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.
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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.