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9 NeutralAbout TakenItSeriously

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 Birthday 03/12/1964
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Silicon Valley

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Problem Solving, Poker, Physics, Engineering, Digital Security

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autodidact

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Physics

Biography
Learned SR, GR, & QM at age 7. Resolved myself to altruism over religion the age of 17. Solved EMI issues for Gigabit Ethernet which had blocked its rollout for two years.

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Retired
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I completely agree that patterns are important in number theory but, in this particular case, rather than looking for patterns indiscriminately and then trying to explain them after the fact, I had first deduced that the harmonic patterns must exist based on the periodicity of prime factors and the resulting patterns had confirmed those deductions. Two points: I discovered an interesting symmetry depending on whether a PFHM starts with 0 or starts with 1. Try the following excercise: Take any PFHM starting with 1 and highlight the prime numbers to reveal the harmonic patterns. You will note that a symmetry exists in the x axis with the exception that the first column on the left is a prime column while the second from the last column is a prime column. When we take the same matrix only start it with 0 instead of 1 the assymetry swps such that it is the second column from the left that is prime while the last column on the right is prime. The second point is that when using a PFHM, one needs not begin at the beginning every time such as with a number seive. That is one of the huge advantages of using a matrix. You can start with the first matrix, the second matrix or the millionth matrix e.g. for a 30x7 matrix we can calculate the primality for the ranges: 1210, 211420, or 209,999,791210,000,000 without needing to calculate the primality of all preceding matrices first! for instance here is the primality of the millionth matrix which I derrived directly without first derriving all 999,999 preceding matrices. Note that there may be errors involved since it did require creating a composite of 1,698 prime factor patterns. I’ve been meaning to look into patterns of semiprimes within a PFHM, though I haven’t had the time to look into it yet. I will post any new results regarding semiprimes if I discover any in the future, however, you should note that my first priority at the moment is to find a method for unbounded data compression. Thanks, I appreciate it. The key to understanding how to create a PFHM are the formulae that are needed to automatically derive the primality patterns within Excell for which there are too many details, in general, to discuss easily within this forum. I may post pics showing the formulae of certain key cells at a later time.

Just because it’s kind of cool to look at here is an expanded view of the animated 30x7 PFHM stack: Figure 2: An expanded view of the prime factor patterns. Above is actually only a partial view of a large array of prime factor patterns in Excel. It starts in the upper left with the harmonic patterns for primes 2, 3, 5, & 7. Each row actually contains 38 PFPs and the number of rows can extend indefinitely until Excel runs out of memory and crashes. Initially, I tried to include enough prime factors to define the primality up to the millionth matrix (numbers from 1 up to 210,000,000) which requires 1700 prime factor patterns for the primality to be fully defined. Oddly it was at the millionth matrix when Excel started crashing. The animation represents matrix levels from 10,000 to 10,033 for 33 frames. I chose 33 frames so that the fifth prime (11) would appear to be smooth when displayed in a repeating loop.

TakenItSeriously started following Real Test Of Genius, Adding Time to 2D PFHM, Why can’t we derive velocity directly from it’s doppler factor? and and 4 others

I thought you guys might find this interesting. Adding Time to a 2D Prime Factor Harmonic Matrix to demonstrate the “behavior” of standing vs moving prime factor “waves” Previously I had introduced the Prime Factor Harmonic Matrix which showed that prime factors behaved like waves or specifically 1 dimensional waves that either behave like moving waves or standing harmonic waves within a 2 dimensional matrix of natural numbers. A PFHM is simply any matrix of natural numbers that is dimensioned according to a primorial. Paul Ikeda's answer to What’s the significance of prime numbers in physics and nature? Finding large Primes using Standing Wave Harmonics When this is done, the pattern of prime factors that make up the primorial behave like standing waves while prime factors that are not part of the primorial would behave like moving waves. In order to better demonstrate this behavior, I added the dimension of time to a 2D 30x7 PFHM which is orthoganal to the plane. Another words I created an animated gif which shows a progression of matrices level by level. i.e. 210 = 2x3x5x7 1210 211420 421630 ... Figure 1: A series of 30x7 matrices of natural numbers such that their prime factors are distributed periodically throughout the matrix. The slot on the left represents the factors of prime number 5, the second shows the factors of 7, the third shows the factors of 11 and the fourth shows the factors of 13. Each frame of the animation shows a progression of levels in the matrix. Note that since 5 and 7 are both factors of the primorial 210, they never move or they behave like standing waves while all larger prime factor patterns each propagate at a different rate or a different “frequency over time”.

Finding large Primes using Standing Wave Harmonics
TakenItSeriously replied to TakenItSeriously's topic in Mathematics
Yes, that’s exactly right. A seive is one dimensional which is why they always need to be started from 0 and very innefficient in terms of storage space while the matrix can be two or three dimensional and the base can be a primorial of any size. The larger the base, the more composite number collumns are segregated out and the greater the probability that the remaining numbers are either prime or semiprime. There are a number of huge advantages over a number sieve. Thanks for the link. It does indeed appear to be based on the same principles though I never intended it to be used as a method for faster prime factorization. My aim, at least in part, was to find a method for a faster primality test for discovering large primes, especially Mersenne primes. I can see how they might succeed using quantum probability analysis to speed up the factorization process though. Prime factors are harmonic which was the basis of the PFHM after all. 
Why can’t we derive velocity directly from it’s doppler factor?
TakenItSeriously replied to TakenItSeriously's topic in Relativity
Yet Relativistic Redshift isn’t accounted for, for galaxies that are receding at speeds appraching the speed of light? That suggests that time dilation isn’t accounted for at those speeds either. Time dilation will cause luminosity to dim which could have easily been overlooked just as length contraction was overlooked for the cause of time deviation in the Twin Paradox. What may seem obvious in hindsite is not obvious in foresite. Please trust me on this. It has been the lifelong bane of my existance. 
Why can’t we derive velocity directly from it’s doppler factor?
TakenItSeriously replied to TakenItSeriously's topic in Relativity
Ah, I see. So your suggesting that if you use relativistic redshift then the numbers don’t agree with the Cosmological data is that correct? 
Why can’t we derive velocity directly from it’s doppler factor?
TakenItSeriously replied to TakenItSeriously's topic in Relativity
I’m not following the basis of your argument. Luminosity which is used to determine distance is essentially the same source and time that relativic redshift came from. So how could light be an invalid source of information in the case of redshift, but be a valid source for distance? In fact light is essentially the only source of information used in this case. It seems as though you are just trying to make the claim that Special Relativity is wrong. 
Why can’t we derive velocity directly from it’s doppler factor?
TakenItSeriously posted a topic in Relativity
Since we can measure the doppler shift, relativistic or otherwise, of a receding galaxy why can’t we use the equation for calculating the Relativistic Doppler Factor (fs/fo) which I will call r for ratio, to derive the galaxies recessional velocity? fs/fo = √[(1+β)/(1β)] r = fs/fo r = √[(1+β)/(1β)] (1+β)/(1β) = r² β+1 = r²(1β) β = r²r²β1 r²β+β = r²1 β(r²+1) = r²1 β = (r²1)/(r²+1) where: fo is the frequency that an observer sees fs is the source frequency that we can find from its spectrographic footprint β = v/c r = fs/fo If the galaxy is in redshift then r > 1 ⇒ 0 < β < 1 If the galaxy is in blueshift then r < 1 ⇒ 0 > β > 1 The negative velocity only means that the objects are moving closer together instead of further apart so we can see that the absolute speed should never exceed c according to Special Relativity. 
A Logical Explaination for the mysterious results of Buffon's Needle
TakenItSeriously replied to TakenItSeriously's topic in Mathematics
Edit to add: Regarding the larger space, I might define a large square for populating the random positions of the universe in a cartesian coordinate system and then I would define a large circle within the boundaries of the square and call it a horizon. Then I would assign random vectors that pass only through those points within the larger circle so that the points in the corners wouldn't create a bias and the horrizon was always equidistant from the circle. This would then preclude the idea of using multiple circles of course. 
A Logical Explaination for the mysterious results of Buffon's Needle
TakenItSeriously replied to TakenItSeriously's topic in Mathematics
The Pics didn’t get into the final draft so here they are now: I’m not sure I would call the Bertrand Paradox all that mysterious so much as confusing. I wouldn’t accept any of the three premises given as valid. Premises should be axiomatic and self evident as far as being valid and the premises given are definitely not axiomatic. My guess is that they are a problem with boundary conditions combined with conflicting properties that cannot be both defined in a non biasing way for both properties at once. It may not be possible to provide a proper definition for random chords to the circle except perhaps in an infinitely large universe which, of course is not practical. For a decent approximation, I might try picking random positions within a much larger space than that described by the circle and then assigned to them random vectors for a random distribution of lines that may or may not pass through an arbitrarily defined circle, but I would use a space that was much much larger than the given circle such that vectors that happened to intersect the circle from a long distance away would make an insignificant contribution. I might also position the circles in a random manor perhaps even using multiple circles with triangles in them. It’s just my first guess at a reasonable approximation of random that would represent an unbiased distribition or a homogenious isotropic environment FWIW. I’m not sure how well it would do in terms of convergence to a unique result. 
A Logical Explaination for the mysterious results of Buffon's Needle
TakenItSeriously posted a topic in Mathematics
When I first came accross the mystery of Buffon’s needle, it was presented as a mystery because, apparently, nobody could understand why it would result in the value of pi or what the problem of scattered needles had to do with a circle. You might actually do the experiment and find that the results really did statistically converge to pi as the sample size grew larger or you might find the mathematical solution would indeed result in a probability that is exactly equal to pi. You might notice that there is a cosine of the angle between the needle and the lines on the table involved. You might even be able to construct a circle to describe how the cosine function relates to a circle using trigonometry, but even then you still probably wouldn’t truly have a clear and direct physical understanding of why the problem of randomly scattered needles should be related to circles. Here, I don’t present the mathematical solution which you can look up online from a number of sources. Instead I present a simple and logical model that explains the problem in the proper physical context which in turn will make it clear why circles are related to randomly distributed needles. Once again, Once you understand the solution it will seem simple to you as all logical solutions that are properly explained will seem relatively simple compared to the math. Perhaps it will even seem like it should be obvious once you understand it and you may not understand why you didnt think of it before but unless you could physically explain it in foresite before hearing this solution, then it clearly wasn’t really as obvious in foresite as it may seem in hindsite. I present this solution to you not just to show off that I have a gift for solving logic problems, but to provide yet another example that shows why logic really is just as important as math and that logic and math are not the same thing. Neither is logic just an alternative method to mathematics for solving problems that can be used as a substitute for math. It actually performs a completely different function from the math as I’ve said many times before: Logic clarifies our understanding of the problem while math quantifies the numerical results of the properties involved that can then be compared to experimental results. In fact math and logic are actually complementary opposites. Another words we cannot truly understand a problem without a logical model that can explain it and we cannot truly know that our understanding is correct without validating the mathematical results with experimental test. Problem: Figure 1: Buffon’s needle is a probabilistic method that can provide a good estimate of π based on random events. Assume that you have a needle that has a length of l and a surface that has parallel lines on it that are all equally spaced at 2l distance apart. If you toss a needle in a random manor on that surface such that it can land in any arbitrary position and orientation, then the probability that the needle lands inbetween the lines divided by the number of times that the needle will intersect with a line will be equal to pi (π). Another words your results will approximate 3.14... etc. with a sufficient sample size and the larger your sample size the better your approximation of π should be. The mystery of this method is why does it approximate π which we know is a constant that must be somehow related to a circle when there seems to be no circles involved with this method of randomly scattering needles. Logical Explaination: There is actually a simple logical explaination for this mystery and to understand it more easily I will provide a probabilistically equivalent scenario to illustrate why. Instead of using needles we can use clear plastic discs that have the needle embedded in the disc such that they perfectly bisect the circumference of the discs. After all it will still represent a random position and orientation just as the needles would. In fact they would probably be more random than the needles themselves since needles are not perfectly symetrical and they may be tossed in such a way that may be biased while the disc surrounding the needle would ensure a more random or unbiased result. Given in this new context, it should now be clear that the source of pi is linked to the circular shape of the disc. Put another way, think of the position of the disks and the orientation of the needles as independant properties. It is the probability distribution of the needle’s orientation that has an even disc like distribution about their center of gravity. By taking all the angles accross the entire sample space then the orientations of all the needles would stack up to be a random sample of all angles between 0 and 2π or between 0 and π if the needle is symmetrical. So you can see that on average, the orientations of all the needles should combine to be distributed in the shape of a disk. If by some extreme long shot, they did not create a reasonable disc like distribution, then you probably would not get a reasonable approximation of pi as your result. 
Betty, Carol, Dan Marketing

Two multiple choice questions
TakenItSeriously replied to bradley55's topic in Brain Teasers and Puzzles
B & C edit to add: I find that these types of problems are often flawed with more then one valid answer. 
A third person can deduce it must be July 16 using all three clues.

Real Test Of Genius
TakenItSeriously replied to Spiri.Of.Genius's topic in Brain Teasers and Puzzles
If my cross was red then it would be trivial for either Wombat or Breeze to know that their cross must be green. Since neither could answer, then my cross must be green.