Just because some encryption mechanisms are crappy, doesn't mean you can't put together good encryption.
SSL with a reasonable key length is essentially unbreakable unless there an exploit in the encryption software.
Some day someone may come up with a trick to defeat it, but there are lots of other encryption mechanisms that are just as secure.
Honestly, I don't get why wireless uses WEP or WPA. We've had VPNs and SSL secure enough for very valuable financial data for a long time; they are proven in the field; and given modern computers, they're not really resource intensive. WEP and WPA are toy security.
I clicked on the replies to the GP to make exactly this point. Somebody mod parent up!
These guys aren't just trying to deal $100 damage to the public interest (by taking a work that might have been popular if it were available for free & legally sharable) to make an extra $1 (by getting that occasional purchase of the restricted work). They would eliminate all sharing of information (with the exception of their advertising) if they could get away with it, because free information might compete with your attention. Attention that they wanted spent on something that put $$$ in their pocket.
Well, I have never deeply understood the incompleteness theorems, so you have me there;-) I've promised myself to devote the effort to do so, but I have never managed to follow through. (Family, full time job, side projects,...)
I agree with you that finiteness of the universe doesn't mean that incompleteness can't apply, but it does mean that it doesn't of necessity apply.
I don't think I've heard the argument that the universe is finite before from an outside source. I've just spent a lot of time thinking about the alternatives that incompleteness offers. Finally I realized that being out of the bounds of applicability of the theorem was one of the alternatives, and it seems well worth consideration.
There is a roughly analogous common argument regarding artificial intelligence: It is commonly argued that the human mind can step outside the incompleteness theorem, therefore it can't be simulated with a turing machine. The counterargument of course is that the human mind may step outside the incompleteness theorem and evaluate the truth of statements outside of the mathematical system in which they are expressed, but that doesn't mean it can do so for all true statements in all mathematical systems. The latter is what would be required for the mind to step outside incompleteness - you can always construct meta-systems to recognize truth. (In fact, if I understand correctly that's largely what the incompleteness theorem is saying.) To go beyond the incompleteness theorem would require that you could recognize the truth of any statement, regardless of the mathematical system, which we obviously can't do.
I am not at all sure that the physical laws are more expressive than peano arithmetic. If the universe is bounded in space and time, and has finite "resolution" (i.e. nothing can be smaller than a Planck length or some similar small length), then there are a finite (if large) number of numbers that can be expressed using the material in the universe.
So the physical laws could be both consistent and complete, because they're weaker than those required for Goedel's proof to apply.
I am not a physicist either, but I do have a BS in Physics.
You are almost exactly right... it is not that the two particles have identical properties, it is that they must have complementary values for properties that are conserved.
For example, the phase of two photons created from an electron & positron collision must cancel out to no phase. I don't remember if that means that they are 90 degrees out of phase or have the same phase... but at any rate, the phase is also indeterminate until measured. If you use two polarized lenses, one to measure the phase of each photon, at distant points, then and if both photons through the lenses, you both know what phase the other measured.
If you randomly flip the lenses between two orientations that are 90 degrees from one another, and tell each other when the photons get through, then you record the orientation each time the photon got through. Now you both have a shared random key for a one time pad.
I'm sorry; that was years ago and it was a RAID controller that was purchased by the sysadmin at my workplace at the time. Those controllers failed, then the replacements eventually failed too.
I should have made it a point to find out, but I didn't.
And what happens when the RAID controller fails and corrupts all of your drives?
Because I've seen that happen more than once.
I'm not saying the more expensive solution is better. I'm just saying that in my personal experience I've seen *more* data destroyed from RAID controller failure than from hard drive failure. I would love to find out the solution to that one.
I do not claim to be a hardware expert or system administrator, so there may be a well known solution (don't buy 'brand X' RAID controllers). I just don't happen to know it.
So, accelerating at 1 g (ignoring relativistic effects, which are less than an order of magnitude), you will get to.5 c in (1.5 * 10^8 / 10) = 1.5 * 10^7 seconds. There are ~10^5 seconds in a day, so this is about 150 days.
If you can handle 2 gs of acceleration, it's only 75 days.
It's not the g forces or the time it takes to accelerate that is the big problem with interstellar travel; it's getting that much propulsive energy on your ship. You have to have either fuel that you pick up on the way (i.e. Bussard ramjet) or antimatter fuel.
To propel your ship to.5 c using only fuel you started with, you need more than half the mass of your ship as fuel, and half of that must be antimatter.
Not even finding something more energetic than matter/antimatter collision would help - by special relativity, energy has mass, so matter/antimatter collision has highest energy density possible.
I have a BS in Mathematics, and quite frankly most of the time I find Wikipedia useless as a reference for Mathematics. This is because I don't understand/remember the terminology they're using! Let me repeat that: I have a BS in Math, and Wikipedia's math terminology is beyond me. (I should point out that I got my degree over a dozen years ago, though.)
As an example, I just looked up the Wikipedia entry on Group Theory. The first paragraph is comprehensible, but virtually information-free. The second paragraph uses technical terms that I would have to look up for them to mean enough to be informative.
From there on out it looks to me as if everything would only mean anything at all to someone who already has a very good handle on just what Group Theory is.
Now, if you skip down to the definition of a group, that's what I remember from my graduate Algebra course and it is more or less readable. Why the hell couldn't that be up top? Moreover, why couldn't the main article for Group Theory essentially be a non-technical rendition of that definition, along with some non-technical examples of where Group Theory is used?
There could be a second Wikipidia article, maybe "Group Theory, Advanced" that reads more like the current main article does.
I've seen some people pointing out that Wikipedia would have to offer some misinformation to be more readable, and that's sufficient reason to not be readable. That's horse crap. Suppose it turns out physics is too complicated for humans to understand accurately without two decades of study. Should we then not teach anyone newtonian gravity, because to avoid misinformation everyone needs to get two or three PhDs to understand it completely?
Read Feynmann's Lectures on Physics. He states up front that he's going to lie to the students a little, so he can present to them some useful tools for solving problems before he complicates it. His audience is physics students at MIT. If Feynmann can simplify things so MIT physics students can get started, Wikipedia can simplify things for their audience of random idiots on the web.
You are absolutely right. Thanks for giving me the impetus to look into this to the degree it deserved, and helping me stop spreading misinformation:-)
Sure, but the problem is that as far as I know all private key encryption currently in wide use is based on factoring large numbers. Which means Shor's algorithm applies. Which means that there's no longer that asymmetric relationship between the difficulty of encrypting data and decrypting it, which makes the encryption worthless.
I imagine that there are well known non-factoring based private/public encryption (elliptical, etc.). We could switch to those. That doesn't help with data that's already out there that was encrypted using old methods, and there's no guarantee that those alternate methods aren't just as vulnerable to some clever quantum algorithm.
Really, the existence of Shor's algorithm is pretty weird. I believe it means that quantum computers are more powerful than turing machines, which turns normal algorithm analysis on its head.
OK, double crap, I think what I said was mostly OK.
Remember, here the N I'm talking about is the number of possibilities, not the amount of data it takes to represent those possibilities. So for 16 million possibilities the N I'm talking about is 16 million, not 24 (the number of bits it takes to represent 16 million possibilities, and the typical usage of N in the O(N) notation).
Of course, you're right that my comment there didn't include the time it takes for f(x) to execute, but for many applications that can be constant time.
I'm just arguing the fine points to make sure my understanding isn't faulty...
Essentially, it means you can solve any NP problem in N^.5 time.
Yeah, crap, I shouldn't have said that. I think the rest of the post is on target, though...
I wasn't trying to claim that Grover's algorithm would let you solve problems in polynomial time. I may well have expressed the time taken incorrectly... hmm, it seems to me that saying "it takes N^.5 applications of the algorithm versus N applications for a classical computer" is equivalent (in terms of the speed) to what you said.
I do think that qualifying Grover's algorithm as being for searching problems is misleading. It's true (it is for inverting functions, i.e. searching for the input that gives the desired output) but GA is useful for much, much more than what most people think of when they say 'search', for example the computer design problem I gave as an example.
It's possible I misunderstood something significant about the algorithm, but I don't think so...
That is not entirely true - a quantum computer can't just test all bit combinations at once and tell you which one has the property you want. See my other post.
Quantum computers don't turn NP into P. I.e. they don't let you solve NP problems (where recognizing a correct answer is very easy but you have to test all answers to see which is correct) in an amount of time that is a polynomial function of the size of the input.
There are two specific algorithms for quantum computers that have a big impact on encryption:
Shor's algorithm lets a quantum computer factor a number in polynomial time. It requires a number of qubits that is some multiple (greater than 1) of the number of bits in the number. So, once we have quantum computers with a few thousand qubits, all encryption mechanisms based on the difficulty of factoring numbers (which is most mechanisms) are broken.
Grover's algorithm lets a quantum computer look up an entry in an unordered dictionary in N^.5 time, where N is the number of entries in the dictionary.
Grover's algorithm, if I understand it properly, is a Big Deal. When they say "look up an entry in a dictionary", they really mean "give an entry for which an arbitrary algorithm returns a desired value". Essentially, it means you can solve any NP problem in N^.5 time. For example, with a simulation algorithm you could find a satisfactory design out of 100,000,000,000,000 different computer designs in 10,000,000 applications of the simulation algorithm, as opposed to the 100,000,000,000,000 applications it could take on a normal computer.
Another example of applying Grover's algorithm would be cracking a password (regardless of the encryption algorithm used). Let N be the number of possible password combinations. On average cracking a password would take N/2 applications of the encryption algorithm using a normal computer; it would take N^.5 applications using a quantum computer.
Quantum computing doesn't invalidate encryption, but real QC would essentially invalidate encryption algorithms based on the difficulty of factoring large numbers and substantially reduce the difficulty to crack any other algorithmic encryption.
Of course, one time pads are still totally unbreakable if used properly...
My entire point is that most Americans identify their country with freedom, an association it does little to deserve. What's more, most Americans (and I'm guessing based on your comment that you're included here) don't really want America to be free.
If you don't fit the bill and you don't even aspire to, you should choose another way of identifying yourself.
I refined my POV in several other posts - I think restrictions like this are OK at the community level. I don't think they're OK at a state or national level in a country that purports to be free.
Sorry, I should say that I would love to see someplace where people were really free to do things that don't harm one another, and still restricted from doing things that do.
OK, scratch my gp response. It is always easy to be misunderstood. I think I've clarified my points so that you, at least, don't misunderstand them any more.
I still think the reply to my original post in this thread was intentionally antagonistic, and I reserve the right to be an ass to someone who's asking for it;-)
You're absolutely right. I wasn't arguing that we should live in anarchy, just that we shouldn't be restricted from doing things that harm no one. (Although, I actually do think local communities should be able to establish a culture, i.e. restrict people from doing things that harm no one.)
My original examples were meant to provide a partial list of things that quite often harm no one (with the possible exception of the person performing the actions) but are illegal.
Slashdot Mirror
Just because some encryption mechanisms are crappy, doesn't mean you can't put together good encryption.
SSL with a reasonable key length is essentially unbreakable unless there an exploit in the encryption software.
Some day someone may come up with a trick to defeat it, but there are lots of other encryption mechanisms that are just as secure.
Honestly, I don't get why wireless uses WEP or WPA. We've had VPNs and SSL secure enough for very valuable financial data for a long time; they are proven in the field; and given modern computers, they're not really resource intensive. WEP and WPA are toy security.
uh, encrypt the traffic...
I clicked on the replies to the GP to make exactly this point. Somebody mod parent up!
These guys aren't just trying to deal $100 damage to the public interest (by taking a work that might have been popular if it were available for free & legally sharable) to make an extra $1 (by getting that occasional purchase of the restricted work). They would eliminate all sharing of information (with the exception of their advertising) if they could get away with it, because free information might compete with your attention. Attention that they wanted spent on something that put $$$ in their pocket.
Well, I have never deeply understood the incompleteness theorems, so you have me there ;-) I've promised myself to devote the effort to do so, but I have never managed to follow through. (Family, full time job, side projects, ...)
I agree with you that finiteness of the universe doesn't mean that incompleteness can't apply, but it does mean that it doesn't of necessity apply.
I don't think I've heard the argument that the universe is finite before from an outside source. I've just spent a lot of time thinking about the alternatives that incompleteness offers. Finally I realized that being out of the bounds of applicability of the theorem was one of the alternatives, and it seems well worth consideration.
There is a roughly analogous common argument regarding artificial intelligence:
It is commonly argued that the human mind can step outside the incompleteness theorem, therefore it can't be simulated with a turing machine. The counterargument of course is that the human mind may step outside the incompleteness theorem and evaluate the truth of statements outside of the mathematical system in which they are expressed, but that doesn't mean it can do so for all true statements in all mathematical systems. The latter is what would be required for the mind to step outside incompleteness - you can always construct meta-systems to recognize truth. (In fact, if I understand correctly that's largely what the incompleteness theorem is saying.) To go beyond the incompleteness theorem would require that you could recognize the truth of any statement, regardless of the mathematical system, which we obviously can't do.
I am not at all sure that the physical laws are more expressive than peano arithmetic. If the universe is bounded in space and time, and has finite "resolution" (i.e. nothing can be smaller than a Planck length or some similar small length), then there are a finite (if large) number of numbers that can be expressed using the material in the universe.
So the physical laws could be both consistent and complete, because they're weaker than those required for Goedel's proof to apply.
I am not a physicist either, but I do have a BS in Physics.
You are almost exactly right... it is not that the two particles have identical properties, it is that they must have complementary values for properties that are conserved.
For example, the phase of two photons created from an electron & positron collision must cancel out to no phase. I don't remember if that means that they are 90 degrees out of phase or have the same phase... but at any rate, the phase is also indeterminate until measured. If you use two polarized lenses, one to measure the phase of each photon, at distant points, then and if both photons through the lenses, you both know what phase the other measured.
If you randomly flip the lenses between two orientations that are 90 degrees from one another, and tell each other when the photons get through, then you record the orientation each time the photon got through. Now you both have a shared random key for a one time pad.
I'm sorry; that was years ago and it was a RAID controller that was purchased by the sysadmin at my workplace at the time. Those controllers failed, then the replacements eventually failed too.
I should have made it a point to find out, but I didn't.
And what happens when the RAID controller fails and corrupts all of your drives?
Because I've seen that happen more than once.
I'm not saying the more expensive solution is better. I'm just saying that in my personal experience I've seen *more* data destroyed from RAID controller failure than from hard drive failure. I would love to find out the solution to that one.
I do not claim to be a hardware expert or system administrator, so there may be a well known solution (don't buy 'brand X' RAID controllers). I just don't happen to know it.
excellent point...
.5 c = 1.5 * 10^8 m/s
.5 c in (1.5 * 10^8 / 10) = 1.5 * 10^7 seconds. There are ~10^5 seconds in a day, so this is about 150 days.
.5 c using only fuel you started with, you need more than half the mass of your ship as fuel, and half of that must be antimatter.
acceleration of gravity on earth is ~10 m/s^2
So, accelerating at 1 g (ignoring relativistic effects, which are less than an order of magnitude), you will get to
If you can handle 2 gs of acceleration, it's only 75 days.
It's not the g forces or the time it takes to accelerate that is the big problem with interstellar travel; it's getting that much propulsive energy on your ship. You have to have either fuel that you pick up on the way (i.e. Bussard ramjet) or antimatter fuel.
To propel your ship to
Not even finding something more energetic than matter/antimatter collision would help - by special relativity, energy has mass, so matter/antimatter collision has highest energy density possible.
I have a BS in Mathematics, and quite frankly most of the time I find Wikipedia useless as a reference for Mathematics. This is because I don't understand/remember the terminology they're using! Let me repeat that: I have a BS in Math, and Wikipedia's math terminology is beyond me. (I should point out that I got my degree over a dozen years ago, though.)
As an example, I just looked up the Wikipedia entry on Group Theory. The first paragraph is comprehensible, but virtually information-free. The second paragraph uses technical terms that I would have to look up for them to mean enough to be informative.
From there on out it looks to me as if everything would only mean anything at all to someone who already has a very good handle on just what Group Theory is.
Now, if you skip down to the definition of a group, that's what I remember from my graduate Algebra course and it is more or less readable. Why the hell couldn't that be up top? Moreover, why couldn't the main article for Group Theory essentially be a non-technical rendition of that definition, along with some non-technical examples of where Group Theory is used?
There could be a second Wikipidia article, maybe "Group Theory, Advanced" that reads more like the current main article does.
I've seen some people pointing out that Wikipedia would have to offer some misinformation to be more readable, and that's sufficient reason to not be readable. That's horse crap. Suppose it turns out physics is too complicated for humans to understand accurately without two decades of study. Should we then not teach anyone newtonian gravity, because to avoid misinformation everyone needs to get two or three PhDs to understand it completely?
Read Feynmann's Lectures on Physics. He states up front that he's going to lie to the students a little, so he can present to them some useful tools for solving problems before he complicates it. His audience is physics students at MIT. If Feynmann can simplify things so MIT physics students can get started, Wikipedia can simplify things for their audience of random idiots on the web.
You are absolutely right. Thanks for giving me the impetus to look into this to the degree it deserved, and helping me stop spreading misinformation :-)
Sure, but the problem is that as far as I know all private key encryption currently in wide use is based on factoring large numbers. Which means Shor's algorithm applies. Which means that there's no longer that asymmetric relationship between the difficulty of encrypting data and decrypting it, which makes the encryption worthless.
I imagine that there are well known non-factoring based private/public encryption (elliptical, etc.). We could switch to those. That doesn't help with data that's already out there that was encrypted using old methods, and there's no guarantee that those alternate methods aren't just as vulnerable to some clever quantum algorithm.
Really, the existence of Shor's algorithm is pretty weird. I believe it means that quantum computers are more powerful than turing machines, which turns normal algorithm analysis on its head.
OK, double crap, I think what I said was mostly OK.
Remember, here the N I'm talking about is the number of possibilities, not the amount of data it takes to represent those possibilities. So for 16 million possibilities the N I'm talking about is 16 million, not 24 (the number of bits it takes to represent 16 million possibilities, and the typical usage of N in the O(N) notation).
Of course, you're right that my comment there didn't include the time it takes for f(x) to execute, but for many applications that can be constant time.
I'm just arguing the fine points to make sure my understanding isn't faulty...
Yeah, crap, I shouldn't have said that. I think the rest of the post is on target, though...
I wasn't trying to claim that Grover's algorithm would let you solve problems in polynomial time. I may well have expressed the time taken incorrectly... hmm, it seems to me that saying "it takes N^.5 applications of the algorithm versus N applications for a classical computer" is equivalent (in terms of the speed) to what you said.
I do think that qualifying Grover's algorithm as being for searching problems is misleading. It's true (it is for inverting functions, i.e. searching for the input that gives the desired output) but GA is useful for much, much more than what most people think of when they say 'search', for example the computer design problem I gave as an example.
It's possible I misunderstood something significant about the algorithm, but I don't think so...
That is not entirely true - a quantum computer can't just test all bit combinations at once and tell you which one has the property you want. See my other post.
Quantum computers don't turn NP into P. I.e. they don't let you solve NP problems (where recognizing a correct answer is very easy but you have to test all answers to see which is correct) in an amount of time that is a polynomial function of the size of the input.
There are two specific algorithms for quantum computers that have a big impact on encryption:
Shor's algorithm lets a quantum computer factor a number in polynomial time. It requires a number of qubits that is some multiple (greater than 1) of the number of bits in the number. So, once we have quantum computers with a few thousand qubits, all encryption mechanisms based on the difficulty of factoring numbers (which is most mechanisms) are broken.
Grover's algorithm lets a quantum computer look up an entry in an unordered dictionary in N^.5 time, where N is the number of entries in the dictionary.
Grover's algorithm, if I understand it properly, is a Big Deal. When they say "look up an entry in a dictionary", they really mean "give an entry for which an arbitrary algorithm returns a desired value". Essentially, it means you can solve any NP problem in N^.5 time. For example, with a simulation algorithm you could find a satisfactory design out of 100,000,000,000,000 different computer designs in 10,000,000 applications of the simulation algorithm, as opposed to the 100,000,000,000,000 applications it could take on a normal computer.
Another example of applying Grover's algorithm would be cracking a password (regardless of the encryption algorithm used). Let N be the number of possible password combinations. On average cracking a password would take N/2 applications of the encryption algorithm using a normal computer; it would take N^.5 applications using a quantum computer.
Quantum computing doesn't invalidate encryption, but real QC would essentially invalidate encryption algorithms based on the difficulty of factoring large numbers and substantially reduce the difficulty to crack any other algorithmic encryption.
Of course, one time pads are still totally unbreakable if used properly...
My entire point is that most Americans identify their country with freedom, an association it does little to deserve. What's more, most Americans (and I'm guessing based on your comment that you're included here) don't really want America to be free.
If you don't fit the bill and you don't even aspire to, you should choose another way of identifying yourself.
I refined my POV in several other posts - I think restrictions like this are OK at the community level. I don't think they're OK at a state or national level in a country that purports to be free.
Thanks; I'll look into it!
Yeah, me too ;-)
Sorry, I should say that I would love to see someplace where people were really free to do things that don't harm one another, and still restricted from doing things that do.
Damned pedants.
OK, scratch my gp response. It is always easy to be misunderstood. I think I've clarified my points so that you, at least, don't misunderstand them any more.
;-)
I still think the reply to my original post in this thread was intentionally antagonistic, and I reserve the right to be an ass to someone who's asking for it
You're absolutely right. I wasn't arguing that we should live in anarchy, just that we shouldn't be restricted from doing things that harm no one. (Although, I actually do think local communities should be able to establish a culture, i.e. restrict people from doing things that harm no one.)
My original examples were meant to provide a partial list of things that quite often harm no one (with the possible exception of the person performing the actions) but are illegal.
And I agree that close relatives should be restricted from breeding. It's harmful to a third party (the kids).