check your script, or go further out than 1M. other, very respectable, tests have shown that the percentage of numbers 0..9 converges to 1/10 each the further out you go in the decimal expansion of pi.
the best tests out there show that the ratio of 5's to 8's approaches 1:1.
that's why mathematicians refer to PI as a potentially 'normal' number as opposed to a potentially 'random' number.
a possible rephrasing of the question could be this: "given only the first n digits in the base b expansion of pi, can you devise a method of guessing the n+1 digit with a probability greater than 1/b?"
you must remember that you must take the digits of pi out of the context of pi - ie, you can't guess the next number by using BBP theorem, it must be based solely on the n digits in your that were given.
actually i have my eye on the Hodge conjecture: "on a projective non-singular algebraic variety over the complex numbers, any Hodge class is a rational linear combination of classes cl(Z) of algebraic cycles"
seems pretty obvious to me...
(ps, my previous post is a slightly reworked and translated quote from Fermat, where he reported in his journal that he had proved that x^n + y^n = z^n had no integral solutions when n>=3... and we all know how that little problem turned out (Wiles). i have no illusion of my total inability (or perhaps the intrinsic intractibility) of the P=NP problem... )
okay, a slightly more detailed number than '1 in a trillion or 10' can be made.
first of all, you need to know all the prime numbers less than the square root of the number you're trying to factor (up to appr 85 decimal digits). Now, due to the prime number theorem (see Riemann for outline, Hadamard & Vallee Poussin for proof) you can know that the number of prime numbers less than 'n' is on the order of n/log(n). Now, the odds you'll pick the correct pair are 2 out of that number, or:
2/[(sqr_root(RSA-576)/log(sqr_root(RSA_576))^2]
now, i just don't care enough to work that out, but i think you'd have a better shot if you started buying superball lotto tickets...
okay, hopelessly math/cs dork question, but have you ever heard of anyone having the answer for question 47 of section 4.5.4 (book 2)? seems doubtful, as it's rated a '50'
i was more interested in addition chains, but that one piqued my curiosity.
what if it's an elderly woman who's son bought her a fenced computer?
radek, however appealing his deadly skills may be, is not the right answer. get the cops. if it is the thief, have him taken out in prison for 4 cases of cigarettes:)
except it was keeping track of nuclear material. were any of the "companies running 6.5 for years with no such troubles" in this line of business?
i don't care if MS FUBARs a database carrying a million orders for widgets, but i do care when the slightest thing goes wrong with a system keeping track of weapons grade plutonium...
i despise bush, and voted for bradley, then gore. i think bush is the worst president since reagan or carter. he's a bumbling fool.
saddam hussein is an out and out murderer, a modern pol pot. he is overseeing the extermination of iraq's kurdish population, and invaded a kuwait soley for the purpose of looting it, to increase his war coffers for fighting iran. he does not imprison political dissidents, he assasinates them.
how spoiled you are to say those things. the freedoms we enjoy are more than most of the world, if not perfect.
I enjoy programming in java, and think it has a lot of promise as a clean, readable, and fast development tool.
I'm also a sports fan (baseball + hockey mostly), and I would die without ESPNs gamecast applet, and i'm beginning to like Yahoo's stattracker... which make me think java's real promise in browsers is to facilitate complicated interactions with server applications w/o involving HTTP. chat programs, stock tickers, etc are all great example of where applets' real strength lies. I know that TIBCo's messaging software comes with a package for messaging between applets and their originating server which seemed really promising... we did some pretty cool stuff with it at a previous company...
much like 'obscene', to paraphrase SCOTUS, i know it when I see it.
and even better yet, how about defining free will as being capable of non-determistic action?
i'd soon argue that human beings do not possess free will, rather than argue computers (which will invariably arrive at the same conclusion given the same input) do possess it...
i may be pessimistic, but you can't possibly think that Survivor, Big Brother, or Temptation Island isn't going to get the award.
the whole reason that this category EXISTS is to placate CBS w/ Survivor, and now that they've created the category, do you think they're going to have a sudden bout of artistic integrity?!
this is a garbage category, and in the grand tradition of hollywood, the 'best reality tv show' will be awarded to the most popular show. which, despite it's following here, is not junkyard wars.
The fact that Junkyard Wars was included means nothing. Survivor is going to take the award, regardless of it's (lack of) merit. This entire reality TV trend makes me ill... in 15 years people won't even know what real is.
...deserves an award for the parody of Iron Chef that they did a while back..
Charlie Sheen was hosting, and was 'American Bachelor chef', and he was challenging Iron Chef Japan (?) played by Horatio Sans... The theme ingredient was Shark heads, and Sans infused some rice with Eel farts (they were 'a little salty').
it was by far the funniest thing I've seen on television in months.
have you seen AOLiza? I think the guy who conceived of the idea is a poster on/.... Kevin Fox i think?
it's the funniest thing... he had an AOL screen name with a high ratio of random chat requests, so he took a freeware version of ELIZA and hooked into into AIM. it's was a truly distressing look at the shear idiocy of a lot of AOL members...
actually, just decided not to be lazy... it is Kevin Fox, and the link is http://www.fury.com/aoliza/... he explains it all on the site. great way to wast 45 minutes (check out #60)...
how about this: a software engineer is someone who has to go through the QA process in the course of coding. if you can make it though that, you deserve some sort of title...
a girl i dated for a while had a too-busy, underqualified campus health center staff diagnose her with 'alcohol poisoning' after she fell down and hit her head while drinking.
this is after she was unconscious for 2 hours, had her heart stop on the way to the local hospital, and had lost 10 pounds in the following 5 days. they kept telling her it was a hangover/alcohol poisoning, in spite of the increasing evidence to the contrary.
eventually, she went to a qualified neurologist when she started losing vision in one eye. he correctly and quickly diagnosed her with a hemorraging blood vessel in her head, which went on to require surgery and cost her some use of here eye.
the moral wasn't not to trust doctors, but not to trust underqualified, overworked doctors (i have deep dislike of HMOs...). a good doctor has worked harder in his/her field than most of us will work in a lifetime (i dropped out of pre-med to go into compsci/math - which ended up being much easier for me).
Is the latter any more plausible than the former ?
well, it depends what you mean. i think it's entirely plausible that a 15 year old is capable of giving 'half-decent' advice on law.
unfortunately, a half-decent legal expert is just about as good as a half-decent surgeon... there is an extraordinary amount of information that a lawyer must take in to be proficient in his or her field. since law is based on precendent, you have to read a TON of densely worded decisions in order to be merely up to date in a given area of law. the decisions are very precisely worded, and in order not to miss any subtleties, you need to have some sort of education in 'legal language' (whether it be formal or legimately self-taught).
so given these 2 aspects of law, i would say that a 15 year old doesn't stand a very good chance of giving good legal advice at all. maybe this kid is the one-in-a-million wunderkid of law, and he will go on to streamline and make more fair IP law, improve the US voting system, and settle the ethical and legal problems in abortion and gun rights.
but i doubt it. i think he probably got lucky that he didn't get anyone in serious trouble.
Slashdot Mirror
you're totally wrong.
omega can be calculated, but it converges extremely slowly to the lower bound. chaitin even mentions this.
check your script, or go further out than 1M. other, very respectable, tests have shown that the percentage of numbers 0..9 converges to 1/10 each the further out you go in the decimal expansion of pi.
the best tests out there show that the ratio of 5's to 8's approaches 1:1.
if you doubt this, i will find you some links.
that's why mathematicians refer to PI as a potentially 'normal' number as opposed to a potentially 'random' number.
a possible rephrasing of the question could be this: "given only the first n digits in the base b expansion of pi, can you devise a method of guessing the n+1 digit with a probability greater than 1/b?"
you must remember that you must take the digits of pi out of the context of pi - ie, you can't guess the next number by using BBP theorem, it must be based solely on the n digits in your that were given.
you come so close to answering your own question...
nah, don't want to spoil it :)
... and we all know how that little problem turned out (Wiles). i have no illusion of my total inability (or perhaps the intrinsic intractibility) of the P=NP problem... )
actually i have my eye on the Hodge conjecture: "on a projective non-singular algebraic variety over the complex numbers, any Hodge class is a rational linear combination of classes cl(Z) of algebraic cycles"
seems pretty obvious to me...
(ps, my previous post is a slightly reworked and translated quote from Fermat, where he reported in his journal that he had proved that x^n + y^n = z^n had no integral solutions when n>=3
ah, i have the updated and revised, but here goes:
f a10fa804ef7ac3ce03d7d3667c4d3e132a24a68e6797fe2865 0dc3adf327474b86b0cbd5387a49872ceo12269a59b3e4b3bd 83b74681a78ad7b6d1772a7451b15b025e2aee095a95425901 84cf62f72b2e8e8dd794aef8511f2591e6bc2c8b8a8e48af1f e04ff2fd933e7309205a3418dbb9bb8c6a7665da309531735f e86c741d1261b34cb2668fa34d0c0c28575a2454e3db00e408 ac7)
4 f2e633f82c88d5224fc4aa6f9104ced2bca810bea76157ffdc 78f9656a0ed9b3f6ccab99001b8b2571f4ebd095925f07f9be e5111e8375dfd71593628ad8d1
'47. [M50] A certain literary quotation x = x1*x2, represented in ASCII code, has the enciphered value (x1^3 mod N, x2^3 mod N) =
(14e97ef5c531d92591b89cdbab48444a04612c01aa29c2a8
in hexadecimal notation, where N is
17b2353b9595eca69fef80940160c4084286d1255ffe49d11
What is x?
okay, a slightly more detailed number than '1 in a trillion or 10' can be made.
first of all, you need to know all the prime numbers less than the square root of the number you're trying to factor (up to appr 85 decimal digits). Now, due to the prime number theorem (see Riemann for outline, Hadamard & Vallee Poussin for proof) you can know that the number of prime numbers less than 'n' is on the order of n/log(n). Now, the odds you'll pick the correct pair are 2 out of that number, or:
2/[(sqr_root(RSA-576)/log(sqr_root(RSA_576))^2]
now, i just don't care enough to work that out, but i think you'd have a better shot if you started buying superball lotto tickets...
P=NP is in fact true...
I've found a remarkable proof of this fact, but there is not enough space in the slashdot comment field to write it.
okay, hopelessly math/cs dork question, but have you ever heard of anyone having the answer for question 47 of section 4.5.4 (book 2)? seems doubtful, as it's rated a '50'
i was more interested in addition chains, but that one piqued my curiosity.
what if it's an elderly woman who's son bought her a fenced computer?
:)
radek, however appealing his deadly skills may be, is not the right answer. get the cops. if it is the thief, have him taken out in prison for 4 cases of cigarettes
yeah, how blase.
except it was keeping track of nuclear material. were any of the "companies running 6.5 for years with no such troubles" in this line of business?
i don't care if MS FUBARs a database carrying a million orders for widgets, but i do care when the slightest thing goes wrong with a system keeping track of weapons grade plutonium...
saddam hussein and gwb have nothing in common.
you are a flaming idiot.
i despise bush, and voted for bradley, then gore. i think bush is the worst president since reagan or carter. he's a bumbling fool.
saddam hussein is an out and out murderer, a modern pol pot. he is overseeing the extermination of iraq's kurdish population, and invaded a kuwait soley for the purpose of looting it, to increase his war coffers for fighting iran. he does not imprison political dissidents, he assasinates them.
how spoiled you are to say those things. the freedoms we enjoy are more than most of the world, if not perfect.
I enjoy programming in java, and think it has a lot of promise as a clean, readable, and fast development tool.
I'm also a sports fan (baseball + hockey mostly), and I would die without ESPNs gamecast applet, and i'm beginning to like Yahoo's stattracker... which make me think java's real promise in browsers is to facilitate complicated interactions with server applications w/o involving HTTP. chat programs, stock tickers, etc are all great example of where applets' real strength lies. I know that TIBCo's messaging software comes with a package for messaging between applets and their originating server which seemed really promising... we did some pretty cool stuff with it at a previous company...
lame response.
much like 'obscene', to paraphrase SCOTUS, i know it when I see it.
and even better yet, how about defining free will as being capable of non-determistic action?
i'd soon argue that human beings do not possess free will, rather than argue computers (which will invariably arrive at the same conclusion given the same input) do possess it...
Mod me a troll? what garbage...
i may be pessimistic, but you can't possibly think that Survivor, Big Brother, or Temptation Island isn't going to get the award.
the whole reason that this category EXISTS is to placate CBS w/ Survivor, and now that they've created the category, do you think they're going to have a sudden bout of artistic integrity?!
this is a garbage category, and in the grand tradition of hollywood, the 'best reality tv show' will be awarded to the most popular show. which, despite it's following here, is not junkyard wars.
The fact that Junkyard Wars was included means nothing. Survivor is going to take the award, regardless of it's (lack of) merit. This entire reality TV trend makes me ill... in 15 years people won't even know what real is.
...deserves an award for the parody of Iron Chef that they did a while back..
Charlie Sheen was hosting, and was 'American Bachelor chef', and he was challenging Iron Chef Japan (?) played by Horatio Sans... The theme ingredient was Shark heads, and Sans infused some rice with Eel farts (they were 'a little salty').
it was by far the funniest thing I've seen on television in months.
i'm thinking that, coupled with a swedish chef filter, could provide days and nights of amusement.
gee, the crap you have to put up with for free content... thanks for sharing, at least.
your analogy about gunpowder is 100% wrong.
, 00.html
see this article and read it: http://search.ebi.eb.com/ebi/article/0,6101,33623
whatever, most of us 'environmentalist wackos' would be just f*king tickled pink if we had a pollution free source of electricity.
their are idiots everywhere, but not every is an idiot...
have you seen AOLiza? I think the guy who conceived of the idea is a poster on /. ... Kevin Fox i think?
... he had an AOL screen name with a high ratio of random chat requests, so he took a freeware version of ELIZA and hooked into into AIM. it's was a truly distressing look at the shear idiocy of a lot of AOL members...
it's the funniest thing
actually, just decided not to be lazy... it is Kevin Fox, and the link is http://www.fury.com/aoliza/... he explains it all on the site. great way to wast 45 minutes (check out #60)...
how about this: a software engineer is someone who has to go through the QA process in the course of coding. if you can make it though that, you deserve some sort of title...
a girl i dated for a while had a too-busy, underqualified campus health center staff diagnose her with 'alcohol poisoning' after she fell down and hit her head while drinking.
this is after she was unconscious for 2 hours, had her heart stop on the way to the local hospital, and had lost 10 pounds in the following 5 days. they kept telling her it was a hangover/alcohol poisoning, in spite of the increasing evidence to the contrary.
eventually, she went to a qualified neurologist when she started losing vision in one eye. he correctly and quickly diagnosed her with a hemorraging blood vessel in her head, which went on to require surgery and cost her some use of here eye.
the moral wasn't not to trust doctors, but not to trust underqualified, overworked doctors (i have deep dislike of HMOs...). a good doctor has worked harder in his/her field than most of us will work in a lifetime (i dropped out of pre-med to go into compsci/math - which ended up being much easier for me).
Is the latter any more plausible than the former ?
well, it depends what you mean. i think it's entirely plausible that a 15 year old is capable of giving 'half-decent' advice on law.
unfortunately, a half-decent legal expert is just about as good as a half-decent surgeon... there is an extraordinary amount of information that a lawyer must take in to be proficient in his or her field. since law is based on precendent, you have to read a TON of densely worded decisions in order to be merely up to date in a given area of law. the decisions are very precisely worded, and in order not to miss any subtleties, you need to have some sort of education in 'legal language' (whether it be formal or legimately self-taught).
so given these 2 aspects of law, i would say that a 15 year old doesn't stand a very good chance of giving good legal advice at all. maybe this kid is the one-in-a-million wunderkid of law, and he will go on to streamline and make more fair IP law, improve the US voting system, and settle the ethical and legal problems in abortion and gun rights.
but i doubt it. i think he probably got lucky that he didn't get anyone in serious trouble.