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[Sean Mirrsen]

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.

[Muz]

Ok question for all you hardcore physics guys.


Do you believe that everything can be predicted with math, as long as you have enough information?

Information is the easy part. Calculating it all is the hard part. Oh yeah, math can figure out what happens when a nuclear weapon hits my house, but I'd need a pretty fricking big computer and some smart people to actually calculate it.

In engineering, you just tend to make some huge assumptions... "Assume that whatever current here is 10 mA." "Calculate the momentum of a plane hitting a building.. but to make things simple, you just assume it as a sphere." "Assume that consonants in speech as random noise."

In short, technically yes, but practically no. In reality, who really cares?

Actually... You got it mixed up; we can calculate it, albiet it would take longer than actually observing it in almost every case, the problem is the starting information. Due to the Uncertainty principle, we can not know both position and velocity of a particle, and as such can only speak in probabilities when it comes to the actual calculations.

Yeah, mathematics helps greatly with that. Especially statistics. Statistics helps us predict and calculate position/velocity accurately enough. Of course, it depends on the degree of precision that you need.

[Neruz]

The important thing to remember with statistics is that they can only be applied to groups; not to individuals.

[Neruz]

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.

Not neccessarily Sean; the computer gives the result that in X minutes, you will get a beer. At the point in time where it made that calculation, this was true. Because when it made that calculation, the results of the calculation it just made were not included, because it hadn't made the calculation yet.

Basically, i take all the information in a given instant and use it to predict what will happen in 5 minutes time. The prediction is 100% accurate, but cannot account for itself, because the prediction did not exist in the instant i collated the information. If i then make a second prediction and take a time after the first, thus including it in my calculations, again i cannot include the second prediction into itself, because the prediction has not been made yet.


A prediction cannot include itself, because in order to include itself it must first be predicted, and it cannot finish being predicted until it includes itself, so you end up with a paradox. Ergo it is impossible for a prediction to include itself within it's prediction.



This is, of course, assuming a mathematical prediction, rather than someone guessing.

[Earthquake Damage]

If there exists a simulator that can and/or does run a simulation of our universe, it certainly cannot exist within this universe.  Moreover, I'd say it cannot exists within the same causal domain (to borrow a term from a previous thread).  In short, we can't interact with it.  If we could, it'd have to include itself in the simulation, implying that an object can consist of more than itself (in terms of "information capacity" as I called it earlier -- as far as we're concerned that translates to energy).

Neruz described a computer that doesn't accurately simulate the universe.  He instead considers a device that simulates what would happen if the simulator itself weren't fucking with things.

This is, of course, assuming a mathematical prediction, rather than someone guessing.

I'm pretty sure we're assuming a device that knows everything about our universe (omniscient, more or less) and can predict with perfect accuracy (as far as natural law permits -- YMMV depending on whether you believe the universe "plays dice" or not, to borrow IIRC Einstein's words) the state of our universe at any given time (or whatever -- I suppose you'd have to input some reference frame, not just a time).

[Neruz]

That's the thing though; no matter what you do you cannot simulate the simulator. In order to simulate the simulator, you need to simulate the result the simulator will get before the simulator gets that result.


To use an analogy, lets say we have an equation, such as 1+1=2, which is sort of what we're looking at here. We work through the equation, add the numbers together and end up with the result, being 2. Now, pretend that 2 is the prediction of the future, and the 1+1 is the present information, in order to accurately include the result, the 2, in our prediction, we would need to intergrate the 2 into the 1+1, but we don't know what the 2 is until we have first evaluated the 1+1.

A simulator can never create a simulation that is affected by itself, because in order to do so, it must simulate the result before it actually gets the result, thus breaking causality in half and causing a nice infinite paradoxical loop in the process.

[Ampersand]

It's only a problem if the simulator wants to be both accurate and faster than reality. If the simulator is only a copy of the state of the universe at exactly present, then the state of the simulator inside the simulation is easy; it's the state of the simulator outside of the simulation.

The problem should be about non-deterministic events that may influence the running of the simulation. There is a problem with the existence of both quantum non-determinism and Absolute Omniscience in the same universe.

This is one of the reasons why I'd argue that if you did actually want to simulate a universe at all, it's physical laws would have to be vastly less random. Computers are not good at random. It'd have to operate more like Clockwork, to borrow from enlightenment era thinking. For an example, In Dwarf Fortress, everything seems to work out randomly, however the seeds provided tell something different. The state of the world at any given moment is determined precisely by the initial conditions at the beginning, and only start to proceed with randomness when we jump in and start mucking with it.

[Neruz]

Well to be fair, to even get to this point we're assuming we've found some way to beat Quantum Uncertainty.

[dreiche2]

On a different note...

Sean, a complete rat brain has already been simulated, down to every single neuron and connection. I believe they're looking to upgrade to a cat brain next.

Seriously?  That's pretty awesome.  I had no idea we'd gotten that far.

We haven't. There was some significant fuss over that misrepresentation in the computational neuroscience community. I haven't looked into it much, so I don't know if the media just misrepresented it, or if the IBM scientists willingly overstated things originally. In any case, here is described what the lead scientist in this case had to say about it, at least in retrospective:

It's not that he's created a cat brain. Every journalist who interviewed him has heard him correct them in the following way: "No, no, it's not a cat brain. A cat-SCALE simulation."

So basically, what they did is to simulate very simplified models of neurons ('point' neurons) with completely random connections in numbers that are in the order of magnitude that you would find in a brain. But otherwise, it's just a pile of simplified, meaninglessly connected neurons.

Saying you simulate a cat brain with this is a little bit like saying you can simulate all life on earth with Conway's Game of Life if you just use large enough numbers of cells.

It's still an achievement in a parallel computing sense, but not a neuronscientific one per se, at all.

Btw, I'm doing a PhD in computational neuroscience / AI, so I know a little bit about this stuff.

[Neruz]

I was actually referring to the Blue Brain Project, not IBM's rather distorted claims of simulating a cat brain, although a quick check appears to suggest that they havn't gotten as far as i thought they had. *Shrug*

[dreiche2]

Yep, they do it in much more details, and they have a cortical column or something, which is something like ten thousand neurons (I haven't followed it lately, maybe they have a million now?). But cortex would be tens of billions of neurons. And, they struggle immensely with getting data about all the details you would actually need to simulate things properly (how exactly neurons are connected etc.). There's a lot of handwaving, guessing and averaging going on. A lot of people say they'll never really get anywhere with this pure bottom-up approach because there are just too many degrees of freedom in the system that cannot be constrained experimentally.

But yeah, it's, on a smaller scale, at least closer to capturing aspects of actual brains...

[Neruz]

I hear they've done something with a 'slice' of a simulated rat brain too, i'm fuzzy on the details, since it was in a New Scientist i read like six months ago.

[Micro102]

In regarding the machine that predicts the future.

If the machine predicts a guy getting a berr, it would predict his reaction to it telling him that, changing its response, but then predicting the reaction to that response, eventually changing it until what it says will be what is actually going to happen.

[Starver]

First of all, nobody's mentioned the Heisenburg Uncertainty Principle or the Planck-sized limit to accurate observation.  i.e. after a while, observing/measuring the system in a classic sense is going to only get so much information out (e.g. position or velocity of particle, not both), and is going to knock the quantum state around while you're doing so, thus invalidating your results.  All the while leaving 'unknown details' in the mix.

So a universe which is deterministic might still be incalculable.  Which is not to say that a simulation can't be sufficiently detailed to provide a reasonably accurate prediction.  But tend towards believing that Butterfly Effects (minor differences, not taken account of or fudged over, between two possible starting states on any simulation) are the deal-breaker and the implied  randomness of result or superposition effects of the quantum world are artifacts of us not able to know the precise rules or configuration of the sub-Planck world underlying that which we can measure to a certain macroscopic certainty.

(Not the reference to that being my belief.  That form of fatalism is probably as close as I come to a practical religion.

Regarding predictions affecting a system, I have been known to refer to self-fulfilling prophecies in the style of Macbeth.  Had the witches not informed the Scottish Lord himself of his destiny, would he (and his wife) have pursued the course of actions that sent him towards the fate that awaited him?  Had they not given him reassurance that only certain obviously ridiculous circumstances could harm him, would he have remained as unconcerned about events until the predictions took place?

Usually I apply the above to philosophical discussions about time-travel scenarios.  Universes that contain closed time-like curves (yes, this time it is time-like that I mean that do not have splintering/branching or other interesting variations on alternate futures must be self-consistent in that "everything that you go back and do, you must have already been back and done", which includes the situation where 'predictions' you make (or warnings) by using information from the future must support the creation of the timeline where this happened.  In fiction, this is usually because of unforeseen interpretations meaning that (in this particular type of unalterable time-line universe) attempts to make changes are the inadvertent cause of the things one wanted to change (or, at the very least, fail disastrously).  The average film-goer can name numerous films that have such self-supporting feedback loops in them, so I won't bore you with a list.  Sometime's it's put down to the Universe "conspiring against" the change, as with the "History will out" types (details change, but the overall run of the game stays the same).

Different uillustrative examples would be the 'new branch creation' types, with the Terminator series as one prime example[1].  At the end of my (unofficial) list of types, there's the Back To The Future types, with Flip-Flop universes and 'fading from reality' effects when things are about to go irreversibly wrong, which then give impetus to your efforts to correct things and allow you to fade back in.

(Illustrative examples only.)


[1] If you don't believe that the information about the timing of Judgement Day might have been deliberately miscommunicated to the past by those sent/sending back to the past...  Not sure if the Sarah Connor Chronicles have anything to add to this argument.

[Huesoo]

I have discovered the answer to DIVIDE BY ZERO

2÷0=∞

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