This post seems made to order to apply recently acquired knowledge. If I come across as pedantic, please attribute that to learner's thrill. From Probability Theory:

"Seeing is inference from incomplete information". -- E.T. Jaynes

Your usual sensory information is inadequate data. You're dealing with that every day. This seems a good starting point to generalize from; brains in vats seem like overkill to approach the question.

Alice and Bob are faced with a scenario of decision in uncertainty. Probability theory and decision theory are normative frameworks that apply there. All the information you've given is symmetrical, favoring no choice over the other.

  • Should Alice or Bob do anything at all ? That depends on the consequences to them of guessing one way or the other, or not guessing at all. If the outcomes are equally good (or equally bad) guessing randomly is optimal.
  • Should they act differently ? There's nothing in the information you've provided that seems to break the symmetry in uncertainty, so I'd say no.
  • Should they circle more than one color ? ... And other variants - you've given no reasons to prefer one outcome to another, so in general we can't say how they should act.
  • If Alice and Bob could coordinate ? They would (as far as I can tell by assessing the information given) have no more definite information by pooling their knowledge than they have separately.

Very well-put, Morendil. The decision one should make here depends on the consequences of erring one way or the other and so there's insufficient information. One quibble though:

Your usual sensory information is inadequate data. You're dealing with that every day. This seems a good starting point to generalize from

It's true, but I don't think there's anything such as "adequate data" to compare to. In a sense, all data is going to be inadequate. David MacKay's cardinal rule of information theory is, "To make inferences, you have to ma... (read more)

0MrHen10yAgreed. Brains-in-vats was one of the original questions that I was pondering and the specific questions were narrowed into goofy sensory data. Narrowing that down provided the two scenarios. What I find interesting is that Bob has more information than Alice but is stuck with the same problem. I found it counter-intuitive that more information did not help provide an action. Is it better to think of Bob as having no more information than Alice? Adding a memory of Blue to Alice seems like adding information and provides a clear action. Additionally adding a memory of Red removes the clear action. Is this because there is now doubt in the previous information? Or... ? Why wouldn't Bob circle both Red and Blue if given the option?

Reacting to Inadequate Data

by MrHen 1 min read18th Dec 200921 comments


Two Scenarios

Alice must answer the multiple-choice question, "What color is the ball?" The two choices are "Red" and "Blue." Alice has no relevant memories of The Ball other than she knows it exists. She cannot see The Ball or interact with it in any way; she cannot do anything but think until she answers the question.

In an independent scenario, Bob has the same question but Bob has two memories of The Ball. In one of the memories, The Ball is red. In the other memory, The Ball is blue. There are no "timestamps" associated with the memories and no way of determining if one came before the other. Bob just has two memories and he, somehow, knows the memories are of the same ball.

If you were Alice, what would you do?

If you were Bob, what would you do?


More questions to ponder:

  • Should they do anything at all?
  • Should Alice and Bob act differently?
  • If Alice and Bob could circle more than one color, should they?
  • Would either answer change if the option "Green" was added to the choice list?
  • If the question was fill-in-the-blank, what should they write?
  • If Bob's memories were of different balls but he didn't know which ball was The Ball, should his actions change?
  • If Alice and Bob could coordinate, should it affect their answers?

Further Discussion

The basic question I was initially pondering was how to resolve conflicting sensory inputs. If I were a brain in a vat and I received two simultaneous sensory inputs that conflicted (such as the color of a ball), how should I process them?

Another related topic is whether a brain in a vat with absolutely no sensory inputs should be considered intelligent. These two questions were reduced into the above two scenarios and I am asking for help in resolving them. I think they are similar to questions asked here before but their relation to these two brain-in-a-vat questions seemed relevant to me.

Realistic Scenarios

These scenarios are cute but there are similar real-world examples. When asked if a visible ball was red or green and you happened to be unable to distinguish between red and green, how do you interpret what you see?

Abstracting a bit, any input (sensory or otherwise) that is indistinguishable from another input can really muck with your head. Most optical illusions are tricks on eye-hardware (software?).

This post is not intended to be clever or teach anything new. Rather, the topic confuses me and I am seeking to learn about the correct behavior. Am I missing some form of global input theory that helps resolve colliding inputs or missing data? When the data is inadequate, what should I do? Start guessing randomly?