The Problem of Solving P NOT Equal to NP

By Herb Wiggins, MD, Clinical Neurosciences; creator/discoverer of the Comparison Process/Methods, Mar. 2014.
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Descriptions are changed into mathematical forms in this way. Each step takes a description to a form of polynomial math solutions, and each step ADDS information, sequentially to the fullest solution. It Translates verbal descriptions into mathematical expressions, throughout. And thus solves the problem, taking NP to P. There are unlimited numbers of such examples, but these are the simplest which show the richest panoplies of what’s possible, much like taking the sensations of vision, feelings, touch, heat, position, etc., including hardness and softnesses to linear, math measuring scales, of same.
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The size of the trial and error sorting problem is also a huge bar to solving many problems. It takes lots of time, as it does evolution, to sort through all the complexisties to find answers to problems. And often, there is not just a single answer, but in complex systems, unlimited numbers of answers. That also can add to the time taken to w/o a solution which is growth capable and useful as well as practical, too.
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The P not equal to NP problem rests upon a very critical juncture of understanding problem solving, essentially math problem solving. There is a $1 M prize for the mathematical proof of this problem, the Millennial Prize.
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Here’s how to solve this problem.  First of all, the structure of the question, P not equal to NP is a significant part of the problem itself.
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Problems not solved go to problems solved. The P not equal to NP is NOT in the proper order to be solved, either, chronologically nor sequentially. It’s, in short, bass/ackwards!!!  Problems not solved go to Problems solved. This is the first major point to be made. The sequence MUST be cast into normal time flow of natural, logical processing..
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Thus all/most all NP is Not equal to P. & Is more properly the question asked.
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The other basic, structural problem is that many solutions to problems cannot be found within logic nor math. Those insights must be supplied from the outside, then incorporated within. Thus the consequences of Godel’s Incompleteness Theorem are once again in the fore. We cannot understand, describe or apply many systems from “within’, but must venture outside & see the problem as more a critical kind of “larger problem” of creativity and its origins. We must take off the blindfolds and see the entire elephant, not just a too small piece of it. We must see the larger, visualized picture, the forest for the trees. Thus to solve such a problem we must figure out how creativity works and how the brain creates information, data, organizes those into knowledge, and further, creates creativities. That being done, the thing is more simply solved.
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Once those are realized then we can take a simple cameo series of solutions and then elucidate HOW the brain solves such problems, i.e., converts NP to P. Here it is.
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We are trying to get from Dallas  to Houston. How do we go about this, verbally and mathematically?  Innate in this question are the multiple solutions to that problem, or HOW we mathematize a verbally descriptive problem to solve it, and WHY, the much deeper question is why we use math at all, compared to verbal descriptions? IOW, we are taking the verbal description which is NP to a polynomial math description equivalent. This is how we create mathematical equivalences to verbal descriptions and in short, how experimental maths are created.
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When Friston, in “Consciousness” shows how the least energy events are mathematical treated reasonably well by Lyupanov numbers, he’s doing the same thing. The repeating stabilities are stable due to least energy. and those are very largely expressed & handled by using Lyupanov math and methods.
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 https://aeon.co/essays/consciousness-is-not-a-thing-but-a-process-of-inference
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When Whitehead writes that “Any society (or group in a society) which cannot break out of its current abstractions, after a limited period of time, stagnates, he can be seen to be describing a series of S-curves, the cubic equations which describe development, growth, market growth, changes, emergence/embryologies, as well as evolution, most all of which are S curves. It also describes an avalanche, the falling of the avalanche growing exponentially & then at last tapering off at the bottom of the hill, the inversions of the S-curve. So there it is again.
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First, from Dallas must find the directions to go to Houston. We can go many different ways to get there, but first the best way is?  That means we have in an IT, Shannon Bandwagon sense, created a sorting of the 360 degrees of direction and found we go about SE. The shortest most direct, least energy and efficient direction. Our solutions then MUST have least energy built into them. this is essential to solving problems and creativity. Also, That adds information to the solution, does it not?  We head roughly in the 75 degrees heading, which is SE. This at once adds information to P.
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Then we must find out how FAR Dallas is from Houston. Well, a friend tells us, it’s about 4 hours’ drive. So we know roundly, it will take us that time, more or less. But we have a car, and we must go that way. Now how FAR is it, we descriptively ask?
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It’s about 250 miles, generally we find out by those who have compared the distance to a set standard, that is measured the distance. That is created the data of about 250 miles in distance
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So, now what? How much gasoline do we need to get there?  There’s a verbal description. We convert that to mathematics by running our car to about 1/2 full on the gas tank dial. Then we go to the nearest gas station and top out the tank. And we find it takes about 7.5 gallons to do that. So we know by a simple algebraic method, it will be 1/2X = 7.5 gals, & thus our tank holds 15 gallons!!!
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Now what do we do with that? We create a proportion, a ratio, a Comparison of the miles driven per gallon of gasoline used. This is like creating Pi, a standard, a constant from comparing the circumference to the diameter of a circle, to create Pi, which we can use to elucidate the truths of spherical geometries, mathematically. Creating that new standard, a comparison, ratio, proportion (the basis of much algebra, so it turns out), allows us to compute the areas, volumes, etc., of roundish objects, to some degree of accuracy. Information has been created and that added to create a solution of spherical algebras, themselves. Comparison processes are algebras.
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So we take the miles/gallon standard, convention, and try to solve that one. Well, we just happened to note, the last time we filled the tank to full, we’d gone about 25,517 odometer miles, and we compare that to the odometer at the gas station we just filled up at, & it was 25,742. So, we compare the two, find a 225 miles difference, by subtraction, another comparison process.
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So we do another algebraic equation,  Miles/gallon = 225/7.5 and that is about 30. Again, comparison processes which drives most all algebras. We, once again, have added information to create a solution.
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We know that Houston is about 240 miles away, and so that means we need about 8 and a fraction gals. to get there, and about 17 gallons for a round trip, plus or minus how much we drive around in Houston.
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So tanking up, will get us there, but not back. At each stage, we are using comparisons to create new information which we can mathematically process by algebra to find answers. This is how we solve not polynomial problems by converting them into polynomial, algebraic solutions, is not?
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At each stage we create relationships, numerical, between real existing events, to treat them. We cannot do this by description, but only partly. The math allows us, in each case, to more accurately treat and understand how to solve the problem. Each relationship gives us answers, creates data from Einsteinian measuring epistemology of a relatively fixed, stable standard/conventions, by which we compare to create data. In these cases, miles to Houston, gallons in our tank. Miles/gallon, and at last, Speeds, which are ratios again, comparing distance over time. Yet another ratio!!!
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How do we use that, then? We know that it takes about 4 hours to get to Houston. We know by asking we use I-45 to get there going roughly SE, because that’s the direction, roughly, I-45 goes.  So there we have it, but for the last, how long will it take to get there?
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IF we travel a fixed speed, say 65 miles/hour, then it will take just under 4 hours to get to Houston. So if to make the 11 AM appointment we have to be on the road by no later than 6:30 to get there 1/2 hour earlier, for getting ready to get to the place, where the appointment is. Again we create and find new information to solve the problem, taking NP to P, adding new information at each point to create a solution.
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Now, how do we find the place we are getting to? We have an address for a place in Houston. & we compare that to a map, showing the alphabetical street name plus the numerical address. We compare the two and find the street by trial and error, relatively by comparison, again on the map. We find the off ramp from the I-45 road to the nearest street that will take us there. Some extra time, going slower than 65 mph, too.
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So THAT is why we use mathematics. It allows us to find, predict and travel more efficiently than merely verbal, not numerical methods of math. It’s precise within some practical limits, and we can plan better with it, than just going SW for 4 hours at about 65 miles an hour. Math is least energy efficient when used in such ways. Words, descriptions cannot do that. That’s why math’s used. It efficiently allows us to solve problems which verbal descriptions alone, cannot.
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The efficiencies of prediction, planning ahead and so forth are what’s going on here. NP becomes P. We convert a verbal problem to a polynomial solution by using these already proven methods.  But note that the map reading is NOT mathematical, at all, though it is comparison processing against the standards of N, S, W, E and so forth!!  So we are still using verbal descriptions with some counting of the street numbers, however.
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And at EACH spot in the problem solving, we are ADDING information, in an Information Theory, Shannon’s Bandwagon sense, where we can solve the problem, confine the data, & thus more completely describe what we are doing!!  Information rises, entropy goes down, and the description using math is far, far more complete than if we used merely words.
But note that we can write and type all words to describe, teach, speak express and use the math, but that math cannot be used to describe much at all of Shakespeare, or written words. It goes one way, words to math, some a limited extent, math to words, but the latter is very limited. This reflects the origins and neuroanatomy of maths in the L Post. Temp. speech centers, where it’s developed, interdigitates with the language processing centers of Wernicke’s area.  when we damage language processing we also damage math, as well. It’s a pure relationship, comparing structure of the brain to the functions which are damaged when the cortex there is significantly damaged or impaired due to various causes. Structure/functions comparisons universally show us how the brain works. As well as for chemical, building, and much other  engineering approaches. Structures of atoms, molecules and even polypeptides and proteins are closely related to their functions. And thus S/F relationships by comparison create information about how events work.
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It’s also how we convert the senses of hot, cold, motion, hard/soft (Moh’s scale and GPA’;s) to maths as well. Most all of our linear scales are NP converted to P, therefore & information is inevitably created as well as added.
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Now compare when we translate a bit of French into English, or vice versa. Are we adding information? Not really in a semantic sense, altho we are showing the information of equivalence of the French sentences to the English. But new information is NOT being added. Translations are thus comparison processes as well. The closest efficiently expressed phrase in each language compared to the other phrases in another language is exactly what translation is.
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Je suis ici.
Ich bin hier
Estoy aqui.
Hic Sum.
I am here.
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& this shows that very, very well, in fact.
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How this applies to the upsetting finding that if Gravity and relativity are quantized, we don’t get anything new is easy. Simply, for the obvious reason, that we are NOT adding any new info, but simply “Quantizing”, read “translating ” into QM. Thus not much info is going to be added. If we want more understanding then we must find more equivalencies, or more relationships in an Einsteinian sense, such that ER is related (but not equal) to EPR. ER bridges are related intrinsically to quantum entanglements. That’s how we learn and create new understanding.
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In order to ADD information we must, as Einstein stated, find new relationships among events (Physics & Reality, 1936). This adds to our understanding, and converts when mathematized, NP to P. Adding info, IOW. But more of that, later. In short we solve the problems first using descriptive, visual models; and then we mathematize the expressions, in order to measure them. This requires some creativity as well, but information is then being added again, creating P from NP.  Einsteinian Relativity was first formulates & THEN Minkowski & he mathematized it. Trying to solve a problem using math only when new relationships are to be found is simply not the way it works. Math follows recognition/relationship creative thinking, but it does NOT create it. Math is not recognition of new relationships, associations, connections, causality, etc.
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This is largely what’s going on here. Have shown how we create the relatively fixed, standard conventions & scales to measure volumes, temps, hardnesses and so forth. how we convert warm, warmer warmest to Hot hotter hottest, or cool, cooler coolest, and cold, colder coldest, as well. It’s a verbal form, linearizing of the temp scale.
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Briefly, we use the freezing point of water, 32 deg. F. versus the boiling point of water, 212 degrees, 180 difference between the two, and find a standard temp, pressure, and conditions to create that measuring standard. The epistemology of Einstein applies. These are NOT absolute, standards, but relative standards. The same for time and space. They have arbitrary units, as well, Km./m. or Miles/gallon, instead of Km./liter, is not?
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& why do we use such standards? They are efficient. But why metric, versus English system of weights and measures?
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Efficiency. It’s easier to use 10 times ten times 10 than 4 quarts to a gallon. 32 oz. to the quart, 2 pints to the quart. It’s least energy efficient, we see. Just as math is least energy efficient to describe better than some verbal terms, how far something is from another, is not?
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Least energy rules.
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 So this is how using our senses of hardness  creates Moh’s scale & is then mathematized to GPA’s.  In degrees it’s 32 F. & deg. C., zero , and  212 boiling point of water, 100 C.  & water is readily available, easy to use and find, as well. It’s an efficient comparison standard,, therefore. And fixed, stable, however arbitrary the units we use, tho in this case, efficient.
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The same is true for the feet, hands, distances and length measures we have adopted, as well.
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This is how we convert NP to P. Creativity using comparison processes of descriptions to maths. NOT the other way round. The distances, in feet, hands, and so forth, became numericized, mathematically using relatively fixed, comparison standards, which are efficient.
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In the same way, we solve mathematical problems by comparison processing. We take NP to P, by ADDING information. and thus all NP is NOT equal to all P, because P contains More information in an IT sense, than NP. In each case this can be shown by comparing the info content of the NP side to the solved, P, side.
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Thus the first person who can use this, clear, descriptive method, to prove, mathematically and logically, that NP is Not equal to P because their information Contents are not the same, will get $1 Million and a lot of interesting outcomes for same. Information Theory is the basic key to this proof.
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We cannot conclude, however, that in some cases NP is equal to P, because that might be possible. With tautologies, and translations it’s likely. But there are most cases in which NP is NOT equal to P because P contains more information.
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But there is this critical point. Each statement be it NP, or P contains information. If more information in an IT sense is found in the solution as seems likely, compared to NP, then it’s very likely that solutions to NP going to P mean that in each Case, NP is NOT equal to P. This simple IT test of info content is sufficient to establish NP is Not equal to P.  And creating the above descriptions which are then translated into polynomial math forms shows this, repeatedly as above.
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Problems can be solved in this way, taking verbal descriptions which create information to math forms which create mathematical measuring forms, which contain more information than the NP side. Thus in most cases, NP is NOT equal to P. Because at each stage we are creating descriptive information changing that into mathematical forms, which measurements (amount of gas in the tank, distance and direction to Houston; how long it will take to drive there, how much gas will be needed) create information to solve the problems, very clearly, and plainly. & in most cases, this occurs, and can be found simply by testing the information content descriptively and mathematically, too.
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In trivial cases of the tautologies in logic, NP is equal to P, is the rule. However, where creativity is required to convert NP into a polynomial form, it’s very likely  the added Info needed to create P makes them not equal.
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Taking the problem of finding out how to solve Archimedes’ problem also shows those unique and critical insights of the comparison process “Ratios”, which the mileage, speed, & in miles/gal., miles/hour, and show how speed is related to travel time, as well. Creating those polynomic ratios does this.
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So for Mass/volume, or in more real terms, gms./cc. we have this. When Archimedes was trying to figure out how to determine if the gold given by the Syracusan king to his goldsmith was completely used, or he stole some, he realized, again, a deep relationship, which could be expressed descriptively. Gold weighs more than silver volume for volume. It’s palpably, by our senses, heavier. (note also how we convert this heaviness sense to a math scale by using comparing of an unknown mass against a known mass in the other balance arm pan!) But when he put his feet, then legs into the water, he realized that he could measure the ratio of mass/volumes, which we call density, to create a standard measurement, that is to create a density measure to more accurately describe this.
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So he could measure both volumes of water, and weights of gold very accurately. And when he compared the mass to the volume, the ratio which also creates like distance to time creates speed/velocity, he created a ratio which followed his verbally descriptive impression that gold is heavier than water as well as to the other base metals. That ratio he could not measures descriptively and it became named in English, density, of mass in gram/cc.  That insight created the solution to the problem, taking NP to P, by adding understanding that a relationship could be created. & with that creative insight, we find the “Eureka” hallmark in most all cases, rom the insights of Darwin and Wallace that led to evolution. From the insight by Kepler that led to elliptical orbits. To the insights by Newton that falling could be mathematized for N=2, and produce a least energy solution, once again, as does the travel description, to the planetary orbits.
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Realizing that the above massive use of and creation of ratios such as miles/hour, or per gallon, or such, create the means to solve these. & those are ALL comparison processes or math ratios, in short.
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Thus, creative activities create information of how, as Einstein states in his “Physics and Reality”, 1936, that understanding is the finding of relationships among events in existence; which are found verbally and descriptively & then if mathematized create greater and more precise measurements, while arbitrary in some sense, are yet efficient, fixed and stable standards. & NOT by in any real way, absolute, but relational, relative and thus most all comparison processing, as ratios, proportions, etc. are. & thus, we find the relativity of the Cortex and that how mathematics of our measuring scales are all created, because NP is NOT equal to P.
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This is the Neuroscience & relativity of problem solving, in a nutshell.
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That’s how it’s done.

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