Apparent uselessness

The illusion of progress, and the difficulty of finding your way in complicated and unknown spaces.

Last year I picked up on Kenneth Stanley’s and Joel Lehmann’s 2015 book called Why Greatness Cannot Be Planned - The Myth of the Objective. In the book they develop an argument for an advanced teleology based on experiments with synthetic processes of knowledge acquisition in the context of AI, ALife, and Learning. The argument roughly says, that if you want to reach a goal, that is ambitious in the sense that the exact sequence of steps (the route) which will get you there, is not known, then accumulating possible steps is a better strategy than heading directly into the direction of the goal. That’s because chances are, that some of these steps will turn out, but unforseeably so, to be precisely what is needed to make the next move when negotiating the route. So far so good, I agree with this line of reasoning.

In the meantime, additional manifestations of that same idea keep popping up urging the collector inside me to collect. Here we go.

  • 2015 Stanley and Lehmann argue that, considering results on “novelty search” in learning experiments with artificial agents, unreflected measures of the distance to a given “goal” are bound to get you stuck in a local extremum in all but trivial cases 1.
  • 1939 Abraham Flexner’s article “The usefulness of useless knowledge” 2, published in Harper’s issue 179 June/November 1939 (available online as PDF). Flexner curiously sketches out a similar line of argument as Stanley and Lehmann reinvigorating satisfaction of curiosity as a sufficient and ultimately fruitful guide in the pursuit of knowledge.
  • 198X The field of media archaeology has been promoting the stance that complex techno-mathematical media can only be understood by reconstructing original forward-looking perspectives and emphasizing the genealogical importance of developments which became “dead media” only in hindsight.
  • 2007 Nicholas Nassim Taleb, deserving a separate comment on the black swan idea (2007), meticulously expounds the difference of the forward and the retrospective narration and substantializes the phenomenon of unpredictability in the domain of complex systems (Extremistan). Honouring this fundamental unpredictabilty we should be highly doubtful about our ability to predict the future utility of any given idea.
  • This is an open list and this entry is a placeholder for things to come …

Realizing the validity of this issue there are fundamental consequences for many areas of human activity, two of which are: autonomous robotic learning (no universal recipe) and funding of professional and amateur scientific pursuits (no maps for uncharted territory 3).

Spectrum of difficulties in reaching goals

Based on my own understanding of different learning problems for artificial agents there exists a spectrum of difficulty, open to the top, along which learning tasks can be positioned. In that spectrum we can draw a line somewhere separating two types of such problems. Update [2016-11-03]: There is a direct correspondence here with the complexity of functional relationships which could be ordered like linear, monotonic, non-monotonic, zero/random. The line that I am referring to above goes through the spectrum between monotonic and non-monotonic problems.

There are those problems, in which the goal-seeker (agent) and the goal are alone in “free space”, meaning that the goal is visible to the agent and the goal can be reached by following a monotonic gradient, that is, by greedily reducing the distance on all axes of space independently, reducing the problem to finding out about the effects of the primitive actions (SMP) available to the agent.

The other type are those in which other objects, usually referred to as obstacles, are present in the same space. Here already no universal recipe whatsoever can be given on how to reach the goal without exploring the space first and building a map. In order to reach a goal or desired destination, the distance to the goal has to increase on at least one axis of the given space at some point (non-monotonicity). This means, that if the wrong distance measure is used, you easily end up in a local extremum.

This issue also seems related to a) convexity, leaving the respective reasoning and diagram as an exercise for a possible later post, and b) to Franz & Mallot’s navigation hierarchy from their 2000 paper 4.

Comments

Footnotes

  1. See this section ↩

  2. Thanks Giulio Sandini. ↩

  3. Please describe in precise steps how you are going to reach an objective (draw a route on a map), which at best is likely to exist and usually is only a vision, and where no one has gone before (on parts of the map labelled “Terra incognita”). ↩

  4. Biomimetic robot navigation. M. Franz, and H. Mallot. Robotics and Autonomous Systems 30 (1-2): 133-153 (2000) ↩

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