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[Sean Mirrsen]

What's 1÷0 then? ∞/2?

No, really, any number divided by a zero is either zero or infinity (infinity and zero being on opposing ends of the spectrum, not taking -∞ into account, and multiplication being the opposite of dividing, dividing by the opposite of infinity would produce the same effect as multiplying by infinity - we then get to the uncomfortably odd point that infinity*0=1?..)

I mean, if you look at the problem logically:

x*∞=∞
x*0=0
x/∞=0
ergo, x/0=∞

[Muz]

No, it's not a number, because it breaks mathematical laws. It approaches infinity as it gets closer to 0, but as soon as it hits 0, it's no longer a number.

The x/0 = ∞ "logic" is pretty much why it's not a number. Otherwise, you can use logic to show that 2 = 5 and such

[bjlong]

Infinity is not a number. Don't use it like one.

Saying that x=inf is not a valid statement. x(t=inf)=inf is more valid, albeit notationally confusing. It's stating that as t gets arbitrarily big, x gets arbitrarily big--infinity can only be thought of as a limit in a number system, not as a number. Basically, whenever you see =inf, replace it with ->inf.

There are plenty of difficult pseudo-classical problems that make direct simulation difficult, such as turbulent flow and brownian motion driving a chemical reaction. The idea is that you end up having to break a large-scale object into lots of very small parts.

[Micro102]

What if x was also 0? inf times 0 still seems to be 0

[eerr]

Mostly, to accurately simulate an object's behavior within a specified time, you need information on everything within the radius equal to how far light would travel in that time. Because of background radiation, etc, that may or may not have an effect on the object. An invisible star in a galaxy far, far away wouldn't matter unless you tried to simulate humanity's working for a few million years. If you did try to, you'd have to take it into account - simply because its mere existance alter the gravity density of that area, and alters radiation passing through.

As to what I meant in regards to the recursive calculation - I didn't mean it'd have to simulate itself. It's just the matter of someone seeing the result. For example, the 'puter takes a snapshot of the universe to see what you'll be doing in the next hour. According to its calculations, exactly in 55:24 minutes from now, you'll be reaching into the fridge for a beer. Now, what happens if you see the result? The first thing you are likely to try is to try and resist fate. So, due to the calculation result, in 53:45 minutes you'll decide to go out for a smoke and forego the beer, even if you actually wanted it. But this reaction is predictable. The computer will predict that you'll try, and so the result is the above action. But you don't know what went on in the computer, and upon seeing the result you'd wonder why it thought that, and don't go for a smoke, choosing the beer option, since that's what you originally wanted. The loop closes. The computer won't be able to give a correct answer, since the answer depends on the answer, creating an infinite recursion that would likely be unsolvable even for a QC, unless it just dumps all possible variations on you at once.

No, this has alot to do with that hypothesis about observing particles.

obviously if you take everything inside the system, and then apply something unexpected from the outside, you can change whatever prediction you have.

it becomes the prediction that "was" true.

obviously if you can predict something will happen, you can change it.

but if you try to include yourself, using the machine's calculation then whatever you were doing was probably going to change it anyway.

That's like saying something is impossible because you can mess it up!

[Sean Mirrsen]

Imagine that you're taking a snapshot copy of a universe timeframe and analyzing it down to the lowest level, then feeding that data into a massive hyperdimensional supercomputer and trying to obtain the result. Even if you remove from the picture the impossibility of a machine that effortlessly gathers data from a given timeframe in the universe and analyzes it without changing it, even then you get the paradox regarding the reply altering the reply.

Let's imagine a situation. There's an airplane that is doomed to crash on its next flight because of undermaintenance. A passenger of said airplane queries the Prophecy-O-Matik^tm to see what will befall him in the future.

Where can the prediction go from here?

1) The prediction he receives will be accurate, detailing the crashing of the plane and death of all passengers. If he pays attention, however, he will notice himself missing from the plane, because he will immediately abandon the idea of flying in that thing, even though any of his efforts to persuade the mechanics to recheck the plane will be for naught.

2) The prediction he receives will be accurate, depicting the plane as safely flying to its destination, after he persuades the mechanics to repair it. Even though he won't know what would happen otherwise, he will follow the prediction to the letter because he understands the supposed importance of the repair and sees no reason to object. This is a borderline case, a self-fulfilling prophecy. Because the first cycle of calculations had the plane crash, and the recipient saw the plane crash, he went to the mechanics and asked them to fix it. The receiver of the final version of the reply does not know what would happen to the plane if he didn't do what he is shown doing, but assumes that following the prophecy is a good way to safely travel to his destination.

3) The prediction he receives will be useless. This will happen if the recipient does not intend to thoroughly look through the reply, only looking whether the plane arrived or not, but is determined to get the plane repaired if it's broken. (or if, for example, the machine is text-only and simply replies to a question: "What will happen during the flight so-and-so?") The first iteration result will be a crash. Due to that result, the second iteration will have a fixed plane and a safe landing. Due to that result and the recipient not receiving vital info, the third iteration will have a crash. The fourth will have the plane fixed again. Because the recipient only sees the "end result", he will not see that his actions have a role in the reply, and unless it's in the machine's power to alter that, the result will be incomprehensible. But then, the incomprehensibility of the result will again likely lead to a crash, starting another cycle. One of the failsafe options in such a case would be a "blank screen" reply, being analogous to "INPUT HAZY, TRY AGAIN LATER". Possibly, it could be a simulated delay to get the user to walk away so he doesn't see the reply. Another would be an "infodump", detailing the specifics of the situation, with all possible outcomes. At that point the machine would no longer be doing predictions, but would simply let the user himself decide what is where.

It's fun imagining quantumly impossible future-foretelling machines. You should try it.

[Micro102]

I don't get your argument, how is there a paradox? If they ask it if the plane will crash or not, it will tell them it will, if they ask it why, it will tell them why.

[Sean Mirrsen]

No, the paradox arises when there is a recursion unsolvable by the machine. An infinitely repeating loop of the same circumstances, induced by the machine itself. In the first two variants, the situation is resolved quickly enough - just one or two calculations on the same matter. However, the third case is complex as the user's reaction is too polar, and produces a different result on each subsequent recalculation. It's the same beer issue - You get one of the two replies, and either compels you to choose the path of the other. For a machine that's supposed to give an accurate answer, this would be unsolvable without some sort of failsafe behavior for such an occasion, which would end the recursion at the cost of producing a false reply.

[alway]

It would likely be more akin to the AI in the Hyperion series. Except that instead of Hyperion being the part of the universe which was inherently unpredictable, it would be the machine itself.

[G-Flex]

What's 1÷0 then? ∞/2?

No, really, any number divided by a zero is either zero or infinity (infinity and zero being on opposing ends of the spectrum, not taking -∞ into account, and multiplication being the opposite of dividing, dividing by the opposite of infinity would produce the same effect as multiplying by infinity - we then get to the uncomfortably odd point that infinity*0=1?..)

I mean, if you look at the problem logically:

x*∞=∞
x*0=0
x/∞=0
ergo, x/0=∞

I can see you haven't taken much calculus. Look up "indeterminate forms" for an explanation on why this doesn't make sense.

For a more reductio ad absurdum style argument:

x/0 = ∞
∞*0 = x

In other words, there would be infinite possible values for x given that 0*∞ = x.

Further, let's say that x < 0. Say, -50.

-50/0 = ∞.

But wait. That's not actually the behavior as the divisor approaches zero.
Example: -50/0.0001 = -500000
In other words, as the divisor approaches 0, the answer becomes -∞, not ∞.


Basically, you can't just define single terms as solutions for things like ∞/0, or 0*∞, or 1^∞, or x/0, or anything similar. Your initial statement of x*∞=∞ is also an assumption on your part, with similar problems; and what exactly happens if x is negative or zero?

[Neruz]

No, the paradox arises when there is a recursion unsolvable by the machine. An infinitely repeating loop of the same circumstances, induced by the machine itself. In the first two variants, the situation is resolved quickly enough - just one or two calculations on the same matter. However, the third case is complex as the user's reaction is too polar, and produces a different result on each subsequent recalculation. It's the same beer issue - You get one of the two replies, and either compels you to choose the path of the other. For a machine that's supposed to give an accurate answer, this would be unsolvable without some sort of failsafe behavior for such an occasion, which would end the recursion at the cost of producing a false reply.

Hence why i said a prediction of the future cannot account for itself.

[Micro102]

No, the paradox arises when there is a recursion unsolvable by the machine. An infinitely repeating loop of the same circumstances, induced by the machine itself. In the first two variants, the situation is resolved quickly enough - just one or two calculations on the same matter. However, the third case is complex as the user's reaction is too polar, and produces a different result on each subsequent recalculation. It's the same beer issue - You get one of the two replies, and either compels you to choose the path of the other. For a machine that's supposed to give an accurate answer, this would be unsolvable without some sort of failsafe behavior for such an occasion, which would end the recursion at the cost of producing a false reply.

I may be missing something as i still don't understand, but let me try saying this.

If everything can be predicted, that man was going to ask that question from the start, so to that computer, the plane was never going to crash because the reply it will give will be to fix it.

[ChairmanPoo]

unless it's a self-fulfilling prophecy.

[G-Flex]

All prophecies need to be self-fulfilling, in that making a prophecy necessarily affects the future in at least a small fashion.

[JoshuaFH]

All prophecies need to be self-fulfilling, in that making a prophecy necessarily affects the future in at least a small fashion.

This is the plot to the game Persona 2.

Man I want to play that game again.