LHanawalt

What follows is virtually unthinkable. Some will call it gibberish--the work of a crank. It can only be imagined from outside of our current agreement about the nature of reality. Those who understand one or more of the following five claims may have a better chance at taking it in. [link removed]

You are right, of course. The next step is to ask for help from someone who can do all the math of dimensionless constants, within the framework of this model. Hiring an M.I.T. graduate student as a tutor might be a way to go. Another approach: see if I can connect with someone about this idea as a framework for an approach to solving the Riemann Hypothesis and accounting for the quantum energy levels of chaotic systems. I don't blame people at all for dismissing this, but I am serious about pursuing paths to validating or invalidating the "hanawalt conjecture". If it proves to be nonsense, I am perfectly willing to give it up and stop being a crackpot, a crank, a mindless troll, etc. Larry.

Bignose, I appreciate your response, thank you. My "project" reminds me of Niels Bohr--if you aren't shocked by quantum theory, you don't really understand it. I think that this shock is a function of the deep mystery of the complex plane itself, without which quantum theory is unthinkable. The complex plane's design is exponential/logarithmic (non-dual, you can't have one without the other). i ln(z) is the inverse of e^iz This link shows the second derivative of i ln(z): http://www.wolframalpha.com/input/?i=i+ln%27%27%28z%29 I think it can be said that i ln''(z) = - i/z^2 is the "imaginary" second derivative or "deceleration" of e^ix...the "real" second derivative is of course minus e^ix... The idea that I want partners in imagining is that -i/z^2 is the source of the inverse square relationship that is attributed to gravity. It actually isn't any more shocking than quantum theory. We have been so attached to Newton's gravitational force that we had to make up dark matter when the math no longer worked. Why not something as impossible to grok as quantum theory was? The real number line is actually defined mathematically by i ln''(z).... This is the only place in the complex plane where the real part is the real number line. The real number line represents the flat, steady-state mean between complex exponential "space" and the complex logarithmic "time". (See bottom about natural log) The only "evidence" for it is that it eliminates the need for dark matter and dark energy, missing mass and missing gravitons, accelerating expansion, inflation, etc. The math works. It's the physical interpretation that boggles the mind. As for the dark matter map, the article says, "Dark matter has never been directly detected, but its presence is felt through its gravitational pull on normal matter". It is a map on where dark matter "must" be to explain the inverse square geometry of things. I really appreciate your response -- even if you now tell me to take this elsewhere. http://betterexplained.com/articles/demystifying-the-natural-logarithm-ln/ The natural log is about time--the time needed to reach a certain level of growth.

Let me start in a different place--with Wigner's "unreasonable effectiveness of mathematics". Is it nonsense to explore the possibility that the nature/design of spacetime and the design of the complex plane might be one and the same? If that doesn't occur for you as an interesting question, I will cease and desist. Larry

In any system satisfying Euler's famous formula e^ix + 1 = 0, the function's rate of change is equal and opposite in sign to the instantaneous rate of change. The function's "deceleration" is a mirror image. It's a tangent to the unit circle that is pointed in the opposite direction from the function's movement. It seems to me that the matter/antimatter mirror image might be considered to have the e^ix + 1 mathematical relationship. Starting with this, I have a new model of light to offer. I will only do that if one or more people indicate some interest. The model eliminates the need for dark energy, dark matter, inflation, exponential expansion, and the idea of gravity as a force that is separate from the architecture of light. Wild, I know. Only for those who are suspicious of received "wisdom". Larry

I once had an experience of light as constituted by equal and opposite exponentials. The second derivative of the complex exponential function (-e^(ix)) and the second derivative of the complex logarithmic function (-i/z^2) seem to provide an analogy. i*ln''(z) = -i/z^2 (as the location of the observer, the model-maker, the measurer) provides the inverse square relationship that we attribute to gravity--"gravity" a function of perception, not force? (The Weber-Fechner Law and other evidence support the idea that all perception might be logarithmic.) It's crazy, I know--but it would eliminate the need for dark energy and dark matter. And a complex exponential "space" viewed from a complex logarithmic perspective ("time") would give us a flat, steady-state rather than an exponentially expanding universe. The flat, steady-state aspect is indicated mathematically by the fact that the real number line is the real part of minus i/z^2...the real number line representing a mean between exponential and logarithmic curves.http://www.wolframalpha.com/input/?i=i+ln%27%27%28z%29 (It would also be an anti-entropic universe. All a very hard sell. But since the current macro-model doesn't work, there may be some tolerance for crazy. At this point I just want to see if the model works mathematically.)

There is an unexamined assumption in mathematical physics about the location of the observer, the physicist--the mind that is constructing the model. Exponential expansion, for example, assumes a location for the observer that is measuring this phenomenon. The following offers a possible location for the observer in complex space. (Electromagnetic, quantum and relativistic phenomena require complex space.) Imagine that the key to the architecture of light is Euler's famous formula e^(ix) + 1 = 0 The real number line is a mean between the complex exponential function and the second derivative of the imaginary logarithm (the inverse of the complex exponential function). The second derivative of the imaginary logarithm = - i/x^2 -- the inverse square relationship that has been attributed to gravity. If you look at i*ln''(x) on WolframAlpha, you will see that the real part is the real number line. http://www.wolframalpha.com/input/?i=i+ln%27%27%28x%29 I am asking you to imagine that light is a non-dual phenomenon constituted by equal and opposite exponentials generating complex space, both physical and mathematical. What would the universe look like if our point of view were imaginary and logarithmic? Looking at a complex exponential curve ("space") from an imaginary/logarithmic viewpoint ("time"), we would see a flat, steady-state universe. I am suggesting that the geometry attributed to gravity may simply represent the mathematical relationship between observer and observed, measurer and measured. This is perfectly consistent with the standard model while eliminating the ideas of accelerating expansion, dark energy, dark matter and gravity as force. I have been thinking about this off and on for nearly four decades, so I am looking forward to feedback from people that are willing to engage with it. Larry