What would you do with an infinitely fast computer?

[roundedge]

If you had a wish from a genie, and you wished for a computer that could do an infinite number of operations in no time, what would you do with that computer?

I'd like to say I'd hack the internet, or something to that extent, but I doubt I'm tech savy enough to be able to do that right off the bat, not to mention the fact that I would probably like to keep such a powerful device under the radar. So the first thing I'd probably do is write a simple cellular automata program, and just run it on a massive massive scale. The next thing I'd do is write a library which simulates real numbers using infinite approximation, and then I'd get cracking at physical simulations which never explode on you.

What would you do?

[Naurgul]

I would brute-force NP-hard problems (and problems from even harder complexity classes) like there's no tomorrow. There probably wouldn't be.

[Ended]

This.

[roundedge]

This.

I think it's unlikely that we could know the original conditions of the universe, even with the right theories. Still, pretty mind bugging story.

[cmd]

Find prime numbers and sell them

[ATCG]

Collect on every still-open Clay Mathematics Institute Millennium Prize Problem. Then again, I'd probably cut out the middleman and ask the genie for the filthy lucre rather than the computer.

[Berengal]

Nothing. It's impossible to use. Any program you run will either not start or enter an infinite loop right away.

[Ended]

This.

I think it's unlikely that we could know the original conditions of the universe, even with the right theories. Still, pretty mind bugging story.

But you could search through all possible original conditions (I get what you're saying, though).

Actually, that raises a question. When you say 'an infinite number of operations', do you mean only countable infinity (like you could evaluate an infinite loop, for example to search for counter-examples to Goldbach's conjecture), or even larger infinities (like you could evaluate a function for each real number)? I assume you get infinite storage space as well?

[quintopia]

Nothing. It's impossible to use. Any program you run will either not start or enter an infinite loop right away.

Not true. Rather, at the same moment you begin the program the results are displayed (or rather, slightly after, since the computer breaks the light-speed barrier, not the monitor). Moreover, there is no such thing as an infinite loop on this computer. All iterations of the loop will be executed instantly in no time as well. (actually, we could say "no time" means "Planck time length" since there is no way to differentiate the two)

This also answers Ended's question I think: with the ability to do an infinite number of operations in zero time, a finite amount of storage should be sufficient for any computation that we care about. That is, any computation with a finite input string.

[achan1058]

Moreover, there is no such thing as an infinite loop on this computer. All iterations of the loop will be executed instantly in no time as well. (actually, we could say "no time" means "Planck time length" since there is no way to differentiate the two)

What about conventionally infinite loops. What will happen to them, then?

[Yakk]

I'd assume it solves the halting problem (on non-infinitely fast computers), which isn't a paradox.

So I'd write a simple proof checker and proof generator in a sufficiently powerful system.

Then I'd write the 'is provable' program, that (if something is provable) it (tells me how long the shortest proof is), and (optionally prints it out).

This would take at least a decade of work. But along the way, I'd solve at least a million dollar mathematics problem, which would keep me funded. (Only one, ideally -- and one that admits a 'counterexample' anti-proof, because I can pretend I got lucky).

I'd recruit a friend who is better at this proof stuff than me, and see if we can make it generate more human-understandable proofs. And start looking up what you can do with a Halt() oracle (which is rather ridiculous).

Probably I could recruit a string theorist, and see if they can produce a computational question that would resolve questions about string theory, etc.

Another interesting idea would be to get a chip engineer and get them to describe the space of possible computer chips. And design a computer chip with a certain set of desired properties, that can be built with current technology, via brute-force search on the space of buildable computer chips. Each iteration would, of course, find errors in the space of possible chips we described, so this might not work, but it would be amusing.

After a period of time, once you had made enough money, you could start funding an actually robust framework of formal mathematics for a computer. Feed it real mathematical systems, and ask it if they are consistent. Do attacks on the space of all computer algorithms to solve particular problems in the most efficient way for a given program and problem size. Etc.

You could do the same with resource allocations for a company.

Note that while some of these problems seem dry, they could have massive effects.

[niteice]

I'd run an infinite loop, of course.

[shieldforyoureyes]

Configure an obscenely large neural net and feed it a copy of wikipedia. Then see what it wants to talk about.

[sje46]

This.

At the end of the story

Spoiler:

why can't they just rewind?
Also, I wonder what would happen if they fast-forwarded it?

[vnfedotov]

cat /dev/urandom|grep finite_loop

[Yakk]

This.

At the end of the story

Spoiler:

why can't they just rewind?
Also, I wonder what would happen if they fast-forwarded it?

Spoiler:

If they rewind, and never play ahead of their point in time, then they will cease to exist.

Fast-forwarding will show your future. Note that this future will take into account the fact that you have seen your future.

At some point, the worlds will reach a stable point. There will be infinitely more such worlds than ones not at a stable point. Thus futures that are likely to contain you having the ability to make decisions that are different than the future you see are exceedingly unlikely, once you hit the fast forward button.

So your free will, and possibly your own perception of your free will, will go away. A simple way to make your free will not happen would be for the universe to be destroyed the moment you hit the fast forward button.

(In effect, it is the time travel problem: if time travel changes time, and it is easy, then time will continue to be changed until the universe is sufficiently altered so that it just happens not to happen, or it is not likely to happen).

Now, by never hitting fast forward, they can hope to be in the universes where there can be at least a perception of free will. Which are more fun to be in.

[crzftx]

Also, I wonder what would happen if they fast-forwarded it?

Not that I know, but I think they could possibly break the universe.
Let's say I look to see what I'm going to do in T seconds. Now that I've seen that, the reality changes. So now, instead of action X, I decide I'll do action Y. But, the simulation would, of course, take that into account. So it says I'll do action Y. But now, the reality changes. ...
I see it like a recursive function. F(0) = 1; F(1) = 2; etc. These numbers represent the action the simulation says I'll do. I'll number each different reaction 1 higher. If ever F(x) < x, I break the universe (because F(3) returns 4, but then F(4) returns 3, the simulation cannot display anything; nothing happens in T seconds). If F(x) = x at some point, the simulation shows I do action x, and as a result, I do action x (the universe continues). If F(x) is always greater than x, I don't know what happens. The simulation can calculate an infinite amount of actions (and reactions) in no time, but I don't understand what happens. It would be like telling it to consider every natural number. Apparently it can consider them all, but I don't understand how it can ever stop...

[Squid Tamer]

Woah! I was considering posting this exact topic earlier today! (Get out of my head roundedge?)

Anyway, I had considered making a simple program to generate other programs randomly, (Just making up random 1's and 0's)and see what happens. Eventually (Within 0 seconds, I guess )Something interesting would happen. But that seems stupidly dangerous.

Other than that, I would just run a simple physics game, and watch as it just never lags no matter what! I suppose it would be possible to run a simulation of an infinite number of whatevers colliding. Might be fun to watch!

And also, since I guess we can assume that this computer has infinite memory as well, I would run a very nice file hosting website. (Infinite GB's for $10 a month!!! An infinitly better deal than our competitors!)

And, as a final thought, I would do this: http://xkcd.com/350/ but with an infinite number of computers.

I guess mine are sort of boring, because most of them are "Oh let's do this, but times infinity!"

[masher]

I guess mine are sort of boring, because most of them are "Oh let's do this, but times infinity!"

Just take the average!

[zombiefeynman]

First off, I'd buy a really big hard drive and a lot of RAM using some new prime-numbers I found. It may have a clock speed of infinity, but it would be nice to evaluate a lot of concurrent programs at the same infinitesimal time. Then I'd actually do stuff.

How about just feed arbitrary sized bits of /dev/urandom into new kernel images, then run them all on virtual machines? Somewhere, the perfect operating system is hiding in random chunks of space. As a matter of fact, so is Duke Nukem Forever! (Yes, Squid Tamer, this is your idea.)

I'd probably use the above approach to get a reasonable AI running. It would take time - not for the computer to generate it, but for me to sort through the infinite false positives write the death-dueling arena for prospective AI's. It would be like Fishtank, but with infinite participants and unlimited knowledge as the prize for the best refugee from the Yarrow Algorithm! I don't know what I'd do with the most theoretically powerful AI, though.

EDIT: and as to the infinitely changing prediction machine based on a simulation of the universe, there are two approaches.

1) Once calculated and displayed, the information is static and doesn't change (as in Minority Report - the short story). This way it can be wrong.
2) Once calculated, it is updated. It will eventually collapse into a Nash Equilibrium-like state ("four" if you know what I mean), and since it is infinitely fast, that equilibrium will be displayed (assuming there is one). I think an equilibrium will exist, but if not the screen will just flicker between the n most probably ones.

[phlip]

I'd learn Prolog... not much point using anything lower-level, at that point. Perhaps something even higher-level than Prolog.

[phider2]

This.

That reminds me of the rock-man comic.

Also, after reading the above post, I'd crack RSA, AES, etc, with QBASIC, just because I can.

[Yakk]

I'd learn Prolog... not much point using anything lower-level, at that point. Perhaps something even higher-level than Prolog.

Use prolog to express the properties of the language you want. Then ask for it.

[davidstvz]

I would write a simple genetic algorithm that relies on an excessive amount of time to increase it's complexity until it is self-aware. Then I'd converse with it. For safety, I would ensure the computer isn't connected to any network.

[roundedge]

For safety, I would ensure the computer isn't connected to any network.

Life will find a way.

[Yakk]

If the AI is smart enough, it will convince you to let it loose.

[afarnen]

http://xkcd.com/329/

Get extra-credit on the Turing test.

Though I'm not sure how it'd be done.

[aeromax]

Write a very simple artificial intelligence program. Allow it to write a second program, and allow the second program to modify the first. Insert a basic IRC client. Unleash on EFnet. Create the ultimate troll.

[flippmoke]

I would install Windows ME, just to see if it would destroy itself.

[zombiefeynman]

Nah. All the bloat in ME was just hidden code that seemed to lag the computer excessively, but in reality all that code was building up for galactic domination. The code was highly obfuscated and hidden by a rogue programmer who sits, still waiting for the last four ME computers to finish the plans, at which point the world will end.

[phider2]

This.

At the end of the story

Spoiler:

why can't they just rewind?
Also, I wonder what would happen if they fast-forwarded it?

Spoiler:

If they rewind, and never play ahead of their point in time, then they will cease to exist.

Fast-forwarding will show your future. Note that this future will take into account the fact that you have seen your future.

At some point, the worlds will reach a stable point. There will be infinitely more such worlds than ones not at a stable point. Thus futures that are likely to contain you having the ability to make decisions that are different than the future you see are exceedingly unlikely, once you hit the fast forward button.

So your free will, and possibly your own perception of your free will, will go away. A simple way to make your free will not happen would be for the universe to be destroyed the moment you hit the fast forward button.

(In effect, it is the time travel problem: if time travel changes time, and it is easy, then time will continue to be changed until the universe is sufficiently altered so that it just happens not to happen, or it is not likely to happen).

Now, by never hitting fast forward, they can hope to be in the universes where there can be at least a perception of free will. Which are more fun to be in.

I think that if they rewind it, they'll just see what happened at whatever point they go to. I mean, they existed before the computer was created in their level, because it had already been simulated. It's like if you're watching a video, and you rewind the video. The later part of the video doesn't cease to exist; you just can't see it.

[DSenette]

look at porn

[_MC_]

I would play Duke Nukem Forever

[M-x shell]

This is obviously a lighthearted thread, but it's worth pointing out that you can't complete an infinite loop, not even with an infinitely fast computer. If you tried to run the algorithm "while(true);" the instantaneous processor would compute that expression an infinite number of times during any interval of time, forever, but would never make any progress. This makes perfect sense, because \infty \div \infty is undefined. In other words, we cannot calculate the time necessary to execute the program by simply dividing the size of the problem by the speed of the processor, and when we look at it in terms of what will cause the program to terminate (in this case, true must equal false), it is clear that nothing will.

Also, the speed of the computer has nothing to do with how much memory it has. If a program requires more memory than is available, at any point during its execution, it simply will not work. Even if all of the operations occur at the same moment, the program must progress through a series of states in some sense. Otherwise, the program isn't actually being run.

That said, having infinitely fast computer would be awesome. To warm up, I'd use programs I have already written to "solve" chess (determine if white can force mate), find large prime numbers, and generate high-resolution fractals. As a long-term project, I'd write a program to work in propositional calculus, and feed it the axioms of number theory. I could have it randomly apply these simple rules to some starting point until it generates a given statement. If the program terminates, that statement is a provable statement of number theory. Having it record the proof, and find the shortest proof, would be only a bit more difficult. It could simply flip through every one-step proof, every two-step proof, and so on. It would start over each time, which would be enormously wasteful in terms of computation, but of course that doesn't matter in the slightest. The important thing is that the amount of memory being used at any stage is no larger than the proof (along with some overhead to keep track of where you are). I don't think it would be nearly as hard as Yakk suggested. The tough part would be understanding the proofs, but they can be proven correct mechanically, without any intuitive "grasp" of what they mean.

[Yakk]

Actually, there are computational models that allow you to "complete an infinite loop".

An example of such a model would be to find the actual limit of any algorithm (ie, impose a topology on the space of answers, and be able to get the actual limit to any degree of accuracy you request), if it has one; or answer the Halting problem. Quite likely these two questions are reducible to the other.

I don't think it would be nearly as hard as Yakk suggested.

I know a friend of mine spent years of study, then lots of work, to generate a computationally verifiable proof of Godel's incompleteness theorem.

Most 'proofs' that you see are full of skipped steps and holes, and the axiom rules we use are full of short cuts. So you need to build a completely computer-checkable system of axioms, and make sure your system is actually the system that you want to check (because you had to mangle it in order to make it computer-checkable).

[HAXUS THE LESSER]

I would calculate fibs and factorials all day long!

[ttsgeb]

Calculate pi.
Oh, I would also have it emulate a full computer that is fully customizable in order to see how things scale.
Afterwards, I would write an infinite loop of 1 second pauses and see if it finishes immediately.
After all my fun of testing it's infinite speed, I would install firefox with every extension and an animated theme and browse the web.
Once the web has all been seen, I would have it plan it's own sucessor that can manipulate space infinitely fast, allowing the robot apocalypse to finally come.

[phider2]

I forgot to say this before: I would play Crysis at full settings.

[quintopia]

Afterwards, I would write an infinite loop of 1 second pauses and see if it finishes immediately.

An infinitely fast computer would almost have to be infinitely parallelized if it contains a timeout instruction. Thus, the infinitely loop of one second waits should take a second to complete. However, such instructions should be the only ones that take positive time to execute, and are provided only to make the computer usable by humans.

Since the computer could just overlap instructions that require it to wait a specified length of time, a more useful usability instruction would likely be "wait for interrupt"

[M-x shell]

Actually, there are computational models that allow you to "complete an infinite loop".

An example of such a model would be to find the actual limit of any algorithm (ie, impose a topology on the space of answers, and be able to get the actual limit to any degree of accuracy you request), if it has one; or answer the Halting problem. Quite likely these two questions are reducible to the other.

I'm not quite sure what you're saying (sounds interesting though). It seems to me that specifying a degree of accuracy would turn this into a finite approximation problem. Could you elaborate?

I know a friend of mine spent years of study, then lots of work, to generate a computationally verifiable proof of Godel's incompleteness theorem.

Most 'proofs' that you see are full of skipped steps and holes, and the axiom rules we use are full of short cuts. So you need to build a completely computer-checkable system of axioms, and make sure your system is actually the system that you want to check (because you had to mangle it in order to make it computer-checkable).

Yes, but having infinite computing power completely changes the problem. Making the proof computer-checkable is trivial, because it is computer generated. You could simply use the same rules. Now, writing a program that forms proofs would still be reasonably difficult, but nothing like trying to do so with finite computation. It isn't that hard to figure out all the things that can be done (I chose number theory because it has a fairly simple set of rules). The main challenge is pruning the tree: getting the program to investigate only the most promising possibilities. That isn't even necessary in this hypothetical scenario. It could just blindly wander the space of all possible theorems and still find the answer instantly. In practice, such a simple approach is useless, even for small proofs. But with an infinitely fast computer, you can just brute-force it.