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tcaudilllg
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biggerUniverse
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tcaudilllg
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 Posted: Mon Aug 01, 2005 11:51 pm Post subject: |
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You might find this funny.
Lightspeed c^8 = 1.43 * 10^42! (in mps)
"Q: What's the answer to life, the universe, and everything? ..."
And c^7 = 7.70 * 10^36, which is actually very significant because that's about the Plank length. (the ratio of a lightwave's wavelength to its energy)
I've got a demonstration in mind to show that this is very relevant to game design, especially pathfinding and AI, but it'll have to wait.
A challenge, LeoDraco: figure it out.
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tcaudilllg
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| Posted: Tue Aug 02, 2005 10:24 pm Post subject: |
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I guess not...? Eh... hope I didn't go over your head there.... (to the degree that you think I did...?)
Anyway, so many people chime with the intuition anyway, and no one's really questioned it. So, quite frankly, the answer to it all appears to be 42.
Or 10^42, at least.
Last night, I prepared a demonstration about what I'm discussing.
The Answer to Life, the Universe, and Everything...
really is 42.
10^42, to be exact.
Which is approx. c^8, the Plank length multiplied by c.
Explanation:
We define a universe that has two particles. We call the transfer of energy from particle to particle 'c'. There are two possible states, one for each particle. The first state is the transfer of the first particle's energy to the second. The second state is the reverse of the first.
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__ __ __ __
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In our universe the law of action/reaction is obeyed: potential energy is exchanged with kinetic energy. Allowing for this possibility, we must see our two particles each in terms of two component particles. The particles in one particle may interact with the particles in the other either as a group or individually. We therefore have four interaction possibilities between our two particles. (c^2)
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| -|> | | | | |_-|>_| |_<|-_|
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To allow our particles to flow in time, we need c^4, or 16, four sequences of the four particle states, one for each moment. We need, therefore, energy enough to move 16 particles. (c^4; note that the particles must obey the path of least resistance, because our particles are flowing in a space-time)
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c^4 = 16 Action/Reaction across time
__ __ __ __ __ __ __ __
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|__|__| |_<|-_| |_<|-_| |_-|>_|
__ __ __ __ __ __ __ __
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|_<|-_| |_<|-_| |_-|>_| |__|__|
__ __ __ __ __ __ __ __
|_-|>_| |_<|-_| | -|> | | | |
|_<|-_| |_-|>_| |__|__| |_<|-_|
__ __ __ __ __ __ __ __
|_<|-_| | -|> | | | | |_-|>_|
|_-|>_| |__|__| |_<|-_| |_<|-_|
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By squaring c again, we end up with enough energy to move our particles through every possible iteration of our four moment universe. Enough energy for every dimension of our two-particle cosmos. (again by the law of least resistance, we end up cycling through another of the possible four moment combinations/dimensions at the end of each set of four moments, not repeating a dimension until the set of all dimensions has been exhausted by the current cycle. Our universe, therefore, is truely continuous)
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c^8 = 256 = All possible action/reaction sequences.
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Einstein's equations are good for any value of c. Therefore, by substituting the speed of light for c, as opposed to 2, we end up with ~1.43 * 10^42 as c^8. The same systems mechanics hold for our own universe. To move all of the particles in our universe through an entire cosmic cycle, that is, from one arbitrary point in time to the moment right before it, we need 1,196,883,216,000,000,000,000 electron volts, the smallest possible unit of energy. To move the universe through all of its possible cycles, we need ~1.43 * 10^42, after which the cyclic sequence repeats.
Now... what does this have to do with games?
Basically, it says that if we look at particles in terms of sprites/polygon models, then we can calculate all of the possible interactions--and sequences of interactions--in our game world using sprites/polygon models ^ 8 bytes. (although my math may be off on that, so substitute "bytes" for a list of memory structures in which the sprites/polygon models is stored). If we allow an AI access to that kind of information, it can pefectly lead players into traps. The difficulty is storing the information: it's completely huge. So we would need instead to use a sort algorithm to limit the AI's predicative ability to a manageable range.
It would also seem possible to expend enough processing cycles to process all c^8 combinations per moment, while cutting down the memory storage to c^4. Does that sound right? Or is it c?
One could split the bill: calculating the dimension of the situation first, when the player enters the room, and using on c^4 processing power/memory to get the job done relative to the situation.
It seems to me a lossy AI in this context would not only be acceptable to the player, but it would even make the AI seem "human."
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XMark
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| Posted: Tue Aug 02, 2005 11:21 pm Post subject: |
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Why didn't I see it before? It's so obvious!!!
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RuneLancer
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| Posted: Tue Aug 02, 2005 11:26 pm Post subject: |
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Let's take a reasonably small scene. 1000 polygones. Although with any experience in 3D you'd probably understand that it'd be more advantageous to compare vertices than actual polygones, so that should be 3000... We'll ignore this for now.
1000^8 = 1,000,000,000,000,000,000,000,000.
Even if your theory were entirely right, can you see the problem here? Just HOW lossy would a real scene with a few hundred thousand polygones have to be to even be possibly implementable? You can't do this every frame, no way in a frozen-over hell: even an empty loop that iterates one millionth of that will cripple the CPU for a few seconds (we're still talking about a mere 1000 polies...) And preloaded? Scenes are dynamic, but ignoring this oh-so unimportant detail and assuming, somehow, every possibility is a bit, that's still 125,000,000,000,000,000,000,000 bytes of preloaded data. I'd translate that to a more manageable equivalent, but I don't know what comes after petabyte. ;)
Even using various shortcuts to cut down, this would never come close to being as efficient as a simple, say, A* pathfinding algorithm. ;) Whatever advantage, if any, it would confer would be absolutely crushed due to speed/memory issues. This is what makes it AI: it isn't brute force, but rather uses an "intelligent" method to organise data and take shortcuts.
Of course, I'd love to see a demo of this. Eagerly awaiting an implementation that'll shut me up. ;)
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tcaudilllg
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| Posted: Tue Aug 02, 2005 11:39 pm Post subject: |
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Right, but the pathfinding algorithm will never yield "real" AI that can beat the player with controlled precision, without violating the rules of the game.
We wouldn't need to do it per-poly: we could do it per poly-model, and get sufficient results. Conside we have eight poly models onscreen, we get 8^8 = only 16.7 million structures. Certainly beyond the pale now, but give it a few years.
Plus, consider the lossy method:
8^4 = 4096. Perfectly manageable, yet effective.
The thing is, you don't need the pathfinding algorithm, because you have the entire universe and all of it's possiblilities already calculated. We accounted for all of the possible dynamic happenings in the equation. (the last squaring of c)
It is certainly possible to make a demo of this... but my mind can't handle it right now.
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RuneLancer
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| Posted: Tue Aug 02, 2005 11:40 pm Post subject: |
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| LordGalbalan wrote: | | It is certainly possible to make a demo of this... but my mind can't handle it right now. |
Eagerly awaiting the time it will be able to. :) I'm curious how you could make this brute-force method more (potentially; every idea has to start somewhere) effective than existing AI theorems.
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tcaudilllg
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| Posted: Tue Aug 02, 2005 11:41 pm Post subject: |
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Question: would c^4 equate to all of the synapse interconnection possibilities in the human brain?
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RuneLancer
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| Posted: Tue Aug 02, 2005 11:45 pm Post subject: |
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Depends what C represents.
The human brain has (IIRC) 10^12 to 10^13 neurons. Most neurons only have a few dozen connections, but some (such as the immensely complex purkinj cell structures in the cerebellum) can have thousands of connections.
It's definitely not exponential. Nor is it linear. AI doesn't work that way: connections are made on a need-to-connect basis in the brain, unlike the current average neural network model which connects every neuron from one layer to every neuron in the next layer and weights the synaptic exchange based on what the network has "experienced".
Edit: As for possibilities, ignoring wether a connection is required or not, that's DEFINITELY not nNeurons ^ 4. ;)
Suppose you have A, B, C. The possibly connections are AB, AC, BC. The possibly connections are nConnections x (nConnections - 1) x (nConnections - 2) x ... x (nConnections - (nConnections - 1)) or, in this case, 3 * 2 *1, 6.
AB, AB AC, AB BC, AC, AC BC, BC
You do the math with 10^12. :)
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Last edited by RuneLancer on Tue Aug 02, 2005 11:52 pm; edited 1 time in total
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tcaudilllg
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| Posted: Tue Aug 02, 2005 11:49 pm Post subject: |
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Using the model I described above, couldn't AI be remodeled then as "I"?
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RuneLancer
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| Posted: Tue Aug 02, 2005 11:56 pm Post subject: |
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| LordGalbalan wrote: | | Using the model I described above, couldn't AI be remodeled then as "I"? |
Not by a long shot. If by intelligence you mean human intelligence, this takes absolutely NOTHING into consideration that the brain actually does. It doesn't even LOOK like a neural network, much less a more functional one than what we currently use in AI.
To boot, intelligence requires training to be genuine. A system which can take data and produce the right answer on its own is called an expert system. A system which can learn how to handle data mostly on its own is AI, and the two most common methods of doing this are through neural networks (mostly for pattern-recognition, as it currently stands) and genetic programming (which, however, typically "evolves" an expert system and not actual AI.)
Cover every possibility is not only wasteful, it does not involve any intelligent decision-making process. It's called brute force, and is about as far from AI as it gets (let's not even consider human intellect!)
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tcaudilllg
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| Posted: Wed Aug 03, 2005 12:00 am Post subject: |
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No I mean, it just seems to me that this formula encompasses the whole spectrum of intellect. Although it does need an accompanying sort to create action.
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Nephilim
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| Posted: Wed Aug 03, 2005 4:02 am Post subject: |
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| LordGalbalan wrote: | | No I mean, it just seems to me that this formula encompasses the whole spectrum of intellect. |
No, all you're doing is describing a snapshot of all possible game spaces at a given moment. For there to be intellect, there has to be choices toward goals. Brute-forcing your way through a problem is not intellect, because you're just computing all possibilities until you find your goal. There's no decision making, except a trivial one (and that's assuming the algorithm can produce that trivial choice).
And this approach doesn't scale. You gave an example where you have eight poly-models, but how many games out there limit themselves to only eight game-level entities? Your typical FPS or RPG has way more than that. (And most entities have many states, which acts as yet another multiplier to your final number.)
And consider this: game state changes any time the player has input into the game world. And the more your player can affect the game world, and the more dynamic and alive the game world is, the more data that changes from frame to frame which has to be brute-forced through.
In addition, having a snapshot of a game universe's possibilities doesn't do you much good if you cannot analyze all those possibilities for fitness. Even if you could get all the possibilities for the next game state for a game, there may not be a clear "best" choice out of those states, or what appears to be the best choice could be a local maximum that traps your algorithm's performance at a very suboptimal place. Brute force is not the be-all and end-all of AI.
Finally, I think your calculations are way off. If you want to compute the number of possible states in a system, you're typically talking factorials rather than exponents, because you're talking combinations and permutations along multiple axes, not just a simple array. Generalizing your observations from a simple system to large systems was fallacious - game worlds can get much more complex than you described much faster than you described, because the interrelations between game objects can have far more than one axis of effect.
On top of all that, you neglected to take into account time - for your AI to "plan ahead," you'd need to extend your snapshot of possible game states many states into the future, and that makes your number of computations grow even faster.
If you don't believe me, apply your theory to a game as simple as Pac-Man. How many computations would you need to do each frame to brute-force your way to a smart ghost?
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tcaudilllg
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| Posted: Wed Aug 03, 2005 9:18 pm Post subject: |
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| Nephilim wrote: | | If you don't believe me, apply your theory to a game as simple as Pac-Man. How many computations would you need to do each frame to brute-force your way to a smart ghost? |
I guess I'll find out. :)
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