Impossible vs Unsolvable Problems

A few years ago I was quoted as the guy who finds ways to solve impossible problems.” And I stand by that. Lately I’ve been working hard to avoiding getting mired in unsolvable problems. There is a difference, at least to me. Let me explain.

Impossible problems look hard because the path is steep and rocky. Most people see a problem as describe it as impossible, but a better descriptor is “impassible.” They can’t see an easy way to solve it, and others have tried, so they label it so. This is perception, driven by lack of creativity. I can handle those, because I usually avoid the straight path.

In contrast, unsolvable problems are of a different kind. Someone who understands the limits of math or order in nature says they can never be solved. You can’t travel faster than the speed of light. You can’t find the next largest prime number. And you can’t rapidly find the optional solution in a fitness landscape (NP-complete).

impossible vs unsolvable

Metaphorically speaking

Imagine climbing a mountain. You can see the summit. From the start, you know which direction you need to go. You know there’s a view at the top. Each step takes you closer to your goal. The climb is hard. These are “impossible” problems.

If instead, someone tells you there is buried treasure in the field, you can strike it rich if only you dig in exactly the right place. It’s easy to know if you are in the right place, if you take the time to dig. But do you want to dig up the whole field? Yet many people do exactly that when they pursue unsolvable problems with no map.

Knowing how to see the difference between these two is the secret to not wasting time. Whenever someone wants a “definitive answer” at applies everywhere, it is usually unsolvable. In contrast, nature takes a creating the perfectly adapted organism. This is why nature is still evolving. It doesn’t look for perfection – but rather – consistent experimentation in which better organisms beat out weaker ones most of the time. Over the long haul, this is more efficient that digging up the whole field. It’s climbing a mountain under clear skies.

Whereas I think it is inevitable that we will write computer programs that will read the emotions on peoples’ faces in videos and transcribe their words into text, accented by the emotions they express audibly, I don’t think we’ll write a program that will interpret what thousands of people are thinking and come up with a solution for global poverty on its own. I don’t think we’ll ever discover the solution to global poverty, period. We will be able to come up with a thousand small tweaks to society and culture and microeconomics and health and education that make poverty less crushing in each coming year, but the end of poverty – not gonna happen (unless we transform basic human morality, but that’s another tactic altogether).

If we assume that our basic human morality remains constant, no optimal combination of “development interventions” will be found. If morality did change, and people began to think of the meaning of life as a journey to become a higher moral being, sacrificing our needs and wealth in that pursuit, a totally different outcome is possible. But without that, we’re better off doing a lot of good small experiments and recycling what seems to work into the next idea as fast as possible. It is not our resources, but our inability to adapt to this new information that remains the barrier to better lives for the bottom billion.

That’s not a palatable conclusion for those who spend so much time seeking out more money to do more stuff inefficiently for people, with no interest in how their limited piece of the total human experience might transform our collective understanding of the problem, writ large. We resist hive learning in favor of individual progress. It feels bigger to move the people you know out of poverty than it does to move everyone’s understanding of poverty a little bit farther, and so knowledge remains fragmented, like loose change in your pocket, not credit in an account.

Feedback Labs

At Feedback Labs, we aim to prove that listening to the people you serve is the right thing, the smart thing, and the feasible thing. But one of these is closer to impossible to prove than it seems.

Feedback is feasible, and it is moral. But I don’t think proving it is truly smart is going to settle the question. It would be better to prove that everything else is dumber, less reliable, more foolhardy, as an approach. Smart solutions fill in a big “problem space” of thousands of possible solutions. Evolution doesn’t look for the ultimate answer to a question, or perfect solution. It looks for the means to spread the question out across tons of parallel examples, each one a possible solution. Then it waits. And when waiting is filled, the best available answer for the time is revealed. In most generations, this answer isn’t very smart. It just needs to be smarter than alternatives around it. And like the tortoise and the hare, evolution wins in the end.


Take a real world example: SpaceX. Author Neal Stephenson recently wrote about the future of rocketry in

…our current proficiency in rocket-building is the result of a hill-climbing approach; we started at one place on the technological landscape—which must be considered a random pick, given that it was chosen for dubious reasons by a maniac—and climbed the hill from there, looking for small steps that could be taken to increase the size and efficiency of the device.

hill-climbing-fitness-landscape-spacexSixty years and a couple of trillion dollars later, we have reached a place that is infinitesimally close to the top of that hill. Rockets are as close to perfect as they’re ever going to get. For a few more billion dollars we might be able to achieve a microscopic improvement in efficiency or reliability, but to make any game-changing improvements is not merely expensive; it’s a physical impossibility.

Stephenson is referring to this fitness landscape model from both evolutionary biology and complexity theory to explain why Elon Musk’s approach is the right way to drive down the cost of space flight. Any given peak in the image represents an optimal solution, but there can be different peaks (i.e. different solutions), some of which are higher (aka better) than others. To move from one local peak to another (higher) peak, it requires a temporary loss of efficiency (or “fitness”) to start scaling the other peak.

This is seen by outsiders as failure. It is an impossible task to optimize from top of any one peak and end up on top of a distant, higher peak without breaking apart the designs and making a lot of inferior intermediate steps. However, given the freedom to fail and the time to iterate, this impossible task can certainly be solved. What is an unsolvable problem is to develop a magical way to jump from one peak to a higher peak far away. Yet leaders in our world manage as if that is the only kind of goal we can live with.


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