## What would you do with an infinitely fast computer?

A place to discuss the science of computers and programs, from algorithms to computability.

Formal proofs preferred.

Moderators: phlip, Moderators General, Prelates

roundedge
Posts: 167
Joined: Wed Jun 20, 2007 3:53 am UTC

### What would you do with an infinitely fast computer?

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
Posts: 623
Joined: Mon Jun 16, 2008 10:50 am UTC
Location: Amsterdam, The Netherlands
Contact:

### Re: What would you do with an infinitely fast computer?

I would brute-force NP-hard problems (and problems from even harder complexity classes) like there's no tomorrow. There probably wouldn't be.
Last edited by Naurgul on Fri May 22, 2009 9:32 am UTC, edited 1 time in total.
Praised be the nightmare, which reveals to us that we have the power to create hell.

Ended
Posts: 1459
Joined: Fri Apr 20, 2007 3:27 pm UTC
Location: The Tower of Flints. (Also known as: England.)

### Re: What would you do with an infinitely fast computer?

Generally I try to make myself do things I instinctively avoid, in case they are awesome.
-dubsola

roundedge
Posts: 167
Joined: Wed Jun 20, 2007 3:53 am UTC

### Re: What would you do with an infinitely fast computer?

Ended wrote: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
Posts: 136
Joined: Thu Nov 20, 2008 5:05 pm UTC

### Re: What would you do with an infinitely fast computer?

Find prime numbers and sell them

ATCG
Posts: 471
Joined: Sat Aug 18, 2007 3:44 am UTC
Location: Straight up the jω axis

### Re: What would you do with an infinitely fast computer?

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.
"The age of the universe is 100 billion, if the units are dog years." - Sean Carroll

Berengal
Superabacus Mystic of the First Rank
Posts: 2707
Joined: Thu May 24, 2007 5:51 am UTC
Location: Bergen, Norway
Contact:

### Re: What would you do with an infinitely fast computer?

Nothing. It's impossible to use. Any program you run will either not start or enter an infinite loop right away.
It is practically impossible to teach good programming to students who are motivated by money: As potential programmers they are mentally mutilated beyond hope of regeneration.

Ended
Posts: 1459
Joined: Fri Apr 20, 2007 3:27 pm UTC
Location: The Tower of Flints. (Also known as: England.)

### Re: What would you do with an infinitely fast computer?

roundedge wrote:
Ended wrote: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?
Generally I try to make myself do things I instinctively avoid, in case they are awesome.
-dubsola

quintopia
Posts: 2906
Joined: Fri Nov 17, 2006 2:53 am UTC
Location: atlanta, ga

### Re: What would you do with an infinitely fast computer?

Berengal wrote: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
Posts: 1783
Joined: Sun Nov 30, 2008 9:50 pm UTC

### Re: What would you do with an infinitely fast computer?

quintopia wrote: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
Poster with most posts but no title.
Posts: 11083
Joined: Sat Jan 27, 2007 7:27 pm UTC
Location: E pur si muove

### Re: What would you do with an infinitely fast computer?

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.
One of the painful things about our time is that those who feel certainty are stupid, and those with any imagination and understanding are filled with doubt and indecision - BR

Last edited by JHVH on Fri Oct 23, 4004 BCE 6:17 pm, edited 6 times in total.

niteice
Posts: 186
Joined: Wed May 02, 2007 4:17 am UTC
Contact:

### Re: What would you do with an infinitely fast computer?

I'd run an infinite loop, of course.
GENERATION 4294967292: The first time you see this, copy it into your sig on any forum, negate the generation, and convert it to a 32-bit unsigned integer. Social experiment.

shieldforyoureyes
Posts: 342
Joined: Sat Apr 19, 2008 9:00 am UTC
Contact:

### Re: What would you do with an infinitely fast computer?

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

sje46
Posts: 4730
Joined: Wed May 14, 2008 4:41 am UTC
Location: New Hampshire

### Re: What would you do with an infinitely fast computer?

Ended wrote: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?
General_Norris: Taking pride in your nation is taking pride in the division of humanity.
Pirate.Bondage: Let's get married. Right now.

vnfedotov
Posts: 2
Joined: Mon May 25, 2009 12:41 am UTC

### Re: What would you do with an infinitely fast computer?

cat /dev/urandom|grep finite_loop

Yakk
Poster with most posts but no title.
Posts: 11083
Joined: Sat Jan 27, 2007 7:27 pm UTC
Location: E pur si muove

### Re: What would you do with an infinitely fast computer?

sje46 wrote:
Ended wrote: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.
One of the painful things about our time is that those who feel certainty are stupid, and those with any imagination and understanding are filled with doubt and indecision - BR

Last edited by JHVH on Fri Oct 23, 4004 BCE 6:17 pm, edited 6 times in total.

crzftx
Posts: 371
Joined: Tue Jul 29, 2008 4:49 am UTC
Location: Rockford, IL

### Re: What would you do with an infinitely fast computer?

sje46 wrote: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
Posts: 220
Joined: Fri Apr 03, 2009 3:59 am UTC
Location: Over there
Contact:

### Re: What would you do with an infinitely fast computer?

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
Posts: 821
Joined: Tue Oct 23, 2007 11:07 pm UTC
Location: Melbourne, Australia

### Re: What would you do with an infinitely fast computer?

Squid Tamer wrote: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
Posts: 211
Joined: Thu Apr 02, 2009 4:16 pm UTC

### Re: What would you do with an infinitely fast computer?

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
Restorer of Worlds
Posts: 7554
Joined: Sat Sep 23, 2006 3:56 am UTC
Location: Australia
Contact:

### Re: What would you do with an infinitely fast computer?

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

Code: Select all

enum ಠ_ಠ {°□°╰=1, °Д°╰, ಠ益ಠ╰};void ┻━┻︵​╰(ಠ_ಠ ⚠) {exit((int)⚠);}
[he/him/his]

phider2
Posts: 71
Joined: Sun May 24, 2009 10:52 pm UTC

### Re: What would you do with an infinitely fast computer?

Ended wrote: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
Poster with most posts but no title.
Posts: 11083
Joined: Sat Jan 27, 2007 7:27 pm UTC
Location: E pur si muove

### Re: What would you do with an infinitely fast computer?

phlip wrote: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.
One of the painful things about our time is that those who feel certainty are stupid, and those with any imagination and understanding are filled with doubt and indecision - BR

Last edited by JHVH on Fri Oct 23, 4004 BCE 6:17 pm, edited 6 times in total.

davidstvz
Posts: 14
Joined: Tue May 26, 2009 6:08 pm UTC

### Re: What would you do with an infinitely fast computer?

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
Posts: 167
Joined: Wed Jun 20, 2007 3:53 am UTC

### Re: What would you do with an infinitely fast computer?

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

Life will find a way.

Yakk
Poster with most posts but no title.
Posts: 11083
Joined: Sat Jan 27, 2007 7:27 pm UTC
Location: E pur si muove

### Re: What would you do with an infinitely fast computer?

If the AI is smart enough, it will convince you to let it loose.
One of the painful things about our time is that those who feel certainty are stupid, and those with any imagination and understanding are filled with doubt and indecision - BR

Last edited by JHVH on Fri Oct 23, 4004 BCE 6:17 pm, edited 6 times in total.

afarnen
Posts: 157
Joined: Mon May 05, 2008 12:12 pm UTC

### Re: What would you do with an infinitely fast computer?

http://xkcd.com/329/

Get extra-credit on the Turing test.

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

aeromax
Posts: 9
Joined: Wed May 27, 2009 12:40 am UTC

### Re: What would you do with an infinitely fast computer?

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
Posts: 11
Joined: Thu Apr 23, 2009 2:08 am UTC

### Re: What would you do with an infinitely fast computer?

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

zombiefeynman
Posts: 211
Joined: Thu Apr 02, 2009 4:16 pm UTC

### Re: What would you do with an infinitely fast computer?

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
Posts: 71
Joined: Sun May 24, 2009 10:52 pm UTC

### Re: What would you do with an infinitely fast computer?

Yakk wrote:
sje46 wrote:
Ended wrote: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
Posts: 2418
Joined: Fri Mar 06, 2009 8:08 pm UTC

### Re: What would you do with an infinitely fast computer?

look at porn
The Righteous Hand Of Retribution
"The evaporation of 4 million who believe this crap would leave the world an instantly better place." ~Andre Codresu (re: "the Rapture")

_MC_
Posts: 105
Joined: Fri May 16, 2008 6:35 am UTC

### Re: What would you do with an infinitely fast computer?

I would play Duke Nukem Forever

M-x shell
Posts: 20
Joined: Thu May 21, 2009 2:07 am UTC

### Re: What would you do with an infinitely fast computer?

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 [imath]\infty \div \infty[/imath] 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
Poster with most posts but no title.
Posts: 11083
Joined: Sat Jan 27, 2007 7:27 pm UTC
Location: E pur si muove

### Re: What would you do with an infinitely fast computer?

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).
One of the painful things about our time is that those who feel certainty are stupid, and those with any imagination and understanding are filled with doubt and indecision - BR

Last edited by JHVH on Fri Oct 23, 4004 BCE 6:17 pm, edited 6 times in total.

HAXUS THE LESSER
Posts: 2
Joined: Mon Jun 01, 2009 3:19 pm UTC

### Re: What would you do with an infinitely fast computer?

I would calculate fibs and factorials all day long!

ttsgeb
Posts: 4
Joined: Sun Apr 26, 2009 1:32 am UTC
Location: Right, Left, Left, Right, Up.
Contact:

### Re: What would you do with an infinitely fast computer?

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
Posts: 71
Joined: Sun May 24, 2009 10:52 pm UTC

### Re: What would you do with an infinitely fast computer?

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

quintopia
Posts: 2906
Joined: Fri Nov 17, 2006 2:53 am UTC
Location: atlanta, ga

### Re: What would you do with an infinitely fast computer?

ttsgeb wrote: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
Posts: 20
Joined: Thu May 21, 2009 2:07 am UTC

### Re: What would you do with an infinitely fast computer?

Yakk wrote: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?

Yakk wrote: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.