Aristo Tacoma
ω
The Supermodel Theory
Illustrated in the Lisa
Programming Language
ω ω
Understanding quantum phenomena,
gravitation, and biological coherence
on a common footing
ω ω
ω
ω
[All software for this book is free at yoga4d.com
ISBN 82-996977-0-1 Publisher: Yoga4d VRGM Copyright author,
all rights reserved. Any reproduction only by written consent
by Stein Henning Bråten Reusch, the author, with A.T. as pen name.
Oslo and Berlin First published 2007 reprinted regularly on demand
To buy more of this and forthcoming books etc cfr yoga6d.com/prices.
Available also at the National Library of Norway, www.nb.no autumn 2007.
The programming language Lisa is developed by the writer of this book
and all programs in this book, as well as the language itself,
are freely available with full sources in an academic spirit.
This book extends the work done first in 2004 (ISBN 82-996977-0-0,
written under pen name Stein von Reusch, also at nb.no),
which in manuscript form is free within the Lisa platform
at yoga4d.com. Illustrations in book from the Lisa performances
on the computer, and so the book can be read, initially, on its own.]
Thanks to:
the Institute of Physics at the University of Oslo for giving me
unlimited access for indefinite periods of time, also so I could have
the volumes at my home, to all its journals, some of which have
been accumulated since the inception of the University in the 19th
century. Other acknowledgements inside the text itself and many,
many more inside the 2004 book where I first launched my theory
of active models or 'supermodels' as a unifying approach for
physics with a perceptive/mind-like element, a book which is in
manuscript form inside my Lisa operating system which also has
my Lisa programming language. This language is here used throughout
as a unifying replacement for the half-working, over-complex
mathematical formalisms which have been attempted to be used
in so-called 'many-body systems' when one treats quantum and
gravitational phenomena together, and, unlike those formalisms,
there is no problem here with infinities.
ω
May we anarchistically break with all categories here; for we must
tweak our theories to fit with nature, rather than tweak nature to fit
with our theories, and each theory presupposes its own categories.
ω
"... In the atom and in the nucleus we have indeed to do with two
extreme cases of mechanical many-body problems for which a
procedure of approximation resting on a combination of one-body
problems, so effective in the former case, loses any validity in the
latter where we, from the very beginning, have to do with essential
collective aspects of the interplay between the constituent particles.
..."
-- Niels Bohr in Nature, Feb 1936 (Copenhagen)
ω
"It is remarkable that Max Planck, who initiated the revolution in
human thought, which is usually subsumed under the term 'quantum
theory', was always somewhat reluctant to accept its final
implications. [...] The success of the very crude theory of Bohr in
which nuclei are treated like liquids seems to indicate that the
alternative description in terms of individual entities may be wrong,
and that some totally new form of description will have to be
discovered before real calculation can be made. This will, of course,
entail some completely new step, even more revolutionary than the
superposition of quantum mechanics on classical mechanics. What
that step will be is still hidden in the mists of the future. ..."
-- Lord Cherwell in Annalen der Physik, Aug 1948 (Oxford)
ω
"<<...Warum glauben Sie eigentlich so fest an Ihre Theorie, wenn
doch so viele und zentrale Fragen noch völlig ungeklärt
sind?...Jetzt bewegen sich Ihre Gedanken aber in einer sehr
gefährlichen Richtung. Sie sprechen nämlich auf einmal von
dem, was man über die Natur weiß, und nicht mehr von
dem, was die Natur wirklich tut...Können Sie den Übergang
von einem stationären Zustand zu einem anderen irgendwie
genauer beschreiben?>> ..."
Einstein to Heisenberg, in conversation with Heisenberg,
from the book 'Der Teil und das Ganze -- Gespräche im Umkreis
der Atomphysik' by Werner Heisenberg, München 1969
ω
"Alla base della teoria sta l'ipotesi di N. Bohr del nucleo
intermedio e la elaborazione quantistica che permette di calcolare
la probabilità di transizione in dipendenza dall'elemento di
matrice della perturbazione. ..."
-- R. Ricamo in Il Nuovo Cimento, June 1951 (Zurigo)
ω
"There is a great conflict, beginning in ancient times and continuing
ever since, between continuity and discontinuity. ..."
-- Nature's editorial, 22 Sept 1928
ω
"Cosmic or galactic noise was discovered by Jansky in 1931; but
its exact origin has remained uncertain. It is generally understood to
originate from collisions in interstellar matter. ..."
-- J. G. Bolton and G. J. Stanley in Nature, Feb 1948 (Australia)
ω
"... Earlier theories due to F. London and Tisza suggest that
superfluidity is connected with the condensation which occurs in a
Bose gas not far from the λ-point. A serious objection to
these theories is the occurrence of entirely analogous phenomena in
superconductors. ..."
-- H. S. Green in Nature, March 1948 (Edinburgh)
ω
"In recent years a considerable amount of work has been done in
the soft X-ray region. In this work several new features foreign to
the ordinary X-ray spectrum were brought to light. According to
Bohr the frequency of the emitted light is in general determined by
the relation ℎν = E' - E'', where E' and E'' are the energies of
the stationary states of the atom. The stationary states appearing in
the X-ray spectra are those in which one electron is missing in an
inner otherwise complete electronic shell. Though the X-ray spectrum
is emitted by the element in the solid state, nevertheless the X-ray
lines are sharp lines especially when both stationary states are
related to inner electronic shells of an element of high atomic
number. ... Theory as well as experiment learns, that the sharp
levels of the valency electrons in the free atom are broadened to
energy bands which belong no more to a separate atom but to the
crystal lattice as a whole. ..."
-- D. Coster and S. Hof in Physica, July 1940 (Groningen)
ω
"If the invariance of light velocity alone, without the requirement
of an invariant length in space-time, be made to define the class of
'physically equivalent observers' then we ought to search for laws
exhibiting conformal invariance in form (i.e., which maintain their
'simplest' form under the whole conformal group). ..."
-- L. Ingraham in Il Nuovo Cimento, Oct 1952 (New Jersey)
ω
WELCOME!
If we are to speculate about the universe, then each element of
the speculation should be open to investigation on its own. That
forms a network of healthy speculations, and we can gather instances
of confirmation or disconfirmation from comparing with research
data and from careful use of our own intuition when it is at its
best. The notion of enquiry by means of a network of relatively
independent insights can also give rise to a whole; this whole,
which I have earlier delievered in more informal work (2004, ref
below), is then not so much a hierarchy as a way to relate a broad
number of insights together coherently.
Only if we assume that we already know the nature of the division
between the individual mind and the rest of reality, can we carry
out the argument that Kant did against the possibility of direct
perception beyond both categories and beyond the confines of the
local sensory origin. Kant's argument against metaphysics is itself
based on a particular localist metaphysics, and involves a circular
reasoning. Metaphysics, in the sense of reflecting over a wholeness
of reality, as meta-physics, may entail direct immediate forms of
perceptive intelligence or intuition which it can be the task of
humanity to call on also in a disciplined, carefully checked (relative
to bias, freedom from dogma and presumptions, and so on) manner.
This means that we must be willing, in contrary to the localist
bias which also Albert Einstein and Karl R Popper had, to perceive
of the possibility of the perception of the whole collective
interplay of phenomena as actual in itself, rather than merely
an aggregate. The direct perception of the wholeness of reality
means that we must not simply turn aside all questions of a metaphysical
nature as something in essence beyond the possibility of careful
checking, but that the nature of this careful checking must go
beyond such confines as was discussed in the Vienna circle of the 1920s,
with such members or occasional participants as Carnap, Wittgenstein
and Russell, and which provided some of the background for some,
but not all, of Popper's commentary on healthy science.
I wholeheartedly agrees with Popper that if we do not have any
possibility of checking a sentence, then adding more of these
sentences hardly constitutes a "progress". I do however think that
Popper, who argued strongly against the Heisenberg Uncertainty Principle
(by Bohr called the Indeterminacy Principle), -- even to an extent
that Einstein had to correct Popper in favor, for once, of quantum
theory (cfr. the letters going between Einstein and Popper
faithfully reproduced verbatim in the later, post-war editions
of his classic masterpiece The Logic of Scientific Discovery) --
if Popper had perceived the essence of nonlocality or alocaliity
(a more generous term, involving the direct concrete action of
wholeness upon its parts, explored strongly by David Bohm esp.
in his 1980 book, Wholeness and the Implicate Order) -- as relevant
for existence as a whole, rather than just as an anomaly inside
a technical particular element of a branch of physics, he would
have conceded that what constitutes an empirical checking can
and must be extended.
As Francisco Varela pointed out to me (in a conversation we once
had in Paris), certain parts of eastern religious thinking have
involved a kind of discipline of intuition which might become
an impulse for western scientific method. However, after careful
scrutiny of many parts of eastern religious thinking I have not
seen there that a sense of the objective and the unbiased in
the realm of intuition or in what C G Jung might have called
'synchronistic perception' have been particularly realized there
in any striking sense. This led me to put forward some elements
of a thesis on just how to evoke unbiased intuition in exploration
of any theme in my 2004 book (which is, as said, in my Lisa
operating system at C:\Yourtext\a.htm). This is a theme which
however goes way beyond the scope of the present text, although
it touches on it esp. in the completing five or so of the
empirical situations we explore here, where we quest for the
essence of consciousness and mind based on an understanding
which is also inspired by general patterns of quantum phenomena
of alocality as well as gravitational patterns, and such
considerations as Einstein put forth in both his special
and his general theories of relativity.
I hope however that the reader, even if rather new to this area
of challenges, can concede that there are open questions at a
very basic nature as for just how we do science still to be
framed, given energy to, and explored, and that it is not
simply a task for philosophers or those who have nothing else
to do. It is a task central to science to persist in enquiry
not just as to established methods of checking theory against
fact, but also on finding out more about the best sources of
fact, and in all this beware the contextual dependency that
some formations of the notion of fact bear with them, without
simply saying that nothing at all is factual.
It is also the task of the scientists to avoid trying to
limit perception of things which the scientist have not
adequately explored. It is just as disgusting to hear scientists
speak of rationality as identical with a particular branch of
darwinistic thought, or as identical with a view of reality
as composed of mechanical forces operating on dumb particles,
as it is to hear a scholar in a religion preach that their
silly old book describes creation in all detail. When
narrow-minded people like Richard Dawkins with his hysterical
pronouncements around Darwin and genes gets so much positive
acclamation around the academies and universities in today's
science world, then science has become substandard, and
anyone who has an established reputation and a conventional
publication record should look askance as to the value of
this, and realize that things have gone astray.
For instance, in July 2007, the BBC World Service reported
that a large number of the science academies in North America
and Europe had voted in favor of discarding all attempts to
critisize darwinistic thought as nonscientific, referring to
those who sought to point out that it may be that the theories
made in the prolongation of Charles Darwin's thinking seemed
hardly adequate to account for the incredible intelligence
and elegance in the 'design' of living organisms such as
human beings -- a perspective which, taken on its own, is
wholly scientific and rational to pursue. Those who speak out
against such a programme (by some called 'Intelligent Design')
do so because not so much of what the programme is stating
explicitly (which is typically very cautiously phrased, full
of honorable question-marks and concepts of wonder, which are
the essence of such open-minded sceptical forms of thought as
Sextus Empiricus also spoke about, cfr pyrrhonism, also Næss
on this), but because they think that they sense that the
hidden agenda involves bible-dogmatism, ie christian or islamist
or something like that. But we must, in science, take people
on their words. If they speak up in favor of a bible, critisize
them for that. If they speak up in favor of doing a serious
rethinking of an established paradigm, or even model monopoly
(as the mechanistic approach to biology connected to darwinism
and neodarwinism most surely is), they should be welcomed on
that. Whatever their hidden agenda might be, if they have
one, it is what they say which must be related to as far as
scientific discourse goes. And when meaningless denials of
alternatives of the established model are hailed as good science,
science as defined by these individuals in these institutions
is no longer good science. Historicians will agree, in all
likelihood, when seen from the future, that the chance of
rescuing the best of science as it is now, in 2007, lies
with those who are not impressed by its current status.
If this is offensive, I beg your pardon, but in the name
of science as an intent of sciere, or knowing by discernment
of reality, please let us not let the politics of viewpoints
in the polemics against the antitheses of these viewpoints
get in the way of pluralistic open-minded dialogue on the
essence of reality.
I also beg apology to the reader that I have found it easier to
do my enquiries almost entirely without relying on existing
mathematical disciplines but rather have developed my own
computer algorithms and my own language for computer algorithms,
and have looked more at empirical reports in rather antique journals
than to that which these days are regarded as prestigous physical
books or magazines, forms of education, and fashionable ways of
talking. I beg apology that I am regarded by some as something of
a rebel against these institutions. I can asure it is not because
I am against the notion of collaborating with many people as
such, for collaborations are one of the sweetest things. But
collaborations must not be what Bohm called 'collusions'
(see his book 'Science, Order and Creativity', 1987, with
F. David Peat).
So, as I said in the beginning:
May we anarchistically break with all categories here; for we must
tweak our theories to fit with nature, rather than tweak nature to fit
with our theories, and each theory presupposes its own categories. This
enterprise of exploration happens on a research-basis which is inspired
by Karl R Popper's notion of the free checking by anyone of anything
which lends itself to checking (so that the gathering of instances
of confirmation for this leads to consistent results, whereas when one
attempts to create disconfirmations one achieves rather in providing
further confirmation of the theory -- this is though a more Carnap-
friendly way of putting it, avoiding the somewhat overbred concept
of 'falsification', which, as Næss pointed out, rarely is possible
due to the many interpretation-possibilities of the connection between
such empirical data and the theories; note however that my use of
the word 'theory' goes along with Popper not Næss in general, for
Popper's use of the word is more inclusive and, as such, more realistic
relative to what scientists are actually doing, whereas Næss appears
to me to give the notion of a theory too many of the criterions which
apply mostly only to such particular frameworks as the General Relativity
Theory of Einstein -- see Øyvind Grøn and Næss in a book on this,
in which I contributed very modestly on pedagogical thema initially).
What lends itself to checking is, qua this capacity to be checked,
scientific; but what defends itself in our thought is mere dogma.
According to Popper (cfr his two-volume book 'The Open Society
and Its Enemies', written 1940-45), anything, even wildly speculative,
is scientific to the extent it can be subjected to attempts of refutation
by empirical study.
It is my feeling that the groundwork done in the first half of
twentieth century, often in a german language context, led to certain
issues of dissent which were not further developed in the second half
of that century because of the strengthening of certain categories,
implying a judgementality as to the limits on what it could be
scientific to speculate about within physics -- which however does
not much accord with the best of the trend of thought represented
by Popper as foundational to all the best of all forms of science
at all time.
What is here presented is very, very far from living up to the
highest standards of checking -- but it is, I feel and hope and
trust, a great beginning on something which can lend itself to more
and more of such checking, or attempts at refutation, as well as
the building of instances of confirmation, and also the refinement
and further development in all directions. The reader who is new to
my work must know that I would have regarded it as embarassing
if I had a high a conventional status; that a scholarly perfect
conventional education with all papers in order is more likely than
not to imply a bias and set a prejudice and a limiting category on the
exploration and the endavour to understand actuality. I regard the
person who attempts to normalize her or his thought within a
category as slightly off her or his rocker; and that the more
free-dancing anarchistically oriented person, is, by that freedom,
also more harmonious. My disgust with the lack of care associated
with the treatment of infinities in mathematics I have rationally
argued for elsewhere (also in the 2004 book).
The breaking with conventional model monopoly categories will be very
evident in the following, which is presented without page numbers,
as a network of questions, freely selected first half 20th century
quotes from physics, suggestions, computer program experiments in
my own newly made programming language Lisa, and comparison both
with empirics in the conventional popperian sense and with empirics
in a more intuitive sense, in what I suggest as a neopopperian sense.
A student about to prepare for an examination in a conventional
university setting in the beginning of the twenty-first century
is likely to get a serious reduction of her or his degree in that
exam if any further reading in this book is attempted. ;)
ω
This book, which is written for the expert and nonexpert alike
(however I assume an intelligent readership, and at least a potential
interest in doing computing in order to think theoretically, although
perhaps the contact with computers in this regard has been
relatively sparse earlier on), is a series of untitled microessays or
comments, with a ω-symbol indicating the transition from one to
the next. The symbol is used, then, to distinguish paragraphs
slightly or somewhat more strongly than a conventional shift in
paragraphs, as occurs on next line. These thoughts were presented
by the undersigned in a smaller book, also available at the
nb.no National Library of Norway, named 'Sex, Meditation and
Physics', in 1999 (yet another pen name was used, based on
my family names: Henning W Reusch, W for Weber), where this
symbol was used to signify what was there called a coordination
field, which is basically what grew into the notion of the
supermodel as used in the present theory. Already when I met
David Bohm first in 1986 I discussed the notion of doing modelling
of physics theories, such as the implicate order, by means of
new forms of computer language (at that time, I called the idea
of a network-oriented language I had for Aspect).
I have here followed the principle that if anything is worth
including in the text at all, it is worth including (instead of
footnotes, endnotes and appendices) inside the text itself, at
the position where it is most relevant -- and this includes
full references. My experience on looking up in old and also
many newer journals to find an article based on a reference
based on issue, page and volume numbers is that these numbers
often mislead, and that the most swift way of looking up often
involves the rough date -- month, if any, and year -- of the
publication along with full name of the publication, or book,
and the author name or names, as there is almost invariably
some kind of content list with author names listed alongside
publication date in each collected volume with several issues
of a magazine. Following a tradition going back to Zeitschrift
für Physik and before, I give (in brackets as the final
piece of information associated with each quote) the city
which the writer gives as his or her location at the time
of writing the article (if any). For Princeton, that would
e.g. by New Jersey. The quotes given here, more for inspiration
than for their actual content, are usually from the beginning of the
intro of their articles, and the references is such as I would
myself have preferred to go to a great physics library, like the
one at the University of Oslo, to locate the journal and read the
rest of the article, if the quote should prove that interesting.
Thanks to the very willing staff at the physics library at the
Institute of Physics I have had exceptionally free access to
ancient and yellow-paged journals accumulated with great care
over more than a century. The present work with the supermodel
theory have taken place admist the sense of early curiosity and
the wide variety of empirical essential research projects done
at the time, and the excitement these authors had in reporting
to each other on what they found, and what they were curious about;
and their curiosity is often of a timeless quality (naturally
relevant also today, in which we find that although additional
decimals have been added to empirical results, and more work
have gone into the theoretical realm, the same issues still stand --
sometimes with more clarity at that time, at other times, as with
the work done around the concept of nonlocality as something
definitely beyond the conceptional boundary of the speed of
light notion, with more clarity later on).
ω
"Current theories of matter are based on the concept of elementary
particles, which are described either as point singularities or as
extended sources of field. The point source models lead to infinities
which must be removed by substraction formalisms; they are
unsatisfactory in their present forms either because of the
arbitrariness associated with the substraction recipes or
because of their reliance on a future theory which is expected to
permit the calculation of certain 'infinite' integrals. On the other
hand, the extended source models, which correspond to cut-off and
strong coupling theories, are not relativistically covariant. ..."
-- R. J. Finkelstein in Physical Review, Sept 1948 (New Jersey)
ω
My own work as indicated in the title of this book involves
an attempt to look at the foundations of physics from a rather
philosophical angle coupled with new computer modelling, utilizing
a unifying concept termed an 'active model' (and earlier on,
'supertext'), which then eventually was called (without any
intended reference to fashion!) 'super models' or 'supermodels';
this work is offered in the sense of open-minded (neo)popperian
research without any pretense of solid grounding in mainstream
physics whatsoever, and whether what I call 'supermodel theory',
as first launched in a book three years ago, will be considered
a contribution to science or to physics is up to others to
find out. The theory is my own, but it has emerged also with the
fantastic help of a vast number of conversations, also with
David Bohm and Arne Næss (several hundreds of conversations
with the latter, also sometimes at Tvergastein, his high mountain
cottage -- often about the questions on where, if anywhere, logical
positivism went wrong, as Næss himself was regarded as a participant
in the Vienna circle), as well as with my own father, Stein Bråten,
whose emphasis on complementarity echoes that of Bohr but with
a more generous sense relative to the visualization of reality,
also helped occasionally by computer modelling, form a bulk of
the background which is referred to in the book in which I first
came with the supermodel theory, and which in manuscript form
is free within the Lisa computer operating system at my
websites.
I refer to the conversations as for the background work on the
supermodel theory, but I do not mean that any mistakes I might
have done is the responsibility of any of those who have advised
me on particular points -- the theory as such is entirely my
own.
I am also grateful for artistic impulses from, I take the liberty
to say, my teacher in painting, Frans Widerberg, and, as I also
take the liberty to say, my teacher in dancing, Monica Emilie
Herstad -- an immense number of conversations with both led
me into exploring things from new angles of the artistic;
I coupled this with my own interest in tantric forms of yoga
and made the computer language Firth Lisa over a decade inspired
by also these impulses.
If, as Einstein is well known to have said, the impulse of
beauty is an essential component in theory-making in science,
then perhaps these esthetical impulses, whether I have realized them
in a good way or not, have a stronger relevance here than my background,
since I was a kid, in programming computers in all ways, back and
forward, up and down. The scope of activity was also strongly
broadened by my chance of making a magazine together with, and
funded by, H B Tschudi, where I, in the capacity of an editor,
had the opportunity, after Bohm had passed away in the early 1990s,
of visiting John Polkinghorne, dean at Queens College, Cambridge,
and himself priest and physicist, Basil Hiley, at Birkbeck College,
collegue of Bohm, Christ Dewdney, at University of Bristol, who
did visualizations of Bohm's quantum potential and hidden position
informations of the electrons by means of Visual Basic, Roger Penrose,
who, with Stuart Hameroff and based on his own interpretation of
Kurt Gödel's work on incompleteness, speculated in the possible
role of quantum coherence in brain circuits possibly relevant for
consciousness, Ilya Prigogine, who was working on broadening the
understanding of the stochastic as an injection of the creative
into cosmos by prolongation of his Nobel-price-winning work in
thermodynamics, at first on "entropy", and many others. Many
conversations in the streets of Manhattan with free thinkers
including Raymond Strano and David Meyer Schonberg on issues
connected to chaos, the quantum, and the relative as well as
mind in the initial phases of making the Lisa programming language
is part of this background; as is the guidance Kristen Nygaard
gave me over coffee in Kaffistova in Oslo after this again. So
this is a part of the acknowledgements in the aforementioned book,
from 2004, in which the theoretical ground of the present work
was first presented from my hand. It was privately published, as
is this volume, but with the help of the ISBN numbering and the
National Library in Norway, it has been there available for loan
since 2004 and that took my mind off the pressure of having to
find any particular place to publish the free-wheeling, and
often tantrically oriented, platform of research I wished to
chisel out without any strong orientation towards fitting in
a particular place in the present mainstream of physics. Whether
what I do can be called 'science', 'physics' or 'research' is not
up to me to claim; I intend the best, and hope for the best,
but the reader can judge for herself/himself on these questions;
and I believe the presence of the now more and more used programming
language of mine, the hybrid between early Forth and early Lisp with
several novel components, also launched in a tantric yoga context
for sensual nonviolent computer games, promises more opportunities
for quickly getting into what I say so that one can independently
consider it. The book from 2004 has an even broader list of
acknowledged conversations, including also with Kristoffer Gjøtterud
at the University of Oslo, and prof. Gunnar Løvhøiden at Cern
as well as the University of Oslo, and Johannes Hansteen and Ladislav
Kohbach, professors at the University of Bergen.
With this easy-to-learn and yet very advanced programming language
for 32-bit personal computers, which is a tremendously satisfactory
size of a computer in a psychological sense, for there is space
for programs of many many thousands of lines with ease, and for
as much data as it makes sense to present during the course of
a programming session on a meaningfully graphical screen with
'pixels' (picture elements) of some 1024*768 in the 4*3 standard
format of the very standard (Y2000-compliant, as it is also called,
meaning it conforms to certain standards which matured right after
year 2000), we have an advantage which was not at all granted the
physicists of the first half of the twentieth century. This
advantage involves going beyond addition, multiplication, and so
forth, into dynamic processes without having to call on statistical
conventions or conventions implying aggregates of infinitely many
infinitesimals and such things which the early physicists had to
struggle with, lacking anything better. The present approach allows
us to go straight from the concept to the program without having
to go through the mathematical convention e.g. as used in S. Wolfram's
Mathematica or in Maple or in any of the numerous other such
packages, which essentially bridge mathematical notation with
numerical performance without calling into question the actual
concepts evoked. One has seen e.g. in the prolongation attempts
of superstring theory that it is easy for mathematics of the
early twenty-first century to wander into complexities on a level
where even most of the most willing of physicists seem to have
got no clue as to what is really, if anything, referred to
empirically. This might however have a certain creative impact,
serving to liberate us from certain elements such as can be called
(in my father's jargon) 'model monopoly', e.g. the way of talking
by physics as established in Copenhagen in the circles around
Niels Bohr. It is in the somewhat creative vacuum that the
present approach is launched; but it is hoped that it is
eclectically honest to in principle all the contributions,
whether theoretically or empirically or in some other way,
of all these scientists.
ω
The principle behind the present text composition involves that of
elaborating certain themes without presuming a common
meaning-horizon which can be readily identified by easy headers and
a hierarchical layout. I invite the reader who wishes to use this
book seriously, for a new type of what I call 'neopopperian' form of
scientific study (see also www.yoga6d.com/caa-academy/science or
similar locations which I have created on other networks in the
future -- but this is correct at least when the book is written, in
2007), to make his or her own content overview, index, and so on.
ω
In addition, the book has a lot of quotes from well-known and not
so well-known physics articles from especially the first half of the
twentieth century, connected to the era of wonder in which the first
new type of post-classical physical theories were being worked out,
sometimes ahead of empirical findings and often trailing after them --
evoking a lot of healthy question-marks. The spirit of enterprise of
that time is worth a lot for those whose passion for physics and for
an understanding of the universe in general is already deep, especially
when we bear in mind that not even half a century or more later has a
really strong theoretical groundbreaking unifying insight occured in
mainstream physics. The contact, found in these early works, with the
sense of curiosity and also with direct simple real research
studies on actual properties of energy, matter, light whatever, is
something which can be treasured almost for its own sake, and quite
apart from whatever particular research aim we might have in this
book. I have taken the liberty of providing these quotes almost
deliberately out of context, because also of the creativeness and
free associativeness and the variety of language lifeworlds which
with luck can be stimulated in a fun way as we also look more
logically at the present proposals for a unified computational
field type of theory incorporating, in a coherent but not overly
numerical fashion, standpoints on all physical phenomena in the
manifest universe and more.
Let me put it in another way: this book has a lot of content which
is complex, subtle and which may not fit at all with many
conventional cultural assumptions nor with assumptions currently
governing that which is regarded as mainstream scientific
academies. Nor does it fit with any existing alternative established
category. What is here said is therefore something which does not
easily invite existing labels or tokens which fleet around; and in
avoiding headers, the book will be honest in shape to that situation:
those who are in a rush to find out what it says, in order to
compare with existing categories, will find that the book does not
yield to that desire. However, those who are interested in actually
listening to what I have put into the book, will suspend their
ordinary categories, perhaps, and decide to take time with it, not
rush through it and categorize it. Then the meaning insight network
will emerge in their minds, and encourage an awakening and be a
stimulus for enlightenment, I should say.
ω
"It is well known that many atomic and molecular properties can be
predicted if we know the relevant accurate wave functions. ..."
-- E. Holøyen in The Proceedings of the Physical Society,
April 1955 (Oslo)
ω
When I use the term 'neopopperian' (see also front pages of my
websites www.yoga4d.com and www.yoga6d.com) I mean by that a
willingness to go first-hand in empirical data contact to a large
extent, rethink absolutely freely and wildly yet soberly theoretical
backgrounds, and carefully check as many predictions as possible
against available empirical data, especially such data which is not
hugely relying on very many ad hoc assumptions. The use of the
prefix 'neo-' also means that I revise what Popper regard as
checking, or refutation, relative even to his most mature works,
The Open Society and Its Enemies, in two volumes. It is clear to me
that Popper has a localist bias, shared with early Einstein. His
references to what he calls 'intellectual intuition' are brittle and not
elaborated nor deepened. The notion of checking a theory against
data which Popper operates with is basically that of comparing with
easy conventional sensory data as provided e.g. by some measuring
machines of a traditional type. I invite intuition as well, but that
does not mean that I include every claim to intuition as intuition;
rather, I call for a quest, open-minded also on that level, as to
what really constitute a checking, and call into question the validity
of implicitly asserting a localist metaphysics (as it is obvious to me
that Popper does) underlaying science. Science must not take (the
answers to) grand questions for granted, but be explorative at all
levels, and not sharply delineate a division to philosophy,
metaphysics etc.
For instance, Popper says that a theory is not by any means
regarded as proven even though there are what he (and Carnap etc)
calls instances of confirmation for it, and no significant instances of
disconformation, as yet.
But that must apply also to Popper's theory that metaphysics
involves only uncheckable sentences. His feeling that metaphysics
involves statements which cannot be checked, however much it is
shared with some other thinkers, is, plainly put, imbecile. The rest
of Popper's work is too good to be discarded. With this revision,
therefore, we say 'neopopperian science'.
Since I have coined the term, I also include in neopopperian science
a sense of connotation of the type of work one easily does when
one engages the Lisa programming language (which is a convenient
way of naming the compiler which is started by the command
FIRTHLIS LISA/NOD501 when my operating system and platform
Lisa_cd is installed on a proper Y2000-compliant 32-bit standard
Personal Computer). My first work in neopopperian science is this
book, which endavours to relate supermodel theory not only to a
program made in Lisa programming language as an illustration, as I
call it (for it is part of neopopperian science not to speak of a
theory as something which is within a formalism, but rather speak
of it as something which is by nature informal, an item of meaning
and quest into reality in the sense of wonder and uncertainty --
where formalisms, such as computer programming languages and
Lisa in particular, are invoked as finite representations merely of
aspects), but also to empirical findings which is so that an ordinary
citizen on an ordinary budget can ascertain these for himself or
herself (ie, without any reliance on supercolliders such as Cern in
Switzerland). I am very grateful to a conversation (at my offices in
Flux, when I was running my little magazine with H B Tschudi) with
physicist Joseph Agassi, a student of and collaborator with Karl
Popper, for pointing out that it is part of what Popper suggested
to insist on simplicity of experiments, and that physics, as he put
it, has had a development in which it has lost contact with simple
empirics in favor of a hyper-complex technological approach where
things are not really checkable in the popperian sense. He pointed
out that the experiments laying the ground for the more interesting
parts of modern physics were generally so that anyone could do
them with relatively inexpensive equipment.
Thanks, as said earlier, to the library of physics at the
Institute of Physics at the University of Oslo, I am in a
position to regularly work in relation to the reports on both
empirics, speculation, and other themes (such as those touching
on the nature of formal languages) e.g. from the first half of
the twentieth century of Zeitschrift für Physik, as well as many
other physics and physics/philosophy journals. The recent work has
also made what Agassi pointed out still much clearer.
More precisely, I realized that the set of experiments
mentioned as classical and ground-breaking for quantum theory and
the relativity theories were but drops in an ocean of empirical
studies and selected not because they at the time perhaps was
generally seen to be ground-breaking, but rather because they fit
well with the theories, illustrating key points in them.
This encouraged me to re-think my relationship to empirics,
and work it out afresh on a neopopperian and first-hand basis.
This accounts for the healthy spirit of the anarchistic choice
in quotes, wishing to widening our sense of that enormously
valuable past of science and the many openings in many directions
found for those who wish to listen -- also to it, complementing
their own direct work with empirics in simple and also not-so-simple
ways.
ω
"A long molecule generally absorbs (visible) light when it is
polarized in the direction of the molecule. ..."
-- Hl. de Vries, A. Spoor and Renske Jielof in Physica, 1953
(Groningen)
ω
It is in physics of importance, I think, to realize the vast
difference between acceptable (by many) ways of talking about
reality and an accurate perception of reality. However difficult the
latter might be (nonetheless it is not impossible), one cannot simply
substitute the former for the latter. One might imagine the
perception of reality a challenge akin to this metaphorical situation:
a secretive variant of the eminent J.S.Bach is heard playing
symphonically in a closed building, occasionally, by passers-by, when
a window is open. Some catches occasionally a tone or even several
tones (read: empirics). They go to a bar (read: university) and talk
about (read: write an article) about what they've heard. Other
people talk about the talk (read: read their articles) and the
majority gets into a way of talking about the music of J.S.Bach with
greater and greater certainty, interpolating and extrapolating the
rest of the symphonies, even giving them names, based on a couple
of tones listened to, and rendered perhaps not very accurately, to
the other people at the bar (read: the way scientists talk about
reality, 'the big bang', 'time' etc).
Then somebody (e.g. Popper) points out -- hey, why not spend
more time in front of the window? But there are opinions about this
in the populace. This has already been discussed, they point out; and
the majority, which, they surmise (confer Ibsen) must be the
wisest, has judged it somewhat peculiar to want to go back to the
window, when insight has "advanced as much as it has" (read: got
complex, full of 'proofs' and 'deductions'). One even has symphonies
performed over what one has 'heard' (read: technology), and some
people seem to like them.
But some people don't give up. They go back to the window and
listen more and more. However, they may find it difficult to listen
if they are too intensely aware of the opinions of the populace over
what they hear (majority mainstream opinion may act as a
mesmerizing force, obstructing perception).
In the words of my father, Stein Bråten, we must then dissolve
the "model monopoly" (or 'modellmakt', as he calls it in Norwegian,
see his 'modellmaktteori' from 1972, cfr the site www.stein-braten.net
on bibliography). The notion of model monopoly is somewhat akin to that
of Thomas Kuhn 'paradigm', although it has a wider application (not
just to science) and it is also, quite unlike both the early version by
Kuhn, and unlike his later work on 'exemplar' as alternative notion,
totally clear from the outset that model monopoly is not at all what
we want. Ie, it is exactly what must be transcended, e.g. by
introducing crossing perspectives, fresh contact with empirics,
alternative formalisms, a re-opened discussions of definitions, and
so forth. I am grateful for this concept, which has been one of my
main compasses in meeting with many brands of theory.
It is part of the dissolution of model monopoly, as I see it, to
prefer the nonsystematic over the systematic except where a
formal language, like my Lisa programming language, requires the
systematic approach in order for it to be machine-readable.
When we look at the science journals for the first half of the
twentieth century, especially before the world war 1940-45, it is
evident that the editors in many nations have pursued their selection
of what articles to publish according to a view of what they regard
as particularly 'hot'. One sees, for instance, in certain North
American journals an emphasis on electricity, and, in the same
journals, one finds, in the 1930s, even relativity theory being
discussed only rarely and then mostly with quotes -- "relativity
theory" -- referring then to the special theory of relativity by
Albert Einstein.
But nevertheless, despite nationalistic and militaristic aims and
divisions, there are many global and insightfully oriented articles,
and one is perhaps struck by the diversity of studies. As Agassi
pointed out, one finds an esthetics often involving a very direct
focus on somewhat more simple forms of empirics than that which
came into fashion by the late 20th century. And in the german
language one finds a slightly "computer-language-like" willingness to
cultivate carefully expressed gestalts of insights and questions,
which even today, especially in an English language context in which
something like Lisa takes the place of the old german systematization
praxis in language, evokes a sense of creativeness, wonder and
suitable philosophical awe of the kind which can act, with luck, to
dissolve model monopolies. I have earlier on voiced concern about
the tendency in the german language to assert structure more than
contact with facts; and my feeling is that any element of focus
on the german language should go hand in hand with a focus on the
laughter and spiritual freedom one naturally comes upon in a
language like english, and with the caution that Popper and others
take great pains to point out so clearly -- that reality must always
have the upper hand, no matter how complicated, diffuse or whatever
it seems to be. It is a crime in science to say that reality cannot
be further analyzed, further visualized, further understood. The
approach of Bohr is therefore here, in that regard, regarded as
Bohr at his most foolish. It was Bohr, far more than Einstein, who
prevented the Bohr-Einstein dicussions from becoming dialogue.
There was a conflict betweem them, but the conflict was not balanced.
Einstein always expressed his viewpoints very clearly, as far as
I can tell. He allowed them to be refuted. Bohr acted as a politician,
eager to win votes from fellow-physicists, degenerating the following
five decades of physics after his dubvious contribution on establishing
his model monopoly. Aside from this, I agree with Einstein that Bohr's
surprisingly accurate traffic rules for the energetic changes of the
atom electrons involved something remarkable, even to the extent it
showed that Bohr was a genius: but this does not justify the
tremendous attempt to block the development of physics by plastering
it with vague words on what is allowed and what is possible to talk
about. One sees the same strain in Wittgenstein's pronouncement that
what one cannot talk about, one must not talk about -- which probably
said more about his shame over his own sexuality than it said either
about logic or science or philosophy (Wittgenstein wrote of his
masturbations in a private language).
The magic of reality is that it can be understood; the magic of
of the heart is that it knows harmony without having to be told it --
and the quest into the spiritual life involves going by heart when
the mind is too occupied with other things to actually penetrate
at an intellectual level (as scientists must do, eventually)
the universe in the sense of wholeness. But the lack of understanding
in any area must never lead to a hype around pronouncement and
declarations, especially not by a Nobel laurate like Bohr, that
the further progress in physics or in any fields lies in avoiding
further analysis, visualization or talk about certain questions --
trends of thought which are found in most of the articles Bohr
wrote, and which are yet themselves so vaguely phrased that I have
heard Bohr's followers, including Gjøtterud, vehemently deny
that Bohr ever said such things. Nor can one at all justify
such meaningless, vehement denials of the reality of how some
have done science and of what can be done next by referring to
the importance of (as some does, I have noticed), 'engagement',
'enthusiasm' or 'feelings'. Feelings of rage, attack, denial,
disgust and such coldness in feelings (which also have been
evident in Arne Næss when he speaks of spirituality) as lead
to sarcasm have no place in science at all -- only in the
treatment of the neurosis called 'egotism'.
The deeper feelings of science involves the cosmic religious
sense of the universe which Einstein spoke about, and which
Spinoza would have called hilaritas, but which need not the
imbecile determinism of either.
ω
My inclusion of quotes is in this spirit and also to
signify my strong acknowledgement to the 20th century
scientific publications and journals, and Zeitschift für Physik in
particular, as I begin my own neopopperian work for real with the
work you have in your hand. The quotes will of course be far
more readable for those with an good understanding of the german
language but the reading of these is not crucial to the formal
content and the discussions around these in informal English
in this book -- they are therefore not translated.
ω
"Es ist die Absicht des vorliegenden Artikels, auf einige
Gesichtspunkte hinzuwisen, die das Expansionsphänomen der Welt
in rein physikalischer Weise zu erklären versuchen. ..."
-- Erich Bagge in Zeitschrift für Physik, July 1950 (Hamburg)
ω
"Die Bindungsenergie der Kernbausteine ist experimentell von der
Größe des Atomkerns nahezu unabhängig, und der Radius der
Kerne variiert ungefähr wie die dritte Wurzel aus der Anzahl der
den Kern aufbauenden Protonen und Neutronen. ..."
-- W. Heisenberg in Zeitschrift für Physik, Sept 1935 (Leipzig)
ω
"In 1937 D. Brown put forward the ingenius idea of using a
strip of sound film as an optical diffraction grating. ..."
-- J. F. Schouten in Physica, Feb 1940 (Eindhoven)
ω
The theory of active models, or supermodels, is my contribution
inside my privately published book, which in manuscript form, as
text file, is within the Lisa operating system, in C:\Yourtext, as
a.htm. It is, since 2004, with ISBN 82-996977-0-0 at the National
Library of Norway (produced under my pen name Stein von Reusch,
published by Yoga4d VRGM, Oslo), in book form (cfr www.nb.no). The
language Forth was there used in a broad and very general form to
illustrate some aspects, because the parallel project of that which
became Firth and Lisa was yet far from completed (the completion
of Firth was in March 2006, and Lisa, which is the way we typically
denote its most ripe form, the LISANOD501, completed July 2007).
It will be extremely clear, on reading that text (esp. its second
part, which introduces the supermodel theory and the Principle of a
tendency of Movement towards Wholeness, or PMW, as we will look
more at here), that there is a respect for key aspects at a very
abstract level of the theories commonly regarded by mainstream
physics as foundational to their science, notably general (as well as
special) relativity theory as by Albert Einstein, and quantum theory,
created by Einstein, Planck, Born, Heisenberg, Bohr, Pauli, Dirac,
Schrödinger, von Neumann, de Broglie, Fermi, and others.
The focus in this book, however, has an intent to engage
more in a first-hand way to empirics and yet do so on the premise
of looking intensely for aspects of the quantum and gravitation, or
curvature-like phenomena (such as acceleration), as well as more
phenomena, of the type one might denote a subtle yet pervasive
macroscopic, or perhaps biological, coherence (or 'nonlocality' as
referred to in that book). I will do so not at all trying to negate the
key importance of such studies as e.g. by Aspect to ascertain Bell's
inequality relative to the Einstein-Podolsky-Rosen article, even
though such studies relies not only on very expensive and
complicated technical arrangements (in order to distinguish finely
between near speed of light and faster than allowed for by the
speed of light limit at short ranges with microscopic quantities of
energy) as well as a brickstone of mathematical deductions and
assumptions. Quite on the contrary, I take it for granted that we
have respect for, and feel gratitude for, all these immense efforts,
including such efforts as trying to find out whether indeed the speed
of light is constant at Earth's surface both in racing towards the
Sun and in racing away from it, and complicated arrangements
(indicating quantum coherence over a timelike dimension which I call
spaceduration) such as 'delayed choice' quantum experiments; and
we must be highly grateful that we have indeed behind us such
things as taking atomic clocks of immense accuracy up in airplanes
and rockets to come to some empirical confirmation of the notion
that gravitation, as well as acceleration, when strong, has a minuscle
but real slowing effect on a precision-manufactored timing device.
The literature covering such studies is immense, and a popular
science writing culture has contributed to this. A person eager to
come into contact with empirics in a first-hand manner would do
well in engaging in a certain amount of visualisation of this empirics
which is in praxis so complicated to reach at the present
technological level of humanity, anyway, for most -- be it
third-hand or fourth-hand, reports of reports of reports -- but it
is a comfort that many scientists have independently gone to the
laboratories in many countries not at all always with the intent to
come up with confirming instances, and several key results, such as
those mentioned above, tend to stand within the present context
fairly well. However it must also be said that the way such studies
are presented is often very subtly dogmatic and one must not let
oneself be seduced by the whole agenda and network of assumptions
running through many of these presentations, and I think my 2004
book should be good in providing a sense of bracketing around
several statements of an over-eager theoretical nature which often
has clothed several of these presentation (for instance, it is
correct that Einstein's work has got many instances of confirmation
but it is not thereby proved, once and for all, that those who
proposed such a notion as an ether proposed something which must
be a laughing-stock of all scientists for all ages to come -- it is
rather so that in the framework Einstein proposed, and which works
not at all for quantum phenomena except by extremely complex
forms of tweaking such as superstring or M-theory, which does not
appeal to anyone oriented towards fresh understanding and
simplicity, I think it is fair to say, this framework does not propose
the ether; but there is no final disproof of any individual concept;
rather, the original ether-framework was found to have instances
of disconfirmation and that does not rule out ether as such --
speaking principally, and there is no reason why one should not
speak principally when one is doing science).
Anyway, the key emphasis on this book is nevertheless
completely different from the typical emphasis when one sees the
word 'quantum' in a scientific context. For I have endavoured to find
what can be found easily, given the present state of commonly
found technology absolutely outside all laboratories, which at least
touches on the quantized aspects of energy; and I do this on the
presumption that those who wish to touch on more classical
quantized phenomena can elaborate further on something much like
the present supermodel formalism as presented here for the first
time. I intend this book to be a platform for infinite undertakings. I
do not presume nor garantee this book will be errorless; but
reports of instances of disconfirmation, if any, will provide further
ground for interesting research for upcoming works. The approach
here is a network of insights, and attempted connections with
empirics, some which may have more to them than others, and it
does not as such stand forth as a hierarchy. The program is the
same, exposed to different input parameters which give different
general model behaviours -- the word 'model', and the phrase
'model behaviour' refers to the computer program, while the word
'supermodel' consistently refers to the theory I have made over the
nature of the universe and by the latter, in contrast to the former,
I explicitly call for a sense of the infinite and the irreducible and
whole.
The model program is meant to be improved upon; and entirely
different programs can be made also inspired by the supermodel
theory. I wish again to say what I said clearly in the 2004 book: the
theory is never its formalisation. A formalisation is an illustration
of a theory, at best. It can in some sense incorporate, mimick or
contain some key aspects of a theory but never all of them,
because insight cannot be put into the shape of a series of
mechanically permutable tokens. These tokens -- such as the tokens
making up a Lisa program -- can have an interesting quality of
encouraging insight into what the theory is all about, but they do
not, in fact never, represent the theory, when we by theory affirm
the important point which I believe also Popper affirmed, namely
that a theory is a semantic item in toto. A formalism, and its
syntax, can be invoked by theory-makers, but not so as to contain
it. One does not record an insight, but one can record a
performance on a keyboard which is inspired by an insight. A
formalisation is in some sense a recording of a performance which
is inspired by a theory.
When I say this so strongly, it is because I feel it is part of the
generous enterprising spirit of neopopperian science always to call
for the childrens' minds to evoke new wonder, ask the big questions
all anew, and cast aside all model monopolies. This they can do with
a compassion that is also an immediate sense of flowing wholeness
and unity, not based on egotism, nor based on a groupism or a
dyadism (a 'twoness' type of egotism would still be egotism). The
wholeness, or compassion, is a universal sense of wonder and open
enquiry which ultimately defies all explanation, and which is part of
a sense of mystery and awe about the universe which is echoed in
the Einstein quote where he speaks of science as a '..cosmic and
religious feeling'. There is a meeting of another individual in this flow
of compassion, as (what I am grateful to my father Stein Bråten for
pointing out) in Martin Buber's Ich-Du poetic vision (which is, as he
often writes himself, also along the lines of my father's scientific
theory of the virtual other, proposed in the context also of
infant research). In this, we see that the sense of individuality, of
one, two, three, four and so on, all comes to happen within
wholeness, or unity, or oneness, that which Jiddu Krishnamurti
referred to, in his many books, as the "love which has no motive;
a love, which has its own intelligence, in which there is no center
such as the 'I'".
ω
"Die Streuung schneller Elektronen an einem
zentralsymmetrischen Felde wurde auf Grund der Diracschen Theorie
bis jetzt von verschiedenen Autoren behandelt. ..."
-- P. Urban in Zeitschrift für Physik, March 1942 (Wien)
ω
"In einer früheren Arbeit konnte gezeight werden, daß ein
Molekularstrahl von Heliumatomen oder Wasserstoffmolekülen von
der Spaltfläche eines Lithiumfluoridkristalls wie von einem
Kreuzgitter gebeugt wird. ..."
-- I. Estermann, R. Frisch, und O. Stern in Zeitscrhift für
Physik, Dec 1931 (Hamburg)
ω
"Schon die alte Hittorfsche Umwegröhre zeight eindringlich,
daß zur Ausbildung einer Glimmentladung genügend Raum
verhanden sein muß. ..."
-- Werner Koch in Zeitscrhift für Physik, Dec 1931 (Berlin)
ω
"Der Ausdruck 'einheitliche' Feldtheorie, der für das erstrebte
Ziel öfters verwendet wird, bezieht sich darauf, daß
Gravitation, Electromagnetismus und vielleicht noch anderes mit einem
Schlag erfaßt werden soll. ..."
-- Erwin Schrödinger in Annalen der Physik, Aug 1948 (Dublin)
ω
"<<.. Sie wissen, daß ich die Vorstellung versucht habe, daß
das Atom von einem stationären Energiewert zum anderen
gewissermaßen plötzlich herunterfällt, indem es die
Energiedifferenz als ein Energiepaket, ein sogenanntes Lichtquant,
ausstrahlt. Das wäre ein besonders krasses Beispiel für jenes
Element von Unstetigkeit. Glauben Sie, daß diese Vorstellung richtig
ist? ...>>"
-- From a conversation between A.Einstein and W.Heisenberg; the
question is put by Einstein; from the book 'Der Teil und das Ganze --
Gespräche im Umkreis der Atomphysik' by Werner Heisenberg,
München 1969
ω
In this book, with the software made for it (and fully
represented inside the book as well as given in an already-
typed-in format at my website as indicated at the frontpage),
the supermodel theory is given an illustration in the form of a
standard computational basis for experiments with various
experimental setups, as determined by extra programs, in which
parameters to the algorithms are given, so as to sketch various
symbolic relationship between processes of various kinds and at
various scales, from microscopic to macroscopic. The Lisa
programming language is of course free, as started with the
command FIRTHLIS LISA/NOD501, on the Lisacode command line, in the
also free operating platform as downloadable from my website
yoga4d.com. The example programs are downloadable as described
further on in this book, associated with each program example.
The book implies that supermodels in some sense can be
considered a concept which is inspired by that of somewhat
'free-floating' algorithms, connecting and disconnecting (indeed, my
initial phraseology was to say 'supratext' or 'supertext').
I would like to make this more precise here. With the advantage of
the work by A. Turing, E. Post, A. Church and others, the notion of
a 'complete programming language' is fairly well defined (albeit
perhaps not with an adequate emphasis on e.g. 32-bit finiteness,
which I, for my own reasons, think it is adamant to put into any
definition of a proper digital programming language). Very vaguely
inspired by Einstein's focus on the unified approach to all of
physics, I wish to make precise a certain postulate, in a context in
which we grant some kind of actuality to something like a
supermodel -- which is an actuality more subtle than mere energy,
of course, in a general and broad way inspired by the reworkings
of pilot waves and other wave functions to nonlocal
manydimensional wave functions.
This postulate is the following:
A supermodel can have associated with it a structure no less
complex and no less dynamic than that of a complete algorithm
written in a complete programming language like Lisa.
I wish it clearly understood that I in no way postulate that the
essential actuality is finite or reducible to the digital. I merely
postulate that this actuality, which in potential (it feels intuitively
right to say) has something essentially infinite about it (in all
senses), also engages in a rather digital-like activity in which
something like algorithms may be a suitable notion of what's done
here.
ω
In this first book in the series calling on Lisa formalism
in science, which will take us into much -- also more on biological
coherence, on the essentials of warp science, and on issues of
geo-engineering and much more, we will look into twenty-seven
27 experimental setups using the computer program,
which are be relevant for theoretical speculation about
a corresponding group phenomena in the real world.
I intend this series often to be more intensely empirical,
and this is a basic work for the CAA-Academy in its science
programme. As far as the empirics go, few of these 27 requires
anything but reflection upon the type of experience and technology
either encountered in a normal daily life, or which is
(like three unattached polaroid glasses) fairly inexpensive
and available, although some are a bit different.
The completing seven or eight increasingly involves
a theory of consciousness, and mind more generally,
but due to the tremendous amount of physical molecules involved
e.g. in brain action, they require a lot more research so that
the particularities of the supermodel theory can be ascertained
in these cases -- or else refuted. This is a first book, of
course, in a series which is of indefinite length, involving
the blending of the Lisa programming language, informal
dicussions, and the insights which are associated with my
supermodel theory, and I try here to sketch outlines for
future research -- and I have had to call upon a trust in
intuition (mine and yours) in chiseling out these examples.
The computer simulations or emulations of some of the key
features of the supermodel theory, however, work on their
own accord, of course -- and that is also a form of empirics,
of course -- valuable in the sense of comparison with actual
world empirics, and with your own intuition. I very strongly
call upon a sophistication of our understanding of intuition
along the lines sketched in many texts on my websites and also
inside the free Lisa platform as a more and more unbiased
research tool -- in neopopperian science.
Especially the two completing points break sharply with
mainstream physics as at the time of writing this book (2007),
and involve a certain number of additional assumptions beyond
the abstract version of supermodel theory, in which
we posit a relationship to the particular macroscopic (in the
sense of biological) processes of our human brains and bodies
with the feature of the supermodel theory called PMW, or
Principle of (a tendency of) Movement towards Wholeness.
While I will attempt to spell out many of these extra
assumptions in connecting to discussing the completing two
points, I will also actually call for intelligent readers
to participate with their own research and write on this.
(1) Supermodel predictions and program example for two
and three polarized glasses with quantum phenomena
(2) Supermodel predictions and program example for weak
exposure on photographic film -- more and more quantum packets
of exposure energy which gradually build up the whole
(3) Supermodel predictions and program example for quantum
refraction of light as seen through water, at an angle
(4) Supermodel predictions and program example for quantum
refraction of white light as seen through crystal with various
colours at various angles
(5) Supermodel predictions and program example for reception
of very weak radio waves in terms of series of quantized sound
bits instead of just weak volume
(6) Supermodel predictions and program example for impact
of sun as noticable on broad bands of wide range radio
(7) Supermodel predictions and program example for the quantum
polarization effect of water on reflection of sunlight
(8) Supermodel predictions and program example for how accelerating
elevator gives gravitation-like pull
(9) Supermodel predictions and program example for inertia in asteroids
(10) Supermodel predictions and program example for constancy of
volume displacement of e.g. large objects in water (Archimedes princ.)
(11) Supermodel predictions and program example for moon (and
satellites in general) in orbit around Earth (or giant-sized objects
in general) -- on curvature and spaceduration
(12) Supermodel predictions and program example for relationship
between amount of 'stuff' and gravitation pull
(13) Supermodel predictions and program example for sunlight
decelerating on hitting earth ground, with a postulate of curvature
arising by it
(14) Supermodel predictions and program example for how fermionic
quality of air bounces airplane-wings up in flying situations
(15) Supermodel predictions and program example for how fermionic
quality of water make curvature either less apparent or less strong:
curvature postulated to be cumulative fermionic effect
(16) Supermodel predictions and program example for how gravitation
does not affect, as it seems, perpendicular motion aspect
(17) Supermodel predictions and program example for quantum resonance
between electrons in electrical wire and electromagnetic waves
(18) Supermodel predictions and program example for mutuality
electricity / magnetism in/around wire e.g. transformator
(19) Supermodel predictions and program example for a new
version of EPR/Bohm/Aspect nonlocality
(20) Supermodel predictions and program example for several
oscillations in guitar / piano string heard best when nondestructive
interference
(21) Supermodel predictions and program example for the
biological/mind phenomenon of gazing at sea, beachside, involving
perceiving relatively nondestructive interfering photonic oscillations
(22) Supermodel predictions and program example with emulation
of some aspects of neuron-like networks for visual perception
involving gestalt-like line segments
(23) Supermodel predictions and program example with emulation
of some aspects of neuron-like networks for auditory perception
of baroque music
(24) Supermodel predictions and program example with emulation
of some aspects of neuron-like networks for perception
within consciousness of thought
(25) Supermodel predictions and program example with emulation
of some aspects of neuron-like networks for perception
within consciousness of feeling
(26) Supermodel predictions and program example with emulation
of some aspects of neuron-like networks for perception
within consciousness of feeling relative to how prolonged
experience of 19 and 20, mind with its increased
coherence can, for the next hour or so, by constantly attuning
to another individual who does the complementing action, come
into the possibility of immediacy of wholeness of mind-contact
(27) Supermodel predictions and program example with emulation
of some aspects of neuron-like networks and the biological
organism as a whole, vaguely, how prolonged experience of
19 and 20, combine with attunments to the experience of over
extremely coherent (read : young) skin, will attain to greater
coherence (read : rejuvenation) due to the modification of the
fluctuations within its causal processes
ω
"It is now generally admitted that the interaction laws of electrons
and photons with matter are sufficiently well known to form a
basis for an explanation of the so-called shower phenomenon.
Carlson and Oppenheimer, and Heitler and Bhaba have shown that a
combination of the processes of bremsstrahlung and of pair
formation gives rise at high energies to a rapid multiplication of
energies. ..."
A. Nordsieck, W. E. Lamb Jr. and G. E. Uhlenbeck in Physica, April
1940 (Columbia and Michigan)
ω
"The visible photo-luminescence of ZnS, activated by silver or
copper, consists of a band in the blue and in the green respectively.
It is already known for a considerable time that these emission
bands gradually shift to the red, when CdS is introduced into a solid
solution.
"More recently S. Rothschild could show that the same holds for
the blue band, emitted by unactivated ZnS, which band is commonly
ascribed to deviations from the stoechiometrical composition.
"In addition J. H. Gisolf, studying the fundamental absorption of
Zns and Zns-CdS mixed crystals, found a shift of the long
wavelength side of the fundamental absorption over the whole
composition range. So emission and absorption seem to be closely
connected. ..."
-- F. A. Kröger in Physica, Jan 1940 (Eindhoven)
ω
"... Bombardment of light nuclei with charged particles has also
shown the existence of resonances. Thus there are resonances for
the emission of γ-rays in proton bombardment of Li, C, F and
similarly there are the well known resonances in disintegration
produced by α particles. ..."
-- G. Breit and E. Wigner in Physical Review, April 1936 (New
Jersey)
ω
"Limited to slow and heavy particles two years ago, the domain of
utilisation of the photographic method is shifting towards higher
energies. The increase in sensitivity brought by the Ilford G5 and
Kodak NT4 emulsions, which made possible the detection of electrons
and minimum ionisation tracks, has opened up a new field of
research. ..."
-- Y. Goldschmidt-Clermont in Il Nuovo Cimento, May 1950
(Bruxelles)
ω
"Bei der photographischen Messung der Intensität von
Spektrallinien geht man gewöhnlich so vor, daß man auf der
Platte außer dem zu untersuchenden Spektrum noch
Schwärzungsmarken erzeught und damit nach
mikrophotometrischer Auswertung über die Schwärzungskurve
zur Intensität der Linien gelangt. ..."
-- Erwin W. Müller in Zeitschrift für Physik, Sept 1935
ω
"As the result of light passing through very thin metal foil,
photoelectrons will be emitted from both sides of the metal
simultaneously. [...] All previous work by the writer and other
investigators who have been interested in the photoelectric
properties of very thin metallic foil, or still thinner and transparent
films of metal was undertaken with cathode deposited films
supported by quartz. [...] The photoelectric currents and velocity
investigations were, however, found to depend too much on the
previous history of the cathode and the potential gradient under
which the cathodic depositing had been made to warrant any
quantitative conclusions. [...]
"In the present work it was found necessary to investigate
metallic films of less than 10-6 in thickness with a degree of
accuracy much beyond that heretofore attained in the above
experiments. It was necessary to provide films of extreme purity
and make electrical contact with them which would exclude the
errors introduced through direct contact clamping between these
very thin films and their supports leading to the electrometer. ..."
-- Otto Stuhlman, Jr. in Physical Review, Feb 1919 (Iowa)
ω
"It is well known that the short-lived atoms of radium A, B, C, and
C' are deposited on the surfaces of objects which come into contact
with radon. Three of them, namely, radium A, C and C', emit alpha
rays. The emulsion of a photographic plate is blackened by these
alpha particles. ..."
-- Ç. Jech in Nature, Feb 1948 (Praha - Bulovka)
ω
"... Some change is produced in the material by the action of
exciting light, and this change persists for a considerable period
after all visible phosphoresence has ceased. In other words the
effect of a given excitation in producing phosphorescence depends
upon the previous history of the phosphorescent substance. ..."
-- Edward L. Nichols and Ernest Merritt in Physical Review, Nov
1907 (USA)
ω
"In einem inhomogen stroömenden Gas mit ungleicher
Temperaturverteilung wird in jedem Volumelement infolge der
ablaufenden irreversiblen Vorgänge (Reiburg und Wärmeleitung)
die Entropie vergrößert. ..."
-- Max Kohler in Zeitschrift für Physik, Jan 1950 (Horb am
Neckar)
ω
"... Sommerfeld has shown in his well-known investigation on the
mathematical theory of diffraction that the diffraction fringes due
to a semiinfinite screen may be regarded as due to the interference
of a system of a series of cylindrical waves emitted by the edge of
the screen with the incident plane waves. ..."
-- Chandi Prasad in Physical Review, jan 1919 (Benares)
ω
"The physical properties of metallic silicon, in so far as they have
been investigated, show this substance to be of peculiar interest.
The position of the element in the periodic system between the
metals and non-metals may explain some of the deviations of its
properties from those of the stronger metals. [...]
"The ends of a silicon rod were copper plated. Upon each end of
this rod were placed two wires, one of copper and one of
constantan. The electro-plating process was then continued until
these wires were firmly fastened to the silicon rod by a bridge of
copper. Pipe stems were used for insulation. [...]
"The direction of thermal current was found to be from Si to Cu
through the hot junction. [...]
"It will be noticed that the thermal E.M.F. generated by a
lead-silicon junction is very large. Another peculiarity about it is
that the curve is not parabolic, being at least to the third degree.
This double curvature may possibly be due to a large Thomson
effect. ..."
-- Frances G. Wick in Physical Review, Nov 1907 (Cornell)
ω
"... Foucault unquestionably succeeded in minimizing his difficulties
by using a very long and very heavy pendulum, but his results may
not have been as exact as some of us have supposed. [...]
"For example, [...] 'La montre à la main, ou voit que, à Paris,
la déviation est un degré en cinq minutes.' Such statements can
not be thought as representing precise measurements. They are
good enough to leave no doubt in regard to the general proposition
that the earth rotates on its axis, but they are not by any means
exact. If success depends upon great length and great mass,
Foucault's results ought to have been very exact. ..."
-- A. C. Longden in Physical Review, April 1919 (Galesburg, Ill.)
ω
We will, after some other discussions, proceed to the
first empirical example, together with the first computer
program performance. In this book you will find
the full Lisa programming language sources for all models called
on, and also the location on the internet where the model can
be collected for free, sparing you type-in time. We will continue
to sprinkle with fascinating quotes from that classical period,
rather pre-1950, and often from a german language context.
We will give a general version of the supermodel theory which
is elucidated in the various contexts, suitable also for the
more biological phenomena we hope to go into, and also the
question of mind in general. It should be clear from the outset
that the supermodel theory involves a certain perception-like
feature which implies that the gap between essential matter
processes and high-level biological and cognitive phenomena,
and also feeling, may, if this postulate holds, not be such
a wide gap after all. However, one must keep in mind that
it is in the current state of science not at all part of the
typical jargon to distinguish clearly between localist-like
phenomena which yields to a causal description of the conventional
kind, and phenomena which in some way can be considered as not
at all limited by the speed of light -- they are in some manner
more 'immediate', but that is not to say that we can with any
scientific certainty lump together all phenomena which do not
yield to the speed of light limit as one type of process. The
differentations we can find here may be at least as important
as the differentiations found e.g. as for the particle masses
of nuclei, and, in a certain further development of the supermodel
theory, I argue that there are indeed many more levels of
discernment of speed beyond the speed of light, as a natural
implication of the concepts which I have found fruitful already
to engage in the essential theory, given certain meaningful
additional postulates.
However, what is a key point relative to biological phenomena
is that the supermodel theory is able to speak of the collective
or holistic properties of quantic systems without asserting that
this feature is grown from below due to extraordinary local
conditions. Rather, this feature is the expression of a certain
type of perceptiveness which is the PMW principle, which generates
and also dissolves the active models, as they act on each other.
This principle, if correct, means that any aggregate of
phenomena can possibly be subject to similar conditions, no
matter how large the aggregate is. However, the subtle wholeness
which flow from an active model must in some sense work together
with the causal (and often light-bound) processes which are in
effect between the constitutent parts. In a situation (such
as superfluidity or superconductivity) in which the causal processes
are small compared to the influence of the supermodel, the holistic
element is macroscopically very evident. In biological situations,
there is a variation, I postulate, in the sense that the holistic
aspect is more subtle. It is this subtlety which the Bohr/Copenhagen
interpretation of quantum theory, which in vague ways has dominated
until now, does not really allow for, since it refers to situations
in which the holistic properties are clear-cut and digitally applied
initially, but does not have a generative principle.
As already indicated, all the phenomena here discussed are worked
on through one single computer program which is made so as to itself,
in its formal shape, provide an illustration of the novel theory
of supermodels. When it performs, it provides various forms of
graphical and numerical representations of the model experimental
emulation, and allows thereby comparison with physical empirical
research data and so forth. It is the contention of this writer
that the future of physics will do well in discerning between
first-hand physics in which the phenomena and theories allowing,
although they often have an imaginary and free speculative content
(e.g. the absolute time of Newton's theories was of course not
an observable part of them), for an as direct formalisation towards
numerical predictions as at all possible. The second-hand and
third-hand (and worse) derivations of abstractions upon abstractions
which commonly has interfered esp. with post-1950 physics when
concrete phenomena has been sought to be better understood does
not impress this writer as science at its best, but rather can
be compared to when assembly language programmers discuss the
best way for sorting bits quickly, or else compare differences
in decimal number compression algorithms. The notion of first-hand
physics must not be confused with a positivist (logico-empiricist)
agenda, in which metaphysics was sought to be cancelled in favour
of trivial data focus with meagre, unimaginative theories put on
top of them. First-hand physics involves first-hand imagination.
This will all be clearer when we work through example after
example, and further acknowledgements will be given as the theory
of supermodels as a unifying, ground-breaking approach incorporating
essentially all of the phenomena of physics is here elaborated in
this the first of an indefinitely long physics and science series
of books utilizing the Lisa programming language from my hands.
In breaking with typical modesty of this writer, I will submit that
I think all of Born, Dirac, Schrödinger, Einstein, Maxwell,
Planck, Bohr, de Broglie, Heisenberg, Feynmann, Mach, Bohm and more
would have welcomed both the Lisa programming language formalism
approach as a unifying approach to physics, and that the theory of
supermodels would have by them been considered a broad and deep
enough concept, allowing of all sufficient details, to handle
both subnuclei phenomena, molecular quantization questions,
electromagnetism, gravitational curvature questions, as well as
pave open the door for a bridge between essential physics and
higher-level biological activity. It is by the passion of the
foregoing that it has become easy to erect it. By its novel
predictions we will have a chance to come to grips as to whether
it truly represents new insights into reality, or is a sideway --
and I challenge all of today's young and active intelligent
thinkers, inside or outside currently respected scientific
communities, to realize the vast implications of this new
approach and both trust it and, in the best scientific spirit,
aim to generate both instances of confirmation and of
disconfirmation.
ω
"...Les deux Mémoires conjoints que M. David Bohm
a publiés en janvier 1952 dans la Physical Review
ont ramené l'attention sur la question de
l'interprétation de la Mécanique ondulatoire.
"... En particulier, il a ramené l'attention
sur la possibilité d'une interprétation de
la Mécanique ondulatoire autre que celle qui
est actuellement adoptée et il a montré
qu'il n'est pas inutile de soumettre la question
à un nouvel examen minutieux.
"... Telles sont quelques-uns des résultats
intéressants développés par M. Bohm
dans ses Mémoires, mais la partie ls plus
originale de son travail est certainement sa
théorie de la mesure que nous allons
maintenant analyser. ..."
-- Louis de Broglie in his book 'Une Tentative
D'Interprétation Causale et Non Linéaire
de la Mécanique Ondulatoire', Paris 1956
ω
"... the interaction between observer and object
causes uncontrollable and large changes in the
system being observed."
-- W. Heisenberg in his book 'The Physical
Principles of the Quantum Theory' Chicago, 1930.
ω
"... Was von den ersten statistischen Interpreten
als ernster Einwand gegen die ganz naiv
realistische Wellenauffassung vorgebracht
wurde: ein System könne nicht zugleich
in zwei verschiedenen Zuständen sein, z. B.
zwei verschiedene Energien haben, das ist von der
neuen, durch die Transformationstheorie und
die Heisenbergsche Unschärfebeziehung
geläuterten Interpretation stillschweigend
assimiliert worden. ..."
-- E. Schrödinger in his preface to the
book 'Elementare Einführung in die
Wellenmechanik' by K. K. Darrow, Leipzig 1929
ω
"... By studying the statistical equilibrium of
a number of such systems in a field of radiation
Planck was led to the conclusion that the emission
and absorption of radiation take place in such
a manner, that so far as a statistical
equilibrium is concerned only certain
distinctive states of the oscillator
are to be taken into consideration. The
particular energy values are therefore given
by the well-known formula En=nℎω
where n is a whole number, ω the frequency
of vibration of the oscillator, and ℎ is
Planck's constant. ..."
-- N. Bohr in his book 'The Theory of Spectra
and Atomic Constitution: three essays', Cambridge
1922, 1924
ω
"... If we come to a region of the order 10-13 cm.,
however, it is quite improbable that the result of
a measurement of such accuracy could be
independent of the means by which it is carried
out, since every particle used for the measurement
will itself have a 'size' of the order 10-13 cm. ..."
-- W. Heisenberg in his book 'Two Lectures', Cambridge
1949.
ω
"... If a system of co-ordinates K is chosen so that,
in relation to it, physical laws hold good in their
simplest form, the same laws also hold good in
relation to any other system of co-ordinates K'
moving in uniform translation relatively to K. This
postulate we call the 'special principle of
relativity'. The word 'special' is meant to
intimate that the principle is restricted to the
case when K' has a motion of uniform translation
relatively to K, but that the equivalence of K'
and K does not extend to the case of non-uniform
motion of K' relatively to K.
"Thus the special theory of relativity does not
depart from classical mechanics through the
postulate of relativity, but through the postulate
of the constancy of the velocity of light in vacuo,
from which, in combination with the special principle
of relativity, there follow, in the well-known way,
the relativity of simultaniety, the Lorentzian
transformation, and the related laws for the
behaviour of moving bodies and clocks.
"... In classical mechanics, and no less in the
special theory of relativity, there is an
inherent defect which was, perhaps for the first
time, clearly pointed out by Ernst Mach.
"... Let K be a Galilean system of reference,
i.e. a system relatively to which (at least in the
four-dimensional region under consideration) a
mass, sufficiently distant from other masses,
is moving with uniform motion in a straight line.
Let K' be a second system of reference which is
moving relatively to K in a uniformly accelerated
translation.
"... It will also be obvious that the principle
of the constancy of the velocity of light in vacuo
must be modified, since we easily recognize that
the path of a ray of light with respect to K'
must in general be curvilinear, if with respect
to K light is propagated in a straight line with
a definite constant velocity.
"... The introduction of a system of reference
serves no other purpose than to facilitate the
description of the totality of such coincidences.
We allot to the universe four space-time variables
x1, x2, x3, x4 in such a way that
for every point-event there is a corresponding system
of values of the variables x1 . . . x4.
To two coincident point-events there corresponds
one system of values of the variables x1 . . . x4, i.e.,
coincidence is characterized by the identity of the co-ordinates.
"...It is not my purpose in this discussion to
represent the general theory of relativity as a system
that is as simiple and logical as possible, and with
the minimum number of axioms; but my main object is
to develop this theory in such a way that the reader
will feel that the path we have entered upon is
psychologically the natural one, and that the underlying
assumptions will seem to have the highest possible
degree of security. With this aim in view let it now
be granted that:--
"For infinitely small four-dimensional regions the
theory of relativity in the restricted sense is
appropriate, if the co-ordinates are suitably chosen.
"For this purpose we must choose the acceleration
of the infinitely small ('local') system of
co-ordinates so that no gravitational field occurs;
this is possible for an infinitely small region.
"...If the ds belonging to the element
dX1 . . . dX4 is positive, we follow
Minkowski in calling it time-like; if it is negative, we
call it space-like. ..."
-- A. Einstein in Annalen der Physik in 'Die Grundlage
der allgemeinen Relativitätstheorie', 1916, as
chapter The Foundation of the General Theory of
Relativity in the book The Principle of Relativity,
New York, 1923, by H.A.Lorentz, A.Einstein,
H.Minkowski and H.Weyl, with notes by A.Sommerfeld,
transl. by W.Perret, G.B.Jeffery.
ω
One of the things which comes forth straight and directly by looking
at Einstein's articles among the massses of other articles produced
in his time is that he relentlessly aims ambitiously to understand the
wholeness of all that is. His informal language is brief, poetic, but
never cold; one senses a warm heart, intent on communicating to
friends, knowing they have great agility of mind and trusting they
also share the good ambition to understand fully and in depth.
It is on the basis of what Einstein calls a 'natural psychological
ground' he offers his formalisms, and they are, despite what some
have claimed as for his skills, at least as high as any other
physicist writing in similar journals -- quite possibly enormously
higher.
One also feels that Einstein has a humility, an awe, in relation to
the universe. His aim does not seem to win among scientists, but to
win over his ego in allowing a pure essence of thought-insight to
come through, if possible, from the universe, through him, toward
the reader, by means of the language skills (formal as informal)
which he possesses.
It is also apparent that although Einstein has spoken up in favor
of emphasizing symmetry and such, his emphasis is consistently
toward an organic simplicity, not a minimalistic simplicity or cold
esthetism at all costs. This organic simplicity may involve more
words and more expressions and he values the psychological realm
-- as many of the superb, eminent jewish scientists with their
kabbalistic sense of unity with a living, feeling universe also do (and
to which I would also include David Bohm, who worked with the
ageing Einstein for two weeks following the publication of Bohm's
grand, systematic (and rather classic) Quantum Theory -- a book
which, when Einstein got it, he reputedly said that this is the first
time quantum theory has made any sense at all to him!). This
valuation of the psychological realm implies (does it not?) that he
sees the human mind as part of the 'masterpiece' which the universe
is, and that anything which is to be presented about this universe,
if it is to be honorable good science, must make honorable good
meaning to the mind -- even if rebellious against previous concepts.
Einstein clearly has a rebellious attitude towards the notion of
time. As Arne Næss pointed out (a long-time admirer of Einstein in
many ways), it was the fashion of very early 20th century (a
fashion which perhaps Einstein helped introducing!) to believe in
determinism and regard motion as mere appearance. This echoes the
view of the classical hellenes.
Prior to the centennial shift, from the 19th to the 20th century,
the good-old-bad tradition in geometry, beginning with Euclid most
explicitly in one of his first axioms, where he speaks of finite
lines, then infinite lines, without suggesting it could be a somewhat
dubvious transition in thought, mathematics had seen Georg Cantor's
work soldifying the sense in which the infinite is a well-treated
concept, to some extent.
With Georg Cantor, one had achieved something like a counting
over infinity, allowing the size, in some new sense, of the infinite
set of all finite whole positive numbers, to be compared, and found
in some new sense, less than, the infinite set of all finite decimal,
or 'real' numbers, including the so-called transcendent numbers. He
had achieved, with the production of a masterful new proof, the
so-called diagonal proof, to show that one cannot line up the real
numbers alongside the so-called natural numbers (ie, the whole
positive finite numbers 1, 2, 3 and so on). This proof Bertrand
Russell struggled with in his youth, then accepted, and apart from a
slight diversion in his little book 'Mysticism and Logic' (a book
devoted to a mystic sense of the infinite, which he later on claimed
was written under 'influence of a woman'!), he believed in it even to
an extent one can say it was one of his foundational beliefs.
So it is not therefore strange that a physicist in 1905 can employ
concepts on the infinite -- indeed, had to, unless he changed job
definition and started being a rebel in mathematics and its
foundational thinking, instead of being a rebel in physics -- such as
we see Einstein do.
And, no matter how mathematical formalism may or may not have
gone astray in its foundation, it may still be, of course, that
continuity, and the rather compatible concept of the infinitesimal,
alongside the actuality possibility of the infinite, can still be totally
applicable to the essence of the universe -- this feeling of a
grandiose origin and nature persistent in existence, in cosmos, I
totally share with Einstein at a certain level.
However, I am eclectically bent. I recognise a model monopoly
when I see one, and I pick it apart, but do not ignore the pearls
within it. There are pearls within Einstein's argument in favor of a
dimensional-twist or bend, higher than the 3d, the three dimensions
of conventional classically conceived space of height, width and
depth. But if we are going to emphasize, as Einstein wishes, a
natural psychological insight, we must also be able to perceive in
quiet the fact that such formalisms do not really penetrate with any
coherent, cogitant clarity what infinity is, or what it does, or
indeed whether it at all can be consistently applied in the way
Einstein hopes to. Much as I respect Einstein for his immense
efforts and superb clarity, do we not see the paradigm of closure
of thought, ignoring the possibility that finitely applicable formalisms
fail when pushed to their infinite, and infinitesimal boundaries, as he
lays out the very foundation thought of the General Theory of
Relativity?
As I have pointed out in the 2004 book, and still more clearly,
perhaps, other places, also at my website, any formal argument
working well with finite whole numbers may completely lack
substance as soon as the apparently innocent principle 'et cetera'
(or the notorious three dots) are added to the concept. Reflection
over this leads to the following grand postulate: while existence as
well as mind indeed may actually involve a sense of the infinite in a
true sense, a formalism which is found to operate well within a
clearly defined finite region with finitely many members of a set or
whatever type of collection are involved, should in no way be
trusted to apply if extended indefinitely, whether to the indefinitely
large or to the indefinitely small. In other words, the notion of the
'limit' as an approach to the infinite is not at all an acceptable one.
My argument is a new one, but the conclusion is shared with, it
seems, quite a few people who have given thought to foundational
themes in logical set theory and that which is regarded as
'foundations of mathematics'. My argument is however so simple it
strikes at the theme strongly enough for me to feel it is honest to
say that it implies that the very concept of mathematics is a
complicated one, if not a fruitless one; but that eclectically this and
that and the other formalism can be extracted from it, and
relegated under other headings, notably the most general one --
'formalism', but also a wide variety will be compatible with the
notion of a mature, 32-bit, within-boundary-defined programming
language.
The idea that any natural psychological argument involving a
blending of formalism with the concept of the infinite, or
infinitesimal, or both, follows directly from the fact that the
following argument seems to me to imply that it is impossible even
to define the set of all finite whole positive numbers 1, 2, 3 and so
on.
I will very briefly indicate how I have done this, with far more
words before. I am grateful to Herman Ruge Jervell, prof. in
language, logic and information technology at the University of Oslo
for informally, during our dialogues, approving of my argument,
although the little thesis I offered to that institute was not formally
approved perhaps mostly because of other professors not agreeing
in the argument.
Assume postulate P1, that X is a collection, a set, whose members
are all of, and nothing at all but, the finite positive whole numbers
beginning with 1, 2, 3 and going upwards.
I will show that P1 leads to the postulate Not P1. In other words,
I will show that P1 implies a contradiction; which means that there
is no such set X. Since the existence of such a set is necessary to
erect such formalisms as Einstein call on for e.g. his general
relativity theory, as well as such formalisms as are involved in the
quantum postulates, I will by this indicate that we do not have a
suitable formalism for physics in any previous endavours at all, at
this essential level. Note that the argument does not rely on Kurt
Gödel's famous second incompleteness theorem, which is another
formal work one cannot push through unless one assumes such
things as the set X.
Argument. If we have set X, we have a set which has no upper
boundary. The argument for this is that given any finite number, we
have the possibility of adding one to this finite number, to produce a
new finite number, along the conventional, established definition of
the addition operator.
Since X has no upper boundary, the amount of members in the
collection X is not finite. Ie, it is infinite.
That means that if we portray X in the following manner, where
the vertical upwards direction indicate additional members of a
larger size,
.
.
.
I I I
I I
I
then the vertical growth direction is limitless, ie infinite. It is also
clear that, when we see how additional members are added, step by
step, in the imaginary construction process of the set X, like in
going to four members,
I I I I
I I I
I I
I
then five members
I I I I I
I I I I
I I I
I I
I
that there is a perfect absolute symmetry between the
height of the triangle the numbers, as represented by vertical
bars, form, and the width of it -- the horisontal topmost line. This
symmetry is perfect and absolute if we stick to consistent writing
of the marks to represent the enlargement of the set towards
infinity, with a suitable selection of font and spacing of course.
But that means that we in fact have two infinite growth aspects to
the triangle, for it to sustain this symmetry: the vertical and the
horisontal. In fact, the vertical and the horisontal are exactly
identical.
This implies that the set X, which must have infinite vertical size
when depicted this way, also has members which are not infinite.
But such members are not members of X, consulting postulate P1.
We are led therefore to Not P1. QED.
Of course many people have been aware of possible complications
whenever anybody invokes the term of the infinite or limitless in
any connotation in mathematics. Some people have sought refuge,
of course, in the concept of, in some cases, almost substituting
the notion of infinity by a particular concept which is somewhat
misleadingly called 'the limit' -- as we know -- which more precisely
can be called a 'flexible limit', involving an oft-used phrase --
'to go as far as we want'. For instance, one has done calculations
not on the beginning of a series of numbers, but on 'any one of
them, x', showing that if one has x, one can also calculate f(x),
which then is supposed to apply for the whole of the series.
This f(x) can for instance be a bridge to the next member in the
series, or it can be an investigation of a property, such as is
called (also by Abel) 'convergent'. The particular advantage of
the limit concept has been in showing that, when one proceeds
to finer resolution in the adding up of gradually
smaller areas or the like, one has been able to show that,
given certain assumptions which were not challenged at the time,
the result sums up to within an error limit. One has, for
instance, such situations as where one can say, given any
error limit p, one can give a resolution m so that, if the
calculation proceeds to this resolution, then it won't appear
to break with the limit ±p if one has any resolution at
all at least as good as m.
This type of reasoning involves no direct talk of the infinite;
it involves what we most generally can call a 'flexible limit',
a variable which can be moved -- upwards, or towards zero, or
towards a particular number or state -- and which certain
formal characteristics seem to follow (and some of the
points of criticism I raise have been of course raised
by the once-existing clan of so-called "intuitionists",
and by Brouwer, who made worthwhile contributions perhaps
mainly so as to make more questions explicit; however I
do not base my work on any of their criticism exactly,
and I have in particular not found that they go even
nearly as far in arguing adequately against the notion
of the set of all finite whole positive numbers as I
do -- nor have I seen anything like the geometrical
argument I have offered in their writings; however it is
not impossible that some of them, in some lesser-known
article, have touched upon this, as my research in the
libraries of mathematics have been far from as complete
as it can be).
When I talk of the limit concept in this discussion on
the viability of trying to achieve a general definition
of natural numbers by means of an infinite set,
I refer to the limit notion in its most abstract sense -- a
generic sense. Here, we do do not necessarily talk of any
error limit or any integrals or anything like that, but
simply address the idea of looking at just some (finite)
numbers at a time, with the notion that these can be
varied, we can 'go as far as we want' applying this condition.
At a very general and abstract level, that is, I think it is
right to say, the way the limit concept did, for a while,
seem to end the feeling of dilemma around the infinity
questions in the 19th and 20th centuries in the foundational
set theoretical / mathematical areas of discourse in science,
meant that a focus could go to technical application of
formalisms, allowing many forms of technology to arise;
pragmatically, that gives of course a limited kind of
support to the notion. However, one must not rashly conclude
from limited practical applicability into the domain of
asking for coherence of our underlying ideas, and sooner
or later this coherence will dictate also practicality,
when the domains are suitably extended. We must therefore
be given the space, and the attention-room, to fulfill
the questioning into how indeed we are supposed to
understand the finite, the infinite, and their
relation, in terms of answering it adequately in our
language at an informal level, and then, if necessary,
revising, a little, or perhaps completely, all our
formal languages accordingly. Indeed, the Lisa formalism
is an expression of such a rethinking -- every extant
element of Firth and Firth Lisa/Nod501 have been forged
in constant awareness that one must respect that something
entirely new can occur as soon as 'et cetera' or anything
like that concept is invoked onto something which by
itself looks clear and well-defined in a finite sense.
For instance, the set-theoretical closure {..} is never
used, but rather (for texts), a version which implies
a sense of the unclosed, namely }..}. And while Lisa
allows the ideas within an algorithm to be grouped
with (( .. )) operators, Lisa is written in my own
Firth with the express statement that such a grouping
is only to assist the reading of the program on a
semantic level and that these operators have no syntatical
application whatsoever. For instance, one can omit to
include a )) after a (( and the program will still work
and this is part of its operational definition. It is
also defined to work in a 32-bit number context with
its whole finite numbers being roughly within two billion,
plus-minus, and furthermore, the context of the language
as occuring on a Personal Computer of the 32-bit hardware
kind with its own operating system context clearly defined
is emphasized (instead of the conventional approach in most
of computer science in which the language is sought to
be defined in abstraction from its hardware). In other
words, the language is boundary-aware. It is a way
to operate a physical digital piece of hardware in a
way which is, practically speaking, roughly first-hand.
Firth Lisa listens to the set boundaries in a first-hand
way, the language is made in contact with the PC hardware.
It is in that sense not a conceptual question involving
infinities when we ask: what is the relationship of our
formalism to our theory? For the theory exist in mind,
while the formalism is engaged to take a particular
manifest apparatus physically existing in our civilisation
and make it assist the semantic formation in our mind of
our theory, but not 'represent' it. In this way, my
conception of the computer language formalism is
fundamentally different from that which Alan Turing
initialized in this sense, for he explicitly states
that the ideal computer involves infinite size of its
recording substance. I do not state such a thing,
in fact I regard it as a result of not paying enough
attention to the infinity concept, for it is clear
to me, based on the attention we already have given
to the question in this book, that it is informally
unclear whether the properties found to apply to
something finite are not negated or else transmutated
when informally applied to that which is nonfinite.
The notion of the flexible, or variable, is somewhat
near the indefinite, which again is very near the
infinite in some senses: but when we speak of a variable
as varying within e.g. minus two billion to plus two
billion, or more precisely, minus two to the thirtyfirst
power to plus that value (plus or minus one, where the
plus minus sign is one bit), which is around plus minus
2147483648, then have conceptually a completely
well-defined finite set at a practical level,
not involving complications as stated above. This is
then a more coherent approach to physics, I submit.
One can still ask questions such as, can we regard
a finite set of numbers as emanating in some sense,
or even in some sense referring into, a movable
infinity of sorts semantically speaking, and one
can also suggest answers to this along positive
lines, without either having to make systems over
such a relationship (which would themselves beg
new questions of infinity versus the finite), nor
consider the meaning of the finite numbers as
something which we have to make any final statement
about. Even if we are as fish swimming in an ocean
of the infinite without initially having clear
concepts about this infinity, we can still relate
to ice floating in it on its own terms, and also
feel free to imagine that the ice is indeed formed
out of the same substance, without this thinking
having to interfere with what we think happen if
we bring e.g. two or three pieces of ice into
close contact. In the same way, an algorithm on
a computer can be considered on its own when we
have a concrete situation without the pretense
of infinity put into its formalism at any point
whatsoever. This consideration on its own means
that we can feel free to say of a computer formalism,
such as Lisa, that it does not represent the world
any more than a Walt Disney cartoon of Donald Duck
represents any particular segment of civilisation --
but represention is not the point. In the case of
the computer formalism, it is a stimulus of mind,
and the stimulus has a relevance for the theory,
when it is coherently made according to that intent.
In the case of the cartoon, it is also a stimulus,
and that stimulus can e.g. have a relevance for
an aim to experience something entertaining.
Representation is not what either is about. This is
what I propose will solve a vast number of hitherto
almost insolvable-appearing questions in science --
this new attitude to the informal; and I think that
the presence of technology in an expensive, standardized
format has made it very easy to say this -- far more
easy than at earlier stages, and so I do think we should
be grateful for this development.
However, let me add here, as I have said before, that
I do think the 32-bit computer has a psychological
advantages above both lesser-sized computers (which
were too small for adequate illustrations), and
larger-sized computers (which, like the 64-bit and
larger, involve memory sizes utterly and completely
beyond what can in pixel- and byte-aware detail
be filled up in a first-hand way by a program
made by hand, line by line). The formal must be
a hand-maiden for the informal. The 32-bit sized
computer is ideally suited to stimulate mind, while
having clear limitations, which (just like the cartoon),
informally serves to remind us of its relationship to
us -- where mind is primary. It is therefore of key
importance to the evolution of science and humankind
as a whole to settle of the Personal Computer standard
of the 32-bit kind with the 1024*768 pixel display
with its 386/Pentium-compatible set of languages and
platforms as a basic item and common reference ground
for all further discussions, whenever a formal language
of a digital kind should be invoked, if we are to
appreciate the fundamental difference, and key
distinction in priority, between the informal, -- where
we make our theories -- and the formal, where we
seek to make illustrations to clarify what we mean
informally, and towards engaging in empirical
testable predictions towards instances of confirmation
and disconfirmation. The standard Y2000-compliant
computer is not a mere step on a ladder towards
indefinitely more digital computer ware, it is,
like the notion of a book, of key importance to
the mind of a human being, and this will always,
of course, be so. The complexities involved in 64-bit,
or billion-bit, or half-nonlocal computers of a more
quantum kind, or merged with biology or plasma or
something else, are so that they do not invite
a clear discernment of what mind is doing and what
formal apparatus on pieces of technology can do
as illustrations, rather than representations.
Put simply, a too powerful digital computing
technology is likely to seduce humanity into
stupidity, and also make features of civilisation
(if they depend on such computer devices) too
second-hand, or, more likely, third-hand and
fourth-hand, to be flexible relative to our
requirements in a first-hand way, because the
vastly powerful, far-more-than-32-bit computers,
or not-quite-digital, will have to require
second-hand, third-hand, fourth-hand programming
languages in which the essential relationship to
the pixel and the byte (and thus to the knowing
of the fact of what the machinery actually does
in a first-hand way) is lost. We must not lose
the 32-bit Y2000-compliant PC; it must be retained
as a key element in all neopopperian science
forever. This follows naturally from all these
considerations and I urge that we all now
soldify these open standards we have got and
do not give in to the companies which, in their
eagerness to try to make people buy more of their
software or hardware stuff, simply make more
complexities of a 64-bit kind and higher-bit
kind just to get new products out each season.
We must combat the notion of progress at all
levels by asserting standards at some levels,
and limit progress to a progress which is humane
and compassionate and responsible within the
levels we soldify, also in terms of "zones of
technology", of which the 32-bit Y2000-compliant
3*4 monitor sized personal computer can be of
extreme significance, for all time, and for everyone,
ultimately.
Having said this, let me again argue more against this
very important point of trying to handle infinity by
means of easy, sloppy concepts, or quick definitions
one has not thought about at all, really. The notion
of the limit, in its most generic, abstract sense (see
above), deserves perhaps more discussion here. For one
might think that the limit concept sort of "solves"
the issue of how to define the set of all finite whole
positive numbers above.
This very abstract notion of limit, including all its more
particular forms, however does not solve the question
conceptually, coherently, as I think it is easy, given
my arguments, to show. And that also means that any piece
of technology based on a formalism which contains the
concept is unlikely to have unlimited domain of application,
and the science involved in it is unlikely to involve a
coherent theory of the universe in the sense of wholeness,
for this seems to call on coherent concepts which have been
through well through -- all the way through.
Exactly on this latter point -- that we must think
coherently all the way through, explicitly, if we are to have
a proper physics theory of the universe as a whole, which we
should indeed aim at, I find that my own general meta-scientific
or meta-physical points cohere perfectly with those of Einstein,
of course. The burden of argument lies with those who argue for
less emphasis on coherence and expliciteness. Science involves
rational dialogue, discussion, emphasis on coherence, on deep
understanding, on the concepts of wholeness; and the technical
permutations of tokens in this context should be consistent,
and reflect the coherence of the semantic understanding. That
doesn't mean, of course, that those who prefer to give themselves
the honorable title of 'scientist', 'physicist', 'philosopher'
or whatever it is are any other than other folks, who just as
easily can give themselves in to the temptations of biased
thinking, bred by selfish emotions, in which rationalism is
merely called on when it serves one own purposes. But if we
appreciate that the scientific attitude is a standard of
excellence, then we will not too easily identify science with
what some people (or some institutions) do, but appreciate
the validity of also what Einstein said in that those who do
science should do well in staying out of 'scientific
institutions' (he himself worked at a patent office when
he was at his most productive, transmitting elegant articles
to german journals and rapidly, within a space of some twelve,
fifteen month, laying strong elements of the foundation of
quantum theory, thermodynamics and his own relativity theories).
At the time Bohm visited Einstein, Einstein was at Princeton,
but without obligations to teach, and regarded as many as
a bit silly for his idea that a theory involving both gravitation
and quantum phenomena could be erected. While he was not able
to do so in any satisfactory way, physicists at large soon
began to appreciate the importance of the idea after his
death.
As Bohm mentioned in his dialogue seminar I co-arranged in
Oslo, he sent his Quantum Theory book both to Bohr and Einstein,
but only Einstein responded; after the weeks with Einstein, who
expressed his misgivings on the lack of picture of reality in
quantum theory, he produced his two articles which outlined
his hidden variable theory. However this not even Einstein
appreciated. Louis de Broglie soon picked it up and announced
it as an important extension of his own thoughts at the time,
which Bohr had persuaded him to drop (according to Heisenberg,
while Broglie was bed-ridden with a flu, Bohr used the
opportunity to nail the arguments for hours upon hours
until Broglie, for the time, gave up resisting the
Copenhagen Interpretation our of sheer headache!), in
particular in relation to how Bohm succeeded in treating
the measurement instruments as part of the physical situation
rather than, as Bohr had often done, as standing outside of
it, and being thought of as representing something which must
be described in 'classical terms'. Bohm's theory of the
quantum potential is however different than Bohr's theory of
the pilot wave in ways perhaps made clearer by the work of
J. S. Bell later on.
Indeed, Bell writes that he did his famous analysis
(the Bell inequality theorem, which involves distinguishing
between implications of classical quantum theory relative
to the question of whether it implies a correlation that,
if analyzed in terms of hidden variables, involves
faster-than-speed contact of some kind, or whether
slower-than-speed contact is enough, at a statistical
level, to accomodate its predictions. He found that
it implies, numerically, a faster-than-speed contact;
and Aspect by a series of experiments late in the 1970s,
as is well known, achieved a confirmation of this)
based on reading Bohm's articles and wondering how
Bohm appeared to circumvent von Neumann's arguments,
put forward to de Broglie decades earlier, that a
theory where position variables are unknown or hidden
is impossible. Bell found that von Neumann implicitly
asserted that all interaction was local, under the
heading of 'given reasonable assumptions'. Bell's
work led to a general realization that nonlocality
-- in some fashion or another -- is part of what
quantum theory is all about. However, as is clear
from the initial quote from Bohr much before Bell's
work in the 1960s, the notion of direct immediate
nonredicble wholeness or interaction of a whole
ensamble has always been part of the flavor of
quantum theory as informally discussed.
While Bohm's theory achieves tehnically the same
as Broglie's updated theory does achieve, the notion
of the reality picture is different in emphasis in the two:
Bohm's quantum potential in general does not look wave-like,
and is supposed to be added to a classical potential, as far
as I understand; whereas Broglie's pilot wave rather looks
more wave-like and represents this sum. In other words,
in de Broglie's approach, one doesn't have a classical
set of variables that clearly. The empirical status of the
pilot wave is however not clearly discussed, because de Broglie
still talks within the framework of conventional physics after
all, rather than rethinking the foundations entirely as e.g.
along the lines of Bohm's implicate order, speaking very generally,
or as I do with the node network of supermodels acting upon by
the contrast-, similarity- and echoing emphasizing principle of
the PMW as in my approach, in which the manifest reality concept
gets an important aura of being part of a greater order which
is coherently thought about.
I should also add that the way I introduce a supermodel
network with a principle of movement towards wholeness --
emphasizing not just similarities, as in Goethe's idea of
evolution of nature, and shared with Rupert Sheldrake's
morphogenetic fields, but also contrasts, and a general
form of echoing reverberances as well -- is eclectically
based on the informal ideas of de Broglie (who I came to
through Bohm's ideas), and of Bohm's implicate order idea
of course, as well as Einstein's general theory of
relativity in particular (but also the pre-Minkowsky idea
of his special theory, before the introduction of the
spacetime schema which Minkowsky produced as a pedagogical
mathematical framework and which led to a strengthening
of the deterministic aspects of Einstein's original, first
theory, which was more axiomatic and more abstract and
thus more open to alternative visualizations). It is
eclectically based on what I think informally works
best together in these and related approaches, and not
directly based on the formalisms in them, since I regard
the discussions around these formalisms as having
relatively little to do with reality, except when
they lead to particular new numerical predictions --
and more to do with the inherent difficulties with the
type of formalism which physics (and science in general)
has seen too much of; difficulties which seem, in many
cases, to have root in the finite/infiniteness dilemma
which soldified itself with the works by Leibniz and
Newton and which leads to a feeling that 20th century
quantum theory, even including de Broglie's and Bohm's
alternatives, more was 'superpositions' upon classical
theory than genuine alternatives; while Einstein
explicitly states that his work is a modification
of Newton's classical scheme. In short, they are all
pretty near the classical even though one gets the
sense that what is hinted at is completely different.
In my 2004 I also quote a number of other influences
for my thoughts, some nearer the core of physics than
others. Bohm's work on the implicate order led to a
large number of interesting metaphorical writings on
physics e.g. the ones by E. Laszlo, who earlier on
worked in what was called Systems Theory, then also
in the Rome Club on the limits of growth, and who
co-arranged the Chaos Pilot school in Århus where
I have once given a seminar for a day; and Lazslo
has strongly emphasized the idea of waves of various
kinds in connection to the local and nonlocal,
trusting this can lead to a new understanding of
mind. Such activities one has seen a lot of without
physics at a core being much impressed; I have for
my own sake seen little, both in Bohm's league and
around Lazslo and others, of relationship to the
popperian questions. Sheldrake has, on the contrary,
tried to prove that biology in classical sense is
predicting something in contrary to his theory, and
have proceeded to attempt to scientifically
investigate very concrete elements e.g. of
brain-to-brain connection between human beings,
but I have not seen in any of these pursuits that
sufficient ample space have been given to taking
into consideration any significant portion of
existing 20th century physics findings and try
to see it all together from afresh. As Bohm
pointed out to Sheldrake in a conversation they
had and which was printed, Bohm's implicate order
allows for something like morphogenetic fields
but does not imply them; and the implicate order
idea is more general and allows for other
possibilities as well.
I do not, however, see any real interest
in the infinite lively creative perceptiveness
of mind in Sheldrake's very strong emphasis
on the repetition of the past. His one single
idea seems to put nonlocality into biology
in a very simple-minded manner, if he forgives
me for pointing it out -- a nonlocality used
to transmit something from somewhere else
to where ordinary biologists did not suppose
it would reoccur, at a matter of form. I
see something of the same in Lazlo's
proposals, who however does not render
nonlocality as truly immediate, but merely
fast, and, in some cases, what he calls
'infinitely fast' -- yet mediated locally
by a special kind of waves.
I cannot say that I find in such proposals
any of the depth I at once found in the
implicate order. They are more to be
compared, at the conceptual level, with
Bohm's 1950 work on hidden variable
causal intepretation of quantum theory
by means of nonlocality, but lacking in
such formal genius brilliance as he had.
The supermodel theory is a far more
concrete theory than the implicate order,
yet just as deep in its framework -- it
perfectly coheres with the vision of
the implicate order, but contains, unlike
Bohm's implicate order work, a clear
bridge between something highly general
and novel, and both concrete numerical
postulates in physics as well as concrete
new predictions, allowing for something
vaguely resembling morphogenetic fields
or even Lazlo's waves as special cases
given certain extra criterions. However,
the vision of the universe as implied in
the supermodel theory is even more
creative than in Bohm's implicate order,
and far more so than in Lazlo's or
Sheldrake's theories, or in Prigogine's
newer works on irreversibility, or in
what I have seen from works in their
leagues and in comparative parts of
the newer forms of thinking about, and
within science, -- for even in Bohm's
theory one can find a kind of determinism,
at least as an unchallenged possibility.
It can still be, with Bohm's implicate
order, that the universe is merely an
unfoldment of something fixed, despite
the enfoldment principle (he calls the
unfolding-enfolding motion for the
holomovement, inspired by holograms,
as e.g. invoked metaphorically in
Karl Pribram's vision of the human brain).
In the supermodel theory, however, there
is a principle, detecting similarities,
contrasts, and echoing reverberances, and
acting subtly to enhance these, or dissolve
earlier enhancements when these are no
longer applicable -- and this principle
is taken to be responsible for all causality
as well as the nonlocality in a way the
examples should make clear; however, it is
explicitly asserted that it may be
certainly well be that a segment of the
fluctuations naturally occurring are indeed
completely free, rather than just relatively
free, so that this principle, operating on
the entire network of supermodels which
unfolds itself as particular, always changed,
manifest region (ie, the universe as manifest),
will act in togetherness with an influx of
something which renders the sum total both
irreversible and indeterminstic, however
not much like the type of indeterminism
asserted by the Copenhagen Interpretation.
Instead, we find that we go along with the
notion of the position as being more real
than asserted by the Copenhagen Interpretion,
yet that we are not making a fully causal
deterministic theory.
However, I will delay a little the introduction of my concrete
ideas until we have looked a little more into the question of
coherence on the notion of the infinite as dealt with through
the limit concept -- as the whole formalisms of all conventional
physics beginning with Newton and Leibniz and continuing up until
the present day in praxis relies on assumptions relevant for it.
For one might think that by introducing the notion of the (flexible)
limit one can simply avoid bringing in the daily life informal
notion of the infinite, and thus avoid the contradiction as
I have very clearly pointed out above. I do not think this is
a proper response to the situation, but it is, of course, worth
a try -- if only for the sake of negating it, so as to move beyond
it.
Suppose that we attempt to discuss the formation of a natural
number set N, beginning with 1, proceeding with 2, and then proceeding
in general by adding 1 to the highest member so far added to generate
a still higher one. This set we call N. We now say of the set N that
given any member in it -- finite, whole, positive -- let's call this
member y -- we can generate y+1. This is a property. We will even
say that it is a defining property. Now surely we have made a strong,
clear, consistent definition of N so as to surely exclude any
possibility of strange non-finite members?
The answer to this question is that we have not made a clear
definition which achieves this, and I will show why.
What we have made is to try to introduce an algorithm for making
N, as the definition of N. This algorithm, this rote procedure,
involves generating a higher member based on an existing member.
It is all well to say that we can build the concept of N initially
by focussing attention to this algorithm of generation, but it is
another theme altogether to say that all properties of N are
clearly elucidated by simple-minded repetition of this algorithm
of generation.
For let us now ask: is N infinite, or not?
Perhaps, those cunningly sticking to the limit concept, will now
say something like this: 'We do not know the answer to that question,
and we do not have to answer it, except in this sense: we have specified
the type of limit -- call it flexible limit if you wish -- and that
is enough. That is what characterises the size of this set N and
I refrain from further comments on it. This is not daily life language
after all, but mathematics. If you like, call that infinite, but I
mean nothing more by that word than that it adheres to this limit
idea. Yes, that is what I suggest: to define infinity as of a set as
equivalent to the concept of the limit as applied to it.'
Apart from the rather obvious sense of paradox in the statement,
I do not think one should be impressed by anyone who suggests that
one should not talk more about something. Such a statement, while it
may have a certain rethorical persuasiveness in some discourses in
science at a very early stage, tend to look shallow later on, when
it was found of inescapable importance to extend the application of
the initial idea beyond their initial contexts. In this case, however,
I think we can find additional applications of the concepts of infinity
by looking to the past of mathematics, enough to show at once that the
answer is inadequate, at least at a level of natural psychological
understanding of what we are at all talking about. I do not claim that
one cannot work consistently at a certain restricted formal level with
such definitions as above. What we are talking of here is whether we
admit that these formalisms should refer to insightful ideas in terms
of their definitions, or whether we are merely throwing tokens around
according to a set game of rules of permutations of them. I take the
stance of semantics: that we are going to do permutations, at a formal
level, based on clear ideas at an informal level, and I do think
implicitly, at least, all philosophically inclined people in all areas
of science cohere with this semantic stance unless they are dogmatically
against it for reasons of their own.
A response to the attempt indicated above to try to identify infinite
with the flexible limit idea is as follows: What then of the notion of
the sense of the whole set in terms of its size? For the limit idea
discusses the relationship between a couple of its members. Even granted
that one can talk of such things as 'any number' without presupposing
that one has, at least implicitly, already granted a different kind of
set definition already (from which one can extract members), the limit
idea does not speak of the size of the set.
Suppose the person infatuated by the limit idea says that 'by the size
I would say it is infinite, again in the sense that the set obeys the
limit idea -- or the flexible limit idea, as you suggest it should be
named.'
But all we have to do at this points is simply to ask: Well, do you
want to say that the size of the set can be measured in terms of a
finite whole positive number?
The person, whose attempts to repeat the definition of a set by means
of such things as a limit concept, will have to reject this, of course --
because the flexible limit idea prescribes a route procedure to make
more members given any such number.
But then, the size is beyond the description which a finite number
can be -- in this sense, the size is not finite.
The limit-oriented person will have to nod to this, of course.
At this point, we bring in the argument above (with my geometrical
presentation of the building up of the set, gradually, beginning with
two or three members, and increasing a little), and I ask whether the
person agrees that the set, at each step, is self-reflective in the
sense that the size of the set is itself, at each step, a member of
the set.
The limit-oriented person will have to nod to the simple rationality
of this point, of course. When we have four members in the set, {1, 2,
3, 4}, the size of it is 4.
The whole set, though, is not self-reflective. I point out that this
has already been admitted by the very fact that the person admitted that
the size of the set cannot be represented by a finite whole positive
number. Again, the person must nod.
And yet in every case of the application of the limit idea in
practise -- ie, the algorithm for generating more numbers, we see
a self-reflectiveness. So where, I now ask, is the coherence here:
the application of generating numbers in each case adheres to the
self-reflectiveness property, whereas the sense of the whole set
involves a clear negation of the self-reflectiveness property, if
we try to speak of the set as defined as consisting only of finite
whole positive numbers. This means that the limit concept does not
adequately define what we mean by the non-finite-ness of this set,
or its infinity, after all. I have not introduced any new domain
of application -- I have simply tried to go along with the idea of
trying to identify the infinity concept with the flexible limit
concept, and what we are led to, by utterly simple, utterly
rational steps, introducing no novel elements at all, just looking
at the implications of what we assert, is the negation of the idea
that infinity can be equated with the limit concept. For the limit
concept as such shows us self-reflectiveness, but the sense of the
set which it is postulated can be generated by it shows us lack
of self-reflectiveness. This is not coherent. This is plainly
incoherent. I therefore regard it as an instance of disconfirmation
against the idea that the limit notion is adequate -- it is refuted.
Perhaps our friend does not give up that easily. He, or she,
worried about it all, tries one more time: 'I hear what you say
and it makes sense. But what if we say that this breaking with
self-reflectiveness is an implication of the limit concept,
even though the limit concept in itself has self-reflectiveness.
It is an implication which comes of the indefinite number of
applications of it. Is that incoherent?'
To this I would simply answer, yes that is incoherent. If one
tries to equate infinity with the limit concept, one must stick
at it. We have shown that one cannot equate infinity with the
limit concept. The limit concept is of one kind, involving
self-reflectiveness relative to the finite, whole, positive
numbers and the set built step by step in this way, while
the set is of another kind, involving -- if it is to be
attempted to be defined as only consisting of finite number --
a breaking of self-reflectiveness; or else, if it is defined
without this limitation, the notion of the limit idea is
inadequate entirely, of course, and the whole idea of
defining the set of all finite whole positive number is
abandoned. But you argument was in favor of not abandoning
that idea. The set you then hope to get breaks with
self-reflectiveness when seen as a whole, a not finite
whole -- a whole not characterized by the limit idea. You
have already tried to say that the whole description of
the set is by the limit idea. So if what we have now pointed
out is not involving an incoherence, then I wonder what
does involve an incoherence.
The set as a whole is not finite -- also called, infinite, --
and this infinity is not described by the limit concept.
If you say 'indefinite number of applications of it', you
are saying something which really amounts to, 'infinite number
of applications of the limit idea'. You are, by that very
statement, already breaking with your own suggested premise,
viz., that of identifying limit with the infinite. For you
did not say, nor can say, apply the limit concept to the
number of times you apply the limit concept. However you
twist and turn it, the limit concept prescribes a
generation algorithm, and does not describe the result;
and even the prescription of the generation algorithm
begs the question of where the set which underlies the
concept 'any number y' or 'any number n' comes from in
the first place. The very notion of speaking about
'any number' refers to an adequate concept of a number;
but if this concept of a number is going to be formed
coherently, it must be formed based on an infinite set
which is, as we have shown, not adhering to the principle
that the self-reflectiveness is broken down at any point
but rather sustained even on to infinity, meaning that
the number concept is so that a sure definition of
finiteness breaks down.
I think at this point, unless the imagined person is
simply not willing to pay attention, and in science we
must be willing, for attention is what drives science and
what gives substance to our rationality, the person will
concede that the limit concept doesn't do the work
after all. However, the person may be confused about
the latter remarks, enough to ask, 'What do you mean?
What is this number concept which is so that a sure
definition of finiteness breaks down?'
To this I will point out, for instance, that any formalism
made by our minds is made by something which is not itself
the result of any formalism that we know of. In some sense,
then, our minds, or Mind, if we wish to emphasize a wholeness
of mind beyond division into the many, involves a sense of
the indefinite. When we as toddlers, as infants, as small
kids, learn to count, perhaps first on our fingers, referring
to toys of various colors or the like, we are emerging some
pointers out of an ocean of possibilities and nuances of
meaning which in a very easy informal sense can be said
to involve something beyond all definitions -- and be
infinite in many ways, of course. So the number concept in
that sense emerges out of a horizon which itself does not
correspond to the number concept. It is erected, we might
say; and when we erect more such numbers, it means we
can put them together and so on, but it does not mean that
these numbers are fundamentally sharply cut out of the
context -- the indefinite, or infinite -- context, out of
which they emerged. The infinite is in some sense
presupposed, tacitly -- but we can also do it explicitly,
and I believe this was the mistake of Georg Cantor --
to imagine that finiteness can in some sure way be put
first, and infinity in some sure way be generated out of
it. Rather, infinite, in an undefined, vague, open sense,
is the ground, and the numbers in some sense represent
structures within the infinite as ice represent
structures within the ocean, still made of the water,
although standing forth. We can compare two and two
and invoke a limit concept, but we cannot try to equate
the limit concept, even if it is flexible, with the
infinite background out of all this emerges.
All this doesn't mean that the technical application of
some definitions to the contrary of what is ultimately
coherently clear ideas cannot work out in some limited
domains, just as a computer program which is sloppily
made can do e.g. wordwrap on some paragraphs but not on
others, something which is not a problem as long as the
domain of application is limited. Physics, on the other
hand, and more broadly the notion of (natural) sciences
in general (but also other forms of sciences), are in their
very nature limitless as for boundary or domain of
application as a matter of principle, as long as we affirm
that we are interested in understanding reality as a whole
(and not merely interested in making a piece of technology
and need an equation to fit with that technology).
This should pave the way for a new type of description of our
physical theories, along the lines I have indicated (also with
somewhat other reasons) earlier in this book. We must then give far
more emphasis on the informal, and, when we evoke the formal, we
must do so without trying to capture more than some finitely
permuatable aspects of the theory (however essential we would like
them to be, we must restrict this consciously to be finite aspects,
and in fact well-defined-within-boundary finite aspects, such as the
32-bit number size, or else we cannot have any garantee that the
formalism will behave in a consistent way -- due to the argument
above, which shows that even very primitive forms of
boundlessness leads to self-contradictions).
I wish to repeat that this does not imply that we cannot have a
theory of an infinite universe with some form or another of
continuity. Much of the thoughts of e.g. Einstein and Bohr may still
be correct. We are however forced to rethink the whole concrete
theory and abandon entirely their formalisms. We must allow for
possibilities e.g. of fourth dimensions without assuming that
something such as differentials, integrals, derivatives of various
sorts and so on (since they are defined by means of infinitesimals
which again are based on the existence of the natural number set)
can adequately speak about them in a consistent way. Some of the
particular shapes of their logical arguments must be considered in a
bracketed form, as possibly right, but also possibly wrong -- and if
right, then right rather for other reasons than what has been
hitherto assumed by some of us.
We can therefore also safely bracket grand concepts such as
'time', 'energy', 'potential', 'position' when they appear in formal
form inside an argument, forming a part of a foundational theory of
physics. When we speak of these concepts informally, we are in a
position to learn from David Bohm's main postulate in his book
Wholeness and the Implicate Order from 1980, namely that quantum
physics indicates 'a new order', in which the manifest forms of
existence are seen to emanate from a completely different order, in
which the previous concepts at an explicate level are seen to no
longer be foundational in the same sense. Bohm is careful enough in
wording this to say 'indicate'. He does not, and of course cannot,
say 'prove'. He merely points out that the complexities and
confusions which trying to understand the universe as a whole after
the decades of existence of both the relativity theories, and also
the quantum theories, indicates that there is a different level of
reality which is so that it is generative relative to the more
experienced reality as conventionally discussed by science and
conventionally empirically studied. This more subtle order is perhaps
exceedingly active, indeed it can be as active as a computer
program relative to that which is on the screen and read from the
keyboard, he points out later, writing with F. David Peat in his 1987
book, Science, Order & Creativity (he was writing on this book still
when I first visited him at Birkbeck College -- I remember asking him
about what the book would say, and he said, 'writing a book is like
making a discovery').
The implicate order concept is sound, but it was never brought
into strong contact with concrete physics by Bohm, or by Bohm and
Hiley in their last book together, before Bohm died (he had a weak
heart and a pacemaker), The Undivided Universe: An ontological
interpretation of quantum theory, published in the early 1990s, with
Hiley doing final corrections.
However, as professor at Bohr Institute in Copenhagen, Holger
Bech-Nielsen pointed out to me in one of our several fascinating
discussions on quantum theory and cosmology, many physicists felt
that Bohm's implicate order concept had more to it than his original
papers where he suggested a causal interpretation of quantum
probabalities by means of making the position variable hidden in the
formalims. And one cannot help seeing that those who have sought to
work in the prolongation of string theory with their many new
forms of mathematical-looking physics theories, with some claims
(perhaps with some meagre justification though) of having a unified
theory of sorts with both gravitation and quantum equations in it --
M-theory and whatever new names they come up with -- in some
sense imply a faith in something like an implicate order.
I began reading on the implicate order a couple of years before I
visited Bohm, and felt it made sense; and at once began talking
about it to all my friends, my father and so on -- and I saw only
fruitful expressions of this discussion coming from it. My father,
who had worked with Process and Reality, the early twentieth
century book by A.N.Whitehead, as an underlaying philosophy for
many of his activities, found many similarities; and Bohm himself
refers to Whitehead as a source in some ways. Again we can see
something like mysticism and the emphasis on the esotheric, as also
in M.Blavatsky and Upanishads and I Ching, Dao, shamanistic
teachings and so on in the whole approach of the implicate order --
but it does in no way mean that one can from such a concept claim
that any particular 'mystical dogma' (if that term is meaningful, as I
think not, for mysticism involves meditative openness, not dogma) is
in any way 'proved'.
The main stream or current of thought is rather this: that reality
is manifold, it flow out from a deeper, grander order which is
probably in constant movement, and which is ceaselessly active
relative to this more manifest order. The emphasis on the very
concept of movement, and the point that movement was a difficult
concept in ancient Greece, is something I am grateful for Henrik
Tschudi for pointing out very clearly in many discussions. The notion
of art involves gestalts, as one sees in the very interesting studies
of so-called gestalt psychology; I studied this during my psychology
exams while comparing with the implicate order, and I am grateful
to Ingar Roggen, a sociologist with an ambitious agenda for
rethinking sociology, for pointing out the validity of thinking in terms
of gestalts when it comes to formalisms and also programming (he
has worked much with the Apple-language Hypertalk relative to
logic).
I think the background for rephrasing the 2004 theory has now
been made very clear. Having sketched it anew, at a general level,
informally, we will see that the program illustration of key finitely
permutable aspects of some parts of the theory has more abstract
concepts than the informal theory, not namely identical, and can in
that way lend itself to more of such 'tweaking' as I promised in the
first sentence in this book that scientific work should concern itself
with. For instance, while informally, the theory speak of
supermodels, the program has the concept SUPERM. Informally, we
will speak of electricity and magnetism, while in the program we
find ELECT and MAG. This means that we are in a position to keep on
exploring reality at an informal level while perhaps finding it
fruitful to bring also this program with us, but reapplied as our
informal understanding deepens and new empirics come in, perhaps
with something else than electricity and magnetism at a new and
much faster level than that of the speed of light (and hence also
more finely woven than that which Planck's constant implies), but
analogous enough to these phenomena that ELECT and MAG may still
be called on, however with new concrete numerical parameters.
For that reason, there is of course in the formal machine no
grandiose 'Laws of Nature' or 'Natural Constants' specifications. The
formalism is rather a question of representing, in a finite,
well-within-a-boundary kind form, certain patterns. These patterns
are supposed to be generically applied so as to connect the informal
theory with concrete numerical data. If this happens with ease, and
if we also get from this novel predictions that turn out to be
accurate, and in general do not get instances of disconfirmation, we
are doing science theory building. This will of course demand
several more books also from my hand, and I am enthusiastic about
the notion of simply keeping on doing this indefinitely, with as much
new development at theory and at program level as necessary to
keep up with whatever findings which come around -- never ever
claiming that anything is finitely proved.
Apart from new quotes, in the next paragraph is a sketch, a
resume, of the 2004 theory of supermodels with its PMW principle,
and in the following paragraph is the general program pattern in the
Lisa programming language, briefly explained in the paragraph
thereafter. Then it is given input parameters suitable to the first
program example, and we discuss the theory, the predictions, the
example, and show an output on the screen from the program
performance to illustrate the activity of the very simple, yet
suitable program formalism for the supermodel theory. It is the
very same program which performs through all twenty-seven
examples, of course, and this is but a tiny subset of countless
possible applications.
ω
"... Die Gesetze, nach denen sich die Zustände der physikalischen
Systeme ändern, sind unabhängig davon, auf welches von zwei
relativ zueinander in gleichförmiger Parallel-Translationsbewegung
befindlichen Koordinatensystemen diese Zustandsänderungen
bezogen werden (Relativitätsprinzip). ..."
-- Albert Einstein in Annalen der Physik, Nov 1905
ω
"Kürzlich hat Dirac en Programm zur relativistischen
Quantenmechanik aufgestellt, das auf den ersten Blick auf einer von
derjenigen der Heisenberg-Paulischen Quantenelektrodynamik sehr
verschiedenen Grundlage zu beruhen scheint. ..."
-- L. Rosenfeld in Zeitschrift f[uur] Physik, July 1932 (Copenhagen)
ω
"Beim Ioniseringsprozeß des α-Teilchens während seines
Durchgangs durch Materie wird immer eine Anzahl von Elektronen
genügend Energie erhalten, um ihrerseits sekundäre Ionen
erzeugen zu können. Solche Elektronenstrahlen wurden zuerst von
J. J. Thomson beobachtet und als ð-Strahlen bezeichnet. ..."
-- Tikvah Alper in Zeitschrift für Physik, May 1932
(Berlin-Dahlem)
ω
"Die vorliegende Untersuchung zum Nachweis des magnetischen
Moments der Elektronen beschäftigt sich mit der zweimaligen
Streuung schneller Elektronen um 90°. ..."
-- E. Rup in Zeitschrift für Physik, Dec 1932
(Berlin-Reinickendorf)
ω
"High field superconductors are characterized by the fact that the
critical magnetic field is so high, that the effect of the field on the
electron spins as well as on the electron orbits has to be taken into
account. ..."
-- P. Fulde in 'Superconductivity', book ed. by P.R.Wallace, New
York, 1969 (Frankfurt)
ω
"Parker's hydrodynamical solution of the solar wind expansion yields
a supersonic plasma flow beyond a critical distance rc from
the sun with an essential constant expansion velocity. ..."
-- H. J. Fahr in 'Cosmic Plasma Physics', book ed. by K.Schindler,
London ISBN 0-306-30582-8, 1972 (Bonn)
ω
"... Was bleibt in einem permanenten Magneten konstant, wenn der
magnetische Widerstand im Bereiche seines Feldes (und damit das
Feld selbst) verändert wird? ..."
-- R. Gans and R. H. Weber in Annalen der Physik, Jan 1905
(Tübingen)
ω
"... Es soll die Frage beantwortet werden: Wie soll man die
Teslaspule dimensionieren, damit das Potential V2 an der
Teslaspule möglichst groß wird? ..."
-- P. Drude in Annalen der Physik, Jan 1905
ω
"Recent investigations have shown that the ionization produced by
the secondary rays arising from a thin metal plate traversed
normally by a primary beam of γ, Röntgen, or ß rays,
is greater on the emergent than on the incident side. ..."
-- Otto Stuhlmann, Jr, in Philosophical Magazine, Aug 1910 (New
Jersey)
ω
"Unter den durchsichtigen Krystallen des Steins, den man in
Deutschland Saphir nennt, [...] den er jetzt aber für eine
Varietät des Corindons hält, kommen einige vor, die ein
besonderes Lichtspiel zeigen, und desshalb von den Liebhaberen
seiner Steine als eine Curiosität gesucht werden. ..."
-- H. Haüy in Annalen der Physik, 1805
ω
"Über die Schwärzung photographischer Schichten durch
Protonen liegt bisher nur eine Arbeit von R. Kollath für den
Energiebereich von 30-1000 eV vor. Das Ziel dieser ersten
Untersuchung (mit Schuman-Platten) richtete sich hauptsächlich
auf die zahlenmäßige Kenntnis der photographischen
Plattenempfindlichkeit, die Gültigkeit des Reziprozitätsgesetzes,
sowie auf die Klarstellung und Beseitigung der Schwierigkeiten,
welche sich durch das Auftreten von Aufladungsercheinungen der
photographischen Schicht ergaben. ..."
-- Peter Brix in Zeitschrift für Physik, April 1949 (Göttingen).
ω
"In dieser Arbeit soll der doppelte ß-Zerfall -- die Emission von 2
Elektronen (oder 2 Positronen) in einem Elementarakt -- untersucht
werden. Ein solcher Prozeß ist in der ursprünglichen
Fermischen Theorie des ß-Zerfalls sehr unwahrscheinlich, da der
dort verwendete einfache Ansatz für die Wechelwirkung zwischen
dem Feld der leichten (Elektronen, Neutrinos) und schweren
(Neutronen, Protonen) Teilchen bewirkt, daß Elektronen jeweils
zugleich mit Antineutrinos, Positronen zugleich mit Neutrinos emittiert
werden. ..."
-- Bruno Touschek in Zeitschrift für Physik, Oct 1948
(Göttingen)
ω
"... Infrared difference spectra have been observed between nerves
in the active and resting stages. The shape of each difference peak
appears to be due to a shift in absorption band on the order of 1
cm-1. ..."
-- M. H. Sherebrin, B. A. E. MacClement and A. J. Franko in
Biophysical Journal, Aug 1972 (Ontario and London)
ω
"... Selvom, iflg. Bohr's teori, ikkelokalitet nok fordrer hel kontakt
lokalt sett aller først, husk at hvis universet har ekspandert fra
en enkelt singularitet, har alle partikler vært i slik kontakt, og
betingelsen kanskje er oppfylt. ..."
-- Kristoffer Gjøtterud at the University of Oslo, Inst. of
Physcs, ito this writer in priv. communication in 1994 (Oslo)
ω
"... The nucleus is responsible for all but about a ten thousandth of
the mass of an atom but its effective diameter is only of the order
of a hundred thousandth that of the electron 'atmosphere' which
surrounds it. ..."
-- G. P. Harnwell in The American Physics Teacher, Feb 1935 (New
Jersey)
ω
"... Die mit kontinuerlichen Raumfunktionen operierende
Undulationstheorie des Lictes hat sich zur Darstellung der rein
optischen Phänomene vortrefflich bewährt und wird wohl nie
durch eine andere Theorie ersetzt werden. ..."
-- A. Einstein in Annalen der Physik, June 1905
ω
"Nach zahlreiche Untersuchungen geht Diamant von etwa 1700° C ab
allmählich in Graphit über. ..."
-- U. Dehlinger in Zeitschrift für Physik, May 1937 (Stuttgart)
ω
"Resonance in room is often confused with reverberation, but
perhaps those who have described 'reverberant' rooms as resonant
ones are not so far from the truth. ..."
-- Vern O. Knudsen in The Journal of the Acoustical Society of
America, July 1932 (Los Angeles)
[This is the first part of the book,
copyright author, an excerpt given
at yoga6d.com/prices. The remaining
parts of the book are found only
within the printed version of it.
The entire book is found, from
autumn 2007, at National Library
of Norway, see ISBN info etc at
yoga6d.com/prices. Please be welcome
to buy this book! This also provides
an element of sponsoring to the
Manhattan Computing and Arts
Academy as planned, encouraging
first-hand programming and artistic
activities for the very young at
a pre-university level, cfr
yoga6d.com/caa-academy. Seminars
in Manhattan, NYC, from 2008,
around this book and the forthcoming
volumes in this series. A.T.]