Get off my lawn. Back in the days of the 386sx, the only reason for more video RAM was so you could get more color depth at a certain resolution (which is X * Y * D bits). There was no 3D, there were no textures.
Memory starting to go?;)
There as no 3D and no textures, true, but there are other reasons for extra RAM. There were benefits to be gotten from having off-screen buffers. At a minimum a good video card had at least double the amount of memory needed to display the screen at a given resolution and depth, so that you could be drawing to the off-screen buffer while displaying the other, then flip. Better video cards often had substantially more memory than that, to support multiple off-screen buffers (ideally, every window could have its own buffer in video RAM, benefiting from faster drawing operations, not consuming main memory, and not requiring a large transfer of data between the two when the window is raised to the front).
Of course, 128MB was unheard of, but there were still beefier cards with extra RAM for things, despite having no 3D or textures.
I have occasionally used "What would your password be if the admins weren't idiots?" This works because the answer is not my password, but it is something probably more secure than the password they forced me to choose. There's a true observation that an 8 character password that uses both upper and lower case letters and a symbol is more difficult to brute force than an 8 character password that does not. However, it is also true that a 16 character password that does not is more difficult to brute force than an 8 character one that does. It's a sign of how stupid many programmers are that many sites will accept at eight character password that does, but tell you your password isn't secure enough when you give it a more secure 16 character password that does not.
I successfully recovered a password from a site recently using this facility because they let me pick my own question, so I did and gave an honest answer. Also made me laugh out loud when this site that I didn't even remember signing up for to begin with popped up the question:
"Hey, what's the idea?"
XD The answer to this question was immediately obvious to me, and would not be to anybody else, precisely satisfying the requirements for a good security measure. If they let you pick your question, it should be easy to come up with something you would know the correct response to, but would leave most people scratching their heads. I didn't remember ever setting this up to begin with, but I knew immediately the one and only possible correct answer to this question (knowing that it was me asking it of myself removed all possible ambiguity about what it meant).
This is pretty secure, actually... except for the storage problem.:( My honest answer doesn't satisfy good password policy regarding symbols, upper/lowercase, etc., so it's probably easy to brute-force even if hashed.
I bet Duke Nukem Forever team members are all philosophers, by now...
Starving philosophers at this point...
(Sorry, that's a bit of an in-joke -- among my college friends, the dining philosophers problem was generally known to as the "starving philosophers problem" after one of them accidentally called it that and the name stuck.)
Supporting organizations and laws that take away the rights from both artists and consumers does not make you "pro-artist", it just makes you gullible if you think it does.
You misspelled "enough" in that variable name. (I'm giving the benefit of the doubt in assuming you weren't committing the far, far worse offense of using Hungarian notation.):p
Maybe that is the intention? Just because Schneier *thinks* it is an average, doesn't make it so. Maybe the device becomes more accurate as more samples are taken, and therefore gives more weight to the last (not the first!) sample.
It damn well better be an average -- having worked with cheap, 12-bit ADC chips before, I know you're getting trash for data if you aren't taking multiple readings and averaging. You must average the readings because the readings are noisy, particularly "in the field". The point of the averaging is to get rid of the noise. The noise doesn't go away as more samples are taken. The average needs to be done properly across the range because if you're giving greater weight to the last reading, your failing entirely to eliminate the noise.
I'm certain it's throwing away that least-significant bits from the 12-bit ADC precisely because they're effectively RNG output. The problem is, that's the wrong way to do it. Keeping the entire value and then averaging properly gives a reasonably accurate value, even from a noisy ADC. You can discard the lower bits after the averaging (it's false precision anyhow), but not before, and you do it by rounding, not truncation. Doing what is described in the article gives you trash.
BTW: This isn't necessarily wrong. Assuming all the measurements are in the same basic range, does this really matter?
If all the measurements are in the same basic range, you don't need to average at all, or maybe only average one or two. If they're bothering to take a running average a substantial number of times, then one of two things is true, (a) they don't need to, so the software is misdesigned to take a running average of 20 readings when it only needs two, or (b) they do need to, so the software is misdesigned to take what's effectively the average of the last couple readings while pretending to average 20. Either way, the software is flawed.
Having worked on field sensors before, I'm suspecting they need to due to a certainly level of noise in the data from the sensor. I've seen this a lot on cheap ADC (analog to digital converter) chips used for mass-produced sensors. You could use a more expensive ADC, but you get the same result by just using the noisy ADC and averaging a number of readings. However, if they were using the averaging method described in the article, the results are basically trash. The result will be thrown off too much by the noise in the last one or two readings.
Without testing the hardware in this case I can't say for sure, but I know from the devices I've worked with, this would *definitely* produce screwy, invalid results.
... Then again the collective "wisdom" of Slashdot was 110% certain that the Ipod was going to be a complete flop so I guess that should say something of the level of understanding about reality here.
The average/. user has a deep and comprehensive understanding of the world... of Warcraft.;)
Sulu offered nothing either and was basically "Harold" (from Harold and Kumar fame) on the bridge of the Enterprise... oh and he could fence. Was that an attempt to pay tribute to Picard or just an excuse to do a pointless and extremely cheesy sword fighting scene (I can't believe CmdrTaco thought this was the least cheesy Star Trek film!) ?
More likely putting a sword in Picard's hand was a tribute to Sulu, who is rather famous for it. You know, I think that someone who apparently never even saw the original series (as you must not have to keep making these weird assertions), you're not really qualified to complain about to what degree they're respecting or destroying canon. You're not even familiar with it...
Checkov bordered on disgraceful. He was made into pure comic relief (which didn't even work on that level).
Um, have you ever seen the series? In almost every episode he appears, he is pure comic relief. Usually though a combination of accent and outrageous claims about Russia. Having him as pure comic relief based on his Russian-ness is being pure and true to the original series.
The relationship doesn't hold true over the first N-primes. It's statistically true over all primes < B^N where B is the numeric base. This will only be true for the first N-primes for very specific values of N, where N is the largest prime smaller than the base to some Nth power.
Um, yeah, when you summarize, you omit details (by definition). When the details you omit are the interesting details, what you're left with is indeed obvious and uninteresting.
It's long been known that primes are more common on the low end. The interesting detail is the mathematical relationship between the actual amounts that end up in the various bins if you divide the range and count them up in each bin. Knowing there will be more in the lower bins doesn't tell you this, it just says there will be more in the lower bins. Benford's law tells you about how many (proportionally) will be in each bin. And it's not in any way an artifict of using a base 10 number system, the relationship remains true regardless of how many bins you use (10, 16, 8, whatever).
Also, this is the reason why large parts of the world has 112 and 113 as general emergency numbers, while Canada and the US (who adopted the Canadian system) has 911.
Yeah, most of the was still using the older style dialing, but touch-tone was becoming the norm in the US by the time 911 was rolled out, so it wasn't as much of a concern.
Right. The usefulness of a statistical observation varies with the size of the set being looked at. For smaller sets, it becomes less useful (ultimately being not noticeably better a predictor than tea leaves for small enough sets). You'll find it much more difficult to find exceptions in ranges of a hundred thousand than in ranges of a thousand (although more easily if you head higher up the number line -- basically, to find exceptions, you need to use ranges that are relatively small compared to the size of the numbers themselves).
I call BS, why would primes care what they look like in base10?
They don't.
And how could something like this be equally true for different base notations at the same time, which is what the Wikipedia article claims.
Quite easily, when you're talking about first digit distributions (and we are), which is basically saying lower magnitude numbers are more frequent than higher magnitude ones. This would (to most people, not you obviously but to most other people) be obviously not influenced by what base you choose to use in expressing the numbers. If lower magnitude numbers are more common than higher magnitude ones, this is simply true regardless of base, so no matter what base you pick, lower magnitude first digits will be more common, and indeed in this case, the distribution of their commonality will vary logarithmically across the digits, regardless of how many of them there are in the base you have chosen, because that's a feature of the set of numbers, not an artifact of their expression.
I mean does this really apply equally to base 2 binary and base 9?
Yes, although base 2 is the degenerate case (all prime numbers start with 1, which is trivial but does satisfy the law).
which, if I understand the "Benford distribution" correctly, is somewhat of a circular argument.
Sort of. To the extent that in any analytic theorem, the truth of the conclusion is essentially contained in the premises, you're just teasing out and making plain what was already there. This is true of all mathematical theorems. That's what makes it analytic rather than synthetic (empirical).
I think I will stick to using prime based crypto for now.
Of course, why wouldn't you? Nothing in the article has any implications for cryptography.
If you're looking for what this taught us about prime numbers that we didn't already know, you're barking up the wrong tree. We've learned precisely nothing we didn't already know about prime numbers.
What's new here is what we've learned about Benford's law.
A better understanding of the "pattern" of prime number could lead to better probabilistic factorization algorithm as well as better random number generation algorithm.
No, not really, at least not in this case. This, after all, did not discover any sort of pattern in prime numbers, it generalized an observation relevant to the pattern of their distribution. So, it might help you make a better prediction of how many primes you'll see in a given range (although, actually not, since we already knew that), it won't in any way help you generate or detect individual primes.
(Again, the news here is that the study of primes helped us develop a generalization of Benford's law. We've learned precisely zero new things about prime numbers, prime numbers have just taught us something new about mathematics.)
... the ability to help predict primes may help reduce the computing cost of encryption, if not decryption, though I doubt it will lead to any additional security.
Your statement is true, but a complete non-sequitur. The GP asked if the research mentioned in the article would have any applications to cryptography. Since the research in the article has nothing to do with predicting primes, your statement is in no way an answer to the question.
It's not that arbitrary. The fundamental reason for that choice was to make it easily divisible. 12 is evenly divisible in a number of ways, but not by five. But multiply 12 by 5 and you get 60, which is evenly divisible by everything 12 is, and by five as well.
Yes, there are 60 minutes and seconds because we decided there should be, but it was by no means an arbitrary decision. There were good, solid mathematical reasons why those numbers were chosen.
How is this any less safe than nuclear powered subs/carriers?
Well, considering you're not planning on taking them into battle, it's probably safer. I've always wondered about all the touted safety of a nuclear reactor on a ship that's likely to have torpedoes shot at it...
I agree to a point, and space is not 'empty', but there's a lot less stuff to wear and tear at a spacecraft when compared to any environment on the earths surface.
True, but there's also a lot more you can do to protect something from wear and tear when you're not concerned about its weight and cost to lift into orbit. It's actually much easier to make something on Earth that lasts that long than it is to make something for space that lasts that long. The reason we don't usually do so is it's even easier to make something that doesn't, and a lot less expensive to just service it as needed.
Slashdot Mirror
Get off my lawn. Back in the days of the 386sx, the only reason for more video RAM was so you could get more color depth at a certain resolution (which is X * Y * D bits). There was no 3D, there were no textures.
Memory starting to go? ;)
There as no 3D and no textures, true, but there are other reasons for extra RAM. There were benefits to be gotten from having off-screen buffers. At a minimum a good video card had at least double the amount of memory needed to display the screen at a given resolution and depth, so that you could be drawing to the off-screen buffer while displaying the other, then flip. Better video cards often had substantially more memory than that, to support multiple off-screen buffers (ideally, every window could have its own buffer in video RAM, benefiting from faster drawing operations, not consuming main memory, and not requiring a large transfer of data between the two when the window is raised to the front).
Of course, 128MB was unheard of, but there were still beefier cards with extra RAM for things, despite having no 3D or textures.
I have occasionally used "What would your password be if the admins weren't idiots?" This works because the answer is not my password, but it is something probably more secure than the password they forced me to choose. There's a true observation that an 8 character password that uses both upper and lower case letters and a symbol is more difficult to brute force than an 8 character password that does not. However, it is also true that a 16 character password that does not is more difficult to brute force than an 8 character one that does. It's a sign of how stupid many programmers are that many sites will accept at eight character password that does, but tell you your password isn't secure enough when you give it a more secure 16 character password that does not.
I successfully recovered a password from a site recently using this facility because they let me pick my own question, so I did and gave an honest answer. Also made me laugh out loud when this site that I didn't even remember signing up for to begin with popped up the question:
"Hey, what's the idea?"
XD The answer to this question was immediately obvious to me, and would not be to anybody else, precisely satisfying the requirements for a good security measure. If they let you pick your question, it should be easy to come up with something you would know the correct response to, but would leave most people scratching their heads. I didn't remember ever setting this up to begin with, but I knew immediately the one and only possible correct answer to this question (knowing that it was me asking it of myself removed all possible ambiguity about what it meant).
This is pretty secure, actually... except for the storage problem. :( My honest answer doesn't satisfy good password policy regarding symbols, upper/lowercase, etc., so it's probably easy to brute-force even if hashed.
I bet Duke Nukem Forever team members are all philosophers, by now...
Starving philosophers at this point...
(Sorry, that's a bit of an in-joke -- among my college friends, the dining philosophers problem was generally known to as the "starving philosophers problem" after one of them accidentally called it that and the name stuck.)
Supporting organizations and laws that take away the rights from both artists and consumers does not make you "pro-artist", it just makes you gullible if you think it does.
You misspelled "enough" in that variable name. (I'm giving the benefit of the doubt in assuming you weren't committing the far, far worse offense of using Hungarian notation.) :p
Maybe that is the intention? Just because Schneier *thinks* it is an average, doesn't make it so. Maybe the device becomes more accurate as more samples are taken, and therefore gives more weight to the last (not the first!) sample.
It damn well better be an average -- having worked with cheap, 12-bit ADC chips before, I know you're getting trash for data if you aren't taking multiple readings and averaging. You must average the readings because the readings are noisy, particularly "in the field". The point of the averaging is to get rid of the noise. The noise doesn't go away as more samples are taken. The average needs to be done properly across the range because if you're giving greater weight to the last reading, your failing entirely to eliminate the noise.
I'm certain it's throwing away that least-significant bits from the 12-bit ADC precisely because they're effectively RNG output. The problem is, that's the wrong way to do it. Keeping the entire value and then averaging properly gives a reasonably accurate value, even from a noisy ADC. You can discard the lower bits after the averaging (it's false precision anyhow), but not before, and you do it by rounding, not truncation. Doing what is described in the article gives you trash.
BTW: This isn't necessarily wrong. Assuming all the measurements are in the same basic range, does this really matter?
If all the measurements are in the same basic range, you don't need to average at all, or maybe only average one or two. If they're bothering to take a running average a substantial number of times, then one of two things is true, (a) they don't need to, so the software is misdesigned to take a running average of 20 readings when it only needs two, or (b) they do need to, so the software is misdesigned to take what's effectively the average of the last couple readings while pretending to average 20. Either way, the software is flawed.
Having worked on field sensors before, I'm suspecting they need to due to a certainly level of noise in the data from the sensor. I've seen this a lot on cheap ADC (analog to digital converter) chips used for mass-produced sensors. You could use a more expensive ADC, but you get the same result by just using the noisy ADC and averaging a number of readings. However, if they were using the averaging method described in the article, the results are basically trash. The result will be thrown off too much by the noise in the last one or two readings.
Without testing the hardware in this case I can't say for sure, but I know from the devices I've worked with, this would *definitely* produce screwy, invalid results.
... Then again the collective "wisdom" of Slashdot was 110% certain that the Ipod was going to be a complete flop so I guess that should say something of the level of understanding about reality here.
The average /. user has a deep and comprehensive understanding of the world... of Warcraft. ;)
Sulu offered nothing either and was basically "Harold" (from Harold and Kumar fame) on the bridge of the Enterprise... oh and he could fence. Was that an attempt to pay tribute to Picard or just an excuse to do a pointless and extremely cheesy sword fighting scene (I can't believe CmdrTaco thought this was the least cheesy Star Trek film!) ?
More likely putting a sword in Picard's hand was a tribute to Sulu, who is rather famous for it. You know, I think that someone who apparently never even saw the original series (as you must not have to keep making these weird assertions), you're not really qualified to complain about to what degree they're respecting or destroying canon. You're not even familiar with it...
Checkov bordered on disgraceful. He was made into pure comic relief (which didn't even work on that level).
Um, have you ever seen the series? In almost every episode he appears, he is pure comic relief. Usually though a combination of accent and outrageous claims about Russia. Having him as pure comic relief based on his Russian-ness is being pure and true to the original series.
Having a lower /. ID does not in any way signify expertise.
Besides, those 5 digit people are n00bs... :p
ur doin it rong! :o
The relationship doesn't hold true over the first N-primes. It's statistically true over all primes < B^N where B is the numeric base. This will only be true for the first N-primes for very specific values of N, where N is the largest prime smaller than the base to some Nth power.
I don't know, it just seems obvious.
Um, yeah, when you summarize, you omit details (by definition). When the details you omit are the interesting details, what you're left with is indeed obvious and uninteresting.
It's long been known that primes are more common on the low end. The interesting detail is the mathematical relationship between the actual amounts that end up in the various bins if you divide the range and count them up in each bin. Knowing there will be more in the lower bins doesn't tell you this, it just says there will be more in the lower bins. Benford's law tells you about how many (proportionally) will be in each bin. And it's not in any way an artifict of using a base 10 number system, the relationship remains true regardless of how many bins you use (10, 16, 8, whatever).
Also, this is the reason why large parts of the world has 112 and 113 as general emergency numbers, while Canada and the US (who adopted the Canadian system) has 911.
Yeah, most of the was still using the older style dialing, but touch-tone was becoming the norm in the US by the time 911 was rolled out, so it wasn't as much of a concern.
Right. The usefulness of a statistical observation varies with the size of the set being looked at. For smaller sets, it becomes less useful (ultimately being not noticeably better a predictor than tea leaves for small enough sets). You'll find it much more difficult to find exceptions in ranges of a hundred thousand than in ranges of a thousand (although more easily if you head higher up the number line -- basically, to find exceptions, you need to use ranges that are relatively small compared to the size of the numbers themselves).
I call BS, why would primes care what they look like in base10?
They don't.
And how could something like this be equally true for different base notations at the same time, which is what the Wikipedia article claims.
Quite easily, when you're talking about first digit distributions (and we are), which is basically saying lower magnitude numbers are more frequent than higher magnitude ones. This would (to most people, not you obviously but to most other people) be obviously not influenced by what base you choose to use in expressing the numbers. If lower magnitude numbers are more common than higher magnitude ones, this is simply true regardless of base, so no matter what base you pick, lower magnitude first digits will be more common, and indeed in this case, the distribution of their commonality will vary logarithmically across the digits, regardless of how many of them there are in the base you have chosen, because that's a feature of the set of numbers, not an artifact of their expression.
I mean does this really apply equally to base 2 binary and base 9?
Yes, although base 2 is the degenerate case (all prime numbers start with 1, which is trivial but does satisfy the law).
which, if I understand the "Benford distribution" correctly, is somewhat of a circular argument.
Sort of. To the extent that in any analytic theorem, the truth of the conclusion is essentially contained in the premises, you're just teasing out and making plain what was already there. This is true of all mathematical theorems. That's what makes it analytic rather than synthetic (empirical).
I think I will stick to using prime based crypto for now.
Of course, why wouldn't you? Nothing in the article has any implications for cryptography.
If you're looking for what this taught us about prime numbers that we didn't already know, you're barking up the wrong tree. We've learned precisely nothing we didn't already know about prime numbers.
What's new here is what we've learned about Benford's law.
A better understanding of the "pattern" of prime number could lead to better probabilistic factorization algorithm as well as better random number generation algorithm.
No, not really, at least not in this case. This, after all, did not discover any sort of pattern in prime numbers, it generalized an observation relevant to the pattern of their distribution. So, it might help you make a better prediction of how many primes you'll see in a given range (although, actually not, since we already knew that), it won't in any way help you generate or detect individual primes.
(Again, the news here is that the study of primes helped us develop a generalization of Benford's law. We've learned precisely zero new things about prime numbers, prime numbers have just taught us something new about mathematics.)
... the ability to help predict primes may help reduce the computing cost of encryption, if not decryption, though I doubt it will lead to any additional security.
Your statement is true, but a complete non-sequitur. The GP asked if the research mentioned in the article would have any applications to cryptography. Since the research in the article has nothing to do with predicting primes, your statement is in no way an answer to the question.
The short answer to the GP's question is, "No."
"One in a million chances crop up nine times out of ten."
It's not that arbitrary. The fundamental reason for that choice was to make it easily divisible. 12 is evenly divisible in a number of ways, but not by five. But multiply 12 by 5 and you get 60, which is evenly divisible by everything 12 is, and by five as well.
Yes, there are 60 minutes and seconds because we decided there should be, but it was by no means an arbitrary decision. There were good, solid mathematical reasons why those numbers were chosen.
If it was in your ROM BIOS, they could never take it away from you. Superior computers always made sure it was there in the ROM.
CALL -151
:)
How is this any less safe than nuclear powered subs/carriers?
Well, considering you're not planning on taking them into battle, it's probably safer. I've always wondered about all the touted safety of a nuclear reactor on a ship that's likely to have torpedoes shot at it...
I agree to a point, and space is not 'empty', but there's a lot less stuff to wear and tear at a spacecraft when compared to any environment on the earths surface.
True, but there's also a lot more you can do to protect something from wear and tear when you're not concerned about its weight and cost to lift into orbit. It's actually much easier to make something on Earth that lasts that long than it is to make something for space that lasts that long. The reason we don't usually do so is it's even easier to make something that doesn't, and a lot less expensive to just service it as needed.