Skip to content
Pathfinding
Blog

Stepping stones in possibility space - by Gordon Brander

Stepping stones in possibility space - by Gordon Brander

Section titled “Stepping stones in possibility space - by Gordon Brander”

Metadata

Section titled “Metadata”

Highlights

Section titled “Highlights”
  • 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)

    • Tags: #favorite
    • Note: Hill-climbing problem
  • 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)

  • 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.)
  • 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. Novelty search isn’t just random, it’s chance plus memory. Together, these ingredients do something 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)

  • 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. Subconscious is 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.