From: Osher Doctorow osher@ix.netcom.com, Mon. June 17, 2002 1:54PM Current physics fads explain the universe and its parts (toward a *Theory of Everything* or TOE) by discrete entities (quanta) and *fields* on the microscopic level and by bending of space on the macroscopic level, with the general opinion (for what it is worth) being that the quantum ultimately will explain everything. String/brane/duality/loop theories add string tension (sort of like how stiff a violin string is) to eliminate paradoxes, of which the standard quantum field theories are full, and to try to relate the microscopic and macroscopic in *quantum gravity*, which so far has not been achieved. Is there something wrong with this picture? I would say yes, but one must look at it quite a bit to come to that conclusion. One way to determine this is to ask what mathematical tools the physicists are using. It turns out that they are almost entirely using algebraic topology and algebraic geometry. Since Creative Genius tends to be most profound when it is across verbal and quantitative fields (like Leonardo Da Vinci), and since Creative Genius tends to be heavily interdisciplinary, the almost exclusive use of two mathematical techniques (which, by the way, provide extremely few intuitive explanatory concepts and are super-abstract) arouses some warning signals. There's actually a good candidate for an alternative TOE right amidst fractal- and chaos-related disciplines provided that we also use many interdisciplinary methods. It turns out that the most characteristic feature of the universe is its expansion (or theoretically expansion-contraction), which is growth, which is quite similar to the growth feature of life. But we know from botany that life solves the *packing with growth* problem of mathematics by putting seeds and buds and so on at an angle equal to the Golden Ratio (also known as the Golden Mean - not the ethical concept). The Golden Ratio in turn is related to the Harmonic and Geometric and Arithmetic Means, especially the Harmonic Mean. Is there an equation which we can PROVE MATHEMATICALLY that might give us some handle on a TOE? Yes. Here it is: 1) (x - y)/(xy) = (1/y) - (1/x) for real x, y, with y < = x. Recall that the harmonic mean h of x and y is given by: 2) h = 2/[(1/x) + (1/y)] I have introduced the *real conjugate* of u + v for u < = v, namely u - v (any real u, v), and I denote it by an asterisk: 3) (u + v)* = u - v for u < = v Now, the universe is divided into three types of events/process (events for short): Rare (R), Fairly Frequent (F), and Very Frequent (V). R corresponds to Lukaciewicz (L) fuzzy multivalued logical implication (x-->y)L = 1 + y - x, V to Godel fuzzy multivalued logical implication (x-->y)G = y, where L and G here are supposed to be subscripts on (x-->y). L, in turn, corresponds to Logic-Based-Probability-Statistics (LBP), G to Independent Probability-Statistics (IPS), and F to Bayesian Conditional Probability-Statistics (BCP). The correspondence continues across proximity-geometry-topology. So if we can rewrite (1) in terms of L and G and either the harmonic mean or the Golden Ratio, we will have related quite a few interdisciplinary fields. Here is the rewritten equivalent version: 4) [1 - (x-->y)L]/[(x-->y)G (y-->x)G] = -2HAR*(x, y) where HAR(x, y) = 1/h. Noting that the left side of (4) is the ratio of *extreme* events in the sense that L and G are rare vs very frequent events, while the third type of fuzzy multivalued logic Product-Goguen (PG) is *mean* or *intermediate* (fairly frequent events), we recall that Euclid defined the Golden Ratio as the solution of the extreme-mean ratio of line segment lengths: divide a line segment or string into two parts, one longer and one shorter, and the original segment is then the longest, the shorter cut segment is the shortest, and the other segment is the *mean* segment. The fraction or ratio of the shorter cut length divided by the longer cut length is now set equal to the ratio of the longer cut length to the uncut length. This yields an equation whose solution is the Golden Ratio. The similarity of extreme and mean lemgths and extreme and mean frequency events is remarkable. Osher Doctorow