The Magic of the Prime Multiples; Insights into Goldbach’s Conjecture

The Magic of Prime Multiples/Quartets; & Insights into Goldbach’s Conjecture
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By Herb Wiggins, M.D.; Clinical Neurosciences; Discoverer/Creator of the Comparison Process/CP Theory/Model; 14 Mar. 2014
Copyright © 2018
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“Almost anything which jogs of us out of our current abstractions is a good thing.”  –Alfred Whitehead
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“If you would discuss philosophy with me, first Define your Terms.” –Voltaire
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Gauss’ Razor:  Mathematics must be constrained by the practical uses of mathematics. AND by those findings which create greater understanding of  how mathematics works.
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Least Energy Rules
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“Understanding comes from finding the Relationships among Events.”  Albert Einstein, “Physics and Reality”, 1936
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The Future of mathematics is Experimental, Empirical mathematics relating to complex systems.
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The fatal, empirical flaw of most Deductive logic is the False Dichotomy.   (Either and only; All White or all Black. But, What of the unlimited greys?)
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“Calling the Universe Non-linear is like calling Biology the study of all Non-elephants.” —Stanislas Ulam
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“Simplify, simplify, simplify”  —Henry David, Thoreau.
“Efficiencies drive the Markets” —Adam Smith, the “Wealth of Nations”
Least energy, Least energy, Least Energy Rules.
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The essential basis of creativity depends upon complex system factors. Pattern Recognition is one high level basis of understanding. This in turn is based upon comparison processes which create information, and by doing so create creativity and understanding. By understanding high level information creation based upon how information is both created verbally (description) and by measuring (empirical mathematics, both thus invoking Einstein’s Relativity epistemology), the requirements of creativity become much, much more clear. This work is an active part of of a new model of cognitive neuroscience, and shows the power of the new understanding of the origins of information, viz. description (Verbal) and Data (counting, measuring), and how those are organized hierarchically & can create unlimited creativity and understanding.
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 Recently there was a found a method which quickly and efficiently sorts through the number line to find the primes. Using the new concept of Prime Multiples (PM), this can be successfully done without limit and very quickly, too. Prime multiples (PM’s) are different from the usual numbers called composites, because they are a simplified number line consisting of n >/= 11, of the numbers ending in -1, -3, -7 & -9. Those 10 quartets make up 40 of the numbers in each centad (100 numbers), and have special properties. All of the primes after  5 end in odd numbers, of the -1, -3, -7, -9 types. So that method clears the number line of all the not primes.
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A Prime Multiple(PM), in its specialized definition, means one of those numbers in the number line which is composed of at least 2 primes mulitplied together, or more, ending in -1, -3, -5, -7, or -9. Those PM’s cannot by definition be primes. This is how those arise & are identified.
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First of all, the number line is generated by adding 1 + 1+ 1 +1 …. to each number, which creates the number line & creates the many kinds of numbers, including the primes. Primes Cannot be generated or created in any other way (except as below, Addendum), altho they can be ID’d and shown to be primes. The primes cannot be created except by using that process of  1 + 1 + 1, etc. Primes (except as below, see Addendum), cannot be generated either by arithmetic. Very quickly we see that the numbers ending 2, 4, 5, 6, 8, and -0’s can be eliminated from the prime lines after 7, very easily using the prime quartet simplification. Simplification of the number line is a key to sorting out and finding the primes. As Thoreau so stated.
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By multiplying the known primes after the 4 numbers ending as above, have been removed easily by using the quartets, because all primes .>/= 11 end in 1, 3, 7, & 9, this becomes possible to reduce the number line to about 26% (73.3333…% of numbers removed) by this means alone.
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Now, because primes Cannot be generated except by 1 + 1 + 1…., added to each number, if 1 is considered prime, then the solution to the Goldbach conjecture that all numbers can be expressed by the sum of two primes becomes a trivial solution.
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However, if 1 is NOT a prime, which is a definition, but not an absolute, & an axiom, then Goldbach’s conjecture becomes much harder to solve. Very likely, Only if we consider 1 not to be prime, then does Goldbach’s problem surface. Goldbach’s is not true then for the 1st even number, 2, so Goldbach’s is NOT completely true. But is true for the rest of the number line to a very high number. That problem will be addressed in the article on proving that Goldbach’s is both true, and not true, conditionally, and broadly.
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However, using the prime multiples (PM) definition it becomes very clear that if we eliminate the PM’s from the number line, then the primes can be simply found.  Because all numbers of the 1, 3, 7, 9, quartets but for the primes are then clearly prime multiples (PM’s). All primes (p) are created by 1 + 1 + 1, but then they begin to repeat at 2p, 3p, 4p, and so forth without limit. But the initial primes are NOT the sums of primes, but of 1’s. Thus all of the numbers but for primes & but for 2 are all odd numbers, & the even numbers can be the sums of two primes, or more. But not quite.
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Each prime starts out as a number not heretofore seen in the number line. As the adding of numbers continues, then the primes begin to repeat as the prime multiples of 2p, 3p, 4p, 5p, etc. By filtering out those repetitions to ONLY the odd numbered PM’s  using the 1, 3, 7, 9, quartets, we can much more easily show how the number line is composed of new primes, and the much larger part, esp. in the very high numbers of 1 billions or more, the PM’s, in which complexities are found, by exclusion of the PM’s, showing the primes. Exclusion is NOT a mathematical function. But based upon a process where numbers not meeting the standard of PM’s are found, then removed leaving the rest, i.e., the primes.
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And we can empirically find two primes which by adding together create the even number line. This is largely true for  the higher primes, that is >/= 11. 7 is 5 + 2, but not all primes for which that can be seen to be true but for the twin primes.
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Because those prime lines are additive, then all but the primes are necessarily prime multiples (multiplication being an easy process to reduce, logically, to additions), and thus Goldbach’s conjuncture is the case, but for all primes & odd numbers. Ergo, Goldbach’s conjecture, to say it another way, is that if the primes & odd numbers are eliminated, we are only left with PM’s & THOSE are the sums of primes, all of them. So Goldbach’s is conditionally, in a limited form, restricted by PM’s, the case. IOW, as in sorting the primes, simplify the problem down, and then solve it.
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This at once shows the power of the Prime Multiples definition, not as composites, but because it clearly can sort out very quickly all the lower primes, altho is laborious, but NTL true. The works of Dugas/O’Connor and Juhani Sipila are very supportive of the finding of primes to very high numbers, (1 billions) using the composites removal method from the number line.
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For instance, there is with the quartets method the clear fact, that all primes create prime multiples of the 1 class numbers ending & being  1 X 1, 3 X 7, and 9 X 9. The -3 class  are 1 X 3, and only -7 X -9; the 7 class, 1 X 7, & 3 X 9; and the -9’s by 1 X 1, and 3 X 7, and 9 X 9. That’s the whole story. And that is why the PM method works. It generates all odd numbers by multiplication only, & removing the PM’s from the quartet line of 40 numbers per centad (1oo numbers group) leaves the primes.
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Further, the powers of the primes all progress with the squares ending ALL in -1’s and -9’s. & then they by a simple, repeating arithmetic/multiplication to ending in the 3’s, 7’s, 1, and 9’s again with each power as each rises.  This is inviolate.
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With the PM’s a number series can be made of an arithmetic series beginning with the quartets with 7 X 7, being 49. Adding 4X7  (4p) to that, then 2p  to that sum, and then repeating the simple two part wheel ( +4p, +2p, +4p, etc.) to  find, create, generate, all the PM’s of 7 to unlimited values. The same pattern is true for all primes beginning with 7, 11, 13, 17, 19, etc. And by using this very simple method, the primes are sorted out very quickly by this simple processor which removes the basic PM numbers from the quartets, leaving only the primes, very efficiently.  See Addenda for the examples of how this sorts out the primes uniquely and completely from the number lines.
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By sorting out ONLY the PM3’s by a simple pattern, it saves many calculations on the odd PM’s and increases the efficiency of this method many fold.
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Because it’s a series of p squared plus +2p , + 4p, plus 2p,  + 4p, etc., the entire line of each prime as its PM’s can be easily found & removed. As the average is 3p, then it proceeds 3 times faster than the E Sieve. And further, because 75% of the number line has been removed, 12 times faster!!!  At least.
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Further, because the occurrence of primes are the case to very large numbers, always greater than 1, the number of primes/centad also means that those primes do not need to be sorted out, lowering the numbers to be processed by 8-16 per 100, thus removing 83.333 to 88% of the number line!!! We need only sort out the PM’s and the primes are left. This speeds up prime sorting again by about 10-15%. Esp. efficiently in the first 10K of 100 centads in the number line, where the primes are greatest in number.
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Then we begin to see the magic. By removing the PM3’s from the quartet number line to 77, we have the primes remaining, up to 77. By then finding the 2p and 4p PM7’s of the primes, those PM’s (77, 91, 119, 133….)  start very quickly being removed, again leaving the primes to 143, where in the PM11’s start to drop out, sorting out more primes. By then generating the PM13 series after 169 (13 Sq.) we find the primes to 191 and then begin removing the PM13’s up to 323, where the PM17’s start continuing the PM removals. This finds a HUGE number of primes, by only using 7, 11, 13!!  The ratio of advantage is by the PM3’s being removed, by the pair of PM3’s in the quartets; which used at once after the 1, 3, 7, 9, quartets are created, & we sort out 61 primes by using only 3 primes up to 323!!! A very good ratio of efficiency.
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 This can be done with the entire simplified number line using calculators or manually. Using this arithmetic progression of the PM’s, it’s possible to sort out the primes into the 15K-20K+ list of numbers on paper, without using a computer or calculators. & it does Not miss one prime at all, if the accounting is exactly done. It’s that simple and efficient.
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When THAT is done, the relationships of the PM’s to each other, creates factorization solutions to the larger problem of factorization. Many numbers are divisible by 2, 3 and 5’s (5 and -0 ending numbers).. But when those are taken out Simple additions of the primes creates the factors to the PM’s embedded in that simple number line. We find interactions, the same numbers with many prime factors, implicit in the series, for instance among the PM 7’s, 11’s, 13’s, 17’s, etc., as below in the Addendum.
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The problems of factorization occur because the PM’s, and in all of their unlimited products. Factoring out numbers by 2, 3, 5, and -0 is trivial. But that leaves the hard, NP problem of the odd PM’s. And when those are all known, and this method creates them, factorization can be VERY fast.
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For instance, 7 X 4 is 49, add 4p or 28 and we get 77, 2 primes, creating the 77, 7 and 11. Adding 2p to that gives us 91, 7 X 13, the next prime; and then 28 again gives us 119 (7X17), then 14 again 133 (7X19), and finally at 143, the 11 PM elimination series then begins. Thus by using ONLY the PM7, after clearing out the PM’s by simple inspection, we have found the first THIRTY primes after 7,  Having cleared out the prime multiples from the number line simply, easily and cleanly.  Dividing the PM’s by the generating +2p, alternating with +4p reveals the Exact primes line, as well, up to about 113, when it becomes more complex.
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At that point in each PM times 113, the PM’s line become the same as the numbers added to the primes. It’s not all  primes, mostly primes early on, but also the PM’s. As single primes  are only used once, but the PM’s then begin to dominate. As in the series of all odd numbers, minus the PM3’s. That’s the line of multiples which then begins. and this creates ALL of the multiples of the primes (PM’s), their squares and powers to p exp. x. This simple arithmetic system  of easy additions, then finds all of the PM’s which can be used to do the hard factorization problems. This means, that factorization becomes a LOT easier, once we remove the even PM’s, and the -5’s/-0’s. THAT’s the hard problem of factorization, the odd numbered PM’s. Solving THAT problem solves and speeds up factorization methods. And that is known, but now it’s seen why due to the quartet systems making the PM’s stand out.
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And note that the 7 X 7 is not prime, the next is 77 or 7 X 11, and then next 7 X 13, 91, & then 7 X17, 119, etc.;  the sums divided by the prime series being used, show the primes as well!!!. That is the first Rem1 quartet of all 2 pairs of primes, 11, 13, 17, & 19. So the prime numbers are sorted out to about 7 X 113, in EACH of the primes starting with PM7 sorting. It’s like magic. & nothing is missed. Not squares, not cubes, not powers of p, not anything. Adding the 2p & +4p’s, this series creates the prime line as well in factorizing numbers to the many higher primes still being used!!!  Those lists of intersecting PM’s provide the raw data for very fast factorization of the number lines. Esp. among the PM5’s which are regularly generated by the system. And in addition those odd numbers of the primes are duplicated EXACTLY for each prime used from 7, 1, 13, 17, 19, to the highest primes known.
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And thus the overlaps between the PM’s lines show the factorization of the number line. Thus, when we eliminate the trivial 2, 3, 4, 5, 6, 8 and -0’s ending numbers, we are left with the bare bones possible prime numbers. Thus the primes find the primes, at least twice, over. By specific exclusion from removing the PM’s from the number line, as well as, by dividing EACH of the PM’s shows the same primes. That is nothing short of Magic, even if we ignore that removing PM3’s by inspection ALSO finds the primes up to 77, of itself. & by using only the PM7 line, the simple adding of the PM’s starting with 7, 11, etc., ALL generates the primes by dividing the PM series by the prime driving that series to 113!!! After that the PM’s are being seen interspersed with the primes, altho there is an easy way round that, as well.  The method has already sorted  out the PM’s by having already ID’d them as NOT primes. Thus leaving the primes in the PM times the series of odd primes and PM’s. And these are the same, exact PM factors for EACH PM series. Thus when we get to 101, we are using the same prime and PM list to create the continuing primes sorting, as well as prime generating sequences. IOW, 101 X 101 (101Sq),  plus 202, plus 404, +202, etc. leaves 101X 103, 101X107, 101X109, 101X 113; 101 X 127 after a few PM’s in the prime gap about 120.
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Thus, once again speeding up the prime sorting by another 30-60%, depending upon how many intersecting PM’s are being created. Adding up the p sq. to the 2p and 4p highlights the primes, too!!!! Thus by a simple process of the 2P and 4p additions, we generate numbers, which when divided by the primes series number base prime,  find the primes by a simple division!!!
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So we can use TWO methods to find the primes, the first creating by arithmetic progression the PM’s, which when removed from the odd quartets leave the primes. And the Second, which is composed of the odd number line created by multiplying the base primes against that. For instance, it all starts out with the prime times the prime, at 7, 49, and then 7 X11, &X 13, 7X 17, and on up till be get to 49, where the prime line breaks, and then up to 71, 73, and then the break at 77, 91, etc. being PM, and then 79, 83, 89, 101, 103, 107, 109, and 113. After that more PM’s are seen, and it gets very much less the primes, only. But as we KNOW what the PM’s are, when those are removed from the Prime times odd number line, bereft of PM3, it gives once again, diving the numbers by the prime series of the 7, 11, 13, etc., the prime line!!!
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This is astonishing. It gives the primes twice, the first time by excluding the PM’s and the second time by dividing the prime multiples by the odd number prime driving that line, less the PM’s, as well. So the one system backs up the other for sorting out the primes.
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Curiously, to state it another way by adding the squares of the primes to the 2p and 4p sums, then dividing many of those, shows the primes.
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Thus, for instance, the number line
7X:  113, 119, 125 127,  (quartet)131, 133, 137, 139, we see the 131 quartet primes and the sole PM 133, which is 7 times 19!!! This continues by removing the PM’s to create the Primes!!!
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And that works for each PM series, too. We are creating the primes by addition of the series of p sq. +2p, +4p, =2p, etc. Bit more complicated than that, but is the case.
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So we get to 7X (quartet) 191, 193, 197, and 199. The PM series create the primes by arithmetic, and faultlessly and without limits.  And by subtraction of the PM’s by a simple pattern, this simple division creates the primes, but ONLY if the PM’s are known. And as the primes are well known before the P sq. plus 2p, +4p gets going, that method also shows the primes, as a b/u event to detect errors!!!
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That’s another of the Magics of the PM methods. Instead of counting up, 1+1 +1 +1, we add up the PM series to find the primes as well. How this occurs is a great mystery, but seen easily. We are finding the primes, by arithmetic progressions, and in every case, too. & then generating the primes by using semi-primes, two primes multiplied together. THAT is the heretofore NOT seen PM effect/phenomenon. And with each number it does this faultlessly AFTER it has found the primes by exclusion.
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So if we removed the PM’s we can find the primes by exclusion once again. Magical, very astonishing and not expected.
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Let/s look at this in the high detail with the PM method uniquely gives us.
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The prime 7 series of PM’s is essentially 7X7=49, then 7×11=77 by 4p addition, and then by 2p addition, 7×13 =91, and then 7X19, 119, and 7X23 is 161.
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So essentially what we are doing is taking out the PM3’s by removing those from the quartet system. But we already KNOW the primes up to 143. So we can use those to remove ever more quickly as we have the prime series of primes & those numbers. This takes the PM’s out of the prime factors created by the arithmetic progression and saves us many steps in terms of checking.
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For instance in Prime series of 19, that starts at 19 squared, and runs up to by 23, 29, 31, 37, 41, 43, 47, etc. through 113 by simple adding.
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So we have 19X 23 which is 4p or 361 + 76 is 437. We ignored the 21 number as it’s PM3. and we have the 49 to use, and have eliminated the 5’s too. so we have this
19X19 = 361
19X23 = 437
19X25 = 475 which we skip
add 19X 29, skipping the 27 as it’s PM3, and get 76 plus that to give
19X29 = 541 well past 23 sq. at 529; and then the 29 times 25 occurs at  575 (5 times 115), and then next is 23X29 at 667, etc.
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So the odd number line proceeds by removing by a simple not mathematical process (saving lots of time) all of those numbers divisible by 3, and only a few by 25 , & 5 of its powers and multiples, which can be ignored. But acts as a sum to add the 2p, or 23X2 or 46 to and we find that overlap which lets us simplify the additions by removing the repetitions, easily. thus increasing the speed of prime exclusions.
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At higher numbers, this becomes more complex, but the overlaps among the PM’s are easily removed by a simple pattern observation.
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Let’s next discuss the PM3 rules by which the primes can be found very quickly. It’s simple, but very tedious to cast out 3’s using the usual adding of digits. But using the quartets methods, we see at once, a pattern of PM3 pairs in the cast out 3  zero remainder, c/o 3 9, and c/o 2, repeating quartets. When zero, the -3 and -9 ending numbers are all PM3’s, because zero plus 3 or 9 is a PM3. When the remainder number is 1, all 4 of the quartet can be primes. When those are 2, then only the -3 and -7 numbers can be primes. Thus we see the repeating primes of the forms, ending in -1, -7, and then in c/o 3 remainder 2 quartets, the 3 and 9. & following this up thru the known primes in the first 200, we see this pattern all the time, too. the 23 and 29, the 31 and 37, the 41, 43, 47, skipping the PM 7 sq. 49, and then the 53 and 59, the 61 and 67, and the 71, 73, % 79, the 77 being 7 X 11. Then the 83, and 89, and the lonely 97. Thus do the PM3’s determine many of the patterns of the primes. And ONLY when the 2 quartets transition to the zero, do we find twin primes, but not withIN the 0, 2 quartets alone, by themselves. And there are possible double twin primes in the c/o3 1 quartets all the time. And then patterns in those patterns.
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Then we begin to realize that in the PM lines we see the route to easier factorization. Even numbers and 5’s, 0’s and 3’s are very easily eliminated by simple inspections. The REAL problems arise with the odd PM’s. But this method shows how THAT can be solved as well. because in the trivial, Even, 3, 5 and -0 ending numbers, the biggest problem is the -1, -3, -7, & -9 ending factors. The PM’s method neatly solves this without limit!!! It creates the factorizations!!! & thus provides new insights in how to apply those findings to more efficiently factor the number line.
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& those can be used as cross checks to the additions, as well. The PM5’s are seen at about 1% and declining with higher numbers. The PM5’s arise as a result of the arithmetic additions of the PM’s. By simply dividing the numbers ending in 5 arising with the PM5 series, we find ever more factors of the PM’s. Those also create the factorizations not including the PM3 5’s multiples. which is just more of the PM magic, too.
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The PM5’s occur at 10 and alternating 20 times the Prime 7 (70 & 140), 11 (110 & 220), 13 (130 & 260), etc., values. so that can also be used to check the accuracy of the PM additions series. If a mistake has been made, then those 10 and 20 times PM5 patterns will not be seen. Thus it’s yet 1 more cross sums checking for the accuracy of the p sq. +2p, +4p series, etc. More magic!!!
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And it also highlights by this simplification the nature of the Zeta function, as well. BTW, except for the very high primes, Riemann’s Hypothesis is very likely correct. His series generation shows the PM’s, and leaves by elimination, the Primes. Implicitly and specifically in the Zeta function, therefore is the p sq. plus 2p, +4p, plus 2p, +4p series. THAT’s what has been missed. and because the PM system of quartets is the case, that is, each sum of 2p and then 4p repeated is mathematically true. SO then is the Zeta function and Riemann’s Hypothesis true. Because the multiplication (by 2p and 4p additions) of the two primes is true, thus the series collection of all the sums, is ALSO true. And Riemann’s is then proven the case. The PM’s show this proof. It’s true, because summing up numbers is true in each case. and the divisions are true, as well, which show the primes, and the PM’s. Whether this also holds in the gigantic numbers can be eventually, experimentally shown.
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Thus do we both provide solid evidence of Goldbach’s Conjecture being conditional, and Riemann’s being likely true by the same PM method.
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Further, When we realize that the prime gaps show us what’s going on, then we reach greater understanding.
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Let’s reconsider once more this important point. If by finding the PM’s we remove those from the 1, 3, 7, 9, quartets, we find the primes, and we do, without a miss, then we know what the primes are. & can use them to extend the primes lines. But if we find that in the PM’s themselves, the product of the single Primes times the odd number line divested of the PM,s also shows the primes, then we have an interesting insight.
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We can remove the PM’s from the factors of the number lines and then directly find the primes, as well.
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The Prime gap of 113 to 127 shows us what occurs, in full details and specifically, in a nutshell, with ALL prime gaps. That’s the first one, and it’s 7 below and 7 above 120, thus 120 +/- 7. That is NO accident. 120 is divisible by huge numbers of primes & PM’s. This again shows us the prime factorization solutions, as well.
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This is very interesting, too. Because when we sum up 2 primes to create the entire number line of even numbers, those numbers show yet again the Rem PM3 zero, 1, & 2  recurrences, the repeating 3 quartets of PM3 driven processes. The 30’s, 90’s and the 60’s, too. The largest numbers of two primes sums creating an even number rises as the even numbers rise. AND there is a 6 repeating series, which quickly becomes yet another 30 series. Such as 8 unique prime sums for 48 becomes TWELVE two prime sums creating 120!!! & with 360, very, very many prime sums. The most up to that number in fact. So the quartet methods shows how that is found & why, too. The PM3’s shape and determine the primes.
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Again, the prime gaps signify the high rate of interference of the numbers which creates the first major prime gap from 113 to 127. And which being extensively created by PM’s is also the case with most all the rest of the prime gaps. & the two prime sums creating the even numbers. These patterns of the sum of two primes giving the entire even number line (as far as can be tested with today’s computer tech) is a very deep insight into why Goldbach’s conjecture is true, and provable. But NOT quite!!!
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And the most of the totals of the two primes sums are also often multiples of 3 and 6 and & 9 & 10.
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When we look at the double pairs which occur with 11, 13, 17, & 19, we add 3 times 30, and get the next double pairs in the c/o 3 Rem 1 quartets. That is 101, 103, 107, and 109. The next is 191, 193, 197, and 199, again, 90 units away. and we find this occurring time and again. This is not explained, but needs to be. The quartets produce a great deal of new information about the primes, which expands our understanding of mathematics, significantly.
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821, 823, 827 and 829 are 191 minus 812, 630 numbers separated, again, 90 times 7. That 90 keeps recurring with the double pairs of primes in the c/o 3 Rem 1 quartets!!! Why?
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In addition, when we sum up the number of primes with respect to the cast out 3, Rem 0, 1, and 2 quartets we find early on that most of the primes occur in the Rem1 quartets. With higher numbers this tends to go back to a balance among the primes in each quartet with respect to how many PM3 pairs are found in each centad. But frankly, because the Rem1 quartet can have more primes than the other two, it’s remarkable that often it has 50-60% of the primes in the quartets in each centad, early on. Altho as stated above, it tends to even out with higher numbers. It’s still clear that if the Rem 1 quartets are checked using primality method such as AKS or ECPP, those still with very high numbers of digits are like to have the most primes in the Rem1 quartets. So with very high numbers where only zero to 4 primes are found per centad, the money is STILL in the Rem1 quartets for finding primes. That’s new information and data about the number line and primes.
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And in the twin prime finding from  Rem2 -9 to Rem0, -1, Those patterns of primes should save lots of time in finding the primes..
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ALL prime gaps are the results of the PM’s creating composites and PM’s in succession which are NOT primes. And the prime sequences of +2p or +4p, such as often seen can be thought of as this. Prime gaps are the reinforcement of the sequential numbers of PM’s, which eliminate using the recurring PM3 structure of the quartets, the number line, leaving the primes.
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In addition, the succession of primes often seen only separated by 2 and 4 such as in 13 to 17, and occ. 6 are the same, and can be conceived of as not reinforcement of the PM’s but break thru the PM blocking patterns in the expression of the primes. Thus the prime gaps are self-reinforcement by the PM’s and groupings of the PM’s; and the lengthy prime sequences seen, are the interference patterns. This is what’s going on, and once again shows the power of the quartet system. This is best seen in the lower centads where primes are still very common. Less often after 20K or so. See Addendum below to visualize those patterns.
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The primes are the cast of the statue, not the statue itself, which are created by the PM’s. And when the statue (PM’s) are removed, the primes remain. This visualizes the relationships of the primes and the PM’s. The PM’s create transient prime patterns because of this, but those do not persist. Only the PM patterns persist and are real and the same throughout the number line. Viz., prime squared plus alternating with + 2p and +4p series to unlimited numbers.
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We can go into the PM3 ordering of the quartets at length, but this also shows the power of the quartet method of 1, 3, 7, 9, too. because invariably all the -1, -3, -7, -9  2 pairs of primes, are seen in ONLY the quartet which is cast out 3 Rem1. In remainder 0 or 2 has a pair of c/o PM3;.  in Cast out 3’s.  The 1 remainder has no PM3’s. And summing up the primes in each centad, we see quickly that the  Rem1 quartets is at least 50-60% of the primes, by itself. the Rem2, and Zero being usually less than 1/2 of the primes. Altho at times it can be a bit more, or even, but not usually.  The 100’s of primes known easily can be separated into the c/o 3, of the  0, 1,  2  groups, and shows that clear cut pattern. The primes LIKE the Rem1 quartet because it can hold up to 4 of them and in any combo from none to 4. 2 twins, pairs, separated by 4, between the -3 and -7.  & many triplets primes, as well. And we see most often early one the -1,-7 ending primes in the Rem0 groups because the -3 and -9 are PM3’s and cast out;  & the similar c/o -1, -7’s, which leaves the -3, and -9 numbers to be primes. That’s why the pattern is there!!! The PM3’s drive the prime patterns.
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So if we want to quickly find primes, we focus on the Rem1 quartets. That has NOT been seen nor understood, either, before. and thus also shows the power of this system to detect the deeper patterns of the PM’s and primes.  Any pattern in the primes ALWAYS reflects the underlying PM3 imposed upon the far more complex PM pattern. And as this can vary, creates pseudo patterns of the primes, but which never, ever recur or easily. The patterns of the primes are always incomplete, and appear random, but for the fact that they reflect the TRUE additive 2p plus 4p patterns which are dominant.
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& is we want to find the primes fasger, check the Not PM3 numbers in the Rem0 and Rem2 quartets.
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The 90’s rule shows this. in the succession of 2 pairs of primes  of 11, 13, 17, & 19, are where they are. The next is 101, 103, 107 & 109. Which is 3 X 30 numbers away. Then we find the next double paired primes in the 191, 193, 197, and 199 again, Rem 1 quartets. 3X30 = 90, again away from the last primes pair. Even at 630 quartets later, we find yet another set of 1, 3, 7, 9 pairs. That shows the power of organizing of the PM3 patterns in the quartets and the primes. This does not hold up, however, as written above. It always breaks down. There are NO steady patterns to the primes, but those which occ. occur as a PM pattern, driving it by exclusions of the PM’s..
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In addition, to close, the number line at ANY place (even to 100’s 1000’s or millions of digits) can be investigated by constructing the 1, 3, 7, 9, quartets, and then using the simple arithmetic progression ridding the number line, most efficiently of upwards of 99+% of the numbers!!!. And thus concentrates the primes. Thusly allowing faster methods, such as the ECPP related methods to find the primes at 10, 100, 1000 and even 10K times faster.  Instead of dividing those numbers of 2, 3, 4, 5…. into the number line, we use the bare bones quartet primes method of PM’s to simplify,  simplify,  simplify the number line. Thus gaining HUGE time savings, by least energy sorting. Many 1000’s of times faster. If the testing for primacy of numbers can be  reduced by 100 fold, or even 1000’s fold. If the calculations of primacy in a large series of many 100’s of digits of numbers takes say 2 months, it’s reduced by the PM exclusions method to a number of hours, not even days, rather. It’s very much faster than doing an E-sieve number reduction up to 150 numbers, say, because by using PM61, the the number line is already reduced by over 95%.
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So let us take a series of 350 digit numbers and we want to find the primes in those. We find, successively the PM3 pairs in the quartets & remove those. Then sequentially remove the PM7, 11, 13, upwards of PM41 to 61, which removes 95% of the not primes in the number lines
with only several primes. If this is expanded further by the PM’s series of primes it very quickly rises.
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That means the number line has been simplified by 1000 times, leaving the primes to be found VERY quickly by AKS or ECPP of the remaining numbers after the PM sieve has processed them in only a very short time. The method Concentrates the primes, first by simplifying down by 60% the number line, then upwards of 73.333% and then with each PM7, PM11, PM13, etc. ever more so, and quickly rising.
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This means that in calculations to find series of primes for encoding credit cards &  bank accounts, a great many can be found very, quickly, with 1000’s of parts upwards of 10K portion of the number line removed by these arithmetic, simple, PM series sieving.
.
This is so much faster than simply doing an Eratosthenes sieve to remove a large part of the number, line, say up to 157, because it rises very much more quickly to clear out and concentrate the primes.
.
That should ALSO significantly shorten finding more and many primes to use in the RSA systems.
.
For number lines in the 100’s of digits, this cuts the primality numbers to be tested by 1000’s fold, for instance. Thus for calculations to find a high primes normally taking many weeks, it only takes several hours or a few days to do the same work.
.
Simplify, simplify, simplify the number line to find the primes. The primality tests cannot do that very easily nor as efficiently as the PM’s method does by simple arithmetic of the 2p + 4p additions. No complex maths. Just an accelerated E-sieve to at least 12 fold or more.
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There are other, almost unlimited numbers of patterns which can be easily detected and uniquely so by using this method of PM sorting. And that is the promise & Magic of the Prime Multiples and the unlimited methods which that can create a better understanding number theory via the (VIP) very important primes.  & also in a practical sense, sort out the primes, much, much faster, to the chagrin of RSA systems. As we have often suspected, but can’t always prove.
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And there are MANY other patterns found here, which time/space do not allow to be discussed and explained. Unlimited new methods regarding understanding the primes, very likely.
.
Here’s the Addendum showing how all of this works.
.
Note the patterns of the primes in Rem1, 2, and zero quartets, which are seen again and again. Note the twin primes being ONLY seen in the move from the Rem2 -9, to the initial _1 in the Rem0 quartets. Note the twin primes being found in the Rem1 quartets consistently, too, and in every variation, as well.
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Note the Prime sequences also seen,  but rarely mentioned in the p plus 2 and P +4 occurrences, and WHY those occur, and why ONLY two pairs of primes can be seen & no more, because the PM3’s make this happen. This new information is very useful in understanding more about the primes, and satisfies Gauss’ Razor by not only being useful in finding primes, but also in understanding the 30, 90, and PM3’s multiples patterns being seen.
.
Addenda:
.
The 1, 3, 7, 9, series will be shown thru the 500’s centad, and then the corresponding primes generator series examples will be shown Adjacent to it.
.
1. Pr means prime;
2. ~ (tilde)3 means NOT prime of a PM3 series sorted out
3. Prime Multiples will be shown by ~( 7 X 73 for instance, thus sorting out the PM’s and showing the remaining Primes.
4. Starts and ends of longer prime sequences twin primes and those Primes separated by only 2 and 4 units shown by *****
5. Rem0, -1, or -2 means one of 3 repeating quartets marked by cast out 3 series
.
Rem 2              PM7 Series
501 ~3             511 +28 (7 X73
503  Prime       539 +14 (7 X77
507 -3              553 +28 (7 X79
509 Pr              581 +14 (7 X83
—-                    595 PM5, +28  (7 X85 (5X17 Overlap
                         623 +14 (7 X89  End PM7 series for centads
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Rem 0
511 ~(7X 71
513 ~3
517 ~(11X 47
519 ~3
——-                PM11 series start
Rem 1              517 +22 (11 X47
521 Pr              539 +44 (11 X49 PM7 overlap, above
523  Pr              583 +22 (11 X53
527 ~( 17X31    605 +44 (11 X55 or 5X121 (End of PM11 series
529 ~( 23 sq.)
23 series starts here  +46 to 575 (23 X25 (5 X5)
—-
Rem2
531~3
533 ~(13X41         PM13 series starts
537~3                    533 +26 (13 X41
539 ~(97 x77(11×7)
—-
Rem0                     559 +52 (13 X43
541 Pr                    611 +26 (13 X47
543 ~3                  etc of PM17, PM19, etc.
547 Pr
549 ~3
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Note same prime progressions, exactly for each successive prime series   that is Exactly the same and extends up to unlimited numbers. Thus, if the 7x  primes and PM’s is known up to the prime #, 601, the same line exactly can   be used to compute the PM’s of every prime up to 601. No point in doing it again & again..
————–
Rem1
551 ~(19X 29
553 ~ (7X79
557 Pr
559 ~(13 X 43 (+52
Rem2
561 ~3
563 Pr
567 ~3
569 Pr
——–
Rem0
571 Pr
573~3
577  Pr
579~3
—-
Rem1
581 ~(7 X83
583 ~(11 X53
587 Pr
589 ~(19 X31
—-
Rem2
591 ~3
593 Pr  *******
597 ~3
599 Pr  ** ( quartet Rem2 to Rem0 twin primes, only twin primes outside of Rem1 quartets
———————–
.
Rem0
601 Pr **
603 ~3
607 Pr **
609 ~3
—-
Rem1
611 ~(13 X47)
613 Pr  **
617 Pr  **
619 Pr ******* end of prime sequence
Etc.
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Table of Contents

Updated 17 Nov. 2018

1. The Comparison Process, Introduction, Pt. 1
https://jochesh00.wordpress.com/2014/02/14/le-chanson-sans-fin-the-comparison-process-introduction/?relatedposts_hit=1&relatedposts_origin=22&relatedposts_position=0

2. The Comparison Process, Introduction, Pt. 2
https://jochesh00.wordpress.com/2014/02/14/le-chanson-sans-fin-the-comparison-process-pt-2/?relatedposts_hit=1&relatedposts_origin=3&relatedposts_position=1

3. The Comparison Process, Introduction, Pt. 3
https://jochesh00.wordpress.com/2014/02/15/le-chanson-sans-fin-the-comparison-process-pt-3/?relatedposts_hit=1&relatedposts_origin=7&relatedposts_position=0

3A.. Extensions & Applications, parts 1 & 2.

https://jochesh00.wordpress.com/2016/05/17/extensions-applications-pts-1-2/

4. The Comparison Process, The Explananda 1
https://jochesh00.wordpress.com/2014/02/28/the-comparison-process-explananda-pt-1/

5. The Comparison Process, The Explananda 2
https://jochesh00.wordpress.com/2014/02/28/the-comparison-process-explananda-pt-2/

6. The Comparison Process, The Explananda 3
https://jochesh00.wordpress.com/2014/03/04/comparison-process-explananda-pt-3/?relatedposts_hit=1&relatedposts_origin=17&relatedposts_position=1

7. The Comparison Process, The Explananda 4
https://jochesh00.wordpress.com/2014/03/15/the-comparison-process-comp-explananda-4/?relatedposts_hit=1&relatedposts_origin=38&relatedposts_position=0

8. The Comparison Process, The Explananda 5: Cosmology
https://jochesh00.wordpress.com/2014/03/15/cosmology-and-the-comparison-process-comp-explananda-5/

9. AI and the Comparison Process
https://jochesh00.wordpress.com/2014/03/20/artificial-intelligence-ai-and-the-comparison-process-comp/

10. Optical and Sensory Illusions, Creativity and the Comparison Process (COMP)
https://jochesh00.wordpress.com/2014/03/06/opticalsensory-illusions-creativity-the-comp/

11. The Emotional Continuum: Exploring Emotions with the Comparison Process
https://jochesh00.wordpress.com/2014/04/02/the-emotional-continuum-exploring-emotions/

12. Depths within Depths: the Nested Great Mysteries
https://jochesh00.wordpress.com/2014/04/14/depths-within-depths-the-nested-great-mysteries/

13. Language/Math, Description/Measurement, Least Energy Principle and AI
https://jochesh00.wordpress.com/2014/04/09/languagemath-descriptionmeasurement-least-energy-principle-and-ai/

14. The Continua, Yin/Yang, Dualities; Creativity and Prediction
https://jochesh00.wordpress.com/2014/04/21/the-continua-yinyang-dualities-creativity-and-prediction/

15. Empirical Introspection and the Comparison Process
https://jochesh00.wordpress.com/2014/04/24/81/

16. The Spark of Life and the Soul of Wit
https://jochesh00.wordpress.com/2014/04/30/the-spark-of-life-and-the-soul-of-wit/

17. The Praxis: Use of Cortical Evoked Responses (CER), functional MRI (fMRI), Magnetic Electroencephalography (MEG), and Magnetic Stimulation of brain (MagStim) to investigate recognition, creativity and the Comparison Process

https://jochesh00.wordpress.com/2014/05/16/the-praxis/

18. A Field Trip into the Mind

https://jochesh00.wordpress.com/2014/05/21/106/

19. Complex Systems, Boundary Events and Hierarchies

https://jochesh00.wordpress.com/2014/06/11/complex-systems-boundary-events-and-hierarchies/

20. The Relativity of the Cortex: The Mind/Brain Interface

https://jochesh00.wordpress.com/2014/07/02/the-relativity-of-the-cortex-the-mindbrain-interface/

21. How to Cure Diabetes (AODM type 2)
https://jochesh00.wordpress.com/2014/07/18/how-to-cure-diabetes-aodm-2/

22. Dealing with Sociopaths, Terrorists and Riots

https://jochesh00.wordpress.com/2014/08/12/dealing-with-sociopaths-terrorists-and-riots/

23. Beyond the Absolute: The Limits to Knowledge

https://jochesh00.wordpress.com/2014/09/03/beyond-the-absolute-limits-to-knowledge/

24  Imaging the Conscience.

https://jochesh00.wordpress.com/2014/10/20/imaging-the-conscience/

25. The Comparison Process: Creativity, and Linguistics. Analyzing a Movie

https://jochesh00.wordpress.com/2015/03/24/comparison-process-creativity-and-linguistics-analyzing-a-movie/

26. A Mother’s Wisdom

https://jochesh00.wordpress.com/2015/06/03/a-mothers-wisdom/

27. The Fox and the Hedgehog

https://jochesh00.wordpress.com/2015/06/19/the-fox-the-hedgehog/

28. Sequoias, Parkinson’s and Space Sickness.

https://jochesh00.wordpress.com/2015/07/17/sequoias-parkinsons-and-space-sickness/

29. Evolution, growth, & Development: A Deeper Understanding.

https://jochesh00.wordpress.com/2015/09/01/evolution-growth-development-a-deeper-understanding/

30. Explanandum 6: Understanding Complex Systems

https://jochesh00.wordpress.com/2015/09/08/explandum-6-understanding-complex-systems/

31. The Promised Land of the Undiscovered Country: Towards Universal Understanding

https://jochesh00.wordpress.com/2015/09/28/the-promised-land-of-the-undiscovered-country-towards-universal-understanding-2/

32. The Power of Proliferation

https://jochesh00.wordpress.com/2015/10/02/the-power-of-proliferation/

33. A Field Trip into our Understanding

https://jochesh00.wordpress.com/2015/11/03/a-field-trip-into-our-understanding/

34.  Extensions & applications: Pts. 1 & 2.

https://jochesh00.wordpress.com/2016/05/17/extensions-applications-pts-1-2/

(35. A Hierarchical Turing Test for General AI, this was deleted after being posted, and it’s not known how it occurred.)

https://jochesh00.wordpress.com/2016/05/17/extensions-applications-pts-1-2/

35. The Structure of Color Vision

https://jochesh00.wordpress.com/2016/06/11/the-structure-of-color-vision/

36. La Chanson Sans Fin:   Table of Contents

https://jochesh00.wordpress.com/2015/09/28/le-chanson-sans-fin-table-of-contents-2/

37. The Structure of Color Vision

https://jochesh00.wordpress.com/2016/06/16/the-structure-of-color-vision-2/

38. Stabilities, Repetitions, and Confirmability

https://jochesh00.wordpress.com/2016/06/30/stabilities-repetitions-confirmability/

39. The Balanced Brain

https://jochesh00.wordpress.com/2016/07/08/the-balanced-brain/

40. The Limits to Linear Thinking & Methods

https://jochesh00.wordpress.com/2016/07/10/the-limits-to-linear-thinking-methods/

41. Melding Cognitive Neuroscience & Behaviorism

https://jochesh00.wordpress.com/2016/11/19/melding-cognitive-neuroscience-behaviorism/

42. An Hierarchical Turing Test for AI

https://jochesh00.wordpress.com/2016/12/02/an-hierarchical-turing-test-for-ai/

43.  Do Neutron Stars develop into White Dwarfs by Mass Loss?https://jochesh00.wordpress.com/2017/02/08/do-neutron-stars-develop-into-white-dwarfs-by-mass-loss/

44. An Infinity of Flavors ?                             https://jochesh00.wordpress.com/2017/02/16/an-infinity-of-flavors/

45. The Origin of Infomration & Understanding; and the Wellsprings of Creativity

https://jochesh00.wordpress.com/2017/04/01/origins-of-information-understanding/

46. The Complex System of the Second Law of Thermodynamics

https://jochesh00.wordpress.com/2017/04/22/the-complex-system-of-the-second-law-of-thermodynamics/

47. How Physicians Create New Information

https://jochesh00.wordpress.com/2017/05/01/how-physicians-create-new-information/

48. An Hierarchical Turing Test for AI

https://jochesh00.wordpress.com/2017/05/20/an-hierarchical-turing-test-for-ai-2/

49. The Neuroscience of Problem Solving

https://jochesh00.wordpress.com/2017/05/27/the-neuroscience-of-problem-solving/

50. A Standard Method to Understand Neurochemistry’s Complexities

https://jochesh00.wordpress.com/2017/05/30/a-standard-method-to-understand-neurochemistrys-complexities/

51. Problem Solving for Self Driving Cars: a Model.

https://jochesh00.wordpress.com/2017/06/10/problem-solving-for-self-driving-cars-a-model/

52. A Trio of Relationships and Connections

https://jochesh00.wordpress.com/2017/08/04/a-trio-of-relationships-connections/

53: Einstein’s Great Subtleties:  Einstein’s Edge

https://wordpress.com/post/jochesh00.wordpress.com/583

54. The Problem of Solving P not Equal to NP

https://jochesh00.wordpress.com/2018/04/28/the-problem-of-solving-p-not-equal-to-np/

55. How to Create a Blue Rose

https://jochesh00.wordpress.com/2018/06/02/how-to-create-a-blue-rose/

56. The Etymologies of Creativity

https://jochesh00.wordpress.com/2018/06/14/the-etymologies-creativity/

57.  A Basic Model of a Unifying System of Most All Knowledge

https://jochesh00.wordpress.com/2018/07/06/a-basic-model-of-a-unifying-system-of-most-all-knowledge/

58. Understanding Psych with S/F Brain Methods

https://jochesh00.wordpress.com/2018/07/11/understanding-psychology-with-s-f-methods/

59. The Wiggins Prime Sieve

https://jochesh00.wordpress.com/2018/08/02/the-wiggins-prime-sieve/

60. The Complex System of Love

https://jochesh00.wordpress.com/2018/08/22/the-complex-system-of-love/

61. The Limits of the Comparison Process

https://jochesh00.wordpress.com/2018/08/27/the-limits-of-comparison-processing/

62.  The Bees, Cortical Brain Structure, Einstein’s Brain, etc.

jochesh00.wordpress.com/2018/09/14/the-bees-cortical-brain-structures-einsteins-brain-the-flowers/

 

63. The Wiggins Prime Sieve, Version 3.

https://jochesh00.wordpress.com/2018/09/15/the-wiggins-prime-sieve-version-3/

64. The Prime Quartets Method

https://jochesh00.wordpress.com/2018/10/04/prime-quartets-method-capabilities-insights-sans-limits/

65. Is Goldbach’s Conjecture True And/or False, Conditionally?

https://jochesh00.wordpress.com/2018/11/17/is-goldbachs-conjecture-true-and-or-false-conditionally/

66. The Magic of the Prime Multiples and Goldbach’s….

https://jochesh00.wordpress.com/2018/11/27/the-magic-of-the-prime-multiples-insights-into-goldbachs-conjecture/

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Is Goldbach’s Conjecture True And/or False, Conditionally?

Is Goldbach’s Conjecture True And/or False, Conditionally?
By Herb Wiggins, M.D.; Clinical Neurosciences; Discoverer/Creator of the Comparison Process/CP Theory/Model; 14 Mar. 2014

Copyright © 2018

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Essentially, we have to explore the primes to find the patterns & information to understand why Goldbach’s is proven, conditionally, as true, and is also not true, conditionally. We must then add the information to show this to be the case, logically.
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As stated before in the NP Not = P article, we must add information to most problems to solve those. Given the amount of Shannon’s information theory quantity of info then NP cannot be = to P. Therefore, in order to solve the hard NP problem of Goldbach’s Conjecture, that the even numbers can all be written as the sums of 2 primes, we must find/add information which can be used to solve that problem.
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And here those are, brought to us by the higher logics of the comparison process, Least energy and empirical, experimental math, the (futures of mathematics) to solve the problems of complex system understandings, as well.
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We must first look at the capabilities AND limits of our logics, and then we make and find some good answers, plural, NOT a single answer. Logic is not complete. Godel’s Incompleteness Theorem showed that important truth,from  80 years ago. Empirically, the EM number line of colours is NOT complete, shown by “The Structure of Colour Vision”.
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First of all, is 1 a prime? Goldbach clearly thought so. & then by solid, empirical, mathematical evidence showed that the even numbers were the sum of primes, & stated, going too far, that they ALL were. However, it’s proven empirically, experimentally, practically up to very high numbers. But not forever, and that will be shown soon, & simply, and why it’s the case.
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But is 5 + 7 = 12 true? Yes. Is 11 + 3 =14, as is 7 + 7 = 14 true? Yes. And the sum of all of these true statements of two primes added together to create the even number line, up to a very high number, are All true, too. The sum and collection of true statements are just as true as the truth of each statement. Thus, to very high numbers, Goldbach’s is true!!
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How DO WE know that 1 is not a prime? And that’s an axiom, an assumption, and how this is the case is based upon the inadequacies and inconsistencies, somewhat arbitrary of Number theory. Goldbach had no problem with 1 being a prime. If 1 is not a prime, then what is it? What’s a Non elephant? Do we not know? How can we? Calling something NOT something does NOT tell us what it is.
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1 is the relationship between all of the numbers in the number line, both above and below a specific number. The number 1 has a relationship, comparison process value, & therefore. It creates the number line, all the odd, even numbers and the primes, and all of the prime multiples, as well.
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If 1 is a prime, then Goldbach’s is easily proven true. We add 1 to each prime and we get a lot of even numbers. We add early on 1 + 1, and we get two. we then add 1 + 2 and we get three, we add 1 plus 3, and we get four, then 6, then 8, 10, and so forth.
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But we note these things. Does adding a prime to another prime create an odd number? Not at all. Adding two odd numbers, except for the case of 1 & zero, can create only even numbers, but empirically, not with odd numbers. Nor can adding any odd number to any other odd number create anything but an even number. That’s basic number theory. Adding a prime, except for the case of 2, which is a special case only works for the 2nd of prime twins to create another prime. and that’s because, also, adding an even number to an odd always creates an odd number. So ONLY by adding THREE primes can we get the odd numbers. & the primes.
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Now, IFF 1 is not a prime, then what is it? Or is math in part, the study of all not elephants, as Ulam’s koan stated?  And that’s the problem, logic doesn’t work for complex systems. It’s not all A and Not A. & Godel’s Proof showed and Hofstadter affirmed that deep truth, “This statement is false” or the many permutations of it, “This sentence is not the case”, creates a real problem in logics. Everything is either all black or white, that is, white or not white. & that is empirically false. What of the unlimited shades of greys? What of the colors, AND the combinations of colours AND the shades of grays? Or DayGlo? The number line of EM spectra, is thus quite as incomplete, as the math is, by Godel’s Proof and empirically.
 .
Thus we have shown that Goldbach’s Conjecture depends upon an unworthy instrument for “proof” in mathematics. A or Not A demanded by logic in math, is not the case, empirically. That model does NOT always work in the real world. The false dichotomy is yet another way in which logic defeats and eats itself, like the Worm of Ouroboros (or the Procrustean Bed of Logics!) thus destroying itself. It’s all not “either/or,  nor true or false, but the unlimited shades of greys, or colours, and their combinations. & what of our visual system? Comparing that to the EM line shows the limits of the EM linear, math lines, What of the combinations of all possible colors? What of Brown and reddish blues? Not on the EM spectrum. The empirical logic of the EM spectrum/structure is NOT complete. Godel’s incompleteness theorem, yet again.  “This statement is not likely to be true”, is the problem. Limits to tools, and their capabilities, yet again. Structural limits to logics.
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Now we must consider negative numbers, to show, once again, these tough number theory problems. Let us take addition in positive numbers. When we add two positive numbers together, we get a sum of even numbers, not quite just like the basis of Goldbach’s Conjecture deals with. And when we start with 2, we count up to 8, and find that we must count up by 6. So we make a table to memorize the relationships of 2 and 8, being 2 + 6 = 8 (equally true, 6 + 2 = 8). And for all the other additions, as well, as that table efficiently (thermodynamics) short cuts “counting up” every time we add 6 to 2 to get 8. It saves us much time and energy. Long Term Memory does that, BTW.
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Then comes the trouble. We then find that the sum of 2   4’s, or 4  2’s is Eight. And that 8 minus 6 or counting backwards, and down, is the same, 2. Thus the generation, source of subtraction. Thus 2 + 6 is 8, or 6 + 2 is 8, empirically by counting. & subtraction is counting down, essentially simplified counting. Thus counting is valid evidence of the truths of the addition tables, is not? And the subtractions tables, is not? And that the relationships of all of the numbers as compared to all of the rest of the numbers can be expressed by counting, the baseline. Then the more efficient, the additions and subtraction tables as well. & thus we do generate arithmetic by comparison processing, which shows the relationships of the numbers to all other numbers, by simple arithmetic, is NOT?
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An hierarchy of counting, then adding, then subtraction; and then the next level, multiplication, and division and then long division, etc. 1’s 10’s, 100’s, 1000′, 10K’s, 100K’s and millions etc. Hierarchical all.
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That’s how arithmetic is created, generated and comes about. Very simply.
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Now what happens when we add  the positive 2   4 times? We get 8. Thus the multiplication tables are validated and PROVEN by this means. A positive number plus a positive number is a positive number. And an odd number plus odd numbers is an even number. and an even number plus an even number is an even number. So we have that consistency. & an odd plus even number is odd.
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Now, comes the trouble. Negative numbers. If we add positive numbers to positive numbers, we, by convention, an axiom, get positive numbers. But if we add an odd number such as -2 to a -2 and up to -8, by the same subtraction numbers, we get the same additions using odd numbers as we do even numbers, do we not? That is the case, and the odd negative numbers plus odd negative numbers give even odds. And the odd negative numbers plus the even’s give odd numbers. and the even negative number plus even negative numbers, give even negative numbers. This is the rule.
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But what happens with multiplication is the trouble with the negative again. (& what of zero? (Oops.)
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So if we multiply an odd number by an odd number we get a positive number. The addition is consistent but the Multiplications are NOT! Using the same conventions, an odd, negative number plus  a negative number should be a negative number, is not? But that’s the problem. & the whole of the imaginary number line is the case. Oops.
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Now if we try to factor positive  numbers, we have not any troubles, But how do we factor large negative numbers such as -12? We cannot!!!!  Because the thing doesn’t work that way, by convention. The Axiomatic problem with number theory is in the way of it. For -12   is it  -4 times -3? Nope it’s +12.  is it -2 -6, nope. Is it minus 4 times +3, to give -12? Or the other way around 4 times minus 3?. Hopelessly complicated and confusing. Something’s not right with the Number Theory because we cannot multiply negative numbers  in any sensible way, NOR factorize them at all. Oops.
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And, what’s more we can add negative odd primes to odd negative primes and get negative even numbers, too!! BUT NOT factor them. There’s a problem here, and it’s what causes the trouble with Goldbach’s. IFF 1 is not a prime, then Goldbach’s arises & trouble with proving it. IF Goldbach’s 1 is prime is the case, Goldbach’s is trivially true.
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So here we are.  5 plus 7 =12? Are 5 and 7 primes? Yes. If Goldbach’s is true, it’s because that’s valid. What of  3 plus 3 being 6? what of 1 + 1 being 2? Not valid due to 1 not being a prime. More Non-elephants we see. So what is the number 1? We are not told.
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So, if we must therefore conclude that 1 is not a prime, Goldbach’s is a problem, because it does NOT allow 1, 2 or 3 to arise. so Goldbach’s Must be true, conditionally, for all even numbers >/= 4. Otherwise, it’s not true. Thus for what we see, Goldbach’s is true with that condition, if 1 is not prime, or a not elephant. Goldbach’s is conditionally the case, AKA true. But not quite, which opens the door for more objections to  Goldbach’s   being true.
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Then we know that since 7 plus 11 give us 18, and 13 + 5 is 18, and 11 + 7 also 18, that Goldbach’s is true. And thus for the rest of the even numbers. If each of the sums of the primes creates the even numbers, then the collection of those statements MUST be true as well, but conditionally, as 1 is not prime.
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Thus we have at least one new piece of information. Conditionally, Goldbach’s is true. Now the next step.
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Let us consider the prime number line and the Gaps in the Primes. Those spots are composed (by composites) of prime multiples and related numbers, which are not prime, and on either side of 120 by 7 units, from 113 to 127, there are NO primes. Now, what happens, assuming that the prime numbers (all but 2 being odd!!) create the positive even numbers when added?
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We have a LOT fewer prime sums, because of that gap in the primes, with which to create the even numbers. Each of the even numbers above 20 have a LOT of prime pairs that when added create those even numbers, NOT just one. So if we add, assuming that 117, 119, and 123 are Prime, for instance, we have a lot more prime sums which create the even numbers. So increasing the numbers of primes, increases the sum of primes for each even number. But since we have a great many primes which can do this, we ask this question. What if the primes thin out? At what point does Goldach’s become false? Here is the solution.
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If we, for instance removed all but 4-5 of the primes in the 100 centad to 200, what happens to the number of prime sums to create the even numbers? They stop doing so!!!. Thus we can prove that if the primes are reduced in number past a certain point, Goldbach’s which was formerly true conditionally above 3, can fail. But does that happen? And the answer is yes!!! Because eliminating the primes in the centad of 100, to create the even numbers does that. Whereas adding more primes increases the prime sums for each even number.
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And that’s the case, and must be. Because we know as the primes begin to fall, with vastly higher number line, we see the inverse log function showing us few, and fewer primes per centad, i. e., groups of 100 numbers such as 101 to 200, and so forth. & we know that the primes must eventually fall to about 0 – 4 primes/centad (and then even less), when the numbers get very large, and this can be calculated. And Proven to be the case. In the regions of 200 there are many primes, upwards of 15 or so. By 500-600 those begin to decline. By 12,000 more so being around 10 or so. & this can be computed out by a special function. Thus we know that the primes begin to decline regularly against an asymptotic limit. We never get to the last prime, but they become increasingly rare as the numbers get into the millions of digits. that is a proven fact, and thus yet another of the pieces of information falls into place to solve Goldbach’s.
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This is the rate of prime density drop off.
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 lim Pn/n =1/ln (n) when n goes to infinity.
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About 1/2 way through this article:
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We’re up against an exponential barrier, asymptotic limits of the primes. Hmm, quite like Cee, 0 Kelvin, the Uncertainty Principle, and that there are NO perfect heat engines; nor in information theory, perfect descriptions, either for the same reasons. Have treated expon bars in many instances on the blog, too, and how those occur and what creates those to some extent.
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In those cases then, just as we see by ridding the number line of the primes in the 100’s, we cannot generate certain positive integers, either. Thus Goldbach’s fails with very large primes, because there are so few of them. But the problem is that calculating those huge numbers is beyond us, & thus the empirical, mathematical truth that Goldbach’s MUST, logically, mathematical fail with very high primes, as they are rarer, and rarer, falling down to 1-2 per centad, is not?  And somewhere down the number line at about twice the size of those fewer primes centads, will be found the even numbers not amenable to creation by adding two primes.
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And that is the solution to Goldbach’s. It’s both conditionally true, but eventually fails. Logic can’t do this requiring either/or. The same is true of Riemann’s Hypothesis about the Zeta function, BTW. Thus the likely Trinary solution of Goldbach’s contributes to the next solution of Riemann’s.
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Thus, Goldbach’s is ONLY conditionally true, but NOT universally true, by yet another instance. Goldbach’s is not the whole case. It’s true if p is >/= 4 or higher, but NOT true for 2. And when the primes get rare, and this can be empirically in time proven, then Goldbach’s at some point must fail, is not? And we know this simply by removing most of the Primes from the 100’s centad and see the sums of primes drop to zero for some even numbers. & we know that by increasing the number of primes also increases the number of prime sums to create even numbers, as well.
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Thus, Goldbach’s is conditionally true, from >/=4 up to very large numbers, but not universally true for the number line at very high numbers.
QED
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That’s the epistemological power of the new complex system, comparison process logics, and how to create creativity. Add information of the right kind and problems get solved. Find that by efficient sorting methods, using comparison process & pattern recognition creating new information, least energy, structure/function (S/F) methods plus the unlimited methods created by the same.
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But rather, there is a Great Race coming resting upon the empirical solution to where Goldbach’s becomes not true, because even numbers will be found very far down the number line, which cannot be created by adding two “known” primes. This is the inevitable outcome of the facts that the sum of two primes will become no longer possible when the primes fall to about 1-4 primes per 100 number centad, & thus unable to support Goldbach’s.
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Because that is in the millions of digits size of numbers, by the inverse log function which shows that. It will be most easily found where a LOT of even numbers in a group, well downstream in the number line, will not be summable by any 2 primes. The first groups of even numbers, failing Goldbach’s, will be far, far upstream from that easier to find even numbers not summable from two primes.
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That will take HUGE amounts of processing power, sorting systems, and efficient programs to find. So the hardware, software and so forth will have to be developed to find out where that goes on. Quantum computers are highly efficient sorters. Those can solve this problem of the empirical test of Goldbach’s failing at very large numbers. Where Goldbach’s conjecture becomes not the case any more. Those empirical findings will cinch the final proof for the understating that Goldbach’s is both conditionally false for 2, then true to very many high millions of digits, but then becomes not the case, well up into the number line.
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And as the saying ago, now The Great Race is on AND, “The Game is Afoot!!!!”

 The Wiggins Prime Sieve, A Prime Quartets Method: Capabilities & Insights Sans Limits  

By Herb Wiggins, M.D.; Clinical Neurosciences; Discoverer/Creator of the Comparison Process/CP Theory/Model; 14 Mar. 2014

Copyright © 2018

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The primes have some patterns, but those are clearly most all the reflections of the underlying Prime Multiples of 3’s(PM3’s) repetitions, as modified by the other PM’s.
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For instance, where there are twin primes those occur in two set patterns. The 2nd commonest is in the 3 PM3’s groups, which repeat every 30 numbers to unlimited numbers. Essentially, each quartet is 1 of 3 repeating PM3 forms.The first is where the -3 and –9 ending numbers are always PM3’s. This allows the -1 & -7 numbers to be primes. Thus there can be NO twin primes Within this PM3 quartet form. The next is the quartet form where there are NO PM3’s and that allows all 4 to be primes, or in any combo of 1, 3, 7, 9, too. The last in this repeating succession of 30, is the PM3 quartet form where the -1 & -7 numbers are PM3’s & the -3 & -9 can be primes. But there cannot be any Twin Primes in these PM3 quartets. This is an absolute (dare it be said!) invariable in the quartet system and is a rule.
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Thus, between those repeating pairs in the 1st and last quartets, in those no PM3’s can be primes. This creates the only possible twin primes ending between the 1st and 3rd PM3’s quartets, and must be -9  in the one quartet and then in the following quartet, the  -1. & indeed those are seen all over the prime lists. Such as 59, and 61, or 149 and 151, without limits. Those twin primes are made possible and driven by the structure of the 2 quartets around PM3 patterns. And because those PM3 patterns are invariable and repeating, there are Twin primes of that kind without limits. This proves part of the twin prime conjecture, very clearly.
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The last half of the twin prime proof is based upon yet again a series of patterns. In the middle quartet there are NO PM3’s exclusions of the -1, -3, -7, -9 ending numbers. Thus all 4, or 1, 2, or 3 or none can be primes. & in ANY combos.  We Also can see NO primes in that quartet, but rarely. And can see -1, or -3, or -7 or -9 only, each alone. Or -1 & -3 twin primes, or -7 & -9 twin primes, or the -3 gap and then -7 patterns. And curiously, if we see the quads, or triplets or twin primes in those patterns we know we have seen the PM3 free quartet once again.
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But there is this caveat. The PM3’s can present with a -1 & -7 pair of primes, As can the middle, PM3 Free quartet. And also the PM3 with an open -3 and -9, can also be seen. But never a -1 and -9 as that only can be seen in the PM3 free quartet. That pretty much exhausts all known possibilities. And conversely NO triples, or -1 & -3; or -3 and -7; or -7 & -9; or -1 & -19 pairs, can be seen in the PM3 two quartets. So it makes finding those very easily in the quartets. Those are the quartet Identifying methods which the PM3 driving patters create.
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At 11, 13, 17, 19, we see that ONLY 4 primes series are possible. Next come the 101, 103, 107, & 109 primes. And next come the 191, 193, 197, & 199 primes. This is no accident, and again, those ALL occur at 90 number intervals. This is PM3 driven, clearly. & we see the 41, 43, 47 prime triplets there, as well. & the 71 &73 twins, as well. As those possibilities exist without limits in the no PM3 middle group of repeating -1, -3, -7, & -9. thus those twin primes can be seen, as can the triples, without limits in the number lines. Thus the twin primes conjecture is proven by the simplifying and universal quartet model of the primes. This is empirical mathematics and creativity.
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But why, additionally are NO more than Four primes possible in the entire number line? Again, the PM3 driving pattern. Because the PM3 quartet form of PM3 of -3 & -9 precedes the middle quartet form all possible 4 primes in a row, and the next PM of  of -1 & -7 ends the PM3 quartet of 4 possible primes, again, this PM3 constraint does NOT permit more than 4 primes in a row!!!
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For instance:
171 PM3
173 Prime
177 PM3
179 Twin prime
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181 Twin prime.
183 PM3
187 PM 11X17
189 PM3
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Then
191  Prime
193  “
197  “
199  “
Then
201 PM3
203 PM 7X29
207 PM3
209 PM11X19
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Thus there cannot ever be a twin prime involving the PM3 mid quartet with a -9 preceding it, or an PM3 free quartet ending with a 9. That is circumscribed by the nature of the PM3 quartet sequences, as well. A sort of lemma of the why there are not any primes longer than 4 in the mid PM3 quartet. It’s impossible to be seen. Thus where the twin primes of -9 and -1 are seen it’s Always after the last PM3 and next to the -1 of the two PM3 pair quartets.
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&  that is not all, so in EVERY case, the prime twins, triples, & quartets can occur & recur without limits in the mid PM3 free series. And where those are seen at intervals of 30’s, always.
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For instance, 821, 823, 827, & 829, are at 630 (90 X 7!) plus 191, 193, and 197 & 199, the double twins. Again, a 3 multiplier and this continues without limits. The double pairs of primes always occur in a pattern, early on, which is 90N plus the initial 11, 13, 17, 19, double twin primes, as well. However, as the double twin primes in the no PM3 quartets rise in values, this breaks down, possibly due to the entrance of the higher prime number multiples, altho it appears occasionally, even then.
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There are the PM3 driven twin primes. And WHY they are there.  It’s not an accident but a deep structure of the PM3’s seen in the prime lines, which would have been missed had not the quartet system shown these deep structures by simplifying down the number line to ONLY those bare bone numbers which can be primes. Simplification is least energy, and a founding part of creativity and understanding.
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& that’s largely what’s going on. The quartet of -1, -3, -7 & -9. show the prime patterns repeating throughout the number line and are very useful mathematical tools to understand how the primes appear and why, in a clear cut, structural, explanatory way.
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There is a lot more to these primes, however. In all cases where the PM3 quartets the one ends in a -9 prime, and then the next twin prime can start with -1. This is the pattern and seen everywhere, without limit. There are NO limits at first to Twin primes and triplets and quadruplets until much higher in the prime lines.
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But a very interesting event occurs as the numbers rise into the 100’s of digits. The number of primes falls to 0 to 5 per 100. And that means twin primes still can occur, but become rarer and rarer. Tho the line is unlimited, those twin primes can still be seen. The same is true for the triple and quadruples. This has broad implications, and proves as well, yet another aspect to the fall off in primes. Which will be addressed, later.
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And there is yet another pattern which is very clear cut and real with respect to the primes in these quartets, which bare bones, stark efficiency of these 3 forms. allows it to be seen. Because ONLY two open spaces exist in the two PM3 quartets, but FOUR potential primes are in the PM3 absent quartet, thus not surprisingly up to 1000, there are about 99 primes in the PM3 free quartet and about less than about 92 , totals in both PM3  quartets. The numbers of primes in the PM3 middle is more than twice as great as the total number of Primes in the Two PM3 quartets. That also does not change, either. but likely gets rarer and rarer as the primes naturally, empirically diminish in numbers per centad of quartets.
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One further repeating pattern found is that the prime quadruples begin at 11, 13, 17, 19, then 90 units away at 101, thru 109, then 90 units away at 191 thru 199. Then a quadruple is not seen again until 821 thru 829. Which is 630 and thus 90 X7. Why this should be so is obvious, but again, will let the astute figure it out for themselves.
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Altho the 90’s intervals break down & get rarer, this is still seen from time to time in the fewer and much higher prime quartets in the PM3 free quartet in the middle of either PM3 pairs quartets.
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There are yet many other interesting patterns, but will let the astute accountants and mathematicians find  those for themselves using the quartets method.
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Recommended testing it for more useful patterns, which are clearly, very definitely there and invariable throughout the number line.
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& that also allows a very, very fast removal of PM3’s thus yielding the other primes 11, 13,17, 19, etc. sequences of the primes, too.
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Commend those interested in understanding much more about the primes to use this method for more study of the primes. Undoubtedly there are many are hidden patterns winch will emerge if looked for by pattern recognition methods of creativity in mathematics, as detailed in “La Chanson San Fin”, which was used to create, find & employ and apply, the prime quartet system.
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The prime quartet method shows the deeper prime structures created by the  PM3’s , and other prime multiples as well, such as the prime gaps. & shows that ALL of those are created by Prime Multiple reinforcement using this method. The prime gaps are prime multiples created, in every case, the first of which at 113 to 127 is very, very clear cut and demonstrative as well. & the PM3 groups make that very much more common than without.
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More on Twin primes
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There will always be twin primes but as primes become rare at the rate of 4/100, those will become much less common, and necessarily fewer repeats of twin primes. This is a matter of empirical fact. Where those twin primes max out will be in the earliest primes, as the patterns show, too. As the primes become rarer, and the 4 primes in a row become rarer, yet still, occasionally, following the 90+ rule, the number of twin primes will fall. But likely will stop when the primes/100 fall at very high numbers to 0-1 prime/100, by common sense. So it will be a low probability of twin primes, but not an absolute, either.
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Thus the maximum number of twin primes will occur early in the number line, and be reduced as the number line gets very large.  That will be found to follow a pattern of 30’s and 90’s, as well. The max number of prime triplets, quads and so forth will also decline. & occur further and further apart in the number line. The number of primes can vary, even at 1 billion by as much as none/100 to as many as 12/100, as shown in the series of 50,847,000 primes found by Dugas/O’Connor. It should not be hard to find a logical reason for this, or proof, either.
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Now that it’s known that the twin primes are driven by a recurring pattern pf PM3 quartets.
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There is one last, huge implication of all of this. That the number of primes will continue asymptotically to near zero, but, like light speed, and 0 Kelvin, NEVER reach that. That exponential, or asymptotic limit is also clear. It will NEVER reach zero, but will get so close as no matter. Comparison process rules create the asymptotes and exponential barriers. & this outcome, like there are no perfect heat engines in TD, or the Heisenberg UP, is part and parcel of the comparison process’ nature, too. Yet another of unlimited asymptotes/exponentials, such as in the S-curves of growth, as well. Unbounded and created by the CP. Such are unlimited using CP methods.
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Thus the twin primes conjectures are easily, uniquely and clearly solved by the prime quartets methods, which greatly simplify down the number line to ONLY those ending in -1, -3, -7, -9 and thus shows the PM3 restrictions which creates that same prime line, too. As well as the PM3 patterns which highly restrict where the primes can fall.
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& it can further describe and improve our understanding of the twin primes, too. Those can ONLY be created in 2 places. The two possible -1, & 3, or -7 & -9 of the middle PM3 free quartets, and between the last, and the first PM3’s pairs quartets sequences.
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To repeat, much more can be found by using the quartets model. It’s essentially unlimited, except by an exponential barrier, which being asymptotic, will in time give the diminishing returns outcome, just like any S-curve or ANY method which is least energy efficient, for that matter.
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The Wiggins Prime Sieve, Version 3

By Herb Wiggins, M.D.; Clinical Neurosciences; Discoverer/Creator of the Comparison Process/CP Theory/Model; 14 Mar. 2014

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Copyright © 2018

 

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The basic concept which best deals with the primes is that of the Prime
Multiples (Prm’s). Those are clearly exclusive of the Primes, and the
primes are by logical definition excluded from being prime multiples. This
is the case. Thus whenever the Prm’s are generated, and eliminated, we are
logically left with the primes. When the language/terminology is better,
the concepts are better, applied more easily and understood better and
faster. There are great and good consequences to good vocabulary and
terminologies. It’s the basis of most all the professional
vocabularies & languages in nearly Every field.
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The method has been tested and works by Dugas and O’Connor to numbers 10
exp.9, & is robust.
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The same by Sullivan through 2000. and my work shows the same outcome to
2700, without missing a single Prm when accurately done. & a similar method
taking 5200’s & 5300’s in isolation, that is, starting at about 5300, and
sorting above and below that point by 100 numbers, showed that the method
works, completely, accurately and clearly.
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So how does this relate to the gaps in the primes? Because the Prm’s
exclude the numbers which are Not Prime. When the PrM’s are consecutive,
the prime gap is consecutive with the PrM’s. And the patterns are very
clear. Take for instance, the huge first primes gap between 113 & 127. This
pattern is blatant, as well. Add 7 to 113, and subtract 7 from 127. We get
120. Now analyze this by the Prm’s methods. 120 is 10 times 12, an even
dozen, which has the largest number of divisors to that point. Then 24 is a
perfect number, and both 120 &12  are multiples of the perfect numbers, 6
and 24.
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Now we take 114, even, divisible by 3’s & ~ Prime. Then 115, -5 ending, not
prime and further, 5 times 23, thus a semi prime. Then 116, even divided by
2, 58, and 29 & 4; then 117, divisible by PrM3’s and 9; then 118, even and
divisible by 2 times 59; then 119,divisible by 7 and 17, again Prm’s. Then
120 and that’s the central magical number, divisible by 2, 3, 4, 5, 6, 8,
10, 12, 15, 20, 30, 60, etc. AND the CENTER of the Prime gap, for sure.
Then we have 121, being 11 squared; &  then 122,  56, 2, 28, 4, 7, etc;
then 123 3 divisors, and then 124 with other many factors, an even number,
62, 31, 4, and so forth; then 125 which is 5 cubed!!!. Then 126, again
even, 63, 2, 7, 9, 3, and multiples of same. And last, 127 prime!!! The end
of the gap of primes.
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The other clear pattern is that  the Prm3’s pairs of 2 consecutive quartets almost always fall within those gaps. Thus those are a major contributor to the gaps, plus the other many Prm’s, too, such as 7, 11, 13, 17, etc. &  this has been consistently found many, many times. Esp. below 2500. So the gaps ARE created by the Prm’s being particularly concentrated by the periodicities of the interference reinforcement patterns of the Prm’s, mostly. The prime gaps are thus generated in toto by large numbers of consecutive Prm’s,  very clearly. It’s that easy to understand, quite frankly.
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This Prm pattern is the pattern of the primes, which is like a cast of a
human face, or a casting system for the bronzes. The cast is the primes.
The face and original forms are the Prm’s, for when they are subtracted, we
get the primes by simple, unlimitedly repeating exclusions.
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& the rest of the gaps are the same. There is NO pattern to the primes, but
for the pattern of the Prm’s. and this allows the primes to be sorted out
exactly and by exclusion when the  Prm’s are created.
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There are many ways of doing Prm creation/generation, efficiently, but the
best heretofore is the Atkins method, altho too many ignored the conversion
of the Entire number line to mod60 and then the laborious conversion back
to Mod10. This means it’s not as efficient as claimed.
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However, there is a better way, and that’s simple and straight forward &
neuroscientific understanding. Our brains/minds are acutely attuned to
finding patterns, regularity, periodicities. & when we find those in
complex systems, we build our understandings on the Long Term Memories
those repeating, stable, efficient, Least energy patterns create, which
naturally are reinforced into our Long Term Memory systems in the cortical
columns. & then we use those standards to better understand what’s going on.
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& that general method repeats without limits, and without constraints.
There are NO limits to the ways that primes can be sorted out. Using the
Prm’s by the long, most direct way, gives us multiples of multiples which
are very time consuming, 7X7’s, 7X primes, 11X11’s, 11, 13, 17, 19, and so
forth. & then the squares of primes, the cubes, etc. That’s what’s going on,
too.
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But the least energy rules of Thermodynamic efficiency state we find the
fastest, best, most complete and which gives the best understanding of how,
in a Gaussian practical sense, “Gauss’ Razor”, we sort the primes.
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So, when we realize the vast fact that ALL primes are odd numbers, always
ending in -1, -3, -7, -9, and never -5, -0, or even numbers, we can thus
exclude 60% of the number line quickly & efficiently.
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We then sort by starting with the primes, 7, 11, 13, 17, 19, then 21, 23,
27, 29. & ever more efficiently by eliminating the Prm3’s, all of them up
to the square of 7, that is 49. We do NOT need to eliminate any other
Prm’s, but the Prm3’s before 49. Which gives the primes to 50!!! At that
time we begin to eliminate the Prm7’s, which are, 77, & 91. That is
7X7, 7X11, & 7X13. And thus have all  primes up to 100. Merely by excluding
the 3 and 7 Prm’s in the first 9 quartets!!!
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Then we do the 101, 103, 107, and 109 quartets, finding those are all
primes, as they are clearly not removed by Prm’s, & by a simple method. too.
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Then we do 111, which is Prm3, then 113, prime, then 117, which is PrM3,
the pattern emerging of the Prm3’s in this method of quartets; and 10
quartets per 100, a centad, that is. Then 121 11 squared, where the Prm11’s
series starts, and 123, Prm3, already done above, and 127, prime, and 129,
Prm3. & we see the repeating, real patterns of paired Prm3’s being
developed here.
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The number line consists of periodicities best described by the Zeta
function. But even that can be simplified down. & this is how it’s done.
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For Prime 3’s we see this pattern: the casting out 3’s method here.
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Add up the digits, and mark Pm3’s as False, the others as T for True
Primes. We find that the Prm3’s are Always in pairs in a quartet, ONLY.
Thus if we find the one, we know that the other is the 2nd following
number. If it’s -1 & Prm3, then the -7 is Prm3. If it’s -3 as Prm3, then
automatically it’s the -9 as Prm3, too. If there is NO Prm3 pairs Ever
found in the first 2 lines ending in -1, & -3, then there are NO Prm3’s in
that quartet. There is NO alternative to this pattern. It’s final, and a
total pattern, without exception.
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That removes by a simple addition ALL of the Prm3’s from the quartets to an
unlimited number, does it not? Far, FAR simpler and less processing than
doing the 3+3+3….. method of the E-sieve. Thus sparing ALL of that. One
to Two simple operations per quartet, at most, one 1/3 of the time, and
thus is massively faster than the E-sieve, which must do 60 more
numbers/100 than this method. that’s the Basic casting out 3’s method using
the quartets. But it’s EVER so easy to make it work faster, too. Using a
simple pattern, actually, the Prm3’s can be removed without even doing more
than one calculation, no matter HOW many digits the number line of quartets
has!!!  & then extending that wheel without limit down the number line of
quartets to as far as needed, into the 100’s of digits, if desired. More of
that incredibly simple system, later.
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Then we have the fast sorter which is of this form. Take a Prime, p, square
it, say 7 to 49, then double 7, get 14, and double that again to 28. Those
are the Prm7 series. by simple, arithmetic function. No lengthy multiplying
of primes together. None of that, at all. All of those multiples of 7, 11,
13, X 17, etc., are not needed. PLUS the primes 7, 11, 13, and their
squares, and cube and p exp. X, without limits, too.
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We find then
49 plus 28
77 plus 14
91 + 28,
119 + 14
133+ 28, etc.
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With 11 it’s 121 plus 22
143 + 44
187 + 22, etc.
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This proceeds at an average rate of Prm7’s by jumps of 14, alt. with 28,
which is 21, average, with Prm7’s. With 11 it’s jumps of 33, on average, and with 17,
jumps of 34 and 68, clearing over 100 digits with only 3 steps, virtually.
As the primes rise in size, the clearing proceeds ever faster. Without
limits. Contrast that to 3, 3, 3, 3, and 7, 7, 7, 7, and 11, 11, 11. It’s
very fast, not having to mess with Prm3’s either.
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We find a few -5 endings but not more than 1% of the Prm7’s, series, and
with each successive Prm# such as 11, 13, 17, 19, etc., the same is true,
and those decrease in number. And this is the method. & it’s robust, but
will over call and find the Prm’s as duplicates in each case as a back up
cross check for the method. So if the computer, or if we use a calculator
makes a mistake, those are real periodicities are not seen and thus the
mistake is quickly seen & correctable. What was thought to be a slow down,
was in fact a checking system, which can create Prm’s very, very much
faster by orders of magnitude if desired.
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Essentially this finds the primes, and then we plow those back into the Prm’s series, finding ever more. By the time we get, for instance, to 19 sq., 361, we have 73 primes to plow back into the Prm’s generators. Well enough ahead to get to at least 130K of the number line and all of those primes, too. Thus this prime sorting system feeds the Prm’s by a huge amount and does not ever run out of primes to find the primes. It’s that easy.
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It can go even faster this way, when the patterns of the successive but not
first Prm’s are located & removed from the number line. Without limits,
too. This is the most rapid way to create the Prm’s and eliminate them from
the number line, leading to a prime list, which grows and grows without
limits, as we reach each prime squared.
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This method is way faster by 3 fold than the E-sieve, and actually advances
faster and faster as the size of the primes are squared and then added to.
Thus it generates quickly the Prm’s and the job is done as fast as possible.
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That’s the Wiggins Prime Sieve in its nearly most efficient form. However,
the Prm’s which are duplicated, can also be sieved out by a simple pattern,
thus making the system even faster, if properly coded.
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& works without limits, too.
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This is what can be discovered with understanding the limitless
capabilities of the brain/mind for seeing patterns, and then more pattern
recognition on top of more patterns. The method can likely be made even
more efficient than this. The Log limit of the E-sieve is thus overwhelmed
and is not efficient, or least energy as this method is, and thus Least
energy methods win once more.
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That’s the basic form of the Wiggins Prime Sieve, which is copyrighted and
which will threaten the cyber security of the RSA method, because when the
prime arithmetic factors are known, huge lengths of digits of primes can be
ID’d and then listed, and generated by computer methods at ANY point in the number line, when properly coded with these new methods.
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And that’s how it’s done. and it’s neuroscientifically supported and robust
as well. Without limits.
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When reviewing the QM equations, which are so complex that they cannot be
solved without huge computer power, we are essentially looking at an
analogous situation with the primes computations. Feynman found ways to
simplify the computations with his diagrams & renormalization. These methods of the Prm’s can
also be applied to the QM wave equation for the higher elements, atoms and
isotopes, & to solve those problems of electron levels and isotopic decay
rates, faster, and faster on existing machines. The way is clear for that,
as well.
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The periodicities of the natural world, whether they be the Roche numbers
of the planetary, complex system orbits, or the rest of the complex system
families of events, can now be more rapidly sorted than ever, using these
methods.
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& that is the Promised Land of the Undiscovered Country of the Complex
Systems. Genetic systems, protein folding and other such periodicities can
then be solved and result in rapid progress in those problems as well. They
way is now clear to understanding much more completely, the limitless
complex systems in our universe.
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And this is the Promised Land of Comparison Processing, which recognizes
Least energy processes, which creates S/F relationships of brain, and the
unlimited methods of CP and LE applications. PLUS within the basic
understanding of Complex Systems, now possible.

The Bees, Cortical & Brain Structures, Einsteins Brain, & the Flowers

By Herb Wiggins, M.D.; Clinical Neurosciences; Discoverer/Creator of the Comparison Process/CP Theory/Model; 14 Mar. 2014

Copyright © 2018

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This title sounds almost silly, but is in fact a very deep, underlying  and least energy connection about how events in our universe are interrelated and work together.

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First of all we look to the bees which create the honeycombs, which are cylindrical cells made of wax, which they secrete from special glands. Then the wax is shaped into the honeycombs, which are repeating hexagonal, cylindrical, regular forms Those are are very famous and of considerable mathematical as well as materials sciences shapes. Just how and why the bees use the repeating hexagonal honeycombs is no longer mysterious, when considered from the least energy principle. The most efficient columnar forms are those of the regular hexagons.
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Those are also seen partially in nature in the nearly hexagonal forms of the basaltic columns when slowly were cooled, worldwide. Devil’s Tower, the Giant’s Causeway, the same basaltic columns in the cliff walls of Yellowstone near Tower Bridge, and even Devil’s Postpile Park in California. Much the same is seen in SE Washington there in the Columbia River Basalts and wherever else massive amounts of basaltic lava flows are laid down and cool, slowly, such as in Iceland.
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Why this should be is very clear. For columns of any kind the hexagonal form is least energy. In other words, the MOST space can be most efficiently enclosed in the hexagonal columns. That is most commonly seen naturally in Honeycombs. Those are not perfect hexagons, but are least energy created to be as close to that as can be done without wasting too much time, materials and effort on perfection. Thus, the geometry of the Honeycomb is a least energy geometry, as those were discussed previously regarding hierarchical arrangements, least gravitational energy forms (water flows downhill) of the riverine systems, world wide, (rivulets/springs, become the little streams, to little creeks, to littler rivers, to bigger rivers, to the massive trunks of the Missouri, Ohio, Mississippi, the Amazon, Orinoco, etc). Or the neurovascular bundles of nerves, arteries & veins, and so forth. & the tree trunks, large branches, smaller branches, sticks, then twigs, then the veining patterns of the leaves, etc. Not to miss the roots of the plants, nor the deltas of the rivers, as well, all of similar, least energy, geographic, topological and biological organizations.
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Thus the honeycomb is least energy geometry and not Euclidean, as the riverine and related hierarchies are also complex system, hierarchical geometries of least energy. It’s in a more general sense, a very tight packing system. Sedimentation layers are also tight packing with least energy forms, as well, and geometries of a type of different particle sizes and densities, driving the layers in that way, as well.
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Examining the Bees more deeply, Von Frisch did several good experiments to find out how the workers were foraging and communicated to where the nectar and pollen were in in how large quantities of each, #’s of flowers, nectar, etc. It turned out that bees were using a landmark system to recall whee the hive was, and NOT getting lost. The bees see UV light, and because of that the sun is visible even when cloudy!!!  And because the sun rises and sets in a consistent repeating, least energy pattern, they use THAT standard to know where the hive is. The movements of the sun tell them time of day, just as it does us, and where the hive is.
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So the worker bee comes back laden with pollen and nectar and communicates to fellow worker bees where the nectar is. Von Frisch put sugar water samples at distances from the hive in many directions and then watched what the bees did upon returning to show the others where the nectar sources were. They oriented themselves to the sun. and if they wiggled fast, it was close and if wiggled slowly it was more distant, and the other collecting bees could then find it looking for the flowers, which not surprisingly ALSO glow in UV light saying, Here we are, nectar and pollen, primarily pollinating most all of our best plants to fruits.
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But, there is a depths within depths to this Von Frisch solution to how the bees communicate by landmarks as to where he nectar is. Which he missed and which was found when trying to solve the Travelling Salesman Problem (TSP). What’s the best route to use getting the packages and sites visited in the least time and distance? Our best computers couldn’t tell us. It was TOO complicated a sorting problem. So, Proverbially, we observed the wisdom of the bees, and the ants. They showed us how to sort thru this problem very quickly. The bees find the closest nectar source, by trial and error sorting (just like we do), and then the mark in their bee brains about where that is from the hive in terms of orientation to the sun, AND distance. They collect as much as can, and if rich it takes a bit of time, but the sun doesn’t really move that much in that time. & bees fly FAST.
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So back to hive, orient their abdomens and bodies towards the sun to tell the other workers where this nectar/pollen largess is, and wiggle at a speed which gives the  distance within less than 100′, approximately. Then the bees rush out in a group, having had this comparison process information created & then signaled to them, and begin to collect more nectar and pollen for the hive. Then they fly back and each gives more and more data which when summed up, is least energy solution to the travelling bee to nectar flowers. Successive approximations to exactly the shortest distances to the pollen and nectar, from flower to flower, which the hive MUST have to live & grow.
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So that was found out, using their strategy of least energy sorting. Go to the first nearest good flower, then the next, then the next. And the next worker bee refines that, until at last, after some 15 periodical reduplications, a math series in a sense of successive approximations, finds The fastest route to the lovely clover plants, which give good nectar to honey. & they are rapidly pollinating the clover, collecting honey, & so forth. They use Landmarks like those found in the grid cell Long Term Memory system of mammals, and they recognize by comparison process standards to where it is and how far out it is. And find a solution within a few minutes to about 75% of likely best possible.
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That’s how the bees do it, and we have followed, using computer driven sorting methods, finding the fastest outcomes. Now what is the value of all of this? With UPS, FedEx and other delivery drivers, it finds the Least Energy, most efficient routes to delivering packages up to a complexity limit of N!, and they save upwards of 40-60% of time, distance, cost of driving wear and tear on drivers and trucks. Least energy Rules, we see. The most efficient methods win. They do lots more work with less time, costs, etc.
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And the necessity of creativity to find those least energy rules to solve the TSP, was shown to us by the bees, and then developed further to greater efficiencies. Create the information by comparison process standards, and then sort to a least energy solution, is the key, fundamental point in understanding most ALL creativity. Information is created by comparing the sun angle and the distance to the points to visit. We use similar comparison standards in Time. We use distance by measuring against relatively fixed set, stable time, distance, i.e., Einsteinian epistemological, related standards. and then against THOSE standards, very similar to what bees AND ants use to find the fastest most direct route to the food, solve the problems.
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It’s how we navigate according to maps, and within the structures of the hierarchies of our understanding. The bees have a grid cell structure short term memory system analogous to our own in function, but much simpler than ours. Look for it in the bees and further show how it works. Same with ants, birds, and all of those creatures which move around by landmarks, even the great whales!!! There’s a LOT of richly rewarding work yet to be done.
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It’s universal, a nearly universally applicable method to solving most ALL problems. That is the power of the comparison process which detects least energy savings in the complex system of the 2nd law of Thermodynamics.
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And that’s how the bees and we are very tightly related in problem solving, creativity, and how the universe is most all of it connected by deep, common, nearly universal standards of getting things done, based upon the enduring & repeating standards/landmarks (which reinforce by those repeats of themselves into our LTM, thus conjoining behaviorism neatly with cognitive neuroscience) of sun directions, time, and distances, used equally by most ALL migrating animals, including the 100’s of bird species, the wildebeests & elephants, and indeed Columbus when he discovered the New World for the Europeans.
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It shows us also that the best,most realistic expression, NP is Not Equal to P. We must add infor to solve the problems. Info content of NP, unless a tautology is NOT equal, but usually less or much less than P. NP is ~= to P. Provably so.
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Simple, elegant, fruitful and nearly universal AND unifying methodologies. It’s that simple.
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So we have the honeycomb. And we must somehow get to the Cortical columns of Mountcastle in the brains of the higher animals, such as porpoises and whales, the great apes, and humans as well. All plumped out, esp. in humans with their gyri and the spaces between the sulci. Most Everyone has seen those patterns when living & fresh brain surfaces are viewed. It’s all tight packing, too. The geometry of least energy, cortical cell columns, which make up the pathology specimens when those are seen in cross section under the microscope.
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There are 6 layers in most all human cortex, as well, altho level 4 is gone or replaced with pyramidal cells in the motor cortex, but still have the same origins as the cortex in the visual systems, the hippocampi, and the rest of the brain. The so called Neocortex. Those columns are packed into tight honeycombed patterns, with 60 degree angles being seen all about. That’s the connection of the bees to our brains’ basic, high level information processing cortical systems. It’s least energy, thermodynamic efficiencies, clearly. The Cortical Honeycombs!!
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The grid cell model of how animals, including humans navigate shows the same 60 deg. angles as the honeycomb structures. Tightly efficient, 3 D, least energy packing, we see. So our brains are also a form of honeycomb tight packing, too. the way Long Term memory is stored in the grid cell patterns. The landmarks are all stored as grid cell patterns. the basic standards of how we navigate in teh real world, reduced to a honeycomb, efficient architecture of structure/function beauty. And teh standards we use to measure and describe out universe, are ALSO stored in those grid cell patterns. The basic standards, conventions and rules are stored in this way, so that we can navigate the hierarchies of our organized knowledge. It all fits into a simple pattern. All the myriad ways of the Least energy tight packing, hierarchical categories of Aristoteles. All the same in normal humans, chimps, gorillas and orangs, as well as our recent ancestors and human relatives, too.
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But it’s way, way deeper than that. When we see the brain of Einstein, with the images of it, which have survived, it’s a very plump brain, somewhat squashed down from the process of fixing in formalin, so the gross architecture is a bit off from usual, too.
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The cortex is where the most of the higher process thinking goes on, in most all cases. Where the great ideas come from. Where the words are stored as ideas, and so forth. When cortex is damaged, in a strict structure/function (S/F) relationship, the various higher functions of speech, math, vision, sensation, movement, geographic navigation, memories and motor programs of all sorts are damaged, specifically into a basic brain plan.
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The brain is organized largely upside down &  reversed right for left in most all cases of the higher animals, including the humans and our cousins, the great apes, the whales esp. the bottlenose dolphins which also take that tight packing of cortical columns to their own kind of apotheosis of organization. And then in the birds, reptiles and likely the amphibians and some leggy fish as well, too.
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Explanandum 3, here:
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This is all well established. But why does the left human cortex of motor and sensory systems, control the right side of the body, and the right cortex the left body? When the left motor cortex is damaged, the right sided movements of the body are damaged, as well, in a strict, Left to right correspondence. Same with Sensations. Vice v ersa with the Right Hemisphere motor/sensory cortices. This is invariable in normal humans, and is the same in the apes, the mammals of all kinds including the marsupials, and the birds and reptiles. A grand design of universal types.
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And the top of the cortex between the hemispheres is where the toes are represented in motor/sensory strips, as well. & then it moves downward because there come the balls of the feet, the insteps and arches, the heels and then the “ankle bones are connected to the leg bones”, the leg bones to the knee bones, and those to the thigh bones to the pelvis and so upwards on the body, and slowly moving down to the bottom of the hemisphere in the brain where the face is represented. Once again. upside down & reversed right for left, we see. But WHY and how is this done?
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After 45 years of working within the neurological and psych fields no one ever, EVER explained why that was. NO one. Ever. Nada, nothing, Kein gedanken.
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So there is way more than that, alone. The motor and sensory nerves cross over, mostly from the left to the right side of the body, and conversely with the right brain via the decussations of the pyramids in the lower brainstem and upper spinal cord. This is also seen invariably in ALL the other mammals, and the rest. Whenever we see this decussation of the pyramids we know, without testing, that the left brain controls the right body, and the right brain, the left. Invariably in all animals and most reptiles and birds, as well.
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When the visual fields are examined. considered as round clock faces, the right visual fields from 12 to 3 to 6 are represented in the LEFT visual cortex. and the converse is true. And the upper visual fields from 9 to 12 to 3 are in the inferior occipital cortices, the visual cortex. And the lower field, from 3 to 6 to 9 in the superior visual cortex. There that is again!! Upside down and right for left. With damage to the right occipital lobes, the left visual field is impaired, and vice versa. Why is this?
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And the kicker? The optic nerves cross over from the right visual field in the right optic nerve, to the left side of brain. &  the left retinal visual field nerves into the optic nerve and do a right crossover. but not quite all fibers, but mostly, again for obvious reasons. And the lower retinal origination fibers in the optic nerve move upwards. and the upper move to the lower, most all (but not quite)l crossing over in a near exact optical nerve replication of the decussations of the pyramids  for the sensory AND motor fibers.
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So why all this complicated crossing over, inversions and left for right change overs? Why does the brain do that? How did that come about? What’s going on? Anyone, anywhere?  Doh…..
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 And when we look at the cerebellum the same right cerebellar hemisphere works on the left side, and the left hemisphere, the right side body movements. A complete S/F correspondence in every case of normal anatomy/function of cerebellum. Surely this is important, but how does it come about. Anybody? Anybody at all who can explain this? Nope, never, nada. Don’t bother us with deep findings.
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That’s what we find.
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And the kicker is, some of the cerebellar fibers are Double Crossed!!! Go figure!!
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But again, throughout the brain, even in the deep white matter structures of the connections, the thalami, the globus pallida, Putamina, internal capsules, and the brainstem. The same, this pattern of the cortex is seen, right reversed for left, & vice versa, and upside down in the deepest structures & connections of the brain. It dominates brains structure throughout all humans and the animals. Now how has this come about? Why?
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And what’s more, the optic radiations as they move from the eyes towards the visual cortex, the lower optic radiations are the upper visual fields, and the left side optic radiations move on the right hemisphere, as well. So we have huge amounts of data that supports this right to left and inverted top for bottom system.
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Now, why?
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And as in most great and good models, it’s quite, quite simple.
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The Eyes Have It!!!
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When we take a double convex lens, and normally use it, it’s a magnifying glass. But when we hold it at arms length we see quite a different picture. The brick house on the right is on the left, and the purple flowered lilac bushes to our left are on the right. And the grass and trees grow down from the top and the blue sky and clouds are on the bottom of the image coming out of the glass. Whoa, now!!! Could it bee?
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Could it be that the double convex lenses in the eyes are WHY the brain is organized upside down & right for left in an EXACT optical and visual relationships to the images cast upon the retina by those lenses?  Indeed, yes! We are visual creatures. Now we know more deeply Why and how. Our brains are organized against the high channel information in our visual images. & when we move that left leg, we move it according to an exact coordination with the lower, right visual field image, too. The same on the right leg, and arm, and face, Reversed right for left and upside down, consistently. All over the body, it’s the same with the brain.
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It’s that simple. We are visual creatures because the vast amounts of information channels in photons of light are that significant to our brains. We do the most with the visual systems, and so the brain is organized to those images of high infomercial channels & processings of information. That’s why this pattern of right reversed for left and upside down is done.
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So the cortical columns of Mountcastle where we do the information processing are also organized according to our visual images.
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And the optic radiations, left and right sides fan out &  also are likely connected to the motor and sensory systems as they pass by so those kinds of corresponding relationships can be even better used. Motor and sensory cortex does some visual processing, very likely.
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But what in the name of all sense does this possibly have to do with Einstein’s brain? Oh, quite a lot in fact. Einstein was a trained mechanical engineer, who examined in the Swiss patent office for much of his post doctoral career, numerous inventions of that visual designs sort. So was his father a mechanical and design engineer. and he was so good at it, he finished the days’ work usually by noon & then spent the afternoon working on his physics, which gave him world renown and fame.
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Sagan shows this in his great “Cosmos” series. That Einstein was a visual thinker, and he could process the complexities of visual images to understand How events in existence worked. To whit, what’s it like to ride on a photon? How is acceleration in a frame of reference like being in gravitational fields? How do photons knock out electrons from the atoms, to create the photoelectric effect, for which he got his Nobel Prize? & only one, BTW.
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And what happens to photons when they enter the very high gravitational field of the sun? Why, they turn a bit, subtlety so, towards the sun. & even billions of light years off, with two galaxies of great size and thus gravitation power and mass interposed on line of sight with observers on Earth, we see the more distant galaxy’s image changed into Einstein crosses and arcs, which the Hubble telescope has images of in the untold 1000’s of cases, too. & gravitational lenses are seen, many times in our own galaxy, which can do much the same, as well, with individual interposed star systems in line of sight with the earth. Right up close & as FAR was we can see.
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As per “Einstein’s Great Subtleties” he was a consummate visual and logical thinker. That’s done in the cortices, mostly. Now how does that get us to his brain?
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Simply. We know he was a very cortically driven and thinking person. We know that in animals of all kinds given a rich visual, stimulating environment that their brains plump out and are richer in sizes and connections than those brains in boring, stultifying environments. Which Einstein did not live in. and so there that is.
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We should expect, because enriched, stimulated, cortically driven & used brains will have more dendritic proliferations, and more synaptic connections made by protein lay downs in long term memory, for richer experience and memories. And for processing those events to meaningful models and understandings, as Einstein so well did. Largely his work was done along the lines of matter at high speeds, velocities and energy near light speed, cee; then again with matter at normal ambient temps, his work on Brownian movements and relationships, which showed the existence of atoms and molecules; and then at the other extreme of the very low energy, velocity, speeds of normal matter, fermions, the Bose-Einstein condensates near absolute zero. The other great exponential barrier, Zero Kelvin, as compared to light, but of very, very low temps, thus particle speeds, too.
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The double S curve of fermion energies from the very high, to the middle, normal ambient temps, to the ultra low. All visualized & explored by him, and pretty much that pattern has been ignored by most scientists. Except for “Einstein’s Great Subtleties”.
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Einstein was a high level, hard working, intensely thinking, cortical processor of all sorts. And an artist with the violin, as well, wherein his spatial relations visual skills were good enough to be not only a very good mechanical engineer and visualizer, but also an excellent violinist, which implies the same thing. Very good, even outstanding at spatial relationships & visual processing in space and time. His special interests. Professionally, and by no coincidence.
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So then we know that Functionally he was a great sorter and information processor, using his cortex, most all of it. And so we can expect WHAT of the structure/function of that same cortex and its unlimited synaptic & nerve fiber connections? Simple. The dendritic processes when compared to normal will be plumper and more of them. & the synaptic knobs which amount to upwards of 10K synapses per neuron within most of the some 50K-60K nerves and much more glia in each of his cortical columns.
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So when compared to the average high school grad’s brain? More connections, more synapses and more dendritic processes in a plumped out brain, and esp. in the visual, parietal & frontal areas, as well. That’s what we can predict and will find, comparatively, on the slides of his brain.
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& those structures/functions which do correlate making him such a great physicist, violinist, and thinker. Simple, S/F relationships of thinking creatively, musical & engineering abilities, as expressed by his plump, highly interconnected brain.
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All organized according to the mammalian plan of upside down & reversed right for left, all over it. But not quite, because if the fibers ALL crossed over to the opposite side but about 10% do not, then how can one side be comparison processed to the other side? & that explains that incomplete decussation of the pyramids, and the optic chiasm and the motor and sensory inputs from the optic radiations, as well. Which also access visual information to compare to motor and sensory tasks.
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Simple, elegant, and predictably fruitful.
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Thus the honeycomb of the bees, weighs in with a deep a very connection to the cortical organization of the cortical columns of Mountcastle, & thence onwards to the size and organizations of Einstein’s brain.
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And now we get to the Compositae. Also related to the above, too.
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Look at the face of the mature sunflower. It can be seen with images from the internet. See the almost geometrical pattern there of the seeds, all lined up in a near perfect geometrical shapes. The Compositae are flowers which have a cluster of a great many little flowers making up the mass of the group. This is a good way to make a LOT of seeds, compared to the near single seeds or few of the grasses, or the one of the coconuts, or the cherries, or peaches, plums, etc.
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Look at the loverly geometrical shapes seen there. It’s yet another form of the same basic, tight packing form, least energy driven, described above with the honeycomb. The central core of the hexagon, then repeated with 6 around it, then 12 around that, then 24 around that, etc., is not? Of course it is. Tight packing, least energy groupings of 100’s of seeds, all created from a single, successfully germinated sunflower seed. Proliferation and growth. Lovely patterns of 4 sided, diamond shaped, seed packing, is it not? Packing in a lot of seeds, in a tiny, little space, too. Efficient, very tight structures. Least energy, for sure.
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& that’s how we get from Bees, to brains, to Einstein and to flowers. Everything in this universe is connected to all else. & the structures of our brains show this, repeatedly with 100K’s of cortical cell columns all tightly, efficiently packed together in the outer brain. & largely connected to all the other parts of brain. So when we find all of those repeating relationships among events, our understanding can greatly rise. And here La Chanson Sans Fin is once again. The Song Without End, the repeating patterns of least energy and efficiencies, thoroughly seen throughout our universe of events. From Bees, to brains, to Einstein &* his methods, & then to flowers. The Compositae are a HUGE family of flowers. & now we know why they have proliferated just like the bees, like our cortices, and our understandings, and the flowers, as well. Most All Least Energy growth and development.
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Beauty is Truth and Truth Beauty.
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 La Chanson Sans Fin.
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Lovely patterns, indeed.

The Limits of Comparison Processing

By Herb Wiggins, M.D.; Clinical Neurosciences; Discoverer/Creator of the Comparison Process/CP Theory/Model; 14 Mar. 2014
Posted 27 Aug. 2018, Copyright 2018.
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It’s been written many times before what the efficiencies and outputs of the comparison process (CP) are. Vast numbers of events in existence which are very similar to each other, & drive the creation of the categories of Aristoteles, the levels of the hierarchies of our understanding. We can detail and compare members of each of those synonymic and word clusters/phrases to each other, and which give a much more efficient and thorough, tho still not  totally complete, descriptions of events. It creates creativity by setting up standards, conventions, rules, laws, etc., against which we describe events both internally and externally. Those standards are compared to events and the differences and similarity among them in wide gradations, allow us to create information. ROY G BIV is an excellent example. ( Do we have a near absolute sense of colour? As we can near perfect pitch? Not absolute but close enough.) So are high, high, highest; low, lower, lowest; hot, hotter, hottest vs. cold, colder, coldest; and the unlimited panoplies of those linear adjectival systems. But the central one is the comparative form, between the base and superlative forms, which generates most all the rest. And that has been missed.

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Math works much the same by creating scales against which we measure using lengths, heights, hardness, softness, warmth, cold, painful or not; and the pleasures as well, as in the Morphine standard for pain meds, the analgesics. By counting we create information. By measuring against our standards and scales we create numerical information, and that is then imported into our brains/minds for further processing. This process internalizes basic parts of the universe and allows us to further find patterns. Much in the same ways as we do our comparison of verbal descriptions, which are vaster, richer, and far, far more flexible in descriptions. & essentially this shows how we’ve mathematized, creatively, our sensory inputs, as well.
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Converting the sensations into mathematical, measuring structures:
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CP creates the recognitions by comparing events of all kinds and flavors, feelings, visual colours and the gray scales,and so forth. Some of which, but most which cannot be measured, such as the loves, hates, and etc., which marks the disparities and differences among the measuring scales versus the vastly greater and more flexible description scales used very largely in biology, medicine, and its subclasses of the exams, diagnoses, and reading most all lab tests, radiological scans and much else.
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So we create the recognitions, then the pattern recognitions, pattern recognitions, pattern recognitions of our hierarchies, without limits. But what of the limits of this method? We know that most all methods, devices and scales have their capabilities and yet their limits and the unlimited ranges in between. & it’s a good craftsman, who knows his tools. And those have been detailed to some degree and before, as well.
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Using this vastly efficient CP series of methods, descriptions and measurements, also shows the limits of them. Just like logic falls to the empirical test of the false dichotomies, of its essential (& maths, too), A or not A. A or B. Hot or cold, and white or black, we see that it misses a LOT of the grays in between those two. It simplifies, and allows to sort by elimination, but misses most all of the rest. Whenever we hear the critique of “oversimplification” we know we’re dealing with a logical limit and likely complex systems. It’s not just Deduction or induction. It’s all of those standards we use, from the moral, to religious, spiritual, legal, mathematical and logical truths, including the empirical logics of the sciences. There are many truths of value, historical and legal, as well, which are closely related. As are the genealogical truths; and the limits to paleontology and archaeology, because data/info decays in time. That is TD, writ large in the limits of our knowledge over times past. And is Essentially WHY the forensic teams get to the crime scene ASAP before more info disappears, as well as managing the crime scene to prevent same, too. It’s TD, again.
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Thus we have some serious limits to logical methods, which Godel showed very clearly in his INCompleteness Theorem, called by the shorter, euphemism, Godel’s Proof. But is not most all our knowledge incomplete? And yet the issues of sorting problems have yet to be more completely addressed regarding most all problem solving methods. & will be in later articles of this key, deep, point. Hofstadter addressed this highly important point in “Godel, Escher, Bach….”,  the “this statement is not true” created the paradox of incompleteness. The global, but not specific negative did so.
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 But comparison processing is not a global negative, but an exclusive sort of info processing. Its work is done by innate, implied or clear cut “exclusions” rather than the negatives, and so is far, far more applicable to events in existence, than limited logics. &  that’s why it’s used by most brains, in one form or the other, daily, and without limits. the limits to our ideas and the methods, devices they are based upon are driven by this incompleteness of logics. Which altho CP has limits by exclusion and by events not being comparable, is so far more capable because it uses relationship, the relational  logics, which go way past what logic can do of itself. & indeed drives the other logics, which create the many truths, as well.
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A detailed examination of this problem of the global negative has already been discussed. The negative, in short is a kind of exclusion, and the global negative, all A or Not A, is of this inadmissible type. Nothing in events in existence is EXACTLY equal to something else. They can be close. But the CP admits this and unless specific exclusions occur, its logic is far more useful & vastly more widely applicable than “A  = B” or “A or Not A”. The Exclusion principle largely disallows those false Identities of logic, which are often the formal logical fallacies, while the CP intrinsically deals with them using similarity, relationships, and so forth, which logic nor math can easily do.
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So there we have it. if logics and math are incomplete, then much else can be also. If in the “Grand Design” Hawking stated from the first, that our physics is incomplete and is the case. & Bell also stated that QM was not complete, as did Feynman. We cannot solve the QM equations for huge complexities. And Feynman also stated the obvious, but missed a deep truth. We cannot develop biology from QM, he said. Which in modern terms means, complex systems elude treatment with maths, and physics. Ulam stated that math must “greatly Advance” before it’s able to describe/model complex systems. & so that is to this day.
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Or do they? The process of evolution, or genetics, and the complexities in each of those cannot be easily figured by those. But we have here good starting answers to Bell, Godel, Hawkings and Einstein’s search for a more complete general theory of physics.
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And it’s very clearly, Least energy, which Einstein alluded to at least elliptically. And how do we recognize least energy conditions? By comparing them to one and the other. The least cost, the least energy, the least materials, the least times, distances, least waste, and the rich panoplies of the 2nd law of Thermodynamics, which more completely describes, as such categories usually do, events in existence, AKA, the complex systems in the universe.
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So there we are with Least energy, the CP, which shows us least energy forms, the structure- function relationships of vast numbers of events in our universe, from the atoms, molecules, organic molecules and much else up the reductionist, hierarchical structure to the brain/mind. Which the latter is best understood by S/F methods. Yet again, CP nearly totally. compares the structures of the brain to their functions, and then back again, and again. thus functional MRI (fMRI) and magneto-EEG’s. And then we compare the outputs of the both, for yet more information!!! Uncannily correct, predictable and we see how the CP creates knowledge. Yet again and again, without limits.
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But we can still ask this huge question. if our knowledge is incomplete, then the main driver of our info/data creating, the CP must also be incomplete. &  knowing that, which in thermodynamics terms combined into Shannon’s IT, we know this. There is NO perfect heat engine. It’s not possible to perfectly use energy sources for doing things with work. Thus complete descriptions are not possible, either, because it means in TD terms, perfect descriptions. Incompleteness of many types makes that very difficult to create. Thus there is a clear, almost blatant TD relationship of our knowledge to “incompleteness” discussions and outcomes.
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But we know that LE creates growth in many unlimited instances. And there are the ways out. Inventions &  devices and indeed cultures & ways of doing things can be improved, that is, made more LE efficient. & this is what drives growth from gravitational bodies getting large and larger (Einstein’s compound interest is the most powerful force in the Universe, ), to evolution, to market efficiencies (least energy) of Adam Smith driving most all market growth, and so forth. Building a better mousetrap is quintessentially a least energy form, is not?
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And that’s the whole point. What do we run up against in most all cases?  We have the S-curves of Whitehead’s Process Thinking methods to thank for that. Growth occurs in additive and exponential curves, of which the S-curves are the unlimited, basic forms. And almost anything which does not break us out of, or jogs our society’s current abstractions, after a limited period of growth, will tend to stagnate. Whitehead’s prescient, verbal form of the S-curve, made real, and mathematical. Showing yet again how descriptions of many kinds can be converted into math, and in this case most all growth, yields math creativity.
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But the limits of finding primes, are basically the most efficient and fastest methods to find, sort out, but not generate the primes. And the best ones are used, again, least energy forms of each when compared to another. How fast does it sort out the primes? Again, showing the LE kinds of sorting problems we get into and escape from. The facts are those can be done more and more efficiently without limits. But we MUST break out of our “current abstractions”, standards, conventions, etc., to do so. And that’s how it’s done. To understand that our methods have limits, and then exceed, circumvent and go “round the impasse”. Creatively. Read the article about the Wiggins’ Prime Sieve, in both the first & then latest, more developed, more complete and more efficient forms, to see this at work, empirically and mathematically. & can be improved without limits.
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This essentially is what’s going on with CP. using linear methods, or lines, we reach limits; light speed, absolute zero, two exponential barriers at either end of the Two connected S-curves of the energies of fermions.  Which Einstein explored rather well, in which, at least conceptually, our universe dwells. Again, Einstein’s Great Subtleties.
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So we know that the exponential barriers, and the perfection barriers of TD, and the HUP barriers to knowledge, and the most of the rest are simply CP limits, and not always real. By creativity we can jump over those barriers in many, many instances, without limits. Is there a limit?
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Yes, in the brain. Which creates by using the CP the expon bars, on in the case of math primes, the asymptotic limits. Mistaking our ideas/words and logics for events in existence is the fallacy of idealism, in a nutshell. And we have no real reason to believe that there are no ways around light speed, such as Quantum Tunneling, and around Zero K, such as negative energies. And nor do bosons have all those limits, either, as photons show. & as matter under Bose-Einstein conditions DOES become more bosonic, too. So there are ways “around” the limits, clearly. and likely without limits, too.
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The CP process limits are clear, the expon bars, and the asymptotes, and the idealistic forms of perfect heat engines. Without those systems, we are trapped, but not forever, as Whitehead showed. &  as our progress as a species has almost always showed, esp in these days of exponential growth of our population, which must come to an end, after a limited period of growth. Until the physical limits of living on our planet instead of most everywhere else, too, must be addressed & are addressed, we will find those “limits to growth”, yet again.
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Before growth resumes after finding new & better performing S-curve of growth, too.
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The limits are between our ears, and the limits to our memories and processing of information, mostly. The limits to logics simply mirror that we cannot compare apples and eggs, very well. So we create the means to measure, and describe each of those. But taste has been ignored.
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“An Infinity of Flavors?”, shows a new approach to those limits and the possibility of mathematizing flavors and smell, too.
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So while our limits are real, Because the universe of vast events does not go as the Big Pot into the  Little Pots, our minds/brains, there is yet a LOT of room for growth, creatively. & this is the problem of the Land of the Undiscovered Country, too. and such is the case, very likely.
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Every generation exceed the limits of its past, because the universe is so very large, and our minds/brains are so very small, by comparison. We give up the idealistic illusions and fallacies of ultimates, finalities, absolutes, certainties and perfections, for the realistic probabilities of complex systems, which promise literally growth without limits. Thus most all our limits are not real, but simply way stations to better methods and ways of doing things, universally, but not quite.
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Beyond the Absolute:
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&  that’s the way it very likely is, over most all fields and endeavors, but not quite……