On Wednesday, February 13, 2013 11:51:32 PM UTC-8, sadovnik socratus wrote: > Euler's Equation and the Reality of Nature. > > =. > > Mr. Dexter Sinister wrote: > > ? I understand Euler's Identity, > > and I know what it means, and I know how to prove it, > > there's nothing particularly mystical about it, > > it just demonstrates that exponential, trigonometric, > > and complex functions are related. > > Given what we know of mathematics it shouldn't surprise > > anyone that its various bits are connected. > > It would be much more surprising if they weren't, that would > > almost certainly mean something was badly wrong somewhere.? > > > > Mr. Gary wrote: > > Mathematics is NOT science. > > Science is knowledge of the REAL world. > > Mathematics is an invention of the mind. > > Many aspects of mathematics have found application > > in the real world, but there is no guarantee. > > Any correlation must meet the ultimate test: > > does it explain something about the real world? > > As an electrical engineer I used the generalized > > Euler's equation all the time in circuit analysis: > > > > exp(j*theta) = cos(theta) + j*sin(theta). > > > > So it works at that particular level in electricity. > > Does it work at other levels, too? > > Logic cannot prove it. > > It must be determined by experiment, not by philosophizing. > > ====.. > > Thinking about theirs posts I wrote brief article: > > Euler's Equation and Reality. > > =. > > a) > > Euler's Equation as a mathematical reality. > > Euler's identity is "the gold standard for mathematical beauty'. > > Euler's identity is "the most famous formula in all mathematics". > > ? . . . this equation is the mathematical analogue of Leonardo > > da Vinci?s Mona Lisa painting or Michelangelo?s statue of David? > > ?It is God?s equation.?, ? It is a mathematical icon.? > > . . . . etc. > > b) > > Euler's Equation as a physical reality. > > "it is absolutely paradoxical; we cannot understand it, > > and we don't know what it means, . . . . .? > > ? Euler's Equation reaches down into the very depths of existence? > > ? Is Euler's Equation about fundamental matters?? > > ?It would be nice to understand Euler's Identity as a physical process > > using physics.? > > ? Is it possible to unite Euler's Identity with physics, quantum > > physics ?? > > ==. > > My aim is to understand the reality of nature. > > Can Euler's equation explain me something about reality? > > To give the answer to this question I need to bind > > Euler's equation with an object - particle. > > Can it be math- point or string- particle or triangle-particle? > > No, Euler's formula has quantity (pi) which says me that > > the particle must be only a circle . > > Now I want to understand the behavior of circle - particle and > > therefore I need to use spatial relativity and quantum theories. > > These two theories say me that the reason of circle ? particle?s > > movement is its own inner impulse (h) or (h*=h/2pi). > > a) > > Using its own inner impulse (h) circle - particle moves > > ( as a wheel) in a straight line with constant speed c = 1. > > We call such particle - ?photon?. > > From Earth ? gravity point of view this speed is maximally. > > From Vacuum point of view this speed is minimally. > > In this movement quantum of light behave as a corpuscular (no charge). > > b) > > Using its own inner impulse / intrinsic angular momentum > > ( h* = h / 2pi ) circle - particle rotates around its axis. > > In such movement particle has charge, produce electric waves > > ( waves property of particle) and its speed ( frequency) is : c>1. > > We call such particle - ? electron? and its energy is: E=h*f. > > > > In this way I (as a peasant ) can understand the reality of nature. > > ==. > > I reread my post. > > My God, that is a naïve peasant's explanation. > > It is absolutely not scientific, not professor's explanation. > > Would a learned man adopt such simple and naive explanation? > > Hmm, . . . problem. > > In any way, even Mr. Dexter Sinister and Mr. Gary > > wouldn't agree with me, I want to say them > > ' Thank you for emails and cooperation? > > =. > > Best wishes. > > Israel Sadovnik Socratus. > > =. > > P.S. > > ' They would play a greater and greater role in mathematics ? > > and then, with the advent of quantum mechanics in the twentieth > > century, in physics and engineering and any field that deals with > > cyclical phenomena such as waves that can be represented by > > complex numbers. For a complex number allows you to represent > > two processes such as phase and wavelenght simultaneously ? > > and a complex exponential allows you to map a straight line > > onto a circle in a complex plane.' > > > > / Book: The great equations. Chapter four. > > The gold standard for mathematical beauty. > > Euler?s equation. Page 104. / > > > > # > > Euler's e-iPi+1=0 is an amazing equation, not in-and-of itself, > > but because it sharply points to our utter ignorance of the > > simplest mathematical and scientific fundamentals. > > The equation means that in flat Euclidean space, e and Pi happen > > to have their particular values to satisfy any equation that relates > > their mathematical constructs. In curved space, e and Pi vary. > > / Rasulkhozha S. Sharafiddinov . / > > ===============?