Goldbachs Conjecture Proof: My Almost-Final Answer

Let us see if it is possible to violate Goldbach's Conjecture. Suppose we take two lines of even, whole numbers, counting in opposite directions, and line them up one on top of the other. If they are 126 long, 0 in one line will be 126 in the other.


6 5 4 3 2 1 0

0 1 2 3 4 5 6


Now suppose we insert a wave of every prime frequency, including 1, into both. At 1 in each, we will get 1, and 1 again at each number through 126. At 2, we will have 2 and 1 - for a total of 2 - at 3 we will have 3 and 1, and so on. At 15, we have 5, 3, and 1, for a total of 3.


0 1 2 2... 3

0 1 2 3... 15


If we load both these number lines with all these frequencies in this manner, both lines will contain the same amount of data in their linear variations, meaning the same amount of entropy or complexity. Complexity is the same, whether you're talking positive or negative space.


But, suppose we flatten these lines, so that they are at either 1 or 0, never 3, like 15. If 15 would be 1, we don't need 3 and 5, just 1's! But suppose we throw away 1's, bar them from our use, and just use waves of prime numbers 2 and higher to fill both from the opposite directions.


The entropy of these lines should be the same, or perfectly opposite, whether you look at their prime holes - meaning 3,7,17 - or their prime frequencies - meaning 121,123,125. They are the same data, no matter how you look at it.


Except for one problem. Each line has a hole in the form of an original 1, which cannot be used as a frequency. And by putting the 1's at opposite ends, it is just impossible to line them up opposite each other! As such, it is impossible to have a hole in 1 line for every frequency in the other.


In other words, each line is theoretically just complex enough, in terms of its time-series variation, to exactly cancel out the other, except each line has an 1 extra hole without a corresponding frequency.


Any time there is a hole left where a prime in the top line sits opposite a prime in the bottom line, that means you have two primes, counting to each of their zero's, which must add up to equal the positive, even sum which is the length of the number line.


Once we elimnate 1's, and the possibility of staggering opposite two-waves by an opposite number, our reduced-entropy linear compaction must marshall the full entropy of both lines to offset. Of course, if we were to allow the vertical stacking variations, the problem would only get worse.


If we used only 3-waves, we could achieve complete smoothness with three staggered lines. But in this challenge, we need to use two lines, so as to measure two primes from one spot to two zeros in two different directions. But the compacted resolution smoothness which could be masked over using staggered two cycles is eliminated using even numbers. And with only two number lines, all remaining frequencies would theoretically be needed to achieve smoothness.


Any number of cycles where, say, the first 10 primes would synch up again - like they were at zero - would invariably take a longer number line than one limited to those primes. Any number line will always contain a sufficiently large prime number that would take a longer number of cylces than the number line itself to fall back in synch with the other primes it is lined up with at zero, and become useful as a frequency.


Another way of saying this is that the complexity is asymmetric, and trapped at opposite ends. Before all the lower prime waves at the wave end will ever fall out of synch enough to disaggregate their complexity, and fill every prime hole at the prime end, an endless stream of new, complex prime holes from the other end will emerge in the middle, to be filled. Every prime is a hole, long before it becomes useful as a frequency.


Notice, I am not saying you need an equal number of holes and frequencies. I am simply saying you need an equal number of out-of-phase frequencies to describe where the holes are. Incredibly, if you use up an extra hole at one end, by using it to describe a hole instead of a frequency - and it does not sit opposite itself in the middle - you end up having two hanging frequencies describing a frequencies, and two more holes which must be used to describe on another.


And, you still always have those two hanging holes at both ends. If you cover them with a frequency, that means there must be at least two hanging holes somewhere in the middle, sitting opposite one another. And that, in addition to the problem that in-phase waves in the middle - where new holes are being created counting from the end - are already creating missing frequencies and extra holes which must sit opposite one another.


So, in summary, an AND hole which is prime to both zeros on an even number line fulfills Goldbach's conjecture. And the naked 1's at both ends guarantee there must at least one such hole somewhere in the middle, since we cannot manufacture an extra frequency without the use of 1's, even with vertical compaction. And the further asymmetries on top of that, guarantee further holes in any number greater than 2.


eLROY

Let us consider the even numbers 18, 20, and 22.


22 has an odd number of holes, because 11 and 11 sit opposite in the middle, and all others pair off. 18 has a frequency in the middle, which seems like it should create two hanging holes - which could sit opposite the original or 1-implicit holes - so it would have an even number.


As such, it makes sense 22 would have 1 fewer holes than 20 - which also includes 19 on its line - but more than 18 - which doesn't have 19. 18 can't single-hole the 11, but it has a hanging frequency in the middle, which balances out its not having 19's when its 17's sit opposite its 1's. Meaning, the 17's are so far apart, and they can't sit with threes, they have to creat a hanging frequency in the middle.


22 has a lot of primes that are not yet fully used as a frequency, 5, 7, 11, 13,17, 19 - if you consider each prime to be "under-utilized" until it reaches its square. And 22 has 2 holes one each side - for a total of 4 apart from its 1-implicit, for a total of the 6 asymmetric and under-utilized frequencies in both directions - which doesn't add up when we take care of 17 - which just really means we have hanging frequencies at like 2 and 20, it all balances out.


Notice, 18 has these same under-utilized frequencies except 19, plus the split 1-implicits, and the hanging 3-wave square frequency in the middle. After each prime's square, the next time it really becomes utilized is as a frequency paired with the next higher prime that has not reached its square. So 3 becomes useful at 9, and then at 15, but is a hole at 3, and covered by 2's at 6.


Any smarties want to correct my work so far?


eLROY

Speaking just for myself, I'm finding your posts very difficult to understand. The one I felt closest to understanding your argument was the one posted at 5:57 A.M. from which the following is an excerpt:


"Therefore, using these axioms, the proof is simply a proof that there will be a prime number higher than any given prime number, but lower than its square, or you get the idea. For an illustration, consider the positive, even numbr 126, which makes separate use of 11,7,5,3, and 2 at its terminus. We already have the prime wave 13 available to describe this region, and we're not even talking half way to the midpoint!"


I suggest you break your argument into pieces, similar to the following:

Axiom 1: Blah

Axiom 2: Blah, blah

......

Axiom n: Blah, blah, blah


Proof (State conjecture)

Given Axioms 1 and 2, it follows that ... and so on.


That is, state exactly what it is you're trying to prove, what your axioms are, and how, given the axioms, the proof would follow. Then we can look at the reasonableness of the axioms and the logic assuming the axioms are true.

tewall,


For a quick up-to-speed, check out my first try in the Stocks forum. You will see my plain error if you start counting down in 3's from 32. They fill both the 29 hole and the 3 hole in the opposite direction, among other things. But it is illustrative of my initial path of thinking, starting at nothing. So, here's my first try:


AXIOM 1: A number line is a linear variation expressing a certain amount of entropy. Look up Huffman coding on the web. It is a sequential collection, to the extent it is unique not just in the number of 1's, 2's, 3's and zeros, but also because of their order.


AXIOM 2: If you take a single wave, its entropy is implicit in its frequency and amplitude.


AXIOM 3: You can populate a number line with linear variations, by starting at zero, and then laying down a 1 at every slot where a prime wave - 5 - or its frequency - 10, 15, 25 - touches down. And you don't need 4's, only 2's. At this point, the entropy of your number line should be the total entropy of all the waves combined. In other words the entropy can really be expressed in terms of each prime hole and its magnitude.


AXIOM 4: When you flatten each slot, to instead of registering the total magnitude of waves hitting it, to only register a binary of whether it has been hit by a frequency or not, you lose - or make - some entropy at "frequencies," so that the new entropy is a complex product of every unique wave interacting. Meaning, the product is now unique based on not just the included waves, but their order, order becomes relevant


AXIOM 5: When you synchronize prime waves to begin at zero - meaning two are not on the same spot on the same number line, and none are a frequency starting at the zero of another, that is a unique entropic collection.


AXIOM 6. The frequencies laid down on the 1-dimensional line should have some complexity which is related to the primes you have included, and their order - meaning their synchronization around one. But where frequencies coincide, but are suppressed, the product must be a simpler strecth of line than if they were not. And since entropy is a concave function of distance in relationshio to conplex objects, in ordered adjacencies, a section which is closer to the suppressed region and further from the out-of-synch region must have less complexity, from its point fo view.


AXIOM 7: To construct the Goldbachs example, we had to deade the vertical component, because all we are trying to do is fill holes on one line with frequencies on the other. But since we are suppressing addition, we have to suppress the 1 frequency, which woudl run rampant across the number line and mask all variation. Two's would do the same thing if we staggered out lien by odd numbers, but fortunately we are dealing with even numbers. Also, Goldbach's Conjecture specifies a sum of two primes, we can forget about zeroes at both ends. But, we have to keep the 1 primes.


AXIOM 8: The total entropy of each line - the suppressed entropy product of the primes included - must be identical. Furthermore, they must be equally complex if inverted, since complexity does not distinguish as to between positive and negative space. Meaning, if you switch every 1 for an 0 and every 0 for a 1, the entropy remains unchanged.


AXIOM 9: The entropy in each separate line therefore remains equal if we switch holes and frequencies, so that, collectively - meaning not in any particular adjacent order - they could cancel one another out, or describe one another. Frequencies in one could be used to describe holes in the other, except two problems: 1, they are laid end to end in opposite directions, and 2) they both have a 1-hole whose frequency is suppressed - meaning frequencies are not a complete product of holes and their order.


AXIOM 10: Therefore, a hole must be opposite a hole somewhere, both because there are 2 extras to match off, and because, suppressed to binary coincision, and at a distance, frequencies are not able to perfectly describe holes. You must subtract an eqaul number of frequencies and holes from both lines, to arrive at a descriptive combination. The way you subtract frequencies and holes on oppiste sides, without using them to describe each other, is by placing them opposite each other in the order. To resolve the asymmetries, there must be at least one hole.


Mind you, this is not my last word. I have to go back through what I have written and brainstormed, and see if I didn't miss or misinterpret a critical axiom somewhere. In any case, and in additionb to any corrections, I would like to add more proof, and more imtermediate axioms, anywhere I can. And I will do so in subsequent posts.


Did I miss something?


I assume I did. I'll go back over everything I've written, and add more.


Thanks for... caring:)


eLROY

Yes, like the definition of an Axiom in your first high school math class.


I don't think you have had any formal mathematics training, and if you want to prove Goldbach's conjecture, it might be a good idea to get some. If you have had some, then you've forgotten a lot of it.


You're wasting your time and ours with this nonsense, but especially yours.


And don't even ask me to try to explain what you did wrong. You have so many of your own definitions and techniques that haven't been properly outlined that it is impossible to figure out what you're talking about. Your writings seem eerily similar to those of schizophrenics, and you seriously might want to talk to a shrink.

Yes, when a unique entity is so complex that no simplification or generalization can be used to describe it or apply rules to it, it remains intractable to a less complex entity.


eLROY


P.S. Why ever would I go pay to sniff chalk dust with a bunch of patch-pants boobs, who have failed utterly to prove this conjecture for the last 250 years, despite every miserable effort?


Your half-brained mathematical "methods" can only be used to prove the exact location of the first hole in any particular series, and only by using a description of that entire series as an input.


Your tools are incapable of uncovering a single common property between any two series of prime waves. And no, I didn't take math in high school, and I had to look up "axiom" in a dictionary just now.


How am I supposed to know what particular axiom some college-trained idiot won't understand? Obviously, I can predict that if any Goldbach's proof is discovered, the axioms used will be alien to the mind of the common limp-wit, or he would have simply assembled them and solved the problem himself long ago.


Of course you don't buy my argument, you moron. But what you don't realize is that you would have the exact same reaction no matter if the correct argument stared you in the face.


Both the correct argument, and an infinite stream of flawed ones would be indistinguishable to you. But you know, good luck, the world needs idiots too.

You wrote:

How am I supposed to know what particular axiom some college-trained idiot won't understand? Obviously, I can predict that if any Goldbach's proof is discovered, the axioms used will be alien to the mind of the common limp-wit, or he would have simply assembled them and solved the problem himself long ago


No, the axioms WON'T be alien to the mind of the common limp-wit. That's the point of an Axiom: its an easily understood statement. Assembling proper axioms in order to reach proof is the difficult part. Understanding the axioms is the easy part. If you've found a new method of proof beyond constructing a logical argument that builds upon basic principles, I'm excited to hear it. That would be more important than proving GC.


Good luck, eLROY, seriously. I read the New York Times so I'll be sure to see the article about you when you finally prove GC.

Each prime wave - 7,13,17 - occurs at its own spot one time. Therefore, a map of 0 through 3, with a binary resolution, will reflect completely the entropy in these waves.


You dead the slots, so that 15 doesn't reflect 3 and 5, but rather only that at least 1 of them was there, you lose some data.


To prove Goldbachs's conjecture, all I need to do is prove that I can't fill - or "describe" - the full-resolution prime holes with suppressed-resolution product frequencies.


And all I need to do to prove that is prove that the product frequencies are less complex than the holes, since, if you take the number 34, it has an 11 hole, but the frequency 11's are buried inside 22's and 33's.


The fact that I also have a 1-hole to describe, but I can't use a 1-wave - or else it would completely pin an entire binary-resolution number line - is just icing.


Or, the fact that, like gravity, complexity is a function of proximity (every code is a subset of a larger code) - so when the lines are overlayed in opposite directions you must have a net complexity gain or loss, not a cancel-out - seems pretty obvious to me.


Is there something strange about the idea that the entropy of a wave is the function of its frequency, such that the higher the frequency, the higher the compelixity?


If we can smooth a number line with three staggered 3-waves, and it only takes two 2-waves, and therefore 2 must be more complex or precise - when it is positioned in proximity or relative to 3 - am I going out of bounds?


eLROY

Don't get mad, but I agree with EssW regarding axioms. However, we can leave that part aside, as an argument can be made rigorous later assuming it's valid.


Basically I'm understanding your argument is:

A) You have a conjectuture which is equivalent to Goldbach's.

B) You have a way of proving your conjecture.


A couple of questions.

1) What is your conjecture?

2) Why is your conjecture equivalent to Goldbach's?

Okay, here's 2 and 3 waves, harmonizing on a binary number line:


. . . . . . . . . . . .

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16


As you can see, they go 3-space-1-space-3-space-1-space. How complicated is that? Moreover, you could bury an 11 in one of these, and, other than at 11, it wouldn't show its face again until 121!


But now lets look at primes, marked out on the same line:


. . . . . . . .

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16


The primes go bang-bang-bang-bang-space-bang-space-bang-space-space-space-bang-space-bang-space... and I'm still not done!


And I never will be.


The primes are the antithesis of frequencies, they literally - by defintion - defy as many waves as possible, no matter how in or out of phase. The primes have no darn harmony whatsoever.


They are literal disharmony sniffers, guaranteed non-cycle detectors, if you don't have every necessary penny of entropy available to you - every penny up to as much as they, themselves describe - they will by law stumble upon at least one way to evade you.


By the laws of physics, one must escape!


Is this not axiomatic?


If this is not axiomatic, I don't know what is. Are we living in 5,000 BC?


eLROY

You know I jsut saw article which says if one can post a correct solution to the goldbach's conjecture you can win one million dollars.


I think the due date is March 15.


You could look here:http://www.mscs.dal.ca/~dilcher/Goldbach/nyt.html.


I suspect it would be easier to work on the "Sklansky" problem.

My understanding of Goldbach's Conjecture - from about a 10-second glance at the Google cache - is that any even number can be created as a sum of two prime numbers. For any even number, there is some prime you can subtract, and get a prime.


Another way of saying that is that if you draw a number line the length of your even number, and put a zero at zero, and another zero at the end - at 32 in the case of a 32-lentgh line - that there must be a spot on the line that is a prime when measured to either zero.


So, the only way this can be not true is if somehow the top number line, running in the opposite direction, can manage to lay down what I call a "frequency" into every prime running the opposite direction - into every what I call a "hole" - in the bottom number line.


But the holes are tragically uncyclical, and the frequencies are tragically cyclical.


eLROY

And that is why a million mathematicians have failed to solve this problem.


Because, put simply, there is no complete mathematical description of a harmonic sequence of prime numbers of indefinite length! And you need to consider the whole line to determine where the first hole will be, before you can determine if one will even be there at all.


My favorite example is 126, where the 11's are 5 out of phase, and the 5's are 1 out of phase, and the 7's and 3's are in 180-degree phase. Implicit in that is pretty much your answer - 13, 113 - but you have to know the specific length of your number line to arrive at it.


There is no rule whereby you can translate from a 20-length line to a 40-length line, by simply recalculating the phase shifts in each prime component. The location of the hole is, like, P+U, where P is the previous line, and I is an unknown factor. So, if you say under a given set of conditions a hole must exist, you have to keep redefining those conditions.


No tricks will shorten it, as all the information has a chance to be reflected at the point you choose. This not unlike Paul Pudaite's bead problem, where the simple answer seems to be the complex one, that considers each combination of beads as a unique entity.


Since I can't tell you where the first hole will pop up, all I did was to show how no pair of number lines could prevent a hole from popping up somewhere. I cannot prove they can make the hole, so much as I can prove that they lack the capacity to prevent it. And so it must exist somewhere.


By definition, there is no fixed amout of math you can use to describe a congenitally non-descript entity. You can't say X = Y - only I have no idea what either X or Y is, and can't plug in a value. In other words you cannot manufacture information out of thin air, or compress indefinite information into finite math.


What puzzles me is why no entropy-coder every came across this problem. I am confident my axioms are their axioms - or at least someone's somewhere. Am I the only open-systemer in the world?


eLROY

A prime sequence sniffs the holes in any cycle, eventually.


And there will be more primes than cycles, given that new primes will be introduced to sniff, long before they emerge from the existing cycle at their square.


In other words, the pattern of the cycle will reflect less complexity, a more simple texture, than the number of primes available.


The construction of a prime number is explicitly the construction of a number that dodges cycles.


Call them "cycle dodgers." Call them "pattern wreckers."


And a cycle is what a pattern of flattened harmonic prime frequencies creates.


eLROY

Let's get something straight.


There are no "math equations" in my proof - not of the kind people expect - because, frankly, I wouldn't have any more idea what to plug into them than anyone else. No one ever will. What we mainly have is logical equivalence and inequivalence, and proofs that things are unequal.


So when we talk about axioms saying two things are equal, or categorizing situations, you won't find any of them here. Because every even number is a snowflake. (Heck, if they weren't, we could save a lot of numbers!) The only things we have to deal with are the top number line, and the bottom number line, of a given even number. And I guess you could do entropy math on any given pair all day. But my proof describes not either one, but rather their generalized relationship.


In order to visualize the deadened or missing entropy in the frequencies - which prevents them from describing the holes even if they happened to somehow be as close as possible to the "right order" (Notice, I am not saying they are in any wrong order, only that they are incapable of being in the right order, no matter how many thigns they have going for them, if they somehow arranged into the right order, the entire universe would disappear) - try picturing a broken-up sequence of irregular flat dots which transision into regularly-space hills or sine waves.


Now, flatten the hills of different sizes, so that all you have left is the lines of their bases, no taller than the nearby, 3-5-7-11 dots. The hills aren't so interesting any more, rather they look like morse code, only they are saying A-B-A-B-B-A-B-A-B-B-A. Meanwhile, the holes coming at them from the right on the top number line are saying X-H-A-J-N-C-P-B-Y-A and, eventually, they will find a hole.


Can you imagine a math equation into which you could plug any combination of prime numbers and it would work?


eLROY

This was clear. You have a number line


0 1 2 3 ..m.n.p 0 which you reverse

0 p.n.m...3 2 1 0 and lay on top of the other one.


You're saying that Goldbach's conjecture is equivalent to saying there must be some prime number m, or n or whatever sitting on top of another prime number beneath it.


You're saying the "frequencies" must knock off all the primes (holes) for Goldbach to be false where "frequencies" are multiples of the primes.


How do you handle 1? One is a prime whose frequency fills in all the holes.

I don't get it...


AXIOM 1: A number line is a linear variation expressing a certain amount of entropy. Look up Huffman coding on the web. It is a sequential collection, to the extent it is unique not just in the number of 1's, 2's, 3's and zeros, but also because of their order.

--

What is a linear variation? What do you mean by entropy? How is such an entropy measured? Given a linear variation, how do you find out how much entropy is being expressed?

--


AXIOM 4: When you flatten each slot, to instead of registering the total magnitude of waves hitting it, to only register a binary of whether it has been hit by a frequency or not, you lose - or make - some entropy at "frequencies," so that the new entropy is a complex product of every unique wave interacting. Meaning, the product is now unique based on not just the included waves, but their order, order becomes relevant.

--

What slot? How do I flatten a slot? What does it mean to "register a binary"? I'm now making new entropy? What is the "complex product"?

--


I'm sorry, but you're not making any sense to me (and seems as if I'm in a majority view here)

"Since I can't tell you where the first hole will pop up, all I did was to show how no pair of number lines could prevent a hole from popping up somewhere. I cannot prove they can make the hole, so much as I can prove that they lack the capacity to prevent it. And so it must exist somewhere."


Isn't a "hole" as you define it a prime? The first hole is 1. The next one is 2. The next one is 3. We know where they are.


What's the argument the holes can't be filled? Run that by as simply as possible.

Except for D. H. Lehmer (who was a tremendous number crunching number theorist in the days before computers), mathematicians don't consider 1 to be a prime (some treat it as a prime power, since x^0 = 1). Lehmer's idiosyncrasy was a bit annoying, because he did things like publishing what he called the first million primes, except it had only the first 999,999 primes.

n/m

In the context of Goldbach's conjecture, it would have to be considered a prime, or the conjecture would be false.

Treating 1 as prime would make the unique factorization theorem messy (e.g., instead of 24 = 2^3 * 3 being the unique factorization, we'd have to explain why 24 = 1 * 2^3 * 3 = 1^2 * 2^3 * 3 = ... doesn't count). Not counting 1 as prime doesn't hurt the Goldbach conjecture. Because 4 = 2 + 2, 2 is the only annoying case, and that's not a big deal because the conjecture is "mainly" about large (even) numbers.

Take 30,250. The first prime, counting left, is 3, or 30,247. But 30,247 is a frequency of 7. The first prime on the bottom line, 30241, is at 9, or a frequency of 3, on the top line. Somewhere, there must be a hole on the bottom that is oppsite a hole on the top. In this case, the first "unfilled hole" is at 30203, 47 but there is no shortcut to "predict" that.


Now, as to the argument the holes can't be filled, I am arguing that the pattern laid down by the "holes" is more complex than the cyclical pattern laid down by the frequencies. Moreover, we don't need to look at interphasing cycles of 2 and 3 compared to a sequence of primes to "suspect" that, rather we can prove it as a result of entropy loss to do loss of resolution at synchronized frequencies.


This body of knowledge, so far as entropy coding and information theory, is really a byproduct of asynchronous serial communciations, meaning the cell phone and Internet revolution. Given a voice pattern, or an image, what is the smallest you can compact it to squeeze it over a slow, low-bandwidth line efficiently? So, for the first time in 250 years, people have been paid to develop some "axioms."


Moreover, I am arguing that we get more information to start with in the holes, because we can't use 1 as a frequency on our binary-resolution line, but have a 1-hole. But, notice I am not saying the total entropy of the two lines, running in opposite directions is unequal. I am saying that when you line them up adjacent in opposite directions, the complexity at the other end doesn't really help.


But again, that may seem obvious, only we need an axiom. So my axiom deals with the nature of complexity and proximity. Why wouldn't a straight-through line, covering every hole and frequency indiscriminately in the other line, cover them with less complexity? Because that straight-through line would have more complexity, given that it is in the same unnoticed resolution, and on the same line, as the awkwardly-spaced holes at the other end.


In other words, straight through is as contrived as any pattern, especially if you're not using a 1-wave. In fact, I might even go so far as to say that, by being next to frequencies, which are next to frequencies and holes which are next to holes on the opposite line (a 2D grid now), the unfilled-hole side becomes more complex. And now the frequency side is across from holes, and down-line from holes, but still not complex enough.


It is also my postulate that if the high-resolution holes were further away from the flattened, cyclical frequencies, the frequencies would be less complex. In an entropy sequence, you achive entropy in combinatipon with neighboring sequences. But I don't even need that to prove Goldbach.


All I need to prove is that the frequencies are less complex than the holes, because our binary line captures the holes whole resolution. Then, when we try to fill every hole on one line with a frequency form the other - so a hole is not opposite a hole that can be traced to zero in both directions - we will tragically fail.


It's not so much that prime numbers sniff out holes in cycles. It's more like the laws of physics require a hole on a hole - and a freqency on a frequency to where the missing entropy cancels out - and a sequence of primes is the only sort of abstract enough human construction that will always meet this without our having to specify or contrive it, and save the universe from paradoxes.


(Notice, there does not seem to be much serial correlation on empty number lines populated by prime-number holes. That is, like, implicit. The filled holes, after you ignore the unfilled holes on one number line, seem to be serially correlated like the frequency cylces on the opposing line that fills them. And just filling holes which happen to fall on an out-of-phase cycle, so that filled holes are cyclical not misbehvaed, won't do it. Hey, maybe the interleaved sequence of frequencies on frequencies, holes on frequencies, and holes on holes, actually takes up the missing or subtracted entropy in its own super-pattern!)


eLROY


(Note: I think I found 30241 by multiplying a bunch of low primes together to get 30240, and just added 1 - knowing that since everything but, like, 3 was in phase there, and 2 can't be odd, there would have to be a hole on one side or the other.)

I'm aware of the prime factorization theory and not counting 1 in that context. I wasn't aware that 1 was discounted in Goldbach's conjecture.

You're just stating what you want to prove in another way. That is, you assert (paraphrasing) that two holes can't be lined up on top of one another because primes generate more complex frequencies than non-primes, or that primes are non-harmonic, or similar things. Why does the fact the fact that primes are more complex mean you can't fill the holes? Unless that's what "complex" means, in which case your assuming what you're trying to prove.


Another question. Why do the frequencies need to be determined by the number line in question? That is, you can get more non-prime frequencies by just considering other number lines (if I'm understanding frequencies correctly as being non-primes that divide the given number).


I think your way of looking at the problem is interesting, BTW.

By slot, I meant a spot on the whole number line.


I guess by entropy I mean the smallest size to which something can be compacted. But, like I said, look entropy coding up on the web.


0010011101010 has linear variation, fluctuating between 1's and 0's. Serial correlation would be if you could guess what the next number would be by starting at some random point in the sequence and looking at a few numbers. If using some subset, even just 1 digit, you can predict what the next number is likely to be - if 1's are followed by 1's three out of four times - the sequence can be compacted, subsituting 1 for 11. So

110110 would become

1010.


Turning

0010032102070 into

0010011101010 would be "flattening."


Binary menas there are two states, 1 and 0.


By complex product, I meant that a 3 6 9 12 15 18... wave combined with a 5 10 15 25 30... wave would have the samee entropy no matter how you staggered them - 2 5 8 11 14, 6 11 16 21 26 - because they woudl just stack up where the coincided. Meaning, at 15, we would "register" the 3-wave and the five-wave, to get 2. But if we flatten, to get just 1 - despite the fact that two hit it - how they synch up, and how much we lose, is a product of whether they are in or out of phase on a finite segment of number line. In the long run, or over an infinite line, they would be equally in and out of phase no matter how you staggered them.


eLROY

I used two number lines so that my hole could be a prime measured to two different even-number spaced zeros. That's all I care about.


So far as my talk of the prime sequence being a "congenital hole-sniffer" and the like, that is just to help you visualize it, we are not "assuming" it is true because I say it is. In fact, last night I was amazed by how stubbornly they sniffed holes, and so that is why I searched for - and found - the underlying mechanics that led to this superficially remarkable coincidence!


I'm not simply assuming that less complex things can't "describe" more complex things, that's a fact. That is the definition of complexity, in the established fields of entropy coding, and information theory. You lose resolution, and never get it back when you try to blow it back up to size. Take your hard drive. The only way you can "fill it" without actually adding any new data is by making endless copies of what is there already. And your copies, no matter how space-consuming, could not "describe" a hard drive with an equal-sized program you don't have.


So, yes, I take this as axiomatic. And then I go on to describe an airtight process which would have to lead to the complexity asymmetry which I need. And then I show how that process and a violation of Goldbach's conjecture are incompatible.


eLROY

Now you are starting to make some sense. But not your proof. (If someone were to ask me to place a wager on your proof, I'd go all-in against it without the slightest hesitation.) However, I am still interested in trying to figure out what you are saying and am still open to the possibility that you may have something of value to say.


If you can go back and define all those words that you are using, then maybe others can understand what you are saying.


For example, there is still not enough information to understand axiom 2:


--

AXIOM 2: If you take a single wave, its entropy is implicit in its frequency and amplitude.

--


Implicit meaning that it's there, but I can't necessarily write it down (like the existence of implicit functions)?


In your axiom 3, "the entropy of your number line should be the total entropy of all the waves combined." Why? You still haven't shown how to figure out the entropy of single wave, so how can you possibly assert that the total entropy is the total entropy of the waves combined? (that is, how do you know there isn't any sort of interference effects?)


(I should interject here to say that, by definition, an axiom is assumed to be true. But then you can axiomatize the Goldbach conjecture and say that it is true.)


I can keep going like this line by line, but I hope you get the idea why the objections to your 'proof' are so numerous. It honestly feels like you're saying a bunch of nothing.