## 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.

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

phlip wrote:
Dason wrote:
fictiveLaark wrote:Everyone seems to have much better ideas but I think I would just want to count to the highest natural number.

As mind blowing as 8000 is... an infinitely fast computer could clearly count to it in 10 or less minutes. However, if you waited long enough you might be able to discover a larger number (8001?)

I thought the largest number was about 45 billion. Or am I getting my references mixed up?

You're confused. Clearly 23 million is larger than 45 billion. You only need to take a look at them side by side to see that.
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### Re: What would you do with an infinitely fast computer?

The highest integer is about 2.1 billion, but the highest positive integer is around 4.2 billion.

http://internetometer.com/give/4279
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Berengal
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### Re: What would you do with an infinitely fast computer?

And the highest natural number is the number that's one more than itself.
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### Re: What would you do with an infinitely fast computer?

No, the real highest number is Ozzy Osbourne, because he is as high as they come.
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fictiveLaark
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### Re: What would you do with an infinitely fast computer?

Wait, can an infinitely fast computer count higher than 2^64-1?

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

Yep. So can I.

2^64-1
-(2^64)
-(2^64)+1
-(2^64)+2
-(2^64)+3

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

phlip wrote:
Dason wrote:
fictiveLaark wrote:Everyone seems to have much better ideas but I think I would just want to count to the highest natural number.

As mind blowing as 8000 is... an infinitely fast computer could clearly count to it in 10 or less minutes. However, if you waited long enough you might be able to discover a larger number (8001?)

I thought the largest number was about 45 billion. Or am I getting my references mixed up?

You're most likely correct. I was too lazy to look it up so I pulled 8000 up (good enough approximation to infinity for me!).

Edit: You are indeed correct. You just brightened up 9 minutes of my day
double epsilon = -.0000001;

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

Good times.

Eh, let's face it. If I had an infinitely fast computer, I'd probably still use it for watching random videos on YouTube.

Code: Select all

`enum ಠ_ಠ {°□°╰=1, °Д°╰, ಠ益ಠ╰};void ┻━┻︵​╰(ಠ_ಠ ⚠) {exit((int)⚠);}`
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userxp
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### Re: What would you do with an infinitely fast computer?

The highest integer is the highest integer definable in one sentence plus two.

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

The largest number is one plus the predicate of this sentence.

http://internetometer.com/give/4279
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fictiveLaark
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### Re: What would you do with an infinitely fast computer?

People might hate me for saying this, but only one man knows the highest natural number, Bruce Schneier, and he will only tell it to you once you've defeated him in battle.

Edit:
Well, it looks like the forum itself frowns upon jokes about the star of Walker Texas Ranger.

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

phlip wrote:Good times.

Eh, let's face it. If I had an infinitely fast computer, I'd probably still use it for watching random videos on YouTube.
Plus rack up some crazy points on Folding@Home

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

Actually, the largest number tends to vary from day to day. Since people started measuring it in 1856, the largest it ever got was 274087721634.46 in August 1920, though geological data hints that there was a short period 34 million years ago where it reached about 1 trillion.
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Dason
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### Re: What would you do with an infinitely fast computer?

I'd brute force all of the Project Euler problems. Stickin it to the man! Finished in under a minute so my algorithm must be fine. Booyah.
double epsilon = -.0000001;

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

Yakk wrote: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).

The halting problem is for Turing machines, which have infinite tape memory, so the halting problem is still there; The "is provable program" can't exist , cause no matter how fast your computer can run, it will never halt. Even if you have a computer with and uncountable amount of memory, the independence of the axiom of choice shows that the halting problem in undecidable, and your "is provable program" can't exist. By definition a proof cannot be infinitely long (because the theorem is the last line of the proof), and the halting problem is equivalent to Godel's incompleteness.

M-x shell wrote: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.

LOL a decade of work? writing a program that forms proofs would still be reasonably difficult? haha we have a formal language that we use as for our proofs: just look at all the proofs of length 1, then all the proofs of length 2, then all the proofs of length 3, etc. Its pretty simple, and its not wandering around blindly, and it would take me 10 min to implement. It would give me a countable infinity of proofs, the last line of each proof is a theorem, and if theorem X and its converse aren't one of them, then theorem X is not provable.

Alrighht so can you tell I only read the first page of this post?
Cmebeh wrote:LOL you computer scientists; isn't it obvious? P = NP is undecidable à la continuum hypothesis

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

cause no matter how fast your computer can run, it will never halt.

Except this computer can run an infinite loop to completion.
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### Re: What would you do with an infinitely fast computer?

Cmebeh wrote:Alrighht so can you tell I only read the first page of this post thread?

To save yourself from further embarrassment, you may wish to peruse the whole thread. It does contain a lot of fluff, but there is also a lot of good discussion on the Halting Problem as it applies to various classes of infinite computer. Also see the Properties and models of infinitely fast computation thread.

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

Cmebeh wrote:Interests: trolling the physicists

Cmebeh, I'm not a physicist.
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Argency
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### Re: What would you do with an infinitely fast computer?

I agree with the people saying you couldn't complete a while(true) loop on this computer.

Imagine a demon (who can move infinitely quickly) coming into your house and messing with your lights. He switches your ceiling bulb on, waits half a second, switches it off, waits a quarter of a second, switches it on, waits an eighth of a second, switches it off, etc... After one second has passed, he's switching it on and off infinitely quickly with infinitely small pauses in between, but he won't ever stop. The light is in the state of being both "on" and "off" at all times t>1. So for an infinite loop, the computer will simultaneously be executing all of the functions required to run the loop at all times t>0, meaning it'll never give you a result.

So you couldn't find the highest prime (unless they really aren't infinite). The Riemann hypothesis is safe. Similarly, function grammar allows for nesting, which means that function space is infinite, so you'd never be able to map it. You could define an arbitrarily high (and therefore functionally infinite) number and get your computer to calculate for all n<x, but that's about it. On the other hand, you >could< solve the halting problem, because any problem that eventually winds down will do it infinitely quickly, so the only programs that take any length of time at all will take an infinite length of time, even on an infinitely fast computer.

With that in mind, I'd probably brute force simulated human brain space. For any finite number of neurons there are a finite number of possible brains. Anyone wanna meet Einstein?
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### Re: What would you do with an infinitely fast computer?

So you couldn't find the highest prime (unless they really aren't infinite). The Riemann hypothesis is safe.

We had this discussion a few pages back, though with the digits of pi instead of primes. You can't find the highest prime number, since that doesn't exist, but you can find all the prime numbers, (which, if you wanted, you could use to prove Riemann.) since your computer has countably infinite processing power/memory, and there are countably infinite prime numbers. (I think. I'm not a mathematician)
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### Re: What would you do with an infinitely fast computer?

Sorry, you're right, I was just coming back to edit in an apology when I read this post. I was being a square and thinking about it all wrong. You can of course calculate all the primes, which means you could prove the Riemann hypothesis, even if you can't calculate the last one. My own argument should have shown me that. So you could map function space as well. I love xkcd because I learn things from you guys.
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### Re: What would you do with an infinitely fast computer?

Argency wrote:So you could map function space as well. I love xkcd because I learn things from you guys.
Only certain functions. There are uncountably many functions from integers to integers, and even more from reals to reals. Any function you could algorithmically describe would be fine of course.
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markop2003
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### Re: What would you do with an infinitely fast computer?

Find the cure to the top 100 fatal diseases then pack the cures into cases and bury them all over the world just to see what the conspiracy nuts come up with.

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

markop2003 wrote:Find the cure to the top 100 fatal diseases then pack the cures into cases and bury them all over the world just to see what the conspiracy nuts come up with.

This involved significantly more than an IFC. Firstly, you'll need a scientist/doctor to help you write the program to find the cures. Then, you'd need to scatter them all over the world.
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### Re: What would you do with an infinitely fast computer?

Seriously? You'd just bury them? There are so many possibilities, e.g.: you could create 5 cure cocktails (each one containing 20 cures, no groups crossing over), and inject each individual in 5 with each set of cures. Tell them they can assimilate the cures of any individual they cannibalise (and engineer it as such) and see what breaks loose. Then just to make it even more of a Highlander scenario, make sure that when all 100 cures are combined into an individual they all react with each other to produce a poison. One of the more irony-laden (and probably evil) possibilities but I'm sure there are better.

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

For the halting problem, would it be possible to make the computer run the program in question and then terminate it if it runs for more than half a second?
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Thesh
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### Re: What would you do with an infinitely fast computer?

I would use it to run apache on linux and display a static HTML page saying "I have all the processing power in the world. I could solve world hunger, cure diseases, colonize space, allow everyone to live like kings. Instead, I choose to display this webpage."
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styrofoam
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### Re: What would you do with an infinitely fast computer?

Thesh wrote:I would use it to run apache on linux and display a static HTML page saying "I have all the processing power in the world. I could solve world hunger, cure diseases, colonize space, allow everyone to live like kings. Instead, I choose to display this webpage."

I'm amazed that there are people who would tease all humanity like a little kid teasing a dog with his hamburger.
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### Re: What would you do with an infinitely fast computer?

Robert'); DROP TABLE *; wrote:
cause no matter how fast your computer can run, it will never halt.

Except this computer can run an infinite loop to completion.

No, it can't. Ugh, it's been discussed in this thread so much I'll not even try.
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Thesh
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### Re: What would you do with an infinitely fast computer?

styrofoam wrote:
Thesh wrote:I would use it to run apache on linux and display a static HTML page saying "I have all the processing power in the world. I could solve world hunger, cure diseases, colonize space, allow everyone to live like kings. Instead, I choose to display this webpage."

I'm amazed that there are people who would tease all humanity like a little kid teasing a dog with his hamburger.

Well, I wasn't really being honest. I would really randomly generate code that designs robots for fighting, and generates the AI. I would then test them against every conceivable situation, and figure out the most efficient way to take over the world and enslave the human race.
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styrofoam
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### Re: What would you do with an infinitely fast computer?

Thesh wrote:Well, I wasn't really being honest. I would really randomly generate code that designs robots for fighting, and generates the AI. I would then test them against every conceivable situation, and figure out the most efficient way to take over the world and enslave the human race.

This one has been discussed before. Randomly generating programs will give you an infinite amount of AIs, and and infinite amount of non-AIs. How are you going to tell the difference? (for any question you test the maybe-AIs with, there are going to be an infinite amount of programs that just happen to give the right answer).
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Thesh
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### Re: What would you do with an infinitely fast computer?

styrofoam wrote:
Thesh wrote:Well, I wasn't really being honest. I would really randomly generate code that designs robots for fighting, and generates the AI. I would then test them against every conceivable situation, and figure out the most efficient way to take over the world and enslave the human race.

This one has been discussed before. Randomly generating programs will give you an infinite amount of AIs, and and infinite amount of non-AIs. How are you going to tell the difference? (for any question you test the maybe-AIs with, there are going to be an infinite amount of programs that just happen to give the right answer).

Simple way is to test against a simulation. If it passes with a desired level of efficiency, it is saved, otherwise it is discarded. You take the first 100 quintillion or so results to pass, and then sort by efficiency. Then you can analyze the top ten results yourself and make your choice.
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styrofoam
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### Re: What would you do with an infinitely fast computer?

Thesh wrote:Simple way is to test against a simulation. If it passes with a desired level of efficiency, it is saved, otherwise it is discarded. You take the first 100 quintillion or so results to pass, and then sort by efficiency. Then you can analyze the top ten results yourself and make your choice.

What do you define as "efficient"? If you define shortness, I can almost guarantee that the top 10 (maybe even top 100 quintillion) are all going to crash in any situation other than the one you set up.
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### Re: What would you do with an infinitely fast computer?

Simulate every situation.

http://internetometer.com/give/4279
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Thesh
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### Re: What would you do with an infinitely fast computer?

styrofoam wrote:
Thesh wrote:Simple way is to test against a simulation. If it passes with a desired level of efficiency, it is saved, otherwise it is discarded. You take the first 100 quintillion or so results to pass, and then sort by efficiency. Then you can analyze the top ten results yourself and make your choice.

What do you define as "efficient"? If you define shortness, I can almost guarantee that the top 10 (maybe even top 100 quintillion) are all going to crash in any situation other than the one you set up.

By efficiency, I mean the combination of cost of building the robot army, testing in tens of thousands of simulated combat situations with scoring based on time to win and casualties, estimated time to take over the world based on many different scenarios, and estimated casualties for both friend and foe. The point of analyzing the AI yourself is to make sure there aren't problems with it.
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TheChewanater
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### Re: What would you do with an infinitely fast computer?

Write a speech-writing program and use it as a teleprompter to politically maneuver your way to world dominance.

I'm pretty sure this is what Obama's doing.

http://internetometer.com/give/4279
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styrofoam
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### Re: What would you do with an infinitely fast computer?

TheChewanater wrote:Simulate every situation.

If you face every maybe-AI with every possible situation? You'll eliminate every program, AI or not. Nobody's perfect.

Thesh wrote:By efficiency, I mean the combination of cost of building the robot army, testing in tens of thousands of simulated combat situations with scoring based on time to win and casualties, estimated time to take over the world based on many different scenarios, and estimated casualties for both friend and foe.

So you're not actually worried about building an AI. You just want a robot army to take over the world. (at least, that's what your algorithm will get you).
Last edited by styrofoam on Fri Jun 11, 2010 12:59 am UTC, edited 1 time in total.
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### Re: What would you do with an infinitely fast computer?

See which passes the most situations in the least amount of instructions.

http://internetometer.com/give/4279
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styrofoam
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### Re: What would you do with an infinitely fast computer?

TheChewanater wrote:See which passes the most situations in the least amount of instructions.

How do you know it won't just crash when you need it most? Unlike programs written by humans, a randomly-generated program may contain self-modifying code, magic numbers that change while the program runs, gotos, parts of the program used as data, or even parts of the program used as data, changed, and then used by the same block of code as data (mahem if it gets executed).
aadams wrote:I am a very nice whatever it is I am.

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

styrofoam wrote:
TheChewanater wrote:See which passes the most situations in the least amount of instructions.

How do you know it won't just crash when you need it most? Unlike programs written by humans, a randomly-generated program may contain self-modifying code, magic numbers that change while the program runs, gotos, parts of the program used as data, or even parts of the program used as data, changed, and then used by the same block of code as data (mahem if it gets executed).

I think their code crashing is actually a good thing for humanity.
double epsilon = -.0000001;