How should we understand the oracle's dilemma in making a prediction?

Question

Let's look at a thought experiment:

There is an oracle who has exact knowledge of the state of a deterministic universe, so her predictions about the universe's future have always turned out to be correct. One day, John approaches the oracle and asks, "Can you tell me whether I will raise my hand in 1 minute?" The oracle, with her uncanny vision, however, sees this: John's brain circuits are in such a state that when he hears "Yes" or anything that he understands as on the affirmative side (such as "Of course", "You will", "I think so", etc), they will react in a way that keeps his hands down, and vice versa. The oracle therefore replies that although she knows the answer, she can't tell him because his brain is in such and such a state. But she can secretly write down her prediction on a piece of paper for him to check that it conforms to his choice later.

At any point in time, the oracle surely knows the future perfectly. So intuitively we would expect her to be able to give us a definite answer to a naive question like whether certain things are going to happen in the future. But the above example indicates there's no way she could achieve that despite of what she knows. How should we understand this? In the following I give my thoughts on this. I'd like to hear your comments and critics. Any other thoughts and ideas are welcome.

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The Yes/No answer (prediction) given by the oracle plays a dual role:

1. As a physical influence on the deterministic world. For instance, a "Yes" travels as some particular vibration of the air and reaches John's brain, causing certain changes and reactions there accordingly.
2. As a piece of information whose semantics stands as a testament to the oracle's prediction.

When the oracle is sufficiently autonomous, not exerting relevant physical influence on the part of the universe she's trying to predict, her prediction plays only role 2. But if she's going to answer John, role 1 becomes inevitable. In the above example, the prediction as a physical influence on the universe happens to cause it to evolve in a way that contradicts the semantics of the prediction. Notice that this reasoning has nothing to do with so called free will whatsoever. It is only the structure of the (deterministic) universe and semantics of language that make the prediction impossible.

But what's the implication? Can we conclude that we can't expect the oracle to answer arbitrary questions about the future, even though, or should we say, precisely because, she is omniscient? Or there always will be questions about the future that will remain unknowable to you, even with the help of the oracle? People have been written much about oracles and prophecies since ancient times. It is interesting to note that many of them work in mysterious ways, writing their prophecies only in the form of obscurely ambiguous poems or nearly inscrutable text. I'd like to think perhaps a real oracle will be just like that, bound to write down her knowledge in a strange way.

Answer 1

In the example, the oracle is part of the universe, that is, she plays your role (1). There are then two options:

1. She is governed by the same deterministic laws as the rest of the universe.
2. She is non-deterministic in some way, although the rest of the universe is deterministic

The latter option seems a non-starter to me -- in that case, given that the Oracle causally interacts with the universe, her being non-deterministic means that the universe as a whole is non-deterministic. There doesn't seem to be any easy way to separate out the parts of the universe which she affects (and thus which are non-deterministic) and those that she does.[1]

So then, the oracle herself is governed by deterministic laws. There might be some contradiction to tease out here, which would prove that such an Oracle is impossible (just like Russell's barber 'paradox' proves that there is no such barber). But I think that everything is consistent. But we need to distinguish between a few kinds of Oracle:

1. She knows every true about the universe; when queried 'p?' she may reply 'yes' or 'no', but she may lie. That is, she may reply 'no' when p is true, or 'yes' when p is false. (Perhaps though, most of the time she replies truly.)

2. She knows every truth about the universe; when queried 'p?' she will give one of three responses:

   1. 'yes', only if p is true
   2. 'no', only if p is false
   3. 'maybe' in any circumstance

3. She knows every truth about the universe; when queried 'p?' she will give one of two responses:

   1. 'yes', if and only if p is true
   2. 'no', if and only if p is false

Your nice thought experiment shows that there can be no Oracle of type (3). (Or that the universe conspires in such a way that the sort of situation you envisage does not arise.)

[1] One way would be to say that anything outside of her forward lightcone is deterministic. But I expect that many complications would result from trying to work out the details of this. I leave it as an exercise to the reader to do so...

Answer 2

I see three serious problems with this oracle machine.

1. She contains a full model of the universe that is informationally isomorphic to it. She herself should be a part of this model as a part of the universe. This part is also equivalent to the universe. And so on - infinite regression in models that are equivalent to the whole. Perhaps, this situation is OK – a familiar fractal behavior, but it looks very problematic.

2. She can predict the state of the universe after 1min. She arrives to this prediction in, say, 0.5min. However, when she runs her calculations she knows at 0.25min the state of the Universe at 0.5min; this means that at 0.25min she knows her answer that she delivers at 0.5min; this means that, in fact, she can deliver her answer in 0.25min. And so on, infinite regression. Therefore, the prediction does not need any time delay at all. The oracle is immediately ready to say everything about the Universe in whole its time existence - the oracle is informationally equivalent not only to the current moment state of the Universe, but also to all its states. Perhaps, one can say that this situation is OK – there are no contradictions; anyway, I find it very problematic.

3. If the oracle machine, which predicts the situation after 1min and delivers this prediction in 0.5min, influences various decisions of the people and disturb her own prediction, she acts as a time machine that gives way for future effects affect their past causes. This means that the hypothesis about 0.5 min delay is wrong and the oracle can deliver her answer not early than in 1min, at that moment when it becomes useless.

(3) seems to contradict (2). Perhaps, there are some holes in these reasonings, but I am pretty sure that this oracle machine is impossible.

Answer 3

Perhaps this explains the particle-wave duality and the two-slit experiment: if we ask the universe to tell us the future, it sidesteps the question.

If John was thinking ahead, he would realize that no matter what the Oracle said, in order to defeat it he would need to both raise and not raise his hand, because prediction leads to an infinite loop in this case. Wisely then, we would become a Zen Buddhist and unask his own question, bow to the Oracle and walk on.

Answer 4

It seems to me that John's humanity is both irrelevant and potentially misleading here, so let's replace him with a machine.

So: Here I have a machine with two buttons labeled B and R. If you push the blue button, it flashes a blue light. If you push a red button, it flashes a red light.

You claim to know everything about how the machine works and everything about your own decision-making.

I say to you: "Okay, let's test that. If you think the machine is going to flash blue, press the R button. If you think it's going to flash red, press the B button. Then we'll see if your prediction is correct."

Or maybe we don't even need the machine. You claim to be able to predict when you'll scratch your ear. I say "Okay, let's test that. If you're going to scratch your ear at 2PM, please indicate that by not scratching your ear at 2PM. If you're not going to scratch your ear at 2PM, please indicate that by scratching your ear at 2PM".

It seems to me that these paradoxes (or pseudo-paradoxes?) are not essentially different from yours, but might help to clarify the issues.