment in time, money, heart, and reputation.
How do you answer those questions? Let’s discuss in the comments.