Wednesday, March 30, 2011

The Map that Reflects the Territory: Rationality and Belief

The map-territory relation is a useful pedagogical tool that I shall be employing regularly. It illustrates the distinction between a model or abstraction and the thing in itself. A map is a model of a territory and the amount of detail is necessarily compressed. When the two diverge, when my map shows a bridge or path that does not exist, territory supersedes map. Territory is invariant; I cannot manipulate the territory by altering my map.


What does it mean to be a rationalist?

Epistemic rationality is the process of forming and updating beliefs that systematically improves the correspondence between your map and the territory. This correspondence is usually referred to as truth or accuracy.

I will get into specifics regarding the process of belief formation and updating in a later post. What is currently necessary to understand is that the goal of the rationalist is to obtain beliefs that correspond to reality as closely as possible.


Why should you care about that?

Instrumental rationality is the process of actually achieving your values.

Try and imagine the many different places you could be a year from now. The smallest decision you make at this instant will influence the opportunities available to you an hour from now, which can themselves influence later opportunities, Ad infinitum. The space of possible future-selves is practically infinite. 

Now imagine where you would like to be a year from now. The number of future selves that you would be happy with given your current set of values, your utility scale, relative to the number of possible future selves is infinitesimally small.

It is our unfortunate condition that we must reach out and pluck the future that we desire from a massive space of possibilities. The odds of success vary based on the strategy employed. Closing our eyes and grasping a future at random, the probability of achieving our desired goal is close to 0%.

Fortunately for us there is a regularity to the system. We can extrapolate probable results of each choice, focusing on those results most likely to converge on our desired outcome. This has the effect of constraining the space of future-selves to a smaller, weighted sample with a much higher desired/undesired ratio.

The extent to which we can accurately predict the results of our choices determines our probability of success. An increased degree of accuracy will increase the probability of success at a greater than linear rate.

To see how this is so, imagine you are walking down a path.

You must start at the bottom and want to reach the destination that is circled in red. The correct sequence of moves is L R L L. If you make a mistake at any point in the sequence you will not reach your destination.

Lets assume that your prediction accuracy is 50%. The odds of you reaching your destination are 1/16 ((1/2)*(1/2)*(1/2)*(1/2)) or 6.25%.

Now lets assume that your accuracy is 60%. The odds of you reaching your destination are 162/1250 ((3/5)*(3/5)*(3/5)*(3/5)) or 12.96%

Finally, lets assume that your accuracy is 70%. The odds of you reaching your destination are 2401/10000 ((7/10)*(7/10)*(7/10)*(7/10)) or 24.01%

The following results continue the pattern:

80% accuracy = 40%
90% accuracy = 65%
95% accuracy = 81%


This is how Epistemic Rationality works to enhance our Instrumental Rationality. The more accurate our map of the territory, the greater our ability to navigate the territory.


  1. That sounds quite rational. But is life rational? What about roadblocks, what about health problems, what about things not anticipated?
    Life isn't just a straight path where you get to choose your destination based on a set of probabilities and percentages, life is complicated and complex. Sometimes quite messy, unpredictable, and ever-changing. ???

  2. It sounds like you're mapping out a car trip to a destination. But cars break down, weather interferes, life just isn't as perfectly organized as your theory suggests.
    So... are you laying the groundwork and I'm jumping the gun? But even the groundwork just sounds too simplistic for real life to me...

  3. What you are noticing is that the amount of information available in real life is severely limited. When planning to make a decision it helps to have as accurate a model of the world as possible, so that your predictive accuracy is maximized. Sure, you won't be able to obtain all the relevant details. If you are trying to get help during an emergency, picking up the phone is still a better choice than attempting contact via astral projection, even if the phone is dead a small percentage of the time.

    For every decision, whether devised under conditions of absolute or imperfect information, there is a strategy that maximizes success. This is called a Nash Equilibrium and I will get into more detail in a later post, but all I was trying to communicate in the current post is that having a more accurate predictive model is always better than having a less accurate predictive model.

    The game towards the end of my post was obviously simplified and used only to illustrate the one point, that in a series of decisions having a map of the territory that is 60% accurate is better than a map that is 50% accurate and so on.

  4. Perhaps it would help if you could quote a specific part of the post that you either disagree with or find unsatisfactory? If your objection is that you don't see how it applies to conditions in real life then I will write several examples for my next post that will demonstrate the principle.

  5. Yes, that's pretty much how I feel; I don't see how this map could really work. Because life, as I have seen it, has a pretty high percentage of unpredictability, and change is pretty much a constant. You can shoot for the moon, and hit the woodpile, so to speak, but to try to figure out your future and your values with mapping and percentages doesn't make sense to me, as well as taking the "life" out of life! Part of the depth and keeping it interesting is the unknown, the mystery of it all. Otherwise we are too similar to robots, and besides being distasteful, that isn't even possible in my mind. Life is wonderful in it's unpredictability, and I don't understand why anyone would WANT it to be predictable and scientific. It's LIFE! And we only have one to live.

  6. You should read the following article. I'll get into your first concern in my next post which will hopefully address the issue. As for mysteries being wonderful, please read the following articles (when you have time). I think they are very important to read and digest.