What would you do with an infinitely fast computer?

[styrofoam]

I think their code crashing is actually a good thing for humanity.

I agree with that, for sure.

[Thesh]

I think their code crashing is actually a good thing for humanity.

Imagine living in a world where there is no risk of overpopulation (I will control breeding, plus the war will likely have a death toll in the billions), no unemployment (every person will be assigned a job and forced to do it, no free loaders), no hunger (food will be rationed and produced in bulk), no money (no need since everyone is given the same rations), no more genetic diseases (if your family has a history of genetic diseases, you won't be allowed to breed).

Sounds like a utopia to me. All men, women, and children will be equal (except for me, I will be considered better than everyone else).

[styrofoam]

except for me, I will be considered better than everyone else

Aren't you describing Soviet Russia taken to it's logical conclusion? And hasn't everybody disliked it, with all the corruption?

[Thesh]

except for me, I will be considered better than everyone else

Aren't you describing Soviet Russia taken to it's logical conclusion? And hasn't everybody disliked it, with all the corruption?

Well, it's not quite the same thing, and I can't speak for others, but I think having absolute power would be absolutely awesome.

[Xanthir]

Your idea of utopia is horrifically anemic. Go read up on real paradise engineering and get back to us. Believe me, you'll be *far* happier in a proper utopia than you would be as the ruler of Soviet Robotopia.

[userxp]

Or you can just use the computer to make a virtual reality and then become master of the universe.

[tekk]

I'd go and use a while(1); to paint the screen completely white by printing #s(This assumes an infinite refresh rate on the monitor)


after that I'd amaze people by having EMACS start in under a minute

[styrofoam]

I'd go and use a while(1); to paint the screen completely white by printing #s(This assumes an infinite refresh rate on the monitor)

Impossible in a theoretical sense. The eye uses light, and light travels finitely fast.

[Rockstone]

Play Crysis and Own Everyone.

And Calculate Pi while I'm owning Everyone in Crysis (Hey- if it can do an infinite number of equations- it can do an infinite number of things with no performance decrease)

[joshz]

Well, the computer won't improve your skills.

[Agent_Irons]

Well, the computer won't improve your skills.

It could beat them for him, though. Brute force the space of scripted bot intelligences(under 1 gibibyte in size, say) for Crysis, compete them in a double elimination tournament, then take the winner and have it aim(and fire and run) for him. The theoretical best Crysis player isn't unbeatable, but it's probably pretty good.

[styrofoam]

The theoretical best Crysis player isn't unbeatable, but it's probably pretty good.

You're forgetting that you can't test every possible scenario (they'll all lose infinitely many times) and any finite amount would result in an infinite amount of programs (the majority of which will malfunction given any scenario that you haven't already tested it with).

There've been multiple pages of discussion on why this wouldn't work.

[Odd_nonposter]

Donate it to Folding@home.

[Josephine]

Donate it to Folding@home.

You don't really have to donate it. Just bring it to wherever F@H's central location is, connect the biggest pipe to their server you can find, wait for the data to transfer, and take it home.

[Agent_Irons]

The theoretical best Crysis player isn't unbeatable, but it's probably pretty good.

You're forgetting that you can't test every possible scenario (they'll all lose infinitely many times) and any finite amount would result in an infinite amount of programs (the majority of which will malfunction given any scenario that you haven't already tested it with).

There've been multiple pages of discussion on why this wouldn't work.

It would work for a computer defined as infinitely fast where infinite is more infinite than other kinds of infinite. Other kinds of infinite computational power are just not as fun. Or a countably infinite computer where there was a given efficiency lower bound(so that you could use these programs outside your secret base where the computer is). Given that a few of the players will just have 'jump' opcodes(in my head they're written in assembler) this gives a maximum size. While large, the space of all crysis players smaller than 'x' where x is big is finite. A good shortcut to uncountably infinite problems is a genetic algorithm, which works for this particular problem.

Something I proposed several pages ago: Discover new branches of mathematics by looking through the space of all programs for short programs that give the same output as reference algorithms, like factoring, etc. A much shorter or more efficient program is probably utilizing a branch of mathematics we haven't discovered yet. This is only doable if you have more than countably infinite cycles to play with. You could try with merely countably infinite cycles, but you'd have to cap checking each program at a few hundred million tries or somesuch, which for complex problems is probably not enough.

[styrofoam]

It would work for a computer defined as infinitely fast where infinite is more infinite than other kinds of infinite. Other kinds of infinite computational power are just not as fun. Or a countably infinite computer where there was a given efficiency lower bound(so that you could use these programs outside your secret base where the computer is). Given that a few of the players will just have 'jump' opcodes(in my head they're written in assembler) this gives a maximum size. While large, the space of all crysis players smaller than 'x' where x is big is finite. A good shortcut to uncountably infinite problems is a genetic algorithm, which works for this particular problem.

With a genetic algorithm, run an infinite amount of times, you either get a perfect program or no program. Also, there's the problem of a fitness function (the perfect program for a FPS game is almost guaranteed to rely on the behaviors of the AI and will give undefined behavior given anything else).

If you really want to try that, you'd have to simulate the universe. Why bother with the robots, then?

[BlackSails]

With a genetic algorithm, run an infinite amount of times, you either get a perfect program or no program. Also, there's the problem of a fitness function (the perfect program for a FPS game is almost guaranteed to rely on the behaviors of the AI and will give undefined behavior given anything else).

The fitness function for an FPS is easy. Its just the kill-death spread averaged over all the maps and many, many games.

[Josephine]

you could do something like this, although it may require a higher infinity than the machine is capable of. You simply have every possible individual fight every other possible individual (or even every possible group of individuals) a very large number of times (could this be infinite too?). After that is done, the single best AI by kill/death ratio. ties are broken by the least time between kills and most time between deaths.

EDIT: come to think of it, that would work for at least a chatbot, if not a full-fledged intelligence. you have all the programs rate each other. the programs that produce outliers for the rating the most are culled. Or something like that. It's not fleshed out.

[userxp]

Crysis is a finite-state machine, so you can compute every possible position, make a game tree and solve Crysis (or any other non-infinite game) in finite time, thus making a perfect unbeatable (if it is possible to win, it will win) bot.

[styrofoam]

Crysis is a finite-state machine, so you can compute every possible position, make a game tree and solve Crysis (or any other non-infinite game) in finite time, thus making a perfect unbeatable (if it is possible to win, it will win) bot.

That's the problem. Crysis is not a complete model of the universe, and the bot will rely on the AI's particular behavior.

[Internetmeme]

Assuming it's linux, go into bash and have it run

Spoiler:

"rm -rf /"

, fubaring the computer instantly.
Also, it's a bad idea to run that command, it deletes everything IIRC.

[joshz]

fubaring the computer instantly.

Unless, you know, you have a live CD or some other image.

[Yakk]

Assuming it's linux, go into bash and have it run

Spoiler:

"rm -rf /"

, fubaring the computer instantly.
Also, it's a bad idea to run that command, it deletes everything IIRC.

Plus, unlike regular computers, infinitely fast (and infinite capacity) computers have a copy of this universe on their hard drive (deep in /dev/random/multiuniverse).

[Xanthir]

Also note that, by the Timmy argument, copies of the universe held in an infiniputer's memory are almost certainly equivalent to the current universe, so that any action taken in the copy occurs in our universe as well.

[styrofoam]

Also note that, by the Timmy argument, copies of the universe held in an infiniputer's memory are almost certainly equivalent to the current universe, so that any action taken in the copy occurs in our universe as well.

More specifically, we reside in the copy on some other infinicomputer where the same action is being taken.

[PM 2Ring]

There's no point differentiating between the original universe and the different levels of copy, as they are in principle, completely indistinguishable, if the copies are perfect. If you can detect any evidence that you're living in a sim & not the base universe, the sim is flawed. (I guess this is also relevant to the Real Life Glitches thread.)

[Xanthir]

The point being made, though, is that, given that there's an infinite stack of simulations, it's almost certain that your universe is in a self-similar region where any changes done on one level are reflected on the level above and below. Thus anything you change in the simulation is almost certain to change in your universe as well.

This is different from what you're saying - it's not about sim vs base, it's about sim vs sim.

[PM 2Ring]

The point being made, though, is that, given that there's an infinite stack of simulations, it's almost certain that your universe is in a self-similar region where any changes done on one level are reflected on the level above and below. Thus anything you change in the simulation is almost certain to change in your universe as well.

This is different from what you're saying - it's not about sim vs base, it's about sim vs sim.

Sorry, I was a little ambiguous. I meant that if the sims are perfect, then all sim levels are indistinguishable from each other, and they are also indistinguishable from the base. I mentioned the base level because if you can prove that your level is not the base level, then it's not a perfect sim.

A closely-related point: since all the levels are identical in every possible detectable way, in a sense, there is only one level. I'm reminded of Feynmann's early idea to explain why all electrons have identical properties: there is only one electron / positron in the universe zipping back & forth through time. But this scenario is a bit different, as electrons can be distinguished by their position & momentum, whereas our sims don't have any properties that differ. I think.

[styrofoam]

A closely-related point: since all the levels are identical in every possible detectable way, in a sense, there is only one level.

The problem is that there are distinguishing characteristics, namely there is no programmer messing with the top level while there is for all the other ones. This is not a characteristic of the universe itself (only what surrounds it) until the programmer messes with the universe he runs and does (or does not) see the effects himself.

It's important to mention that it doesn't really matter that, since the top level isn't being affected, they're going to treat the second level differently, because the top level doesn't HAVE to simulate the second level precicely. Since the chain is infinitely long, the whole system will reach a stablization point eventually.

An interesting related problem is that, since the probability of any one universe being the top is 1/infinity=0, then there cannot be a top. (a paradox). It also means we're GUARANTEED to be beyond the stablization point. (there are a finite amount of unstable universes and and infinite amount of stable ones, and infinity/infinity=1)

[BlackSails]

I dont see why its taken for granted that it has to stabilize somewhere. It could end up being some sort of cycle.

[styrofoam]

I dont see why its taken for granted that it has to stabilize somewhere. It could end up being some sort of cycle.

Simple observation. If you're simulating your own universe, it isn't a cycle.

[Xanthir]

I dont see why its taken for granted that it has to stabilize somewhere. It could end up being some sort of cycle.

To expand on what styrofoam said, once you simulate your own universe, that simulated universe will simulate it its own universe, which will simulate its own universe, and so on. A universe that wants to create a simulation of itself *creates* self-similar regions in the simulation stack. The closer the simulation is to 'reality', the larger the self-similar region will be (because it will take longer to diverge sufficiently to no longer want to simulate itself).

An interesting related problem is that, since the probability of any one universe being the top is 1/infinity=0, then there cannot be a top. (a paradox). It also means we're GUARANTEED to be beyond the stablization point. (there are a finite amount of unstable universes and and infinite amount of stable ones, and infinity/infinity=1)

Use the proper mathy terms - it's almost certain that we're not the top. It's almost certain that we're beyond the stabilization point. That's how you refer to things where something isn't impossible, but the chance of it being true are 0%. (That is, the set of outcomes where it's true has measure 0 in the set of all outcomes. Any finite set in an infinite set does this, frex.)

The stable section isn't necessarily infinite, if there are properties of the computation that make it impossible to simulate reality with perfect fidelity. Small changes will mostly damp out, but occasionally will build up and create a non-self-similar region which can go on for an arbitrary length of time before stabilizing again. Almost all of the non-self-similar regions will look nothing like our own universe, though, precisely *because* we're likely to simulate ourselves. Thus once a universe similar to us appears, a self-similar region is basically guaranteed.

[styrofoam]

The stable section isn't necessarily infinite, if there are properties of the computation that make it impossible to simulate reality with perfect fidelity.

Then it's a simulation of a similar, but not identical universe. Don't know why you'd want that, given an infinitely powerful computer, since you can evalulate to infinitely many decimal places. And you must have an infinitely powerful computer, in order to include infinite universes inside it,

[TheChewanater]

I'd simulate the universe and kill the virtual me in it.

Before I get the supercomputer.

[Axidos]

How to survive an infinite-depth simulation of your own universe without inconvenience:
1. Run the universe to the end of life itself (just because that final lifeform could, by some chance, be you, and avoiding erasing yourself is the whole point of this exercise). Your simulator simulated the entirety of existence this far, there is no reason at all it can't continue in time and thus simulate the future.
2. Shut down simulator before new life has a chance to appear.
3. Live happily.

If you happen to be the guy in reality who ends up simulating a universe, please please do #1 and #2 so that the top-level universe can do #3.

[Xanthir]

The stable section isn't necessarily infinite, if there are properties of the computation that make it impossible to simulate reality with perfect fidelity.

Then it's a simulation of a similar, but not identical universe. Don't know why you'd want that, given an infinitely powerful computer, since you can evalulate to infinitely many decimal places. And you must have an infinitely powerful computer, in order to include infinite universes inside it,

"Evaluate to infinitely many decimal places" is not equal to "reproduce every interaction exactly".

For example, some phenomena may not be possible to perfectly emulate, if they're based on random processes.

[Yakk]

The stable section isn't necessarily infinite, if there are properties of the computation that make it impossible to simulate reality with perfect fidelity.

Then it's a simulation of a similar, but not identical universe. Don't know why you'd want that, given an infinitely powerful computer, since you can evalulate to infinitely many decimal places. And you must have an infinitely powerful computer, in order to include infinite universes inside it,

"Evaluate to infinitely many decimal places" is not equal to "reproduce every interaction exactly".

For example, some phenomena may not be possible to perfectly emulate, if they're based on random processes.

They have to be based on "random" processes over a continuum, and there cannot be a countably dense subset with sufficiently continuous behaviour. (ie, a process that randomly picks out a real number from 0 to 1, then if it is transcendental it does one thing, and if it isn't transcendental it does another)

Otherwise, you just simulate every element in the countably dense subset. And in the above case, you'll note that there where only two possibilities -- you need an uncountably large set of possibilities that are fundamentally different (ie, not related to each other in smooth ways).

Of course, defeating that kind of thing simply requires a computer that is an order of infinity "faster" and "bigger". (which opens up yet more complex models that need even larger computers)

[Xanthir]

Ah, right. For some reason I was thinking of a single universe simulation. That would indeed work.

It would also, by the by, simulate every possible universe derivable from the same initial conditions through physical processes.

[Yakk]

Ah, right. For some reason I was thinking of a single universe simulation. That would indeed work.

Hence /dev/random/universes/....

[Meteorswarm]

(Arise, dead thread)

Having just learned about Turing machines, I have an idea I'd like to ask you:

Suppose we have a particular infinitely fast Turing machine (infinite tape) like was discussed here, that takes a year to perform its first step, 6 months its next, 3 months, 45 days, ... halving each step, so that any computation can be completed in 2 years. The catch is that the only data you can get out of the machine is its final state: Yes, No, Halt or Diverges.

We only have one of the machine. What problems would you feed in to it?