J. Mod. Phys., 2010, 1, 70-76
doi:10.4236/jmp.2010.11009 Published Online April 2010 (http://www.scirp.org/journal/jmp)
Copyright © 2010 SciRes. JMP
The Possible Dimension, Additional to Space-Time, which
Physicists Ignore
Arie S. Issar, Shaul Sorek
Ben-Gurion University of the Negev Israel, Blaustein Institutes for Desert Research, Israel
Zuckerberg Institute for Water Research, Environmental Hydrology & Microbiology
E-mail: {issar, sorek}@bgu.ac.il
Received February 23, 20 1 0; revi sed M arch 25, 2010; accepted March 25, 2010
In response to Wheeler’s challenge to find an element that is: “something that itself has no localization in
space and time…pure knowledge … an atom of information” we suggest to account for Information as a di-
mension. Its degrees of freedom are arithmetical (+-) and logical (if-then) forward and backward steps.
While Space refers to gaps in distance, Time refers to change in instances, Information refers to a sequence
of notions measured by the number of steps made (or bytes used) by a computer in order to perform (de-
scribe or solve) a certain logical sentence or a sequence of logical sentences. In the attempt to quantifiably
formulate the incorporation of Information into physical laws, we refer to Hamiltonian extended stationary
principle in terms of Space, Time and an additional degree of freedom, suggested as an information state.
The obtained Euler equation is demonstrated for the case of a thin rod under longitudinal vibrations, investi-
gated by dimensionless analysis. It is shown that depending on the value of information and its rate, one may
obtain dominant forms conforming to Poison’s equation in Space vs Information, wave equation in Time vs
Information and the expected wave equation in Time vs Space.
Keywords: Information, Hamiltonian, Dimensionless-Analysis
1. The New Dimension Wheeler Foresaw:
“If we’re ever going to find an element of nature that
explains space and time, we surely have to find some-
thing that is deeper than space and time—something that
itself has no localization in space and time. The amazing
feature of the elementary quantum phenomenon—the
Great Smoky Dragon—is exactly this. It is indeed some-
thing of a pure knowledge-theoretical character, an atom
of information, which has no localization in between the
point of entry and the point of registration. This is the
significance of the delayed-choice experiment.” [1].
Following Wheeler’s call [1] we maintain that Infor-
mation should be (along which intelligence is measured
as well as instinctive knowledge) added, independently,
to space and time. At first it was thought by Issar to call
this dimension1 either thinking or ‘intelligence’, but after
investigating these options it was found that thinking is
the description of moving and ‘intelligence’ are structures
along degrees of freedom along a more substantial di-
mension. The introduction of a new basic dimension will
enable to describe intelligence as a feature or even a
structure constructed from the addition of fundamental
steps of observation and logical conclusion. These, are in
fact the basic steps of arithmetic addition (and subtraction)
and the basic logical conclusion of ‘if-then’, forward and
backwards. Generalizing this suggestion will say that the
adding one to another of a few basic conclusions, which
brings to the arriving of a more general structure, is actually
a construction along a dimension, which constitutes 4
degrees of freedom. The more intelligent is the living
being, the more will be its ab ility to increase the build ing
composed of elaborate structures of knowledge added one
to another and put together by logical steps, to form wider
and higher stru ctures of i nt e l l igent t hi nki n g and behavior.
This conclusion brought to search for an altogether
new dimension along which the movement while taking
these fundamental steps can be described and quantified.
After investigating various options the conclusion was
that the most appropriate term will be: ‘Information’.
Thus, change in location on space is quantified by steps
1An intrinsic independent property, representing the minimum number
of directions needed to specify either a point on space, an instant on
time and a notion when considering Information.
Copyright © 2010 SciRes. JMP
of the foot or by a meter, duration of time is quantified by
the movement of shade on the sun-dial or by a clock,
while progress on the Dimension of Information is quan-
tified by the length of mathematical or logical sentences
needed to describe a certain idea or number of bytes used
by a computer t o perf orm a certain logical sentence.
Space has six degrees of freedom namely along or
spins around three coordinates, in two directions i.e. for-
ward and backwards, Time one degree of freedom from
present to future (the perspective from present to past
actually refers to knowledge and thus is regarded as the
Dimension of Information), while the additional dimen-
sion of Information has four degrees of freedom [2],
which are: addition and subtraction and induction and
deduction (i.e. ‘if-then’ and ‘when-then’). Altogether the
evolution of the universe is along a three dimensional
continuum of Space-Time-Information, having 11 de-
grees of freedom.
The introduction of this new dimension enables to an-
swer a question that many outstanding physicists came up
with and which Albert Einstein [3] brought up in his
lecture before the Prussian Academy of Sciences, namely:
“How can it be that mathematics, being after all a product
of human thought which is independent of experience, is
so admirably appropriate to the objects of reality? His
answer to this enigma was by accepting as a fact that
Mathematics is intrinsic both in Nature and in the human
mind. Yet while the human mind can build wonderful
logical structures with the aid of this mysterious tool,
these structures are not factual if not cross-checked by
empirical observations. In Einstein’s words: “In my
opinion the answer to this question is, briefly, this: as far
as the propositions of mathematics refer to reality, they
are not certain; and as far as they are certain, they do not
refer to reality [3].
In his Herbert Spencer lecture at Oxford, Einstein [4]
manifested his faith in mathematics as the skeleton of the
edifice of nature, and thus the power of abstract mathe-
matical thought to reveal the secrets of the laws inter-
connecting our observation of natural phenomena. He
stressed the role of mathematics as a bridge between
mind and nature. In his words: “Our experience hitherto
justifies us in believing that nature is the realization of
the simplest conceivable mathematical ideas. I am con-
vinced that we can discover by means of purely ma-
thematical constructions the concepts and the laws
connecting them with each other, which furnish the key
to the understanding of natural phenomena. Useful ma-
thematical concepts may well be suggested by ex-
perience, but in no way can they be derived from it.
Experience naturally remains the sole criterion of the
usefulness of a mathematical construction for physics.
But the actual creative principle lies in mathematics.
Thus, in a certain sense, I take it to be true that pure
thought can grasp the real, as the ancients had dreamed
He did not touch, however, upon the basic question:
How comes that mathematics is on one hand the brain-
child of the human b eing and on the other hand is intrin-
sic in the framework of the universe? When he did refer
to this question he admitted failure from the start “One
may say “the eternal mystery of the world is its compre-
hensibility” [5].
It can be concluded, thus, that for Einstein, this ques-
tion was solved once he accepted the philosophical world
view and thus the “God” of Baruch-Benedictus Espinoza,
who argued for the unifor mity of the terms of “God’’ and
“Nature”2. Espinoza and thus Einstein , took it as granted
that being a Supreme Mathematician is one of the infinite
attributes of “God” i.e. Nature.
Eugene Wigner [6], not being a Spinozist, brought this
enigma to the level of an absurd in the title in his paper
“The Unreasonable Effectiveness of Mathematics in the
Physical Science”, in which he restated the problem by
touching on the super-natural. His claim was that “The
miracle of the appropriateness of the language of
mathematics to the formulation of the laws of physics is
a wonderful gift which we neither understand nor de-
serve.” [6].
Indeed the achievements of the theories of Einstein,
which were applauded by the world of science on the
occasion of the hundred anniversary of Annum Mirabelis,
had confirmed his trust in the power of mathematical
thinking to unveil the many faces of nature.
One of the famous cases of forecasting, which was
confirmed by many observations, is Einstein’s General
Theory of Relativity. In 1922 by developing the equa-
tions of this theory the Russian physicists Alexander
Friedman [7] showed that these equations demand either
a contracting or an expanding universe along space-time
dimensions, which Einstein tried to stabilize by intro-
ducing his ‘cosmological constant’ [7]. Hubble’s obser-
vations showed that this constant is redundant. Running
back the “motion picture”, namely turning expansion to
contraction on space-time dimensions brought cosmolo-
gists to conclude that all started with a singular event,
namely the Big Bang, after which the cosmos expands
continuously to this day and into the future.
2. The 5th Dimension along Which Our
Universe Expands
All the computerized models used by the physicists to
contract the universe to reach the pre-Big Bang singular
point and expand it to its present dimension s and beyond
were dictated by mathematical procedures, demanding
2Einstein’s response the telegrammed question of New York’s Rabbi
Herbert S. Goldstein in (24 April 1929): “Do you believe in God? I
believe in Spinoza’s God, Who reveals Himself in the lawful harmony
of the world, not in a God Who concerns Himself with the fate and the
doings of mankind.
Copyright © 2010 SciRes. JMP
various assumptions at various stages. The basic assump-
tion, following Einstein’s basic conceptual model is that
our universe is four-dimensional, (three orthogonal spa-
tial coordinate system and time which has only one de-
gree of freedom from past to future). This continuum is
measurable by an observer using a meter and a clock.
Yet, Einstein’s, Friedman’s and their colleagues, in-
vestigating the implication of the General Theory of
Relativity, like the Dutch Willem de Sitter [8], and the
French Georges Lemaitre [9], were all following the
same laws of mathematics, which they assumed that the
universe is following. However, it never occurred to
these physicists to ask the following questions:
1) Along which dimension evolve the mathematical-
logical structures they have constructed and were run-
ning in their brains an d later on their computers.
2) Is it not possible that this sequ ence of ideas in their
brain while thinking and trying to understand these theo-
ries is running along a dimension addition to space-time?
One will not be surprised, however, that any physicist
adherent to the mandate of his profession i.e. investigat-
ing the physical world along the physical spatial-temporal
dimensions, using a meter and a clock will revoke these
questions, claiming that they belong to the field of ‘me-
ta-physics’ and endangers the objective approach to sci-
ence. In other words, once the subjective individual sit-
ting in front of his computer becomes involved in the
program being run on this objective machine, the results
may be biased. This approach makes further questions
redundant, like: The knowledge gained allowing the exe-
cution of a program by a computer every few years be-
coming faster than its previous ancestor, is it not due to
progress in information (hard ware an d so ftw are) ?
It goes without saying that we suggest that once such
advancement is noticeable, it should be measured along a
dimensio n of information.
Speaking about this additional dimension one comes
to the ‘fifth dimension’ (i.e. the three spatial directions
and the direction of time) introduced in by Kaluza in
1919 [10]. Although Kaluza was able to show that by
introducing a fifth dimension then both gravity and elec-
tromagnetism can be described from the same underlying
framework, and albeit Einstein’s interest and pr eliminary
acceptance [10], this 5th dimension was not acceptable
among physicists. The main reason, to the present au-
thors’ opinion, being that the 5th dimension was a
mathematical innovation and the physicists could not
‘see it’ ‘measure it with their rulers’ and clocks. No
physicist, including Einstein, who pondered about the
mystery of mathematics, dared to ask, how is it that a
mathematical 5th dimension is capable of unifying the
electro-magnetic and the gravity fields. Is it not possible
that the 5th dimension is along the dimension of mathe-
matics? Klein [10], a theoretical-physicist, proposed a
solution to the physical deficiency in Kaluza’s (1919)
suggestion by attributing to the mathematical 5th dimen-
sion a spatial character of curling it up into a small
enough space to escape ordinary detection.
Curling up dimensions and thus making them “physi-
cal”, is a plausible solution from the point of view of the
physicist, who configures with “four dimensional” uni-
verse. Yet his brain is free to roam multi-dimensional
universes. In other words what Kaluza showed the phy-
sicists is that mathematics is a vehicle enabling to add
dimensions and thus expanding beyond Space-Time.
The curling up of space, was also criticized by Hawk-
ing [11], in the case of discussing the multi dimensional
(ten or twen ty-six) space-time universe, suggested b y the
string theory [12,13]. His question is: Why should some,
but not all, of the dimensions be curled up into a small
ball? It is beyond the scope of the present article to dis-
cuss the answers that Hawking [11] suggests, the com-
mon factor of which is that these are all physical
space-time dimensions. On the other hand the need to
invent the conceptual model of the ‘string theory’ [12,13]
and add a non-observable dimension to the space-time
continuum, may be regarded as a hint, what sort of a di-
mension it should be. More-overformulation s accounting
for Information as an additional dimension will also
address the 11-dimensional M-theory [13] that requires
space-time to have eleven dimensions.
3. The Dimension not Accounted by Darwin
While investigating the geology of the Quaternary, i.e. the
layers deposited during the last two million years, of the
Coastal Plain of Israel, the first author of the present arti-
cle got acquainted with the evolution of the stone tools.
These tools show evolution from primitive pebble tools,
which were just pebbles etched at one end to become
sharp and pointed, to the evolved flint arrow heads. In
other words: a body showing a rise of spatial-complexity
along the dimension of time. The evolution of this com-
plexity expressed, as we know, also progress in the intel-
ligence of its manufacturers. The question then arises
whether this trend of evolution could be explained in the
framework of the conventional Darwinian to Neo-
Darwinian paradigms, i.e. evolution through the process
of random mutations filtered by the constraints of the
hostile environment, which condemned to disappearance
form the stage of existence the less fitted.
Thus, while success in the process of Darwinian selec-
tion, i.e. survival of the fittest, can be measured according
to the number of similar forms of life and their distribu-
tion in space-time. The question which bothered the first
author was: What about the ability of these forms of life
who were able to change the hostile environment. As the
ability to change the environment, in the case of the
hominids, was a function of the evolution of their intelli-
gence, the following question was: How should the sur-
vival of the more intellig ent forms be measured? In other
Copyright © 2010 SciRes. JMP
words, who are more successful from the point of view of
the Darwinian paradigm, the hominids or the beetles?
The general question which follows is: By which units
of measurements the evolution of intelligence can be
quantified (when IQ tests are not feasible) and on what
dimension can evolut i on of intelligence be m easured?
Generalizing these questions, it can be said that the
Darwinian paradigm explained beautifully the evolution
of forms, i.e. spatial changes and the spread out of the
forms along the space dimension as time passed, i.e. the
time dimension. Now, at a certain point on the dimension
of time the hominids branched off from the primates and
started to produce tools. These tools became more and
more sophisticated as time progressed and as the homi-
nids multiplied and spread over the globe. The dimen-
sions on which this progress on the tree of evolution is
described, by conventional measures, are either temporal,
i.e. the time passed since the first pebble-tools were pro-
duced, or spatial, i.e. the spatial features of the hominids
and their tools, as well as their geographical range. All
these data are along space-time dimensions and the ques-
tion is: Once pr ogress of intelligen ce became do minant in
the evolutionary process should not an additional dimen-
sion be added to properly address this progress and eva-
luate it?
While the questions started with relation to hominids,
in due time this question was generalized for the entire
bio-world. Thi s happened after coming upon the results of
the research carried out by the psychologist Morton E.
Bitterman [14], who found that the evolution of intelli-
gent behavior in the bio-world correlates with the place of
the species on the evolutionary tree. This meant that the
increase of intelligence is parallel with the appearance of
new forms of life on the geological timetable. Thus ver-
tebrates are more intelligent than invertebrates, saurians
than fishes, mammals than saurians, etc. Bitterman [14]
investigated the level of intelligence by “the ability to
develop a new way of reaction when an entirely new situ-
ation comes up.” The question, which came up after
reading this conclusion was whether there exists a dimen-
sion on which intelligence can be measured, except by the
time needed to learn to push a button or find food in a
maze? Moreover, once experience is gained and turned
into instinctive behavior or abstract knowledge on what
dimension can this be presented and evaluated, in addi-
tion to the spatial-temporal scales?
The answer to these questions is: The Dimension of
Information”. Yet this dimension is not necessary just to
describe the evolution of intelligence in the bio-world in
general and that of the Homo sapiens-sapience in par-
ticular, but is also essential to describe the rise in the
complexity of the physical world [15], namely the
growth of the complexity of the structures composed of
information bits, which means on one hand more infor-
mation bits, as well as higher levels of organization of
algebraic-logical sentences.
The above definition of Information actu ally describes
the coordinates along which the intelligibility of a mes-
sages sent through any system of tele-communication
can be measured either by telephone, telegraph, e- mail or
internet. In this context it is generalizing the term of ‘in-
formation’ as defined in the theory developed by Shan-
non and Weaver [16]. In their theory they suggested that
the loss in the intelligibility of a messages sent through
any system of communication, namely its increasing
distortion by ‘noise’, can be described in a similar for-
mulation to Boltzman-Maxwell’s formulation of the
physical Second Law of Thermodynamics. Thus, one
cannot avoid the general conclusion that the loss of
meaning (decrease in the number of ordered sets of bits
of information) of a certain message is th rough a process
similar to that which determines the increase of entropy
in a thermodynamic system. The addition of the Dimen-
sion of Information measured along the - informa-
tion/time/space - dimensions, enables this loss of mean-
ing to be expressed in physical-mathematical terms.
Physically-mathematically speaking, an increase in
order is equated with increase in complexity and with
organization, and is defined as negative entropy. Thus
the Boltzman and Planck expression for the entropy of a
system ln
S denotes the statisti-
cal entropy of a closed system,
denotes Boltzman’s
constant and W denotes the number of independent
quantum states) can be regarded as strictly a thermo-
dynamic statement.
On the other hand when the same expression is pre-
sented as
 (where Pdenotes the
probability that the system exists in the microstate i) it
becomes a measure of the probability of the system, i.e.
the measure of our ignorance of the actual quantum state
of the system. Such a measurement is also along the di-
mension of information, or more correctly, the exponen-
tial value on the dimension of information. This is pro-
portional to the level of organization of the system. In
other words, the more information and the higher is its
exponential value so is the system of lower probability,
and thus lowers entropy.
Instead of the expression for
S, a more general
form [16] can be
 wheren
the total information derived from a system where lni
expresses the total contributions of each subset of which
the system is composed of, weighted by its probability.
In conclusion, the adding of the Dimension of Infor-
mation enables to understand better the physical obser-
vation made by Shannon that the noise (reciprocal to the
quantity of Information) in a communication system be-
comes greater the longer are the dimensions of space-
Copyright © 2010 SciRes. JMP
4. A Few Words of Encouragement from
Although we foresee the difficulties facing the undertak-
ing of building a bridge between the space-time measur-
able world of the physicists and the one containing also
the dimension of Information, still a blink of hope exists.
This emerges from the fact that quantum physicists are
becoming aware of the need to introduce the observer
and an additional dimension, similar to that of Informa-
tion, to their conceptual model in order to explain “bi-
zarre” phenomena, in the micro-world. This can be seen
in the following citations, which we believe can also be
regarded as a support to the space-time-Information
conceptual model:
1) “We have already considered with disfavour the
possibility of the universe having been planned by a bi-
ologist or an engineer; from the intrinsic evidence of his
creation, the Great Architect of the Universe now begins
to appear as a pure mathematician.” [17].
2) “No, it’s a new kind of wave which I call ‘active
information’. The notion of active information is already
familiar to us from computers. Also, if I tell you some-
thing and you do something, that’s obviously active in-
formation. If `I shouted ‘fire’, everybody would move, so
we know that in living intelligent systems, and in com-
puters, active information is a useful concept. Now what
I am proposing is that matter in general is not so differ-
ent.” [1].
5. Formulation
As already mentioned physicists and mathematicians
strive to formulate the multi-dimensional continuum in
the framework of the conceptual model of the multi di-
mensional string theory. The following formulation is
more modest and is exercised in the framework of the
Hamiltonian extended stationary principle in terms of
Space, Time and an additional degree of freedom, all as
independent stationary variables. It is suggested that this
degree of freedom may be regarded as an information
Thus, let us denote the information state by
, we
postulate that similar to Hamilton’s extended stationary
principle, there exists a functional ()
being a func-
tion of its integrant
between an initial information
level 0
and that of a final one f
I, in the form
00 ,,, ,,,
It dIdtd
 
 (1)
Note that in (1) we consider time
space , to be independent of information. Accord-
denotes the dependent function with
its: information derivative
  , time derivative
 and spatial derivative
 .
The spatial domain is assumed to be fixed. The neces-
sary and sufficient condition to obtain minimum for
is that the dependent function
satisfy Euler’s
equation, namely
 
 
  (2)
In what follows, we will investigate the implementa-
tion of the theory to a 1D problem.
6. Example
Let us consider a thin rod under vibrations along
0,xthe longitudinal direction with U
,,UItx as its wave amplitude.
For this proposed example, we relate U with
and choose
in the form
22 2
 
 
 
FItx denotes the specific external
driving force over a unit area, ,
 and
coefficients associated with the second partial derivative
of U.
For example, let
denotes the travelling speed of the informa-
tion wave in the
-vs-t plan and VC
for the ratio
and C the speed of a traveling wave in
-vs-t plan. In view of (1), (3) and (4) the func-
to be varied, will be in the form
Ut FUdIdt dx
QUZUdt dx
 
where Q and
denote, respectively, generalized
source and conductance terms on the boundary envelope
in space and time.
Upon varying
, we describe an extremum process
to define the U function in ,,
tx terms that will
minimize the
functional. Assuming that the bound-
Copyright © 2010 SciRes. JMP
ary conditions in (5) are fulfilled, we follow (2), Euler’s
equation, and obtain a modified wave equation in the
11 0
 (6)
In what follows, we will consider different dominant
forms that may be obtained from (6). To do this we will
refer to nondimensional analysis.
6.1. Dimensionless Analysis
Let us denote the characteristic value of a property by
()C. We choose the characteristic value so as to allow
the dimensionless terms, *
[] , be of a unit order. This
will allow the comparison between the scalar factors
multiplying the dimensionless terms.
The dimensionless form of (6) reads
** *
22 2
22 2
LtIx t
 
 
 
 
 
where C
L denotes a characteristic spatial increment and
t denotes a characteristic time step. In view of (7)
and the relative order of magnitude of its scalar numbers,
we may obtain different dominant forms. To investigate
these, let us also define:
as a characteristic velocity,
as the characteristic amplitude rate,
as the information density,
as the characteristic traveling velocity of information,
as the characteristic aspect ratio.
6.2. Traveling Wave in Space and Time
Consider the possibility that,
In view of (13), the approximate form of (6) conforms
to a traveling wave in the form,
 (14)
Note that the driving force is amplified by the square
of the ratio between traveling velocity of information and
the velocity of the aforementioned traveling wave.
6.2.1. Traveling wave in information and time
Consider the possibility that,
In view of (13), the approximate form of (6) conforms
to a traveling wave equation in the
-vs-t plane
 (16)
It is worthy to stress that (16) occurs when the charac-
teristic velocity is of greater magnitude than that of the
traveling wave velocity and the ratio between the ampli-
tude rate and the driving force be also of greater magni-
tude than the traveling velocity of the considered wave.
6.2.2. Stagnation in Space and Information
Consider the possibility that,
By virtue of (17) the dominant form of (6) will be-
 (18)
The amplitude surface which is obtained by the solu-
tion of (18), may exhib it craters and/or peaks, depending
on the driving force which, as a function also of informa-
tion, acts as a sink/source term.
7. Questions and Conclusions
The mathematician Kaluza in 1919 suggested that if the
world was five dimensional (3 spatial + time + 5th) then
electromagnetism and gravitation can be described by a 5
dimensional geometry. The physicist Klein [10] ex-
Copyright © 2010 SciRes. JMP
plained the invisibility of this extra dimension, by adding
to this geometric description, the principle of “perspec-
tive” namely that this dimension which we do not ob-
serve is because it is rolled up to a tiny size. Klein [10]
computed the circumference of this tiny corpuscle to be
about twenty powers of ten smaller than an atomic nu-
cleus. The revolution of adding dimensions continued
when the nuclear forces were discovered and the ques-
tion rose whether to achieve a general theory these forces
should not be incorporated into a Kaluza-Klein’s [10]
theory by this reducing all the forces of nature to pure
geometry? This brought to the multi-dimensional string
theory [12,13] which brought to the formulation of the
11-dimensional M-theory [13]. Yet in the various articles
discussing the physics of a multi-dimensional continuum,
one can not find any suggestion of a dimension which is
not spatial-temporal.
Focusing just on the period from Newton to Einstein
to Kaluza-Klein [10] theories, every physicist will
probably agree that there was evolution in the complex-
ity of the physical conceptual model. Yet, the question,
which should be asked, is: What about the evolution of
human thinking, which became more complex since it
had to address additional concepts. On what dimension
did human thought evolve ? Was it just on space-time ?
The evolution of the biological sciences and especially
that of the processes of heredity and genetics has even
made these questions more relevant. Does the informa-
tion contained in the DNA molecule described just by its
space-time structure? Or just by its chemical configura-
tion? Moreover, even if these descriptions are sufficient
to pin-point a certain congenital trait, do they describe
the past history of the evolution of these traits? These
questions are now hotly debated, between the proponents
of intelligent design, creationism, and Darwinism [18].
Generalizing these questions will be: Isn’t it possible
that there exists a non spatial-temporal dimension, which
the physicists and biologists ignore because it is not ob-
served, yet science on the whole is built and is continu-
ously progressing along it? Our suggestion is: Indeed this
is the Dimension of Information.
8. References
[1] P. C. W. Davies and J. R. Brown “The Ghost in the Atom
Interviews with John Bell, David Bohm and Basil Hile,”
Cambridge University Press, Cambridge, 1986, p. 128
[2] A. S. Issar, “Evolution of Intelligence in the Bio-World.
Divine Action and Natural Selection: Questions of Sci-
ence and Faith in Biological Evolution,” In: R. Gordon
and J. Seckbach, Ed., World Scientific, Singapore, 2008.
[3] A. Einstein, “Geometry and Experience: Lecture before
the Prussian Academy of Sciences on January 27, 1921,”
In: A. Einstein, Ed., Ideas and Opinions, Crown Publish-
ers, New York, 1954.
[4] A. Einstein, “On the Method of Theoretical Physics,” In:
A. Einstein, Ed., Ideas and Opinions, Crown Publishers,
New York, 1954, pp. 270-276.
[5] A. Einstein, “Physics and Reality,” Franklin Institute
Journal Ditto, 1936, pp. 290-322.
[6] E. Wigner, “The Unreasonable Effectiveness of Mathe-
matics in the Natural Sciences,” Communications on
Pure and Applied Mathematics, Vol. 13, No. 1, 1960, pp.
[7] A. Friedman, “English Translation in: On the Curvature
of Space,” General Relativity and Gravitation, Springer
Netherlands, Vol. 31, 1999. Original article in: T. Kaluza,
“Über die Krümmung des Raumes,” Zeitschrift für
Physik, Vol. 10, No. 1, 1999, pp. 377-386.
[8] P. Kerszberg, “The Invented Universe: The Einstein-De
Sitter Controversy 1916 and the Rise of Relativistic
Cosmology,” Oxford University Press, 1989.
[9] J. Farrell, “The Day without Yesterday: Lemaitre, Ein-
stein and the Birth of New Cosmology,” Thunder’s
Mouth Press, New York, 2005.
[10] P. S. Wesson, “Five-Dimensional Physics: Classical and
Quantum Consequences of Kaluza-Klein Cosmology,”
World Scientific Publishing, Singapore, 2006.
[11] S. W. Hawking, “A Brief History of Time—From the Big
Bang to Black Holes,” A Bantam Book, 1988.
[12] J. Polchinski, “String Theory,” Cambridge University
Press, Cambridge, 1998.
[13] M. Kaku, “Strings, Conformal Fields, and M-Theory,”
Springer-Verlag, New York, 1999.
[14] M. E. Bitterman, “Phyletic Differences in Learning,”
American Psychologist, Vol. 20, 1965, pp. 396-410.
[15] S. A. Kauffman, “The Origins of Order,” Self Organiza-
tion and Selection in Evolution, Oxford University Press,
New York, Oxford, 1993.
[16] W. Weaver and C. E. Shannon, “The Mathematical The-
ory of Communication,” University of Illinois Press, Ur-
bana, 1963.
[17] H. J. Jeans, “The Mysterious Universe,” Cambridge Uni-
versity Press, Cambridge, 1930, p. 134.
[18] A. S. Issar, “Evolution of Intelligence in the Bio-World
Divine Action and Natural Selection: Questions of Sci-
ence and Faith in Biological Evolution,” In: R. Gordon
and J. Seckbach, Eds., World Scientific, Singapore, 2009.