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Ernst

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    Programming and maths enthusiast. Author of Introduction to Dynamic Unary Encoding.
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    Just reading about it actually.
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    Ernst Berg
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    Modesto Junior College
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  1. I am considering reworking the "Attractor Finder" program I wrote back in 2004 and publishing something of a list of cycles of the dynamic system [3X+Y,X/2] is there any interest here in advancing our understanding of these dynamic systems? We simply must expand our conceptual foci.
  2. You know I see that the last version of the Attractor Program here is dated 2005 so I am wrong about how long ago it was. Also I see that I didn't have as grand a format as I remember??? I guess I spent time editing the output. So, I'm thinking I should rework to take advantage of multicore programming. However, I am going to cut and paste the output here so my Collatz friends can see that there are an infinity of cycles and that only addends that are a power of three have a single cycle and the rest have more cycles. Therefore there are many "sets" the inputs divide into. Obviously I present a big clue about this Collatz Conjecture in that I am sharing the bigger picture. Attractor Finder program by Ernst Berg June 2005 Report for the Y of 1 is a power of 3 and a single attractor system Report for the Y of 3 is a power of 3 and a single attractor system The attractor >> 1 has been added. Run had 5 steps and the X is 1 The attractor >> 19 has been added. Run had 18 steps and the X is 3 The attractor >> 5 has been added. Run had 4 steps and the X is 5 The attractor >> 23 has been added. Run had 9 steps and the X is 23 The attractor >> 187 has been added. Run had 47 steps and the X is 123 The attractor >> 347 has been added. Run had 44 steps and the X is 171 Report for the Y of 5 -------- The value of Y is now 7 The attractor >> 5 has been added. Run had 9 steps and the X is 1 The attractor >> 7 has been added. Run had 4 steps and the X is 7 Report for the Y of 7 -------- The value of Y is now 9 Report for the Y of 9 is a power of 3 and a single attractor system The attractor >> 1 has been added. Run had 9 steps and the X is 1 The attractor >> 13 has been added. Run had 28 steps and the X is 3 The attractor >> 11 has been added. Run had 4 steps and the X is 11 Report for the Y of 11 -------- The value of Y is now 13 The attractor >> 1 has been added. Run had 6 steps and the X is 1 The attractor >> 13 has been added. Run had 4 steps and the X is 13 The attractor >> 131 has been added. Run had 43 steps and the X is 19 The attractor >> 211 has been added. Run had 26 steps and the X is 99 The attractor >> 259 has been added. Run had 13 steps and the X is 123 The attractor >> 227 has been added. Run had 16 steps and the X is 147 The attractor >> 287 has been added. Run had 21 steps and the X is 159 The attractor >> 251 has been added. Run had 16 steps and the X is 163 The attractor >> 283 has been added. Run had 14 steps and the X is 283 The attractor >> 319 has been added. Run had 14 steps and the X is 319 Report for the Y of 13 -------- The value of Y is now 15 The attractor >> 57 has been added. Run had 20 steps and the X is 1 The attractor >> 3 has been added. Run had 5 steps and the X is 3 The attractor >> 15 has been added. Run had 6 steps and the X is 5 The attractor >> 69 has been added. Run had 11 steps and the X is 41 The attractor >> 561 has been added. Run had 49 steps and the X is 241 The attractor >> 1041 has been added. Run had 46 steps and the X is 337 Report for the Y of 15 -------- Simply change the Addend to the current Y value and run that with the distinguished X value to verify the data.
  3. Thanks Mark for that addition. The conflict between Edison and Tesla is classic. Guys I will be digging out my attractor finder program to generate a new list of all the cycles of the [A(X)+Y,X/2] since I cannot find the old list. I remember that there is a single cycle for all odd Y addends that are Powers of three such as the famous Collatz where Y=3^0 I wrote that program 14 years ago. My my how time goes by when one works on this challenge. I can generate all the cycles into the millions of odd Ys' with the Workstation I now have so if anyone wants are really long list of all the cycles let me know otherwise I will cut it off at about the first 10,000 ys'. I will post it on my site and if I can figure out how to work the download add-on I can make it a downloadable file otherwise there will be as many as the editor will hold. @Greg No specific question at this time I simply didn't want you to feel left out of the group if you are not actively working on it. "Collatz friends" are important to me. Oh and what I was thinking of doing is only applicable to Ys that are powers of three so that is not a global solution although we can divide the input into more than one set. If you are interested in a quick proof of more than one cycle simply work with 3x+5 with input set {1,5} you will see (8 4 2 1) and ( 20 10 5 ) Also Cycle notation is different from set notation as we do not use commas in cycle notation.
  4. It occurred to me that I should write a paper on this subject. I ask of you, those of you that have read what I have posted in this thread, to let me know if any one else has written these things down. I do not wish to repeat prior Art. Also Greg, Are you done discussing the Collatz as well? For the rest of your life or is it that what you wanted to do do didn't pan out when you talked to that tutor? I'm thinking of making the question of "Did Lothor Collatz" get it wrong. What do you think?
  5. Not Ready? Well, not really because we humans are basically the same humans genetically as those that lived 2000 years ago so we humans can understand the answer. What happens is that we resist change. Science is rife with examples of good minds balking at change like Tesla slamming Albert Einstein and Edison slamming Tesla. Just look at what crap Cantor was subjected to and the most famous in my mind was http://en.wikipedia.org/wiki/Giordano_Bruno . I have experienced "The Slam" first hand when I introduced Dynamic Unary to the world, before the paper was on arXive and even before the subject was relieved. A well respected Data Compression person wrote a reply to my announcement that I would be sharing something with everyone soon that flat out stated that my paper would never be read by anyone and that I should accept that as the way it is. Looking back now I wish I had replied that his "Freudian slip" was showing and I could see his cute little agenda but I was polite and wrote that I would be thankful that it was on arXiv if nothing else. Dynamic Unary generates dynamic integers by the way so they are bonafide mathematical objects just like ordinary numbers are,. So I disagree with Paul Erdős on the grounds that we must first believe in the change before we can change. I restate that the Collatz is just one of an infinite set of systems (dynamic equations) which are differentiated by the addend in the function 3X+Y where X is the current value of state and Y is the odd addend. The proof of this is in the parity language structure where if the 3X+Y is represented with one parity and the X/2 is represented by the opposite parity. Through iteration then a relationship to the Fibonacci series is observed because no consecutive 3X+Y functions occur. Thus although the sequences of values are different for the same X but different Ys' the common parity language structure is proof that all odd Y belong to the same set or best said 3X+1 belongs to that set of all odd Y So, we must change our perspective here and that therein is what I feel Paul is really saying and not that we are too dumb to figure it out and somehow the humans of the future are somehow smart enough. Changing talking points here, I have written many C language programs using these dynamic equations so they are very useful and of mathematical significance. Therefore "We are indeed Ready for it." For anyone interested in Cryptography I point out that you can encode and decode data using this Parity language. So there is a Cryptography application right there. Been there done that.... Again "We are Ready for it." We just need to think in terms of iterations(dynamic) and not in just the linear (A+B=C) mathematics. The Linear I think is the approach most have taken in trying to produce a solution to the Conjecture. . The answer already exists so it's on us to change in order to see it So.. Keep on Banging those Rocks Together my friends. http://en.wikiquote.org/wiki/The_Hitchhiker%27s_Guide_to_the_Galaxy Ernst
  6. I see... After all the time I have worked with this I have little doubt. It's the simplest and it's all true. Okay, if you will refrain from deleting this post; Anyone interested can contact me at [email protected]
  7. I'm giving thought to how to formulate the transit of value and I welcome any help with that maths. The obviousness of the cycle of the Y of 3X+Y hasn't been included in what I have read from others attempting proof. So, I think this is the right direction for a proper proof. The "Goes to One" may be a misnomer. Should say has a cycle on One or a cycle on the Y of 3X+Y That divides the elements into two sets. Those that are part of that cycle and those that are not. Of those two sets there is only one common element to both 3x+y and x/2 and that is the first even after the 3x+y So, cycle of Y, all others are transit values that decline in value over distance. One element in common between the two functions in the algorithm of if odd or if even. That's what I got out of the past 18 years of working with this.
  8. I think it's simpler then we have assumed. Collatz may have had it wrong. Let's go with the http://en.wikipedia.org/wiki/Occam%27s_razor approach. Here is where I can stand some help and clarity. How can we show the equation-proof of relative value descending towards zero? Given some integer we apply the [3x+1,x/2] correct so it "grows" in value if odd and it "shrinks" in value if even. Now what is the mathematics that explains the decent towards zero? I mean it's obvious that the value of X does reduce over a distance right? So what maths do we write to show this relationship between the two functions of { 3X+1, X/2 } ??? You see if we can show it always reduces over distance then to explain why it cycles on the 3X+odd is obvious too and so the function simply '"steps through" descending towards zero in value over distance until it "hits" one of the cycle values. Remember Collatz was studying the Cycle of 1/3 when he made this famous conjecture. So what maths works here? How can we define the overall reduction in value over a distance for [3X+1,X/2] ??? I do think this is the correct direction of "proof" and that the "proving the path to One" is a "Red Herring." Anyone agree or not? Reasons?? Please share. This could be much simpler then we have thought. Thus it is a reduction in value over distance separate from the cycle generated by the odd addend. Ernst
  9. That's how it has gone for the past 20 years. I really think trying to prove the number to next to one is not the way. Y'all probably have better maths skills. Can we show that given any number not in the cycle that the value descends towards zero over the distance? Once we can show the X/2 wins over the 3X+1 and we show that there is a cycle on the value One we can show that once the value of our x becomes one of the cycle values that it gets stuck in cycle and not that it "Goes to One." Proof of this is that for any 3X+Y where Y is odd there is a cycle of the Y We must prove for all Odd Y not just Y == 1 I understand conformity is a powerful influence.. How can everyone be wrong for so long right? Well no one has a solution who has conformed now do they? Take a walk on the wild side here. What maths shows the over all value through iterations in [3X+Y,X/2] <-- my notation for cycle here I mean 3X+Y and the value goes up then X/2 and the value goes down. It seems obvious to me X/2 wins out over the distance. I just need some help with the math on that. The cycle is obvious.
  10. Well, y'alls maths looked to be similar to work I have seen before yet I wonder if you two accomplished any advances? Anyone find the suggestion I made worth a second consideration?
  11. Well, I had one email about the possible solution to this so I'll just spill the beans here. I believe that we are asking the wrong question when it comes to Collatz Conjecture. By that I mean we needn't prove that integer X ends on integer y but let me explain and I welcome your comments. We try to prove that A goes to B and with little success however what is really happening is that some numbers create a Cycle and the rest do not. I believe you all will find that Collatz in the form of [3X+Y,X/2] is just one of an infinite set of Y==ODD. So 3x+3, 3X+98466894651694615 and so on. What we see when we process any integer for any Y is that in the Cycle the Y is seen. So what we have is a Struggle between 3X+Y and X/2 until an integer that cycles is reached. I propose the following as the foundation of a Proof. 1: That the X/2 part wins over the 3X+Y part. That this process necessarily reduces all unsigned integers towards zero. 2: That a Cycle of integers occurs when the input to this dynamic system is the Y of the system. So it can be broken down to integers that cycle and the process of the struggle between two functions with one growing the value and the other reducing the value. Also noticed is that the even number generated by 3X+Y is the only element that belongs to both the 3X+Y part and the X/2 part. So, it is not to prove that all numbers go to one it is that the [Ax+y,x/2] A=3 reduces value towards zero over the long run and that when a value that is in the cycle of the Y is reached an endless cycle occurs. That is what I have come to believe since being introduced to Collatz Conjecture in 1992. Now how do we show that the value reduces towards zero? I need help with that. I think I can describe the cycle action but that is open to share too. I have written my first scientific paper which introduces something new so that is a proof of sorts but I have not written a proper proof so I need help with that too. Are we ready for a Solution to Collatz Conjecture?
  12. It is good to see that people have an interest still in this. I have an idea for a possible proof and I sure can share such a thing but I would like to work semi-privately with others. My email is [email protected] if you would like to consider an approach that I have not seen done before. Call it an exploratory group email conversation. I have enjoyed the Collatz stuff since 1993 and I often include the mechanics in experimental software design so I am not so new to it but will benefit greatly from maths smart friends when it comes to writing things down. Now to go back an reread the newer posts here. Again great to come here and be a part of such an interesting and honourable quest.
  13. I term Cycle in the Collatz and ilk as the part where the integers repeat. In the 3(x)+1 form we have a { 4 2 1 } cycle. in 3(x)+3 we have { 12 6 3 } Collatz conjectured all integers "go to one' I see it as a cycle of elements and not a "GoTo". So you have been looking at the Collatz for about a Year? LOL it hooks ya.. Remember there are systems for all + odd in 3(x)+Odd-Integer. So we are not limited to 3(x)+1, 3(x)+3 and so on.. At some point a cycle of values will be seen. We also can have systems of minus the odd value as in [3(x)-1,x/2] Perhaps we might need to restate : no matter what integer input a cycle of elements will occur. Also if we represent the odd action as a set bit and the divide by even action as 0 then the stream of bits emit from any integer processed to cycle is a parity language that is Fibonacci in structure.
  14. If I may, I love the Cycle. I have been attracted to all things that cycle. I spent many years on the Collatz Conjecture. I studied it. for Collatz it's in a class of [A(X),+/-Y,X/2] Where Y is odd and X is usually 3 for this new form [A(X+/-Y),X/2] where the A scales for A > 0 when A = 1 the cycle is { 2 1 } cycle notation doesn't use commas when A = 2 the cycle is { 4 2 1 } So the cycle structure is there. independent of the two forms. Cycle may well be a force in Nature. Elementary particles spin and so on. If you guys like you can check out http://arxiv.org/abs/1405.2846 Introduction to Dynamic Unary and see a lot of cycle that scale from 1 to infinity. If you have questions you can contact me at [email protected] the website is eberg.us I worked with [[A(x+1),x/2] yesterday and I feel it is as stable as Collatz. True it is not Collatz in it functioning but it works well in a 1 to 1 bit ratio for input number size and output number size when the actions odd = 1 and even = 0 are captured as a file I have experimented with Collatz to make data transforms and this form ( Berg? ) seems mathematically true as well.. I am still searching for Prior art on [A(x+/-Y),X/2] I mean I would love to say I saw it first but have I? In conclusion the study of these dynamic equations is the study of Cycle which may well be a force of Nature. Thanks for the ramble. Ernst
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