International Journal of Modern Research in Engineering & Management (IJMREM) ||Volume|| 1||Issue|| 4 ||Pages|| 17-29 ||April 2018|| ISSN: 2581-4540
P=NP Proved, Disproved, Varies Based on Problem or issue, and Indeterminate Based on Similarity between Checked and Find, Consideration of the Similar Planetary Diameter Problem, Consideration of Non-Deterministic Process Always Different than implementation, Some Questions Not Solvable in Polynomial Time, P Questions Always Different than Non-Deterministic Polynomial Time Processes James T. Struck BA, BS, AA, MLIS Affiliation- President A French American Museum of Chicago, President Dinosaurs Trees Religion and Galaxies, Researcher NASA, Assistant Midwest Benefits Contact at PO BOX 61 Evanston IL 60204
-------------------------------------------------------ABSTRACT----------------------------------------------------We consider Dr. Stephen A. Cook’s P=NP Relation with regard to P=NP being an algebraic relationship, a relationship between being able to check a solution and find a solution and its other possible relationships. We find the relation to be provable, disprovable and varying based on problem or issue and in some cases, in which for example the value of N is not clear, to be indeterminate or uncertain. We use the field of combinatorics to show that a problem like P=NP can have more than one solution. Disproving P=NP I was able to show that problems such as "What, How, When, Are planets similarly sized, can you check for the book, can you find the mail in the mailbox, is there a God, did you like the movie, where is the bathroom, How did life begin?, How will life end?" show that Polynomial time processes can be different than non-deterministic polynomial time processes, these problems can be the same as each other and not understandable according to checking and finding concepts and not distinguishable between checking in finding in some cases. “Why?” is a question in which P=NP have an unclear relationship not involving equality disproving the conjecture’s equality thesis. When one process NP involves guessing and another P involves what a computer can deal with, those processes are clearly not equal. P does not equal NP as the processes to get somewhere are different. We, as Stephen Cook did, can still imagine P=NP though. ---------------------------------------------------------------------------------------- ----------------------------------------------Date of Submission: Date, 18 March 2018 Date of Accepted: 24 March 2018 ------------------------------------------------------------------------------------------------ --------------------------------------I. INTRODUCTION We first consider algebraic relationships of P and NP as algebraic symbols, then case studies on the issue of checking and finding where NP is for checking and P is for finding. We consider abstract cases where a computer is restricted from doing finding or checking, so that the other process is faster and then concrete examples like we can find a computer, but cannot easily check its operation, check for a book but cannot easily find the book, can find a mailbox but cannot check for the letter in the box and cases in which we cannot easily find or check for something such as in response to the query “What? or Why?” What operation is easier is not clear? Are we to check for or find something or how do the words differ in function? The field of combinatorics is concerned with the idea that there are multiple solutions to problems. As we show different questions and issues and problems explored, we can obviously expect multiple answers. P can sometimes equal NP, but P does not have to equal NP. We can set up a process a computer cannot do, so the P and NP do not have to relate.
II.
METHODOLOGY
We first consider algebraic relationships of P and NP as algebraic symbols, then case studies on the issue of checking and finding where NP is for checking and P is for finding. We consider abstract cases where a computer is restricted from doing finding or checking, so that the other process is faster and then concrete examples like we can find a computer, but cannot easily check its operation, check for a book but cannot easily find the book,
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P=NP Proved, Disproved, Varies Based on Problem… can find a mailbox but cannot check for the letter in the box and cases in which we cannot easily find or check for something such as in response to the query “What? Or Why?” What operation is easier is not clear? Are we to check for or find something or how do the words differ in function? The field of combinatorics is concerned with the idea that there are multiple solutions to problems. As we show different questions and issues and problems explored, we can obviously expect multiple answers. P can sometimes equal NP, but P does not have to equal NP. We can set up a process a computer cannot do, so the P and NP do not have to relate.
III.
DISPROVED
P Does Not Equal NP is based on the idea that a P is not equal to an NP. There are different algebraic symbols or quantities on both sides of the equation. A P is not an NP. Something guessed is not something processed. With different variables or algebraic symbols on the sides of the equation, there would not be equality. We were taught this in kindergarten, “When you sit legs crossed and guess, you are not engaging in a computer process.”
IV. PROVED P=NP is based on the value of N=1, in which case P=NP. Indeterminate or Vague As we do not know the value of N, it cannot be determined if P=NP or P does not equal NP This is an algebraic symbol consideration of the equation. Based strictly on seeing the NP as algebraic symbols of something, we can see the equation as provable, disprovable and indeterminate. Relationship Varies on Case Studies or Problem Being Considered-Solutions vary based on problem being studied Case study Proof of P=NP based on identical definitions of finding and checking solutions Checking and finding a solution to a problem can be seen as identical. Checking for something can be seen as the same as finding something, in which case the relation P=NP could be seen as proved in that checking can be seen as the same as finding. When I check for God or a bird or myself, I can be seen as doing the same thing as finding God or a bird or myself. Case study Disproof where P Does not equal NP: I can set up a computer in which checking a solution can be done but finding a solution cannot be done. The machine’s algorithm is that checking is doable but finding cannot be done. Therefore, NP can be seen as done before P as P is not permitted. Case study where NP or checking can be done faster than P-I can be sitting at a library circulation desk and be asked “Can you check if that book is held by or owned by the library?” I can check the catalog and find that the book is held by the library or in the library consortium. Finding the library book on the bookshelf or somewhere would be harder as I have to check the shelf or the patrons (possibly millions of them in major cities like Tokyo, Mexico City, New York, Los Angeles, Chicago, and Shanghai) for the book. Checking for a book can be easier than finding a particular book. Case Study where P or finding Can be Easier than Checking for something or NP -I put a piece of mail in a mailbox in front of someone, but it is unlawful for a non-mail carrier to go into the box and retrieve my letter. I then ask “Can you find the mail box?” which the person could as I put the mail in the box in front of him. I then ask “Can you check for the letter?” which he or she cannot do as he is not supposed to go into the mailbox. He can find the letter, but he or she is not permitted to check for the letter by the jurisdiction’s laws. Case Study where P is possible but NP is not - I set up an algorithm on a computer and tell the computer to find P but not to check for NP. Therefore, on that computer, P is possible but NP is not possible. Case study where the P or NP being faster is not able to be determined? The relation can be indeterminate in a specific case for P=NP. I ask someone www.ijmrem.com
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P=NP Proved, Disproved, Varies Based on Problem… “What?” What is there to check or to find? That is unclear so the relation between P and NP cannot be determined. I ask someone “Is there a God?” God can be checked for and found in dictionary, Encyclopedia and as a word in many books, but what is the difference between checking for God and finding God? The difference in the words is not clear or cannot easily be determined. Does God mean Paul Tillich’s ultimate concern, does God mean all things as in Spinoza, does God mean being as in Martin Heidegger’s work, does God mean first mover, creator as in the work of Thomas Aquinas Summa Theological. Word meanings are unclear so the relation N=NP can be seen as indeterminate at times as someone’s meaning of problems, checking for process and finding process can be unclear. Someone finding God through meditation, prayer or guessing are doing different processes. The guessing process is not the prayer process. The non-deterministic guessing for God is not praying to find God. The non-deterministic NP guessing processes is not finding God in the Almanac or text book or Encyclopedia. Guessing is different than a computer process! A computer that I guessing does not find the same answers as a computer following a program. Case study of Checking or NP faster than finding or P-I can teach someone the word checking or NP in which case they know how to check for something, but they do not know the word find so they are not able to find something. Checking for would be faster than finding. Inverse finding easier than Checking- We can teach someone the word finds in which they can find, but not the word check in which case they can find but cannot check for. A non-deterministic guess at a process can be defined to be different than a process a computer does to find a solution. Guessing can find a different answer than the process a computer does in time. Case Study of finding easier than Checking-I ask someone to find a computer, which they see in front of them. Does the computer operate? The checking for the operation of the computer would be more difficult than the finding of the computer and vice versa. A computer on Andromeda Galaxy is neither easy to find or check. Case study of Checking on a solution simpler to find than finding a solution-I am asked I need you to say “thank you” to Stephen A. Cook for his P=NP article. It is easy for me to check or find for Stephen A. Cook on the internet using a computer; checking and finding can be the same process. If I had tried to take the Edmund Fitzgerald iron ore carrier in Thanksgiving 1975, I would have probably died on the ship with the other sailors. Finding Stephen Cook to say thank you to him would involve more work, more difficulty than imagining that sailing on the Edmund Fitzgerald would result in me sinking to the bottom of the Great Lakes in 1975. Checking for something like “what would have happened if I would have taken the Edmund Fitzgerald to say thank you to Dr. Cook?” Can be easier than finding something like actually saying “Thank you, Dr. Cook” after travelling on the Edmund Fitzgerald in some cases. Say I guessed “There is some chance I will sink on the ship to say thank you to Dr. Cook across Lake Michigan and Lake Superior.” The guess is a different process than the process of actually sailing on the Ship. A polynomial time process of going on the boat to Toronto does not have to be the same as guessing about how to get Toronto. The P=NP issue varies based on topic being studied. “Are there any Dodo Birds?” A guess “No” will be wrong as there are museums of natural history with DODO birds, so guesses differ than processes. By the way sometimes the guess is better than the process. The computer guesses “There are Dodo birds in natural history museums”, but the computer tells us there are no dodo birds. Guesses can be better than answers in polynomial time or vice versa. Computer answers can be better than guesses but the processes are not the same! V. CONCLUSION The P=NP relation then can be seen as proved, disproved, and uncertain varying based on the issue or problem presented to the relationship. There is not one clear answer to the relation P=NP, but rather the relation can be proved, disproved and found to vary based on problem presented to a computer or problem solver. The way the P=NP relation is understood is also shown here to vary as well. www.ijmrem.com
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P=NP Proved, Disproved, Varies Based on Problem… Treated as a strictly algebraic relationship, we are also able to show provable, disprovable and uncertain relationship between P and NP. Using case studies, we are also able to show P=NP to be provable, disprovable and uncertain based on issue studied. Recall that the whole discussion of HAL by Arthur C. Clarke and Stanley Kubrick in 2001: A Space Odyssey revolves around the issue of the computer HAL resolving the issue independently of humans; HAL and its alien friends create a new star near Jupiter and the moon Europa around Jupiter to settle or bring peace to a Central American war. A computer or human can actually be designed to think for itself, like humans, in which it does not have to solve or verify following the programs or algorithms we give the computer or human. P can be seen as unrelated to NP, P=NP, or P does not equal NP, or one can see the issue as mystery or mysterious or unclear a different kind of relationship. The field of combinatorics is concerned with the idea that there are multiple solutions to problems. As we show different questions and issues and problems explored, we can obviously expect multiple answers. P can sometimes equal NP, but P does not have to equal NP. From Wikipedia.org accessed 2/9/2018 “Combinatorics is an area of mathematics primarily concerned with counting, both as a means and an end in obtaining results, and certain properties of finite structures. It is closely related to many other areas of mathematics and has many applications ranging from logic to statistical physics, from evolutionary biology to computer science, etc. [1] There can be more than one solution to a problem; we can count more than one solution to a problem like P=NP. P=NP P Does Not Equal NP, P has No clearly defined relationship with NP for questions like Why? Or How? P solutions found do not need to be related to solutions checked for issues in which one only wants to check or find a solution. P=NP are different given the algebraic language involved so P does not equal NP, P can be the same as NP if we consider N=1, We can easily write programs only involving checking and programs only involving finding in which P does not relate to NP for a particular computer program or operational problem. I can write a program that does not check or find and does not guess or only guesses, so a program does not need to do either or anything. P and NP do not need to be considered for certain questions. I really do not need to find or check anything for questions like “Why?” or “Be!” A program can be written so that nothing is being processed and nothing is being guessed. P and NP do not need to involved in some programs. P and NP are not involved in all computer function. James T. Struck BA, BS, AA, MLIS Reference List 1. https://en.wikipedia.org/wiki/Combinatorics accessed on 2/9/2018.An earlier discussion by me Disproof and Proof of P versus NP Problem Postulated by Stephen Cook By James T. Struck BA, BS, AA, MLIS Quoted from “THE P VERSUS NP PROBLEM STEPHEN COOK” accessed on 2/21/2017 “Problem Statement. Does P = NP?” Different Verified versus Solved Computer Invention Disproof - James T. Struck argued from 2010-2017 that one can invent a different computer which will always verify a solution differently than the solved computer solution. As a disproof, solved solutions can always be worked out differently than verified solutions. I can develop a computer so that any solution that someone has will give a different verified solution. That is a disproof would be that one can develop a computer so that every solution is not what is verified, every solution is different than what gets verified. Different computers would have different answers to P=NP. P does not NP with the case study of the different verification method computer invention. Computer program is that all guessed NP solutions are tossed and the program only allows the process solution, then P does not equal NP. Same Computer Proof of P=NP- Further, one can develop a computer so that when there is a computer guessed solution it is the same as the verified solution. A solution can be both always different than a verified solution and always the same as a verified solution. Stephen Cook's www.ijmrem.com
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P=NP Proved, Disproved, Varies Based on Problem… conjecture. Same Computer Disproof of P=NP. Does P=NP can be easily disproved by developing a computer where solutions do not equal what is verified. But one can also develop a computer where every computer guess is the same as what is verified or the same as the process. No Objective or single Solution to P=NP. Dr. Cook and solvers possibly forgot that there is no objective answer to the query. Of course, a conjecture is just a hypothesis to discuss and debate not a belief! P a solution can be the same as what is verified and can be different than what is verified. The P=NP conjecture is both provable and deniable based on the computer that is used to test his theory. P can equal NP but P does not have to equal NP. Every process solution can yield a different result than what might be guessed. P again does not equal NP. The computer does not guessing and does no processing. That is neither P nor NP are needed or occur in some computers. Method or Path Disproof of P=NP. In addition the routes through which we gain solutions can be different than verified solutions, but they do not have to be different routes. P can be achieved the same way as NP, but P does not have to equal NP. I can have solution A=B but then verify it using a different method. The Method disproof is a legitimate type of disproof. Paths to solutions do not have to equal paths to verification. Method or Path proof of P=NP. On the other hand, I can set up a path to a solution to be the same as the path to verification. I can have solution A=B and verify on the same computer that A=B. Easily Provable and Deniable based on computer, verification method. Computer selection based proof and disproof- every computer would be a different type of finding and checking. Verification method proof and disproof; every computer would be a different verification method as they are different computers. What is guessed on computer A can be seen as not the process on a particular computer! Certainly each computer is not verifying the same as the guess as they are different computers possibly. Even on the same computer, the guess process is not the implemented process. There is no objective solution to Dr. Cook's query, in some cases P=NP and in other cases P does not equal NP. There is not one proof, but rather the conjecture is Provable and deniable. Answers vary on method, computer, verification, question, issue. Proof and disproof based on subject, issue or question or topic? Here we are solving God while that would have a different P=NP answer than adding. P=NP varies in being proved or denied based on issue studied. So not only does computer, method, verification, question, guessing process vary, but the whole Conjecture is subjective based on what surface, geometry, question is being queried. P =NP or P could =NP for 2+2 but P not equal to NP for queries about God, for example. P=NP can be proven and disproven for subject matter issues. Is there a God? I or you design a computer to say yes. Then it verifies the Yes. So, P does =NP. Is there are a God? I or you design and computer to say maybe. Then it verifies no. Then it verifies yes. Cook’s conjecture is deniable as what a computer solves is not what it verifies. A guess does not need to be the same as the process. Is 2+2=4? I or you design a computer to say no. That within 2 there are an infinite numbers and 2 is an Arabic numeral not necessarily needing to equal 4. The 2 rocks break up and become an infinite number of rocks. The computer provides different verification, guesses and solution. The computer is programmed to always guess NO, so when asked is 2+2=4 the computer says NO. Is 2+2=4. I or you design a computer to not give a solution. Then the computer verifies that 2+2=4. My solution is not what is verified. Is 2+2=4? My computer solves that 2+2=4 but then verification is programmed to show that 2+2 does not equal 4 due to an infinite number of pieces or decimal numbers within 2 and 2 and 4. Solved is not what is verified. Does P=NP? Stephen Cook forgot that computers, methods, issues, subjects, paths vary. P can equal NP, but P does not have to equal NP. If I were to walk directly North of where I am now I would end up in Ontario Canada to thank you Dr. Cook for his conjecture. I am trying to solve the Problem “can I say thank you to Dr. Cook?” But if I took a car my method would get me to Ontario at a different time. If I took a boat, I might sink like the Edmund Fitzgerald in 1975. www.ijmrem.com
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P=NP Proved, Disproved, Varies Based on Problem… If I take a plane I would say thanks to Dr. Cook earlier if my plane did not crash like about 2 crashes recently and 6.8 crashes in the US in 1972 each day. My solution will vary by the path taken. Solution can be same as verification method, but solution does not have to be the same as verification. P=NP and P does not equal NP. My plane could crash therefore my verification method would differ from my solution. I can assert that I can send Dr. Cook an email, but to verify that I could use different computers to send the message, or different email systems from Gmail to yahoo to Hotmail to twitter to Facebook etc. If I ever get to Toronto to discuss the issue with Dr. Cook my solution is different than verification method. Thank you is different than Thank you very much and both those are verified differently Thank you is understood differently than Thank you very much. P=NP, but P does not have to equal NP. P=NP and P does not equal NP. The conjecture is both provable and deniable. Linguistically I can say for example P=NP. Linguistically I can say P does not equal NP. With color I can say P=NP with the same color. P does not equal NP with different colors. P does =NP with the same or different colors. Solution and verification can be the same method, but solution and verification do not have to be the same. Some problems cannot Be Solved or Verified, Guessed or Processed; these problems are Neither P nor NP. Program- “The computer cannot guess or process” that program is not P or NP. By the way a different solution is that certain computers cannot verify or solve a question? For example, for the question “Is a Dog a cat?” Or the problem “How” or “Where?” or “When?” or “What?” or “Do not operate or function.” A computer can choose not to verify or solve. Computers and human beings can make choices too to not solve or not check. There is not one answer to Cook’s P=NP as algorithms vary based on questions and problems so that P’s relationship with NP also varies. How something is solved varies in its relationship with how something or a problem is checked, so the solution to Cook’s P=NP query is that the relationship would actually vary based on problem asked. Variation is something we celebrate; diversity makes life interesting. P=NP and the Similar Planetary Diameter Problem by James T. Struck BA, BS, AA, MLIS Introduction I was reading a New York Public Library Desk Reference on 2/6/2018 and noticed that planetary diameters were vaguely similar. (The New York Public Library Desk Reference by New York Public Library Hardcover, Second Edition, 930 pages Published November 1st 1993 by MacMillan Publishing Company) [2] The Planetary diameters of Jupiter and Saturn, Uranus and Neptune, Earth and Venus, and Mercury, the Moon and Mars were vaguely similar. After I made this observation or discovery, I decided to use the Similar Planetary Diameter problem to study the issue of P=NP raised by Stephen Cook and Leonid Levin and other scientists. The Clay Mathematics Foundation states the problem as “P vs NP Problem http://www.claymath.org/millennium-problems/p-vs-np-problem” accessed on 2/6/2018 “Suppose that you are organizing housing accommodations for a group of four hundred university students. Space is limited and only one hundred of the students will receive places in the dormitory. To complicate matters, the Dean has provided you with a list of pairs of incompatible students and requested that no pair from this list appear in your final choice. This is an example of what computer scientists call an NP- problem, since it is easy to check if a given choice of one hundred students proposed by a coworker is satisfactory (i.e., no pair taken from your coworker's list also appears on the list from the Dean's office), however the task of generating such a list from scratch seems to be so hard as to be completely impractical. Indeed, the total number of ways of choosing one hundred students from the four hundred applicants is greater than the number of atoms in the known www.ijmrem.com
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P=NP Proved, Disproved, Varies Based on Problem… universe! Thus, no future civilization could ever hope to build a supercomputer capable of solving the problem by brute force; that is, by checking every possible combination of 100 students. However, this apparent difficulty may only reflect the lack of ingenuity of your programmer. In fact, one of the outstanding problems in computer science is determining whether questions exist whose answer can be quickly checked, but which require an impossibly long time to solve by any direct procedure. Problems like the one listed above certainly seem to be of this kind, but so far no one has managed to prove that any of them really are so hard as they appear, i.e., that there really is no feasible way to generate an answer with the help of a computer. Stephen Cook and Leonid Levin formulated the P (i.e., easy to find) versus NP (i.e., easy to check) problem independently in 1971.” [2] I want to say in opening that I question that there are more ways of housing 400 students than atoms in the Universe. I would disagree with that hypothesis first as the Universe is vast and immense and large! In opening that is a problematic troublesome assertion! Abstract Here I use the Similar Planetary Diameter Problem to discuss P=NP. I am able to show that, Found can = Checked, Found does not have to equal checked, Found can be similar to checked, Found does not have to be similar to checked, Found in books can be different than checking with radar or signaling, Found in books can be different than using looking in Space or the Universe to check, We can invent new planetary systems where planetary diameters can be checked to be the same as planets found, We can invent new planetary systems where planetary diameters can be checked to be different than planets found, Found does not have to equal checked for other planetary systems, A problem like this can be impossible to prove as we can have a planetary system with no diameters in the planets hence checked and found can be impossible to establish when a planetary system has no planetary diameters. A system with no planets; we can check and find but the process would be different than the guess. We can design a computer in which the solutions are easier to find than check, we can design a computer in which the solutions checked are easier than found, we can look at planetary diameters and debate about their similarities. That is checked and found can be debated about rather than easily determined, We can have planets change into stars which would change the checked versus find issues; fusion just needs to begin, We can have the planets collide and become one planet, which would change check versus found, We can have the planets collide into millions of pieces which would alter check versus findable, We can have the planets collide into the Sun so that the planets no longer exist changing found versus checked, We can have no relation between P and NP. We can have a time, event, problem-based relationship between P and NP. Discussion I invented the planetary diameter 2-2-2 Rule that Jupiter and Saturn, Uranus and Neptune and Earth and Venus have similar diameters. This rule can be seen as similar to the Third law of Johannes Kepler. The planets Mercury, Mars, Pluto, and the Moon also have vaguely similar diameters. The 2-2-2 Rule of Planetary Diameters is presented to show that discoveries similar to Johannes Kepler's Law of Harmonies can still be argued for. Here is what the discovery is based on from the data at the end of the article and other sources. The planets then have similar diameters in groups or sets of 2 planets. Venus is 7,521 miles; Earth is 7,926 miles. Uranus is 31,763 miles; Neptune is 30,778 miles. Jupiter is 88,846 miles; Saturn is 74,898 miles [3] These discoveries or measurements can be argued about too and disagreed with. Why for example should we not group another group of objects like Mercury, Mars, Pluto and the Moon into a group of 4? I raised the query to show that general observations of the solar system and its planets can be made and discussed where guesses are not the same as verified. The 2-2-2 Planetary Diameter Rule can be seen as similar to Kepler’s Three Laws. A guess the 222 Rule is like Kepler’s law would show that that is not what is verified. Guesses do not equal processes or solution. Non deterministic polynomial www.ijmrem.com
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P=NP Proved, Disproved, Varies Based on Problem‌ time can differ from P solutions. From wikipedia.org here are Kepler's three laws-"In astronomy, Kepler's laws of planetary motion are three scientific laws describing the motion of planets around the Sun. The orbit of a planet is an ellipse with the Sun at one of the two foci. A line segment joining a planet and the Sun sweeps out equal areas during equal intervals of time. The square of the orbital period of a planet is proportional to the cube of the semi-major axis of its orbit." [4] Finding these three laws would seem to be easier than checking these three laws. I can open any book and find them, but checking them would involve careful astronomical observations. Finding then is sometimes easier than checking. I can do all the checked found relationships established in the Abstract Here I use the Similar Planetary Diameter Problem to discuss P=NP. I am able to show that Found can = Checked. Jupiter and Saturn have similar diameters, Found does not have to equal checked, as the diameters of Jupiter and Saturn are different, Found can be similar to checked. Jupiter and Saturn have similar diameters, Found does not have to be similar to checked. Jupiter and Saturn do not need to be seen as with similar diameters, Found in books can be different than checking with radar or signaling. We can find the diameter of Venus and Earth and then look in space with signaling and the process of checking is harder than finding. Guessing can be different than process as a guess “222 Planetary diameter law is different than Kepler lawâ€? would forget that both are hypotheses. Found in books can be different than using looking in Space or the Universe to check. When I look in a book, I find Uranus and Neptune to be similar in diameters but looking in space I find something different. We can invent new planetary systems where planetary diameters can be checked to be the same as planets found. We define a new planetary system where all the diameters of planets are the same. Because we invented this planetary system, checked and find are the same. Checking and finding involve the same process as we invented every planet to have the same diameter. We can invent new planetary systems where planetary diameters can be checked to be different than planets found. We invent a planetary system where all diameters are different. This system where all the planets are different is like our current solar system. Although the planetary diameters are sometimes similar, all the planetary diameters are different. Found does not have to equal checked for other planetary systems? We invent a planetary system so found solution is always different than checked solution. A problem like this can be impossible to prove as we can have a planetary system with no diameters in the planets hence checked and found can be impossible to establish when a planetary system has no planetary diameters. We can design a computer in which the solutions are easier to find than check. We invent a computer so that the diameter of the planet is easy to find as in our solar system, but it is hard to go into space to check that problem. We can design a computer in which the solutions checked are easier than found. I can more easily check all these diameters against the chart below and debate about them than I can find the diameters. We can look at planetary diameters and debate about their similarities. That is checked and found can be debated about rather than easily determined. We could debate about each of these found and checked relationships so the determination of found and easier to check is something vague or debatable. We can invent a planetary system so the checked solution is always easier than the found solution. I have an easier time checking the fact sheet than finding all these diameters. I can invent a planetary system so the found solution which can be seen as data like the fact sheet is always easier to find than it is to check. This is a system where checked and found easier is always debatable and the subject of discourse. We can find a solution easier than we can check a solution. The found diameters below are easier to find than check. Checking would involve throwing satellites and missions into space to determine if the found solution is correct. Checking would be more costly. Or finding would be more costly depending on how you define find and check. I can make a computer to look at planetary diameters which always gives a different answer. Here is my computer which gives variable answers to checking and finding. Computer can www.ijmrem.com
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P=NP Proved, Disproved, Varies Based on Problem‌ you find the planetary diameters to be similar? NO is the answer the computer always gives Or Yes is the answer the computer gives Computers can be designed in such a way that they can give computer programmed answers Vague as the computer can always define find and checked as the same. Checked can be seen as having the same meaning as find. P=NP. Computer programming can be done so the answer to a question is determined by its programming. I can program this as a computer to show find always easier than checked. See the fact sheet as a computer. Finding the fact sheet is easier than checking the solutions as I need to throw up billion dollars launch satellites faced with risks of space junk problems or launch problems to check the solutions. Finding can be programmed through the fact sheet computer to be easier than checking. Checking the fact sheet can be easier than finding it, or finding the fact sheet can be seen as easier than checking the answers to the planetary diameters. Based on how we define find or check, checking and finding can vary in how easy the process of finding or checking is to do. Checking and finding can be seen as the same process too. Based on lack of terminological definitions of checking and finding, we can see the P=NP problem as too vague to really solve. Data that Planetary Diameter 2-2-2 Rule is based on Q: What are the diameters of the planets? A: Quick Answer The diameters of the planets are as follows: Mercury is 3,032 miles; Venus is 7,521 miles; Earth is 7,926 miles; Mars is 4,222 miles; Jupiter is 88,846 miles; Saturn is 74,898 miles; Uranus is 31,763 miles; Neptune is 30,778 miles. As a result, the largest planet by diameter is Jupiter and the smallest is Mercury. Accessed at: https://www.reference.com/science/diameters-planets-3538c28cffe3507b [5] and When we look at his fact sheet, we can be seen as both checking and finding at the same time. P can be seen as equal to NP sometimes then too. Planetary Fact Sheet – Metric https://nssdc.gsfc.nasa.gov/planetary/factsheet/ accessed on 2/6/2017 [6] Author/Curator: Dr. David R. Williams, dave.williams@nasa.gov NSSDCA, Mail Code 690.1 NASA Goddard Space Flight Center Greenbelt, MD 20771
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P=NP Proved, Disproved, Varies Based on Problem…
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P=NP Proved, Disproved, Varies Based on Problem…
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P=NP Proved, Disproved, Varies Based on Problem‌ VI. CONCLUSION The case study of planetary diameters shows that P=NP can be proved, disproved, varies based on problem or issue, and can be seen as indeterminate and vague based on similarity between checked and found. Seeing a fact sheet as a type of computer, checking and finding can both be seen as easier than the other based on how we define checking and finding. Checking and finding can also be seen as the same process. We can also prove P=NP when we see that checking and finding can be seen as identical based on the computer design! As the letter P is not equal to the letters NP, we can see the P process as easier than the NP process as the P process is shorter. When I check and find planetary diameters, if I use certain data sets or computers, the process of checking planetary diameters can be seen as the same as finding planetary diameters or P can be seen as equal to NP. But if I use a rocket to check and find planetary diameters, checking and finding can be seen as entirely different processes. The book solution P is entirely different than the rocket, radar, or radio based checking involved with NP. NP guesses are different than how the issue is verified. But if we invent a new set of planets which all have identical planets, P=NP as we designed the planets that way. Recall we can define a planetary system with no planets so P and NP cannot be done as there are no planets. P does not have to have a relationship with NP. No Planets and I cannot either check or find the planetary diameter differences! Many stars do not have planets. P and NP would change their relationship based on planetary evolution. Here I do more discussion of the issue. Why we can see NP not equal P-All Problems are Not NP complete as Polynomial time cannot complete all questions and NP Procedures are not the same as P implementation by James T. STruck BA, BS, AA, MLIS 1. A P is not an NP 2. A number of questions are not computable in polynomial time. "Why, Where, When, How, Who, What if? How did it all begin? How will it all end? How long have we existed as a Universe?" have answers that are too complicated to be made into a simple polynomial computations simply as the answer or procedure to "why?" varies across many people and other variables such as what is meant by "Why?" 3. If we labelled the question "Why?" NP complete that would be incorrect as "Why?" does not have the same answers for many people. Polynomial time procedures vary across situations and questions. Guesses are not the same as verifications or Polynomial computer processes. 4. The question "How many atoms are there in the Universe?" involves checking and finding issues that make checking and finding similar processes although we cannot currently complete the actual process of counting. In polynomial time, or time “that a computer can deal with effectivelyâ€? [7], I or anyone cannot actually count all the Universe's atoms. We have no current method of travelling the distances to do computation physically. The procedure is not always doable. The calculation is not the same as the counting and finding. 5. Suppose I call "What is God?" NP complete, I would be saying that in polynomial time I can develop a process of answering the question. But say God is, as some theologians (St. Anselm etc) infer or imply, beyond everything we see or hear or can calculate or can make a procedure regarding. I would be simplifying a number of questions like "What is God?" by making the question into a polynomial time problem that is open to procedure when the question is not open to calculation or procedure.6. Similarly I hypothesize, "I've invented a number which cannot be computed, calculated or guessed beyond infinity not open to a procedural process." You cannot invent a way to make this question NP complete as the question involves a number which cannot be computed, guessed or open to process. It would be incorrect to make something that is not guessable or not computable into something computable. Whatever procedure you invent, I assert my number is not found by that procedure. The NP complete procedure does not equal the P procedure as I will always say that my P procedure is not what you set up with your NP procedure.7. NP complete processes vary in their polynomial time solutions. As there are multiple possible NP processes that shows NP is different than P as there can be multiple NP processes. As there is not just one NP process, NP and P are different. I can find more ways to get the apple from the tree. As there is more than one way to get the apple out of the tree, the NP completeness varies from a P solution. One P solution does not equal the many NP complete processes to do a P solution. I guess we will have passenger pigeon fly the apple over. There are not passenger pigeons so my guess is not doable. 8. Many problems have no relationship with P and NP. For example, solve the problem of Being. Being
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P=NP Proved, Disproved, Varies Based on Problem… or being yourself is not computable via polynomial processes, but to be existing or being, life is more complicated than polynomial processes. To live, our lives will always be different than any polynomial process that someone finds or NP guess. 9. Existentialism denies the NP=P relationship. Any NP complete processes always will be different than the existing person's solution to a problem. A Computer is trying to find a computation or procedure of life, but that is not what the Person chooses. The NP completion program is different than the Polynomial time lived solution of being. 10. NP does not actually equal P. As I or Cook describe one as polynomial and one as not polynomial, the polynomial side of the equation does not equal the non-deterministic polynomial side of the equation. Algebraic language shows the 2 sides are different. Stephen A. Cook's The Complexity of Theorem Proving Procedures, written in 1971, would have us believe that NP completeness shows problems as solved by a polynomial time procedure. If we are going to live life and truly live as independent beings, we have the right to see our lives as independent and different than any polynomial time procedure that a computer might set up. Live life and understand that the computers procedures or guesses do not need to define your life and existence. That goes for the Peregrine Falcon, the passenger pigeon, the imperial woodpecker, the Mexican Grizzly, the Auroch, the buffalo, the Dodo bird, the Irish Elk, the mastodon, the Brontosaurus, the diplodocus and the extinct seal. All life has a right to not be the solution that a polynomial time procedure might set up or determine. A computer example of a Peregrine Falcon, woolly mammoth or passenger pigeon does not need to act out the polynomial time procedure that an NP complete procedure finds, so NP does not equal P. NP completeness is not the same as polynomial time procedures. None of those creatures exist; computer guesses are not the same as the imagination of the animal. The bird does not act as you guess it does also! Life can be different, vastly different than its program, guess or procedure. Thank you Dr. Stephen Cook for trying to raise the query, but we can and have been showing every problem in NP is NOT solved by just one polynomial time procedure. Our lives, all lives and solutions and procedures are independent of whatever a computer determines or guesses as a procedure. The simple difference between the NP complete procedures and the living or acting out or running or implementation of the procedures is enough to show that NP does not equal P! “According to Cook, an NP problem was said to be NP-complete if the discovery of a polynomial-time procedure to solve it would imply that every problem in NP could be solved by a polynomialtime procedure.” [8] Since many problems are different, the discovery of one polynomial-time procedure to solve an NP problem would not imply that every problem can be solved by a polynomial time procedure. Non deterministic polynomial time procedures involve guesses, polynomial time procedures involve problems computer solve. Guesses are not the same as problems computers can solve. Recall on a broken computer that the non-deterministic polynomial time procedure would certainly not play out the same on the broken computer. Therefore the guess is really different than something a computer can deal with. Sometimes the guess procedure linked to NP might actually work better than what a broken computer can deal with!
ACKNOWLEDGEMENT I would like to thank my mother Jane Frances Back Struck who died 7/15/2017 for teaching me to live as an independent human being independent of some of the procedures that an NP complete solution might set out for me. Anyway, the NP complete solution is acted out entirely differently in me than acted by others than acted out by different computers. The many NP complete solutions that a computer can guess are implemented variously by computer processes. P does not equal NP. But we still can imagine that P =NP as we can imagine anything.
REFERENCE LIST [1]. https://en.wikipedia.org/wiki/Combinatorics accessed on 2/9/2018 [2]. The New York Public Library Desk Reference by New York Public Library Hardcover, Second Edition, 930 pages Published November 1st 1993 by MacMillan Publishing Company 2. http://www.claymath.org/millennium-problems/pvs-np-problem” accessed on 2/6/2018 [3]. https://www.reference.com/science/diameters-planets-3538c28cffe3507b accessed on 2/9/2018 [4]. https://en.wikipedia.org/wiki/Kepler27’s_laws_of_planetary_motion accessed on 2/7/2018 [5]. https://www.reference.com/science/diameters-planets-3538c28cffe3507b accessed on 2/9/2018 [6]. Planetary Fact Sheet – Metric https://nssdc.gsfc.nasa.gov/planetary/factsheet/ accessed on 2/6/2017. Author/ Curator: Dr. David R. Williams, dave.williams@nasa.gov NSSDCA, Mail Code 690.1NASA Goddard Space Flight Center Greenbelt, MD 20771 [7]. Devlin, Keith. The Millennium Problems The Seven Greatest Unsolved Mathematical Puzzles, NY New York, Basic Books, 2002. P. 120 [8]. Ibid, p.125.
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