Stepping stones in possibility space
A luck maximization algorithm
In Possibility Space, we looked at the creative process as a search problem, an exploration through the space of possibility. For example,
Imagine this giant room in which every image conceivable is hovering in the air in one location or another, trillions upon trillions of images shimmering in the darkness, spanning wall to wall and floor to ceiling. This cavernous room is the space of all possible images.
Yet this presents a challenge. Our room of all possible images contains Mondrians, the Mona Lisa and van Gogh’s Starry Night, but it also contains a lot of noise. How best to navigate this possibility space? How do we get to the good stuff?
AI researchers Kenneth Stanley and Joel Lehman explore exactly this challenge through their work on Novelty Search algorithms. In their book, Why Greatness Cannot Be Planned (2015), and in their published research, they offer many insights into how we might effectively navigate possibility space. Let’s take a look…
So, one common strategy for navigating possibility space is the warmer-colder game. To play, you pick an objective, and then measure your progress toward that objective. Line goes up and to the right? Do more of that thing. Line goes down? Do less of that thing. Many of businesses and projects are managed this way.
For the warmer-colder game to work, you need a neatly organized possibility space. If you can travel in the direction of more and more stars, more and more impressionism, and more and more swirls, until you arrive at van Gogh’s Starry Night, then warmer-colder is a good strategy. This kind of neatly organized possibility space is called a continuous search space.
A problem emerges when you apply this method to possibility spaces that are not neatly organized, that are discontinuous. What does a discontinuous possibility space look like? In their paper Novelty Search and the Problem with Objectives (2011), Stanley and Lehman offer the example of navigating a maze.
If you try to navigate this maze by the warmer-colder method, you’re going to move toward the objective, and get stuck against the first wall. Every other direction will look worse, because it will take you further away from your objective. Paradoxically, you must be ready to repeatedly walk away from your objective if you are to have any chance of reaching it.
The idea that an improving score guarantees that you’re approaching the objective is wrong. It’s perfectly possible that moving closer to the goal actually does not increase the value of the objective function, even if the move brings us closer to the objective. (Stanley, Lehman, 2015. Why Greatness Cannot Be Planned)
This challenge of navigating discontinuous possibility spaces is not uncommon. In fact, it turns out that many possibility spaces are discontinuous. Take the history of computing. It is full of discontinuities:
For example, the very first computer was built with vacuum tubes, which are devices that channel electric current through a vacuum. However here’s the strange part: The history of vacuum tubes has nothing to do with computers. People like Thomas Edison who were originally interested in vacuum tubes were investigating electricity, not computing. Later, in 1904, physicist John Ambrose Fleming refined the technology to detect radio waves, still with no inkling of building a computer. It was only decades later that scientists first realized that vacuum tubes could help build computers, when the ENIAC was finally invented.
So even though vacuum tubes are a key stepping stone on the road to computers, few if any could see it coming. In fact if you were alive in 1750 with the objective of building some kind of computer, you’d never think of inventing a vacuum tube first. Even after vacuum tubes were first discovered, no one would realize their application to computation for over 100 years. The problem is that the stepping stone does not resemble the final product.
(Stanley, Lehman, 2015. Why Greatness Cannot Be Planned)
It gets worse. These discontinuities are not a fluke in the history of computing. It seems discontinuities are the rule, rather than the exception. Breakthroughs come from unexpected directions. Reality itself is a discontinuous possibility space!
In such a situation, objectives are worse than useless. They get you stuck.
Objectives actually become obstacles toward more exciting achievements, like those involving discovery, creativity, invention, or innovation… In other words (and here is the paradox), the greatest achievements become less likely when they are made objectives.
(Stanley, Lehman, 2015. Why Greatness Cannot Be Planned)
So if a possibility space is discontinuous, objectives don’t work. What does?
Stanley and Lehman offer us a thought experiment. Imagine a lake. Scattered across the surface of this lake are stepping stones. You want to cross the lake by hopping from one stone to another, but a thick fog hangs over the water and you can only see one or two steps ahead before the fog shrouds your view.
The stepping stones closest to the shore fade gradually as they wind into the fog. As you walk along the course of stepping stones over the water, the shore dissolves from sight behind you even as the other side remains cloaked behind the mist. But here’s the hard part: eventually you come upon a fork where a choice must be made.
Because of the fog, you don’t know where either path leads. For all you know, one might lead you to a dead end while the other eventually might reach the other side of the lake. But even if you make a lucky choice, chances are that more forks will appear sooner or later. When crossing stepping stones in a fog, many critical decisions must be made with little knowledge of where they lead.
(Stanley, Lehman, 2015. Why Greatness Cannot Be Planned, ch 4.)
What are these stepping stones? They are strategies within the possibility space that have been found to work—or as evolutionary philosopher Daniel Dennett puts it—good tricks for survival. Vacuum tubes, clock-making, weaving, semiconductor physics, and the exploration of mathematics for religious reasons were all unexpected stepping stones in the evolution of modern computing.
Some stepping stones might head in one direction before doubling back. Others might loop into paths you have taken before. Sometimes a stepping stone might look like a dead end, only for the fog to later clear and reveal that it leads to stepping stones that were previously out of reach. You never know where a stepping stone might lead.
Another way to look at ambitious problems is to say that their solutions are more than one stepping stone away. (Stanley, Lehman, 2015)
If we try to cross this lake by following only the stepping stones that lead toward our objective, we’ll soon get stuck. But what if we let go of our objectives? What if we focused on trying to find new stepping stones instead? This is novelty search. Instead of looking for something specific, you look for something new.
Novelty search isn’t just random, it’s chance plus memory. Together, these ingredients do something interesting.
Because eventually you have to acquire some kind of knowledge to continue to produce novelty, it means that novelty search is a kind of information accumulator about the world in which it takes place. The longer the search progresses, the more information about the world it ends up accumulating. And of course information and complexity go hand in hand—more complex behaviors require more information.
(Stanley, Lehman, 2015. Why Greatness Cannot Be Planned)
In fact, evolution itself is a kind of non-objective search, in the same family of algorithms as novelty search.
…nature is a stepping stone collector, accumulating steps towards ever-more complicated novelties, marching onward onto the mist-cloaked lake of possible-life-forms, heading eternally both everywhere and nowhere in particular. That’s the signature, now increasingly familiar, of processes that produce amazing innovations.
(Stanley, Lehman, 2015. Why Greatness Cannot Be Planned)
Stepping stones are also combinatorial. Each new stepping stone we discover expands our potential to find even more stepping stones. Collecting stepping stones is a luck maximization algorithm. By collecting and combining stepping stones, we might arrive at our destination by accident, or somewhere more interesting!
Collecting stepping stones isn’t like pursuing an objective because the stepping stones… don’t lead to somewhere in particular. Rather, they are the road to everywhere. To arrive somewhere remarkable, we must be willing to hold many paths open without knowing where they might lead.
(Stanley, Lehman, 2015. Why Greatness Cannot Be Planned, ch 4.)
What if we reimagine note-taking through this lens? Every note you take is a stepping stone, expanding your combinatorial space of possibility.
From this point of view, Subconscious is about building a stepping stone collector. Geists, search-or-create, backlinks… every feature we are building toward is aimed at collecting and combing stepping stones to generate yet more stepping stones. A serendipity engine.
In other news…
Programmable notes: Maggie Appleton explores the idea of notes-as-software. It touches on Subconscious, as well as many other threads we’ve pulled on here, including SCAMPER and Oblique Strategies. It’s great!
Subconscious Alpha 0.0.3 is rolling out with fixes to focus management, animations, and markup rendering. Thanks for the helpful bug reports! “I’ve got to admit it’s getting better, a little better all the time.”
ObservableStore 0.1.0 (new open source release). We’ve been developing this little Elm-like store as the backbone for Subconscious. This release includes new features, refactors, and improvements, based on what we’ve been learning from using it in what is becoming a nontrivial codebase. The new helpers for composing update functions are getting a workout in our code.