Replies

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  Roaring Lovely March 4, 2016 at 6:35pm

  Wings,
  The situation of an expanding gas apply when the gas is left alone to do so SPONTANEOUSLY. Likewise, I am not saying that the toruses never change speed. I am saying that AS LONG AS NO ENERGY INPUT, THE TORUS SPINS STEADILY. Here the growth is solely due to the entropic force which happens spontaneously, with no other forces as in gravity, electromagnetism etc. What I think I have shown here is that under such conditions, the plus toruses spinning steadily, the mere law of entropy gives rise to golden spirals.
  
  You can see why torus is a perfect candidate to relate entropy to spiral, its spinning and the fact that it has 2 radii. Holding the 'toroidal radius' constant, we explain entropy. Holding the 'poloidal radius' constant, we explain time dilation. Keeping both constant, we explain Planck's Constant!!! This torus has amazing explanatory power, mainstream physicists are yet to understand!
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    Feather Winger > Roaring Lovely March 5, 2016 at 3:22pm

    the amazing torus..
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  Roaring Lovely March 4, 2016 at 4:59pm

  ANGLE AND ENTROPY
  Actually, it is strait foward. As long as we stipulate that entropy is increasing steadily and that toruses are also spinning steadily, then S/K=A/a. Where 'a' here is the initial angle and K is the innitial entropy.
  
  EXPONENT:
  
  Let me sketch for you why given that dv/dE=v/KT, then v=ue^(E/KT)
  
  In the equation, y=e^x, when y changes by a tiny amound, dy, x changes by a tiny amount, dx. So we have:
  
  y+dy=e^(x+dx)
  
  or dy=e^(x+dx)-y
  
  or dy=e^(x+dx)-e^x (substitude y=e^x)
  
  or dy=(e^x)(e^dx)-e^x (applying the rules of indices in multiplication).
  
  or dy=ye^dx-y (again substituting y=e^x)
  
  dy=y(e^dx-1) (factorising y)
  
  so dy/dx=y(e^dx-1)/dx
  
  so if we define e such that (e^dx-1)/dx=1, or e^dx=dx+1,or e=(1+dx)^(1/dx)
  
  then dy/dx=y
  
  That is to say that as long as rate of change in y is proportional to y, we are sure that y is given by y=e^x, provided e=(1+dx)^(1/dx), which is indead true. That is the definition of the base of natural logarithm, e. It is an irrational number we get close to as we wish by making dx very small. Try it. Let dx say to be 0.000001. Then you get e to be something like 2.718. The more you increase the decimals for dx, the more correct you get the value of e (you get it correct to more decimal places).
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    Feather Winger > Roaring Lovely March 4, 2016 at 5:28pm

    the torus does seem to change speed frequently....thanks for all your patient explanations..
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  Roaring Lovely March 4, 2016 at 2:46pm

  Wings, good! I was waiting for someone to notice that my story is hanging so I may be sure that someone is following it and am not just talking to myself.:) Congracs for following the math. Its beautiful. When the container is a torus, here it goes:
  
  S=klogW.
  
  We have seen two important things,
  
  a)S=E/T, i.e entropy is just energy per given temperature.
  b)W=V/v, i.e the ratio of multiplicities is equal to the ratio of volumes (the volume is expanding due to entropy).
  
  The volume of a torus is given by:
  
  V=(4/3)p^2R^2r
  
  so if the torus had radus a befor expanding, We find that V/v is just r/a.
  
  Punching in to the Boltzmann's entropy, we have:
  
  S=Klog(r/a)
  
  Remember that the torus is spinning both toroidaly and poloidaly as a grows to r. Now this has come very close to the logarithmic spiral equation:
  
  A=blog(r/a)
  
  Relating the increas in angle, A, during growth of the spiral, to the increas in entropy. I will justify this more.
  
  Now, Wings, the only reason they call it 'axis of evil' is that it utterly destroy their beleifs about the universe. Otherwise there is nothing evil at all about the thing. It is very cool.:)
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  Roaring Lovely March 3, 2016 at 8:31am

  THE RELATIONSHIP BETWEEN THE SPIRAL AND THE TORUS
  
  You can understand Boltzmann's equation this way:
  
  a)If you compress a given volume of gas, its molecules begins to vibrate faster and faster. Hence its temperature increases. So temperature of a gas is corelated to preasure which in turn is corelated to volume. Preasure is given by:
  
  p=f/A, i.e force per given area.
  
  The work done, which equals the energy used is fx, where x is the distance moved in compresing the gas. Then Ax will be the change in volume due to the act of compressing. So if we rewrite preasure as p=fx/Ax, we can relate the change in energy and the change volume with preasure as p=dE/dv, or dE=pdv. The change in energy of a gas is proportion to both the change in volume of the container and the preasure (force per given area) the gas exerts on the walls of the container. Our aim is to investigate what happens if the container in question is a torus. But first, lets understand Boltzmann's entropy.
  
  Now the temperature of the gass is inversly proportional to its volume and directly proportional to its preasure. We say p=TK/v, T=temperature, K=constant (related to the famous Boltzmann's constant). So lets punch in to our formular, dE=pdv. We have (TK/v)dv=dE. If you knew elementary calculus, this should ring a bell!! We write dE/KT=dv/v, or dv/dE=v/KT. This a rate of change that obey logarithmic equation, when the change in a quantity (in this case the volume) is directly proportional to that quantity itself, then the quantity increase, or reduces exponentially. We simply write v=e^(E/KT)+constant or E/KT=logv-logc.(Take simple calculus to understand this). Entropy, S is just E/T.
  
  Doing the simple math will help you judge for yourself whethe entropy has anything to do with DISORDER. It has non!! That was Boltzmann's way of understanding it by comparing the logarithmic equation with an identical one in STATISTICS. He could have as well compared it with the golden spiral and understood entropy as growth!!
  
  A physicist gotta be carefull with math!
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    Feather Winger > Roaring Lovely March 4, 2016 at 2:03pm

    thanks...and what happens when the container is a torus...
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  Roaring Lovely March 3, 2016 at 6:29am

  Or rather better, the second law of thermodynamics is caused by particles spiraling out tracing the golden spiral. So yes, as Malcolm says, the spiral is corelated to how free energy flows.
  
  Try to understand entropy using the spiral, and not the vise versa. Then drop the steriotype that associats entropy with disorder. Entropy is about DIVERSITY and GROWTH, not DISORDER. The latter is just an interpratation that suits the atheistic mind our scientists tends to buy into.
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  Roaring Lovely March 3, 2016 at 6:22am

  The equation of the logarithmic spiral reads:
  
  r=ae^(bA)
  
  What this mean is that one way of drawing a accurate spiral is as follows: Consider two lines intersecting. Let one line, call it h, lie, horizontally and let the angle between them be A. Call the other line g. Then a distance of r along line g, that is related to A by r=ae^(bA), will touch a point along the spiral. Do so for all the values of A, i.e keep turning around in circles as you increase r. i.e spiral out wards. The values a and b are constants that determines how big the spiral is (or rather how quick it grows). The number 'e' is the base of natural logarithim and you gotta be able to see now what is 'natural' about this logarithim.:)
  
  But the curious part I like you to not is this: rewrite the equation in logarithm form as:
  
  A=(1/b)log(r/a)
  
  Compare with Boltzmann's equation for entropy:
  
  S=KlogW
  
  Then you gotta get a grip why this spiral is so dorminant in nature. It is because things growing obeys the second law of thermodynamics.
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  Roaring Lovely March 2, 2016 at 9:00pm

  The biggest logarithmic spiral known is now one formed not by stars but by galaxies!! Truely, the spiral is a blue print of nature. It is not at all far fetched to say that the universe itself is the spiral! What else? There is now a sturning evidence; 'axis of evil'. The most reasonable explanation is that the entire known univers spins about the axis!! This major spin produces the minor spirals. It has been observed that, to the amazement of astronomers, the galaxies in the north not only tend to lie along the same axis, but they tend to spin in one direction and the galaxies in the south spin at the other direction!!
  The bell is ringing very clearly: there are no accidents in this universe! The picture of the universe we tend to hear from science, that so apeal to atheists is simply not there. 'Corpenicus' would like stars being sprayed carelessly like dust. Such a universe can be seen as a huge chance in pointless colition. He would like such structures as spirals to be insignificant and purely accidental, while universe at large is just a heep of dust scatered aimlessly. Wrong!! All the way from atoms, leaving things, Stars, galaxies, galaxies of galaxies etc are so well arranged like it were, the works of unseen genius!