JSH: Prime gap equation consequences
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From: JSH on 24 Jul 2010 15:15 On Jul 24, 11:31 am, Mark Murray <w.h.o...(a)example.com> wrote: > On 24/07/2010 18:26, JSH wrote: > > > On Jul 24, 10:04 am, Mark Murray<w.h.o...(a)example.com> wrote: > >> On 24/07/2010 16:30, JSH wrote: > > >>> If I'm correct then further "research" on prime gaps is specious. > > >> What if you are /not/ correct? How would you tell? > > > Yuck, you know no math, failed when challenged to show your work, > > trotting out an answer from a computer program, and now you ask a > > stupid question. > > So what? The question was answered, and it wasn't the answer you were > hoping for. > > > Answer is: my prime gap equation would fail against the data if wrong. > > So, if your equation were out by say, 12%, it would be wrong, > correct? No. And I WILL apologize to you here because I've been deliberately harsh when a lot of the problem appears to be your perception of where you are, who is reading, and what the mathematics says, versus the reality, so it's probably not really fair for me to just beat up on you verbally. So I apologize for some of my harsher words to you today. And the answer here is, no, it's the correlation that matters. Now ponder that for a while, understand why I don't worry a lot about a claim of a probabilistic equation supposedly often being about 12% off, and if necessary brush up on probability and statistics, which I think you really should do. To people with scientific backgrounds it's not even an issue you debate as it's so obvious, and for any adults who wish to understand scientific discussions where the issue of probability comes up it IS important to know it and understand it, or you're lost on things like, is our climate really heating up? How close do the statistical models REALLY need to be? From your posts I'd assume you'd think that perfection is required or NO, not global warming! But it's not that simple. So it's not a minor issue, and if it helps, again I apologize! Knowing these things is not trivial. Understanding probability and statistics is not intuitive. James Harris
From: Mark Murray on 24 Jul 2010 16:02 On 24/07/2010 20:15, JSH wrote: >> So, if your equation were out by say, 12%, it would be wrong, >> correct? > > No. And I WILL apologize to you here because I've been deliberately > harsh when a lot of the problem appears to be your perception of where > you are, who is reading, and what the mathematics says, versus the > reality, so it's probably not really fair for me to just beat up on > you verbally. I don't understand all of that, but I note the apology, and I accept it. Thank you! > So I apologize for some of my harsher words to you today. Again, Thank you! > And the answer here is, no, it's the correlation that matters. > > Now ponder that for a while, understand why I don't worry a lot about > a claim of a probabilistic equation supposedly often being about 12% > off, and if necessary brush up on probability and statistics, which I > think you really should do. I'm very familiar with the concept of experimental error, ant the statistical processing thereof. This requires a formal study of statistics, albeit not at the level of a major as degree level. A consistent 12% is cause for concern, and needs to be dealt with, and posters here (MichaelW and Penny Hassett) have both pointed out papers that explain this 12%. They have shown that apart from this 12%, your equation is correct, by showing it in a paper. > To people with scientific backgrounds it's not even an issue you > debate as it's so obvious, and for any adults who wish to understand > scientific discussions where the issue of probability comes up it IS > important to know it and understand it, or you're lost on things like, > is our climate really heating up? If my experiment differed from the theory by 12%, I'd look to explain the 12%. > How close do the statistical models REALLY need to be? That is open-ended. Statistical tests-of-significance are well understood. If theory predics a value, and an experiment produces a result with a standard deviation of error that encompasses this value, the experiment could be deemed successful. This holds even if the result is reasonably far off, but the error is explained (formally) as large (enough). Of course, if the error is too large, it may invalidate the whole process. > From your posts I'd assume you'd think that perfection is required or > NO, not global warming! You assume wrongly. > But it's not that simple. > > So it's not a minor issue, and if it helps, again I apologize! I accept your apology with gratitude! > Knowing these things is not trivial. > > Understanding probability and statistics is not intuitive. Yes, I agree. It was the subject I had the most difficulty with. The intuitive assumptions were invariably horribly wrong. M -- Mark "No Nickname" Murray Notable nebbish, extreme generalist.
From: JSH on 24 Jul 2010 16:31 On Jul 24, 1:02 pm, Mark Murray <w.h.o...(a)example.com> wrote: > On 24/07/2010 20:15, JSH wrote: > > >> So, if your equation were out by say, 12%, it would be wrong, > >> correct? > > > No. And I WILL apologize to you here because I've been deliberately > > harsh when a lot of the problem appears to be your perception of where > > you are, who is reading, and what the mathematics says, versus the > > reality, so it's probably not really fair for me to just beat up on > > you verbally. > > I don't understand all of that, but I note the apology, and I accept > it. Thank you! You're welcome! > > So I apologize for some of my harsher words to you today. > > Again, Thank you! You're welcome again! > > And the answer here is, no, it's the correlation that matters. > > > Now ponder that for a while, understand why I don't worry a lot about > > a claim of a probabilistic equation supposedly often being about 12% > > off, and if necessary brush up on probability and statistics, which I > > think you really should do. > > I'm very familiar with the concept of experimental error, ant the > statistical processing thereof. This requires a formal study of > statistics, albeit not at the level of a major as degree level. > > A consistent 12% is cause for concern, and needs to be dealt with, No. That's just not correct! > and posters here (MichaelW and Penny Hassett) have both pointed out > papers that explain this 12%. They have shown that apart from this > 12%, your equation is correct, by showing it in a paper. Mathematics is a HUGE subject. No one can be an expert on it all. But you can't just think you can read posts on Usenet and get a firm grasp of something and then just refer back to other posters when called on your error. Quite simply, you are wrong here. Worse, you are wrong in a way that shows a very dismal lack of understanding of basic probability and statistics. And you are insistent in your error. I am a world figure for a reason. You are not. There is no safety net for you here. Sorry, yet again. If apologies help you then fine. But you cannot will probability and statistics into something it's not. There is not that power in the world, and there shouldn't be. James Harris
From: JSH on 24 Jul 2010 17:29 On Jul 24, 2:10 pm, Mark Murray <w.h.o...(a)example.com> wrote: > On 24/07/2010 21:31, JSH wrote: > > > You're welcome again! > > :-) :-) :-) > > >>> And the answer here is, no, it's the correlation that matters. > > >>> Now ponder that for a while, understand why I don't worry a lot about > >>> a claim of a probabilistic equation supposedly often being about 12% > >>> off, and if necessary brush up on probability and statistics, which I > >>> think you really should do. > > >> I'm very familiar with the concept of experimental error, ant the > >> statistical processing thereof. This requires a formal study of > >> statistics, albeit not at the level of a major as degree level. > > >> A consistent 12% is cause for concern, and needs to be dealt with, > > > No. That's just not correct! > > Please explain (in detail). The stuff that MichaelW pointed out is the > same equation as yours, except for the constant 1.12... factor. Please > explain why that equation matches actual data much better than yours > does (or /vice versa/?). THAT is about an empirical formula which appears to match the data well. My result is derived from the prime residue axiom. Understand now? Or did that just whiz over your head? I CANNOT give you a college education on stat mech in Usenet posts!!! You CAN take a course on the subject. > >> and posters here (MichaelW and Penny Hassett) have both pointed out > >> papers that explain this 12%. They have shown that apart from this > >> 12%, your equation is correct, by showing it in a paper. > > > Mathematics is a HUGE subject. No one can be an expert on it all. > > Goes without saying. Thats why folks get together in discussion groups. > If I get something wrong, there is usually someone here who can help me > get it right. You are naive aren't you. Dude, you're entertainment now. There are people I'm sure who read this newsgroup just to wait until I finally let loose upon the latest poor sucker who decided to step into the fray. For every one poster who MAY seem to help you--and where are they now?--there may be thousands of readers around the world, looking to be entertained by you or someone like you. And it's so weird, I asked once years ago to see what people like you think, and this poster replied back that he thought roughly a dozen people were paying attention to my posts!!! Google Groups claims over 5000 reads in the last 7 days. That JUST Google Groups though, and however they get those stats as to what they consider a "read". When I post actively I push search results in any number of areas impacting people all over the world--especially if they happen to have THEIR research in those areas. Posters like you accept that as if it's normal but for the professionals it must be disconcerting. I draw attention at the level of a small university--all by my little self. > > But you can't just think you can read posts on Usenet and get a firm > > grasp of something and then just refer back to other posters when > > called on your error. > > No, but I consider the material referred to inhttp://groups.google.com/group/sci.math/msg/d07daf82d9238778 > persuasive, in support of MichaelW having accurately displayed the > 12% discrepancy and provides a reference to a paper that contains > an equation very similar to yours, except for the 12% correction. Empirical. My result is *derived* from the prime residue axiom. > Penny Hassett concurs, I do believe. If the poster posting on the newsgroup IS Penny Hassett--I have my doubts--you need to read a little more carefully. > > Quite simply, you are wrong here. Worse, you are wrong in a way that > > shows a very dismal lack of understanding of basic probability and > > statistics. > > Please check the above papers. The most relevant one is published by > The Mathematical Association of America. These are not idiots. LOL. You are so trusting. You're looking at empirical results. So people look at prime gaps and try to find a formula that matches, and correct it as they look at more data. In contrast I derived a result from my prime residue axiom. So my research is about 'why'. I answer why. THAT is the point. When you see empirical results you need to understand what you're facing which is about, sorry, education. Mathematics is a HUGE subject. And you're on a worldwide forum with a guy who gets attention from over 100+ countries. Sorry but while your world may be silly in many ways, it's not THAT silly. People like me get that level of attention for a reason. And I'm taking time out to help you as I fear you may have been caught in the gears of a rather large machine you just don't understand. In a sense, maybe this will help--it's like you're on something like a reality television show with a worldwide audience, but it's just not like others, so it is more like a stealth show, and I'm pulling away the curtain for you.... James Harris
From: MichaelW on 24 Jul 2010 19:49
Since there is some overlap between this thread and the "three years grace" thread I am copying in a post I just made in that thread that relates to the 12%, empirical results and the relationship with existing research: On Jul 25, 1:19 am, JSH <jst...(a)gmail.com> wrote: > Interesting. What if you shifted to 32? In the same interval? How > close is the count then? See below. > And if you're curious you MIGHT then consider what my prime gap > equation says for both. I'll admit I am not doing any actual math in > this area as the very title of this post is about my 3 years grace. > But hey, I can't stop others, eh? If you look at the equation then it creates two values. The first is a probability of a pair occurring at a particular prime when the gap is a power of 2. The second is the Corr value which adjusts for the prime factors of the gap. The product of the two gives the final probability. The result is that for any particular interval (say, 10^6 to 10^7) there is a number J that will be the predicted number of pairs for a gap of 2,4,8,16,32 etc; this J is the sum of the probabilities over the primes in the interval. The count for 6,12,18,24,36 etc (gaps with only 2 and 3 as factors) will be 2*J since Corr=2 in this case. The count for other gaps can be discovered by calculating Corr and multiplying by J. The need for the Corr multiplier comes out of the maths and has been known at least since the 19th century. If you see this link http://en.wikipedia.org/wiki/De_Polignac%27s_conjecture then the same calculation can be see in the discussion of C_n. The hard part is to determine J. I used this formula: Pi_2(x) = 2*C_2*x/ln(x)^2 where C_2 is the twin prime constant. Better is the Li_2 integral but I could not find a calculator for this integral online. > To really thoroughly check though, you'd check for EVERY prime gap > possible within that interval, and that is what I've meant above. And my point has been that you don't need to check for every prime gap as once you have J you have all the values. Note that this is a direct conclusion from the prime gap equation that you posted so I am agreeing with your maths regarding this point. > Computers don't care. They'll do the work without screaming at you. > The tables are around so every single prime gap possible from 10^6 to > 10^7 can be checked against my prime gap equation, or for any other > interval for which a table is available. THAT check isn't amenable to > rationalizations, and the standard theory collapses under it, with > horrible results in comparison (I hope, eh?). Could you provide a link for a table of prime gaps? Google has not been my friend. Regarding standard theory; we have three processes for calculating J: (1) Pi_2(x) given above (2) Li_2(x) which is the integral in the Wiki link above (3) Your probability function You seem to be implying that (3) is somehow superior to (1) and (2). I will agree that subject to the need for a constant multiplier (your equivalent of C_2) that (3) gives a much better answer than (1). Regarding (2) I have a conjecture: Equation (3) gives a close approximation of (2); they are in fact essentially the same. > That type of check is what can yank checks out of professors hands and > have them scrambling to find new ways to make money to feed their > kids--as the government dole which I call white collar welfare goes > away--pay their mortgages and keep their wives in decent clothes. > James Harris If my conjecture is correct (and I have proved it to my satisfaction) then in fact your prime gap equation reinforces standard theory. For reference Li_2(10^7) - Li_2(10^6) is 50506. The prime gap equation before constant multiplier gives 56537. The actual number of pairs for g=2 is 50811, for g=32 is 50369 and for g=18 is 101012 (giving a J of 50506). Regards, Michael W. |