It Must Be Said

   I write to announce return of Geometrical Dimensional Analysis,
technique of producing physics maps that are simultaneously concept,
factor, and unit systems maps and the logical evolution of Napier's
logarithm tables into multidimensional use of language that should
have occurred more than three hundred years ago.  Happ's flowgraphs
organized into lattices of logic, Corrsin's dimension space expanded
and elaborated upon, reassessment of Birge-Bond diagrams to augment
the least squares method of fundamental constants adjustment, the
embodiment of de Boer's claim that unit systems can be treated as
vector spaces, roadmaps for Feynmann's declaration that mathematics
is the language that takes us places, it is also the purest of art:
shaped by the math itself.

   Of immediate interest will be the four dimensional depiction of
the MKSA core and majority of the modern International System.  It
shows all the dimensionless constants which that system can project,
it shows every concept as the end result of all possible factoring
procedures from every other concept, it shows every unit in the
system as all possible combinations of all the other units, and it
will shed new light on the relationship between gravitation and
electromagnetism.  Without reservation I say that some version of
this one diagram should be available to all students and that it
will show all experts the physics they thought they knew like they
never saw it before.

   As "numbers don't lie" validation, one subsidiary map depicts the
atomic system of units projecting the environment of the Bohr atom
and another space is defined by the choice of Planck units as unit
vectors to structure that natural unit system.  Further, through an
"overlay" method, with the elements in one map as numerators to the
elements in the second as denominators, a third mapping is produced,
and all the points in all three spaces are thereby related.  Seeing
any individual map as a vector space, where derivation of any single
formula characterizes all similar vectors, all similar formulas, the
overlay approach is vector space multiplication of whole structures
of logic to produce entire formula arrays derived all at one time.

   I also include a table of numerical values expressed as powers of
ten and listed in absolute value order.  Modern manifestation of
Gunter's logarithmic line of numbers, the invention abridged by and
overshadowed by development of the slide rule, it is an enlightening
device on its own, as much of "ease the burden of calculation" and
"let the numbers speak for themselves" as the log tables that Napier
and Briggs published in columns and rows.  The whole vista, not just
a window as is the slide rule, this evolution of Gunter's approach
allows pattern recognition and discernment of numerical coincidence
almost as readily as graphics in two, three, and four dimensions.

   While all the maps argue against the use of scientific notation
in physical quantity factoring, where the unit of measure part will
be dealt with logarithmically, a whole listing of fundamental values
as logs is especially important today, decades after that smaller
window of the electronic calculator has outmoded use of log tables
and slide rules.  The double context of scientific notation itself
is not only tailor made for conversion to and from the mantissa and
characteristic that logarithmic numerical expression already is, as
log tables and slide rules formerly required, it forces emphasis on
the fine tuning portion of a value over its magnitude, it takes more
space, and it forces involvement of yet another context if numerical
values are compared to their own or other reciprocals.

   Just as in a city where streets are numbered, not named, and the
map becomes its own reference grid with navigation unfettered by
arbitrary nomenclature, these graphics use the math itself as both
map and calculating device to create a density of information which
facilitates speed and comprehension.  As an accomodation, I employ
symbols and unit labels which will be called unconventional.  Such
exclusive use of alphanumeric characters not only addresses the fact
that current use of symbology is an impediment, it also opens up the
discussion to those without the software collections or printing
office needed to supply all the subscripts, superscripts, bold and
italic letters, multiple fonts, foreign language characters, and
graphics demanded by official standards and publishers.  Compatible
back to the typewriter, if minimal English hypertext markup language
can be called a world language, then here is expression of formulas,
numerical values, and labels for units that can work with browser,
search, and optical character recognition software the world over.

   You may not think much of my conventions, of the low resolution
of my graphics, or of my obvious disappointment with establishment.
You may not like the obvious learning curve or time spans involved
as I worked my way back and forth across the country, from society
meeting to conference, from government lab to institute of higher
teaching, from closed door to closed mind, too busy, too skeptical,
too egotistical, too greedy, until I myself learned enough and found
references enough to document the conviction that these tools would
promote more efficient teaching and greater understanding, until I
myself had developed enough of the potential in the technique to let
it speak for itself.  You may think it impolite if I point out that
my work required no megabuck contracts for architectural wonders,
fishing ponds, or deer management programs, that I have no racks of
free brochures or free photos testifying that the working man's tax
money is being well spent, that no one made any fortunes from the
salvage yard sales, that there are no escalating grant budgets as
"non-profit" researches dovetail further and further afield to keep
the money coming in.

    Whatever you might think, however, KNOW this:

1.  I dare anyone in the world who has used the timeline of history,
the tree of life in biology, chemistry's periodic table of elements
or any street map to objectively examine my material, my hundreds of
references, any other work, and then to declare that the foundation
science with the units of measurement at its core has no need of
such a common ground visual aid, memory aid, and calculation device.

2.  I dare anyone, after examination, to declare that the technique
which I have stumbled upon is not the most logical, most pertinent,
the most elegant approach for the mapping of physics that exists.

3.  I challenge everyone to seek the limits of the potential in this
meta-language tool: My work is public domain.


    John Aikman
    The Outlaw Map of Physics