From: Osher Doctorow osher(a)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
