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I just posted the following to the NKS
Forum.
The view of the relationship between Theory and
Reality sketched therein mirrors that of Keynes in his 1922 definition of The
Theory of Economic Science.
Gunnar
?Einstein?s Unfinished
Revolution? Introduction Last January, my wife and I picked
up our nine-year old grandson from a special session for GT kids at a local
college. ?What is GT?? I asked
him. ?It stands for gifted and
talented,? he replied ? and added, ?all are gifted and talented in their own
way.? On the way home, he told me
of this, that, and the other, including the idea which he had been discussing
with a friend ? ?that there is only NOW in all TIME.? As it happens, Albert Einstein
racked his brains over the same idea ? it lies at the heart of what physicist
Paul Davies has termed ?Einstein?s Unfinished Revolution?: ?Even Einstein confessed, near the
end of his days, that the problem of the now ?worried him seriously.? In conversation with the philosopher
Rudolf Carnap, he conceded that there is something essential about the now,? but
expressed the belief that, whatever it was, it lay ?just outside the realm of
science.?? (?About Time, Einstein?s Unfinished Revolution?, Penguin Books, 1995,
p. 77) As detailed further below, I agree
(a) with my grandson ?that there is only NOW in all TIME,? and (b) with Einstein
?that there is something essential about the NOW? ? something which, indeed,
lies ?just outside the realm of science.? For the NOW mirrors the PERMANENCE
which is the defining attribute of the Cosmos as the grounds of what has been
termed ?the permanent possibility of perception? ? that is to say, the Cosmos as
non-observed sub-stratum of all our spatio-temporal experiences which comprise
?the realm of science.? ?The Realm of
Science? And what, precisely, is ?the realm
of science?, and how does the concept of ?time? relate thereto in the first
place? Here is how Einstein
sketched his answers to these questions in the opening paragraph of ?The Meaning
of Relativity?:
?The theory of relativity is
intimately connected with the theory of space and time. I shall therefore begin with a brief
investigation of the origin of our ideas of space and time, although in doing so
I know that I introduce a controversial subject. The object of all science, whether
natural science or psychology, is to co-ordinate our experiences and to bring
them into a logical system.? (Fifth
Edition, Princeton University Press, 1974, p. 1) Thus, the ?theory of space and
time? and ?the problem of the now? come into play when we attempt to construct
in our minds in logically coherent fashion a spatio-temporal representation of
external ?events? revealed to us through our perception of photons of lights or
other forms of external sense stimuli. ?Scientific
Theory? In ?A Brief History of Time?,
Stephen W. Hawking seconded this view of ?the realm of science? ? albeit in
curiously ambiguous terms ? as follows: ?In order to talk about the nature
of the universe and to discuss questions such as whether it has a beginning or
an end, you have to be clear about what a scientific theory is. I shall take the simple-minded [?] view
that a theory is just a model of the universe, or a restricted part of it, and a
set of rules that relate quantities in the model to observations that we
make. It exists only in our minds
and does not have any other reality (whatever that might mean).? (Bantam Books,
1988, p. 9) In fact, there is nothing
?simple-minded? about this concept of ?scientific theory? ? scientists of first
rank, including Kepler, Galileo, This practice itself is without
warrant in epistemology and comes at a very high cost, as indicated by Einstein
in 1949: ?Science without epistemology is ? insofar as it is thinkable at all ?
primitive and muddled.? (?Reply to
Criticisms?, in ?Albert Einstein, Philosopher-Scientist?,
?The structure of the system
[theory] is the work of reason; the empirical contents and their mutual
relations must find their representation in the conclusions of the theory. In the possibility of such a
representation lie the sole value and justification of the whole system, and
especially of the concepts and fundamental principles which underlie it. Apart from that, these latter are free
inventions of the human intellect, which cannot be justified either by the
nature of that intellect or in any other fashion a priori.? (?On The Method of
Theoretical Physics?, reprinted in ?Ideas and Opinions?, Dell paperback, 1976,
pp. 265-266) Thus, the ?structure [of the
General Theory of Relativity] is the work of reason? in the form of mathematics
whereby certain underlying ?concepts and fundamental principles? are related to
associated ?empirical contents?.
With respect to the latter, Newton stipulated the following ?Rule of
Reasoning in Philosophy? at the outset of ?The System of the World in
Mathematical Treatment? in Book Three of ?Principia?: ?We are certainly not to relinquish the
evidence of experiments for the sake of dreams and vain fictions of our own
devising.? The grounds for
Einstein?s theory represents such
?empirical contents? in terms of a mental picture as Leonardo da Vinci?s ?Mona
Lisa? does the ?real? Mona Lisa through paint on canvas; there exists no warrant
in either case for inferences to be drawn about any aspects of ?reality? which
are not so represented in the picture or the painting. ?Primitive
Science? ?The whole modern conception of
the world is founded on the illusion that the so-called laws of nature are the
explanations of natural phenomena,? Wittgenstein noted in 1921 (Op. cit., para.
#6.371). A few years later, Cornell
philosopher E. A. Burtt concluded that the ?illusion? was a by-product of the
fact ?that men cannot do arduous and profound intellectual labour in the face of
constant and seductive distractions [of an epistemological nature ?
insert]. The sources of distraction
simply had to be denied or removed.
To get ahead confidently with their revolutionary achievements, [the
creators of modern physical science] had to attribute absolute reality and
independence to those entities in terms of which they were attempting to reduce
the world. This once done, all the
other features of their cosmology followed as naturally as you please. It has, no doubt, been worth the
metaphysical barbarism of a few centuries to possess modern
science.? ?Why did none of them see the
tremendous difficulties involved??, Burtt continued. ?Here, too, in the light of our study,
can there be any doubt of the central reason? These founders of the philosophy of
science were absorbed in the mathematical study of nature. Metaphysics they tended more and more to
avoid, so far as they could avoid it; so far as not, it became an instrument for
their further mathematical conquest of the world. Any solution of the ultimate questions
which continued to pop up, however superficial and inconsistent, that served to
quiet the situation, to give a tolerably plausible response to their
questionings in the categories they were now familiar with, and above all to
open before them a free field for their fuller mathematical exploitation of
nature, tended to be readily accepted and tucked away in their minds with
uncritical confidence.? (?The
Metaphysical Foundations of Modern Physical Science?, 1924/1932, Doubleday
Anchor Book, 1954, pp. 305-306) The ?illusion? was manifested in
the nineteenth-century Laplacian construction of Newtonian Mechanics as
explanatory of UNIVERSAL gravitational interaction rather than descriptive of
LOCAL solar-system phenomena and, incongruously, it survived the advent of the
General Theory of Relativity with its ?explanation? of the same set of phenomena
in terms of non-Newtonian ?curved? space and ?relativistic? time. Thus, the ?illusion? that
?scientific theory? is explanatory rather than descriptive of the ?realm of
science? remains entrenched in the minds of modern physicists AS IF the
relativity revolution never happened ? as if Einstein had NOT demonstrated ?that
distance and duration, and all the physical quantities derived from them, do not
as hitherto supposed refer to anything absolute in the external world, but are
relative quantities which alter when we pass from one observer to another with
different motion,? as Arthur Stanley Eddington summarized Einstein?s achievement
in 1922.
?The most we can hope for from any
frame,? he added, ?is that it will not have distorted the simplicity which was
originally present whilst an ill-chosen frame may play havoc with the natural
simplicity of things.? (?The Theory
of Relativity and its Influence on Scientific Thought?, reprinted in ?Albert
Einstein?s Theory of General Relativity?, ed. by Gerald Tauber, Crown
Publishers, Mind-Space as Theory
Frame The General Theory of Relativity
represents ?the natural simplicity of things? by a set of ?concepts and
fundamental principles? whose internal relations specified in
logico-mathematical form give LOGICAL UNITY to the theory in any observer?s
Mind-Space. This construction is IMPLICIT in Einstein?s comments in a London
Times article in 1919: ?The chief
attraction of the theory lies in its logical completeness. If a single one of the conclusions drawn
from it proves wrong, it must be given up; to modify it without destroying the
whole structure seems to be impossible.?
(?What Is the Theory of Relativity??, reprinted in ?Ideas and Opinions?,
p. 227) As far as I know, however,
Einstein never arrived at an EXPLICIT conceptualization of the subject matter
along the above lines. Yet, the fact that the problem of
the now ?worried him seriously? late in life AND that he readily conceded that
the axiomatic premises of the General Theory of Relativity might not be tenable
(see my post ?Einstein?s ?Scientific Testament??) indicates very strongly, to
the point of near-certainty, that Einstein?s thinking was moving towards
explicit embrace of the concept of ?Mind-Space as Theory Frame? as defined
above. While the concept has been part of
my intellectual ?tool kit? for years, the following statement thereof by Ludwig
von Mises impresses me as exceptionally lucid: ?Logic and mathematics deal with
an ideal system of thought. The relations and implications of their system are
coexistent and interdependent. We may say as well that they are synchronous or
that they are out of time. A perfect mind could grasp them all in one thought.
Man's inability to accomplish this makes thinking itself an action, proceeding
step by step from the less satisfactory state of insufficient cognition to the
more satisfactory state of better insight. But the temporal order in which
knowledge is acquired must not be confused with the logical simultaneity of all
parts of an aprioristic deductive system. Within such a system the notions of
anteriority and consequence are metaphorical only. They do not refer to the
system, but to our action in grasping it. The system itself implies neither the
category of time nor that of causality. There is functional correspondence
between elements, but there is neither cause nor effect.? (?Human Action: A
Treatise on Economics?, 1949, Part I,
Therein lies the crux of the
matter insofar as ?the problem of the now? is concerned ? as ?free inventions of
the human intellect?, which aid in our mental construction of a representation
of ?events? in the ?realm of science,? neither ?time? nor ?space? are attributes
of that ?permanent possibility of perception? ? that NOW or PERMANENCE ? which
is the Cosmos ?just outside the realm of science? itself. ?Realistic
Mathematics? In turn, this conclusion implies
that ?the realm of science?, while co-extensive with the domain of what Hermann
Weyl termed ?realistic mathematics?, is not ?the one REAL world? as he
supposed. ?It is impossible to
discuss realism in logic without drawing in the empirical sciences,? Weyl
suggested. ?? A truly realistic
mathematics should be conceived, in line with physics, as a branch of
theoretical construction of the one real world and should adopt the same sober
and cautious attitude towards hypothetic extensions of its foundation as is
exhibited by physics.? (?Philosophy
of Mathematics and Natural Science?, 1949, Appendix A, ?Structure of
Mathematics?, p. 235) The identification of the domain
of ?realistic mathematics? with ?the realm of science? lays bare the root cause
(superior and, hence, infuriating intuition and intellectual integrity) of
Einstein?s painful isolation within the physics community of which Max Born
wrote as follows: ?He has seen more
clearly than anyone before him the statistical background of the laws of
physics, and he was a pioneer in the struggle for conquering the wilderness of
quantum phenomena. Yet later, when
out of his own work a synthesis of statistical and quantum principles emerged
which seemed to be acceptable to almost all physicists, he kept himself aloof
and sceptical. Many of us regard
this as a tragedy ? for him, as he gropes his way in loneliness, and for us who
miss our leader and standard-bearer.
I shall not try to suggest a resolution of this discord,? Born
continued. ?We have to accept the
fact that even in physics fundamental convictions are prior to reasoning, as in
all other human activities.?
(?Einstein?s Statistical Theories?, in ?Albert Einstein,
Philosopher-Scientist?, p. 163) That is, ?Einstein is completely
cuckoo,? as J. Robert Oppenheimer put it in 1935. The record indicates that
Einstein?s early command of the epistemological aspects of science did not match
his intuitive grasp of the essence of ?realistic mathematics? as reflected in
the following two statements made in 1918 and 1933, respectively: (1) ?The supreme task of the physicist is to
arrive at those universal elementary laws from which the cosmos can be built up
by pure deduction.?; and (2) ?I am
convinced that we can discover by means of purely mathematical constructions the
concepts and laws connecting them with each other, which furnish the key to the
understanding of physical phenomena.? (?Ideas and Opinions?, p. 221 and p.
267) The first statement defines the
task of theoretical physicists in ?the realm of science? (mis-labeled ?Cosmos?)
and the second expresses the intuitive conviction of scientists of first rank
from Kepler, Galileo, and Newton to Planck and Einstein that, as Newton observed
with respect to Newton?s Rule, ?we are not to recede from the analogy of Nature,
which is wont to be simple, and always consonant to
itself.? In the context, Newton?s ?Nature?
is synonymous with Einstein?s ?realm of science? alias the ?empirical contents?
of Wittgenstein?s ?World? introduced at the outset of his ?Tractatus
Logico-Philosophicus? as follows:
1. The world is all that is the case. 1.1 The world is the totality of facts,
not of things. 1.11 The world is
determined by the facts, and by their being all the facts. 1.12 For the totality of facts
determines what is the case, and also whatever is not the case. 1.13 The facts in logical space are the
world. 1.14 The world divides into
facts. In other words, the World denotes
?our experiences? transformed by Intuition into ?concepts and fundamental
principles? and ?[brought] into a logical system? in Mind-Space by
Reason. With respect to the World so
defined, Wittgenstein?s following statements hold true: 3.
A logical picture of facts is a thought. 3.001 ?A state of affairs is thinkable?;
what this means is that we can picture it to ourselves. 3.01 The totality of true thoughts is a
picture of the world. 3.02 A thought contains the possibility of
the situation of which it is the thought.
What is thinkable is possible too.
3.03 Thought can never be of
anything illogical, since, if it were, we should have to think illogically. 3.031 It used to be said that God could create
anything except what would be contrary to the laws of logic. The truth is that we could not say what
an ?illogical? world would look like.
3.032 It is as impossible to
represent in language anything that ?contradicts logic? as it is in geometry to
represent by its coordinates a figure that contradicts the laws of space, or to
give the coordinates of a point that does not exist. Here is my own, less formal,
short-hand _expression_ of the like view, born of research in theoretical physics
and economics in the 1970s: Theory
is an axiomatic structure of thought based on some given set of axioms which are
consistent, coherent, and complete for the purpose at
hand. That is to say, ?theory? is a
UNITARY structure in Mind-Space such that ?A perfect mind could grasp [it] all
in ONE thought,? as noted by von Mises.
Therein, I suggest, lies the mystery of INTUITION in the work of
path-breaking scientists such as Kepler, Galileo,
?Gödel?s Incompleteness
Theorem? The concept of ?theory? as a
UNITARY structure implies that ?Gödel?s Incompleteness Theorem? is NOT
applicable to ?realistic mathematics? ? for UNITY is akin to a POINT in
Euclidean geometry with respect to which the ?incompleteness? issue cannot
arise. In a recent talk on ?Gödel and the End of Physics?,
Stephen W. Hawking concluded otherwise on grounds that ?we and our models are
both part of the universe we are describing. Thus a physical theory is
self-referencing, like in Gödel?s
theorem. One might therefore expect
it to be either inconsistent or incomplete.? (Internet text.) ?The Uncertainty
Principle? The concept of ?Mind-Space as
Theory Frame? also belies Hawking?s statement in ?A Brief History of Time? that
?it SEEMS that the uncertainty principle is a fundamental feature of the
universe we live in. A successful
unified theory MUST therefore necessarily incorporate the principle.? (pp.
155-156)
In the context, Hawking?s
rhetorical escalation from ?seems? to ?must? serves in lieu of reasoned argument
for the proposition that a particle can be at some given point while in motion
relative to such point ? a logical absurdity embraced also by modern String
Theorists (a ?typical? string is a Point ?smeared? out to one Planck Length) but
derided for 2500 years through Zeno?s Paradox in implicit support of the key
tenet of the Eleatic school of philosophy that the universe is one, eternal, and
unchanging. That is, the ?universe? as grounds
of ?the permanent possibility of perception? ? of the NOW which lies ?just
outside the realm of science.? ?String
Theory? The concept
of ?Mind-Space as Theory Frame? blows to smithereens the foundational premises
of String Theory as summarized by Brian Greene in ?The Elegant Universe?:
?The
unified framework that string theory presents is compelling. But its real attraction is the ability
to ameliorate the hostilities between the gravitational force and quantum
mechanics. Recall that the problem
in merging general relativity and quantum mechanics turns up when the central
tenet of the former ? that space and time constitute a smoothly curving
geometrical structure ? confronts the essential feature of the latter ? that
everything in the universe, including the fabric of space and time, undergoes
quantum fluctuations that become increasingly turbulent when probed on smaller
and smaller distance scales. On
sub-Planck-scale distances, the quantum undulations are so violent that they
destroy the notion of a smoothly curving geometrical space; this means that
general relativity breaks down.?
(W. W. Norton and Company, New York, 1999, p. 152) It is nuts
to suppose that the ?space? and ?time? aspects of ?scientific theory? which
?exists only in our minds? can undergo any ?quantum fluctuations? whatsoever.
?Objective
Truth? ?We may now say that our discourse
about the nature of the universe has an end,? Plato began the final paragraph of
?Timaeus?. Insofar as there is ?an
arrow of time? in ?the realm of science?, it is one that flies through
Mind-Space from Ignorance to Knowledge of what Parmenides termed ?Objective
Truth?. In an essay ?On Nature?, he
has a Goddess explain that ?arrow of time? as follows: ?Youth, attended by immortal
charioteers, who come to our House by these mares that carry you, welcome. For it was not ill fortune that sent you
forth to travel this road (lying far indeed from the beaten path of humans), but
Right and Justice. And it is right
that you should learn all things, both the persuasive, unshaken heart of
Objective Truth, and the subjective beliefs of mortals, in which there is no
true trust. But you shall learn
these too: how, for the mortals passing through them, the things-that-seem must
?really exist?, being, for them, all there is.? ?Our revels now are
ended.? Francis
Bacon began his essay ?Of Truth? with Pilate?s question,
?What is truth?? As indicated
below, the Shakespeare Opus, conceived at the dawn of the scientific age, may be
construed as vehicle for conveying Objective Truth to a Brave New World. The argument is complex, but three
points may serve to convey its thrust.
First. The theme of ?the things-that-seem? is
echoed in Act I, Sc. ii of Shakespeare?s play in the words of Hamlet, who
advises the Queen, his Mother:
?Seems, madam! Nay, it is; I
know not ?seems?.? The theme is
picked up again in Act III, Sc. iv when the Ghost visits the Queen?s
Apartment. ?Do you see nothing
there??, the Prince of Denmark asks his Mother. ?Nothing at all; yet all that is I see,?
replies the Queen.
Second. Inscribed on a statue of William
Shakespeare erected by Alexander Pope et. al. in Westminster Abbey in 1741 is a
mangled version of magician Prospero?s words in Act IV, Sc. i of ?The
Tempest?: ?Our revels now are
ended. These our actors, As I
foretold you, were all spirits and Are melted into air, into thin air: And, like
the baseless fabric of this vision, The cloud-capp?d towers, the gorgeous
palaces, The solemn temples, the great globe itself, Yea, all which it inherit,
shall dissolve And, like this insubstantial pageant faded, Leave not a rack
behind. We are such stuff As dreams
are made on, and our little life Is rounded with a sleep.? Third. Inscribed on a memorial statue of
Francis Bacon raised by his secretary, Dr. Thomas Meautys, is a Latin text
which, in the context of the Shakespeare Mystery, may relate the end of ?the
things-that-seem? and the advent of ?Objective Truth? to the concept of
?Mind-Space as Theory Frame? set forth herein. In
translation: Francis Bacon, Baron of Verulam, Viscount St.
Albans or, by more conspicuous titles, of Science the Light, of Eloquence the
Law, sat thus. Who after all Natural Wisdom And Secrets of Civil
Life he had unfolded Nature?s Law fulfilled ? Let Compounds be
dissolved! For ALL IS
ONE. ©Gunnar Tómasson November
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