The power of chance |
| My
interest in natural science dates back to my early childhood. My
father, a school teacher (mathematics, industrial arts, physical
exercise) was always ready to answer the usual questions of little ones
in a satisfying way. Soon, I developed my own theories on the world
around me. When I switched from elementary to secondary school, I was
conviced that our physical world was an endless row of universes. I
imagined our solar system as an atom with the sun as nucleus and the
planets as electrons. Similarly, I was speculating about inhabitants on
the planets in our body and all objects around, living on the electrons
of the atoms constituting ordinary matter. |
| I
was careful enough to keep this theory to myself, as long as I had no
proof for it. Nevertheless, I was ready to propose a much easier way to
look for extra-terrestrial civilizations than to struggle with
distances of dozens and hundreds of lightyears and the rather limited
velocity of light. We just should keep an eye on our own microscopic
worlds and explore in more detail the surfaces of its electrons. The
final nail in the coffin of my secret Matroschka theory of the world
was convincingly provided by quantum theory. But every time when I
think about a 'theory of everything', this old concept of mine comes to
mind. |
| Also
another approach to deal with our reality has deep roots in my
curriculum. In the early eighties, during my thesis, evaluating the
results of experiments was still predominately some paper & pencil
work. My old lab notes are full of hand-made diagrams. When I was
confronted with the problem of fitting experimental data to a
non-linear function with 4 parameters, I turned to our high end
electronic instrument, an HP 35 pocket calculator. Based on intuition,
I wrote a program that allowed the iterative adaptation of the 4
parameters according to random numbers ('Monte Carlo simulation'). I
obtained plausible solutions after hours of run time. |
| Unfortunately,
it soon turned out that the results of each run differed from each
other considerably. It took me days and weeks of calculation time to
explore a landscape of plausible results, pointing to the existence of
an absolute minimum. At this stage of my endavor I looked for help at
our IT department, where I was introduced to the iterative curve
fitting methods as used by Gauss & Newton already at the beginning
of the 18th century. I was granted access to the local 'super-computer'
and introduced to the fabrication of punched cards ('Lochkarten') to
enter my data. |
| Happily
I retured to the lab with a stack of computer printouts and enjoyed the
now accessible 'true' values, including even the standard deviations
(from the diagonal elements of the matrix). I was able to teach our
famous pocket calculator the new technique. Basically, the procedure
solved 4 equations with 4 variables. Even secondary school knowledge
would have allowed me to do this, some hours of careful pencil &
paper work included (the calculator was done with it in a few seconds). |
| In the year 2020, the COVID-19 crisis rekindled my interest in fitting data to non-linear functions. I collected the pandemic-related death toll
from 28 nations (Wiki, WHO) and fitted the time course to an
exponential function with an increasing number of terms. I started with
the good old Gauss-Newton algorithm on my HP 28S; later, I switched to
the more powerful web site
originally conceptualized by John Pezzullo. When the emergency state
was over, I used the data as material to resurrect my old idea: fitting
parameters in a random way. |
| Some time courses resulted in multiple solutions of
almost identical fitting quality. I came to these results offline on an
old notebook (Microsoft Excel 2010), after having written the first
'macro' in my life. Fitting reached Gauss-Newton quality after run
times of 30-60 min. Most functions consisted of 4-6 terms each
requiring 3 parameters. This was quite some progress in comparison with
my first allempt of random fitting back in the eighties. This time, the
'Monte Carlo' approach added some specific quality to the matter,
something the Gauss-Newton method was unable to yield. |
| Extracting
facts on the basis of data and models is always an insecure procedure.
Data contain measurement error, and models are mostly chosen by
intuition. Allowing random variation during complex fitting procedures
adds a certain quantum of realism into the analysis. On the one hand,
the obtained result will disappoint our hope for clarity; on the other,
it will prevent us from premature conclusions. It is old mathematic
wisdom that you cannot secure more parameters out of an analysis than
the number of independent relationships analyzed. The essence is to spell out all
relationships in precise detail, but often knowledge about them is
limited (if not totally missing).. |
| In
case of further dimensions in addition to our conventional
4-dimensional space-time (as suggested in earlier accounts of mine), we may collect data on the influence of
observation and communication, but analysis will be hampered by the
absence of any formalism expressing potential connections or
dependencies. Instead of expecting direct relationships allowing the
setup of equations, we rather may be left with stochastic approaches. In the
realm of observation and communication it is mostly a question of yes
or no (digital instead of analog). Instead of measurement, the
preferred tool will probably be the (very rough) estimate of
probabilities. |
| Of
course, we will not get out more than we invested. Also the (hopefully)
obtained results will treat more dimensions than our conventional
space-time. For hard-core natural scientists, they will have some
casual, non-scientific appeal. This would not be the case, if we would
interact with non-terrestrial civilizations by speed-of-light channels
(which is not possible). Interaction with non-solar civilizations (see link below 'On the likelihood...') will
only be possible in a full-dimensional way (whatever that means). |
| 2/25 < MB (3/25) > 5/25 |
| On the likelihood of rare events back to At the border between fiction and reality |