Science Forums  # Don Blazys

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## Everything posted by Don Blazys

1. That's very strange indeed. I too noticed that numbers very close to $\sqrt{3}$ do seem to occur more frequently than expected in equations involving the fine structure constant. Don
2. Quoting "turtle": Of course that is what I mean! Let's be perfectly clear about this. Here is the polygonal number counting function: $\varpi(x)\approx\left(\left(\sqrt{\left(\left(1-\frac{1}{\left(\alpha*\pi*e+e\right)}\right)*x\right)}-\frac{1}{4}\right)^{2}-\frac{1}{16}\right)*\left(1-\frac{\alpha}{\left(6*\pi^{5}-\pi^{2}\right)}\right)$ where: $\alpha=\left(\left(A^{-1}*\pi*e+e\right)*\left(\pi^{e}+e^{\left(\frac{-\pi}{2}\right)}\right)-\frac{\left(\left(\pi^e+e^{\frac{-\pi}{2}}+4+\frac{5}{16}\right)*\left(\ln\left(x\right)\right)^{-1}+1\right)}{\left(6*\pi^{5 3. To: Jess (Pascal), I checked out Valery Tsimmerman's site. Very impressive! Please give him my regards. Better yet, invite him to become a Hypographer and join us here on this thread! You see, I finally got a chance to do a little research on periodic tables, magic numbers, shell theories, the theoretical "island of stability", etc. and what I found is that both the fine structure constant and the counting function for polygonal numbers of order > 2 do indeed seem to tie into those things. For instance, Quoting Valery Tsimmerman: Well, our polygonal number counting function s 4. To:Lars(LBg), Running the counting function beyond [math]x=10^{15}$ we find that its upper and lower bounds are as follows: For $x<10^{19.0324}$, the upper bound is $\varpi(10^{n})=.640362739400577657*10^{n}$ which is in exellent agreement with your findings. (Actually, the more fitting word here would be remarkable, because that upper bound occurs slightly after $x=10^{19}$ which is ten thousand times beyond where we are now!) For $x>10^{19.0324}$, the lower bound is $\varpi(10^{n})=.64036273685156*10^{n}$ D
5. Quoting Jess: It may be that those behaviors only appear anomolous because the entire system involves, at its core, a sequence of numbers that is erratic and essentially unpredictable. A while back, you mentioned string theory. Google searching phrases such as "polygonal numbers in string theory" or "string theory polygons" shows that polygonal numbers are not only at the very core of string theory, but ubiquitous throughout it, so it should not be all that surprising that the fine structure constant should emerge naturally when we try to develop an honest counting function for polygonal n
6. Quoting LBg: Looks really interesting. Seems to match my results quite nicely. Please stand by. Don.
7. Quoting Jess: Congratulations! If those mappings do indeed work without exeption, then what you have discovered is a pattern which may very well be the consequence of some underlying principle which describes the entire system. In and of itself, that pattern or "law" is as important as it allows us to make further predictions. At some point, you should compile all your findings in one location, such as a website. After all, it's a lot easier to put together a jig-saw puzzle if all the pieces are on the table rather than scattered about in different rooms!
8. Hi Lars, I'm sure that when our fictional MOTHER said that to her equally fictional DAUGHTER, she was talking about my website. :D But seriously Lars, words cannot express the gratitude that I feel. Thank you. Don.
9. To: Jess Tauber (Pascal), Quoting Jess: Slugfests are a waste of time. Boring too! Hopefully, we can make some actual progress in answering some really tough and interesting questions. Quoting Jess: The fine structure constant gets larger as the energy scale increases. At zero energy, the estimates range from: $\alpha^{-1}=137.036$ to: $\alpha^{-1}=137.03604(11)$ At the lowest energy scale of the electron mass, it is $\alpha^{-1}=137.035999084(51)$ At the high energy scale of the W boson, it is $\alpha^{-1}=128$ and at unification energ
10. Quoting "turtle": Fiction writers write fiction, but in reality, I am indeed a legend in my own mind! Don.
11. Hi Lars (LBg), Somehow, an error occured when you "copied and pasted" the equation for $\alpha$. Please change that "201" to a "2". Anyway, thanks for making my point with such outstanding eloquence and humour. I can easily imagine that hypothetical dialogue between MOTHER and DAUGHTER continuing as follows: DAUGHTER (surprised) Wow mommy, those equations sure do look pretty. Heck, I would even go so far as to say that they appear downright elegant! However, I'm afraid that I can't quite understand them because I'm still just a little kid. Look, all I want to know is exact
12. Quoting Turtle: I disagree. Polygonal numbers have been studied since before the days of the ancient Greeks, yet, polygonal numbers of order greater than 2 or "regular figurative numbers" as they are otherwise known, have only been counted up to $x=10^{15}$. That's only one billionth of the value of $x$ to which prime numbers have been counted, so clearly, our mathematical literature is desperately in need of higher tables of $\varpi(x)$, (the number of regular figurative numbers under some number $x$). That's utterly shameful, because even y
13. Quoting 7DSUSYstrings: Having a value of the FSC that is "close enough on a local level" is one thing, having a bonifide mathematical function that requires the FSC is quite another. Functions can be modified, incorporated with and applied to other functions (such as the Lorentz functions) which describe other aspects of reality. In other words, functions allow us to explore. Of course, I agree with you that any prospect of accurately determining the "big picture" does indeed seem bleak when we take into account things like dark matter and dark energy. Experimental data on this
14. To: Jess, Do you have a website? Don.
15. Quoting "Pincho Paxton", In order to determine the value of the fine structure constant, Professor Gabrielse measured the electron magnetic moment, not the electron mass as you seem to think. Moreover, Gabrielse's ingeneous experiments are now universally regarded as the most accurate verification of any prediction in the entire history of physics! Now, when the results of physical experiments become that accurate, then it is time for mathematicians to "rise to the occasion" and develop constructs which not only describe those results, but allow new results to be predicted as well.
16. In order to demonstrate the uncanny accuracy of my equations, let's extend them several decimal places beyond $\alpha^{-1}= 137.035999084(51)$, which is by far the most precise experimental value of the fine structure constant ever determined. The results are as follows: $\alpha_b^{-1}=137.03599913476=(A^{-1}*\pi*e+e)*(\pi^{e}+e^{(\frac{-\pi}{2})})-\frac{1}{((M_n/M_e)*e^{2}-2*e^{\frac{5}{2}})}$ $\alpha_s^{-1}=137.03599908378=(A^{-1}*\pi*e+e)*(\pi^{e}+e^{(\frac{-\pi}{2})})-\frac{1}{(6*\pi^{5}*e^{2}-2*e^{2})}$ $\alpha_L^{-1}=137.03599903278=(A^{-1} 17. As we have seen, each and every version of my counting function remains extraordinarily accurate to at least [math]x=10^{15}$. However, I do believe that the following version: $\varpi(x)\approx\left(\left(\sqrt{\left(\left(1-\frac{1}{\left(\alpha*\pi*e+e\right)}\right)*x\right)}-\frac{1}{4}\right)^{2}-\frac{1}{16}\right)*\left(1-\frac{\alpha}{\left(6*\pi^{5}-\pi^{2}\right)}\right)$ where: $\alpha=\left(\left(A^{-1}*\pi*e+e\right)*\left(\pi^{e}+e^{\left(\frac{-\pi}{2}\right)}\right)-\frac{\left(\left(\pi^e+e^{\frac{-\pi}{2}}+4+\frac{5}{16}\right)*\left(\ln\le 18. Chris Langan in his theory of everything which can be found here: http://megafoundation.org/CTMU/Articles/Langan_CTMU_092902.pdf postulates a somewhat similar construct. Don. 19. Quoting mpc755: http://aether.lbl.gov/image_all.html Hmmm... so it appears that in a sense, the topological properties of the universe are identical to that of a condom! Well, now that we all know what the universe "really" looks like, let's all celebrate! Don. 20. For all we know, our region or sector, which we call "the observable universe" may be spinning or rotating merely as a consequence of gravity acting upon it from another, more distant region or sector which happens to be spinning or rotating in the opposite direction due to some kind of cosmic "instability", the cause of which has yet to be determined. This idea is rather abstract and hard to describe, but perhaps a somewhat decent analogy might be found in the mathematics of fluid dynamics. Then again, you know what they say... "a picture is worth a thousand words". Don. 21. Hi Laurie, Interestingly, there are now several theories floating about that the fine structure constant at infinite energy is [math]\frac{1}{4*\pi}$. Here's one of them: http://arxiv.org/pdf/hep-th/9904158.pdf You sort of lost me here... "c" (as in "the speed of light") is not a dimensionless constant. Don.
22. Quoting Laurie AG: You ain't just "whistling Dixie"! Personally, I think the "night doubling" question is fundamentally undecidable because there can be nothing "outside" the universe which can be used as a "measuring stick". I agree, and the two most important dimensionless constants are the fine structure constant $\alpha$ and the proton to electron mass ratio $\mu$. Now, by far the most accurate determination of the fine structure constant ever made was by Gerald Gabrielse, and the following derivations (from another thread) match his exactly, so I hope
23. Quoting pascal: I really don't know. Probably some yet to be discovered mechanism at the quantum level. Nature is extraordinarily efficient and seems to store and display information in ways that prevent it from being lost. For instance, we can deduce both $\phi$ and the Fibonacci sequence from a sunflower.
24. Quoting Turtle: So do I. :) Quoting Turtle: That's perfectly understandable. Ever since I proposed the problem of developing a counting function for "regular figurative numbers" or "polygonal numbers of order greater than 2" as they are otherwise known, I too have found it very hard to believe that the fine structure constant should in any way be involved. That said, as a mathematician, I must investigate all possible constructs, and as it turns out, the constructs that do involve the fine structure constant are infinitely more accurate than the constructs that don't. That's just a
25. Quoting CraigD, Yeah! If there is no challenge, then life quickly becomes very boring. This is true even when it comes to movies and other forms of entertainment. Imagine a James Bond flick in which .007 finally retires and the entire film is about him just relaxing by the pool and drinking vodka martinis "shaken, not stirred". :cocktail: Heck, we would all be fast asleep! It would be a complete and utter flop! No one would go see it! Don.
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