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 make assumptions." No matter how much data you get, it's going to be building on a prior. The data must be interpreted in light of the prior.

Human cognition has been refined over the evolutionary history to start from very good priors which allow it very accurate inferences from minimal data, and you have to go out of your way to find the places where the priors point it in the wrong direction, such as in optical illusions.

I wouldn't call it a quibble: I agree. There is a lovely tension between the idea that all perception, not just seeing, is "inference from incomplete information"; and the peripatetic axiom, "nothing is in the intellect that was not first in the senses".

The only way to have complete information is to be Laplace's demon. No one else has truly "adequate data", and all knowledge is in that sense incertain; nevertheless, inference does work pretty well. (So well that it sure feels as if logic need not have been "first in the senses", even though it is a form of knowledge and should therefore be to some extent incertain... the epistemology, it burns us !).

Reacting to Inadequate Data

by MrHen 1 min read18th Dec 200921 comments

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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?

Variations

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?

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