Natural Science Forum / Physics / General Physics / July 2008

From Osher Doctorow

A few years ago, Sir Michael Atiyah of the U.K., renowned discoverer
of K-theory and much else, wrote in the Bulletin of the American
Mathematical Society (AMS) more or less that one of the main problems
for the future in mathematics/physics in memory.

The simplest memory scenario is two-step-back memory because one-step-
back memory is known as "memoryless" Markov Chain type memory or its
relatives, which roughly speaking says that the computer or automaton
or observer or whatever just remembers one time step back and not
further back.   That type of memory, by the way, is generated by
Conditional Probability, the main rival of Probable Causation/
Influence (PI), because Conditional Probability "fixes" or "holds
constant" the previous step when calculating the next one.

PI, on the other hand, doesn't hold anything fixed or constant, and so
deals with arbitrarily n-step backward or continuous past memory, n =
0, 1, 2, 3, ....

The simplest number of steps of 2 or more steps backward memory is 2-
step Memory, of which again the simplest type is the Fibonacci Numbers
or Fibonacci Sequence generated by sqrt(5), and the ratio of
successive Fibonacci Numbers approaches the Golden Ratio/Golden Mean
as n approaches infinity, where the latter again is a function of
sqrt(5), this time (1 + sqrt(5))/2.

If we regard Quantum Gravity as completing Unification and TOE, which
is rather plausible, then to say that 2-step Memory characterizes
Quantum Gravity is to say that the Universe fundamentally has the
simplest type of non-Memoryless Memory.   This is quite plausible,
both intuitively and theoretically.

The indications, however, appears to be rather surprising.  If Gravity
is really a "step beyond" Non-Memory or Memoryless scenarios, then
Gravity may be what characterizes Biology, as Erwin Schrodinger seems
to have anticipated long ago.

Osher Doctorow

PI