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the Shadow of the Torah)
Posted November 10, 2002
- Ferber and Branover
Hebrew words B'Ohr Ha'Torah mean In the Light of the Torah. This
is the title of a lavishly published journal whose Editor-in-Chief Herman
Branover is a professor of physics at Ben-Gurion University in Beersheba,
Israel. As is indicated on the title page, this journal (whose periodicity is
not revealed) is published by an organization called SHAMIR, "the Israel
Association of Religious Professionals from the former USSR."
announcement on that title page says that this is an "international forum for
all Jews who want to understand how the Torah permeates everyday life, from
personal behavior and social mores to scientific and artistic creativity."
the above statement it seems to follow that contributions from non-Jews are not
welcome; likewise those Jews who do not accept the Torah as the depository of
the ultimate truth apparently need not apply.
to the above statement, I am not one of the potential contributors to the
journal in question. Indeed, I tend to view it in a light different from its
acceptable contributors. Hence the title of this essay; in my view many
articles published in that journal show that their authors, often highly
competent specialists in various fields, are actually benighted by the
uncritical a priori acceptance of the Torah as a source of infinite wisdom and
unlimited knowledge about everything, from what a Jew is allowed to eat and
drink to the most intricate problems of the theory of relativity and of quantum
mechanics. In my view their discourse is often characterized by myopia which is
due to the deep shadow (Tsel in Hebrew) from the Torah story hovering
over their minds.
have no intention of arguing against the role the Torah played in the history
of the Jewish people (while also having exerted enormous influence on many
other nations, Christian, Muslim, and some others) or against the poetic power
evident in that greatest bestseller of all times. I do not believe, though, that
the Torah is a source of scientific knowledge and all attempts to reconcile its
story with the data of science is, in my view, an exercise in futility.
have chosen for my review issue number 13 of the journal, published in 2002 (no
indication of the month of publication). The reason for this choice is that it contains that part of the
Proceedings of a December 1999 conference that took place in Miami, Florida,
devoted to the relation between modern science and the Torah story. The motto
of that conference (which is conducted biannually) was "Absolute Standards in a
World of Relativity." The absolute
standards, as the conference's organizers believe, are given in the Torah,
while scientific knowledge is relative.
all of the authors of the articles in that issue have impressive scientific
credentials. All of them are firm believers in the inerrancy of the Torah and
try to show that modern science is fully compatible with the Torah. In that, issue 13 of the journal may be
viewed as a sequel to or an updated version of the collection Challenge:
Torah View on Science And Its Problems edited by Aryeh Carmell and Cyril
Domb, published by the Association of
Orthodox Jewish Scientists (via Feldheim Publishers of NY and Jerusalem) in
1976 and again in 1978 and critically reviewed at TalkReason
and The Bible vs. Science.
will not review each and every article in that issue, since it would be too
long a discourse, and, moreover, some of the material in that issue lies beyond
the subject of the relation between modern science and the Torah. I will,
though, try to discuss the salient points of those articles wherein their
authors endeavor to interpret both the data of science and the Torah story with
a preconceived confidence of their perfect mutual compatibility.
the journal's cover we read the following lines, which apparently encapsulate
what in the editor's view is the most important thesis covered by the issue's
articles: "Adam & Eve collapse the quantum wave function? THE ROLE OF HUMAN
OBSERVER IN NATURE."
several articles in the issue discuss in detail the above thesis, and I'll
devote a substantial portion of my review to its discussion.
first paper in issue 13 is titled And G-d Said, "Let There Have Been
a Big Bang." Its author is a physicist, Dr. Avi Rabinowitz.
starts his discourse by claiming the following "creation axiom":
"In a free-willed act an
all-powerful being designed and created a natural universe containing entities
that are morally responsible for their choices."
beginning portends the gist of Rabinowitz's article, where we cannot expect to
see an objective analysis based on facts and logic since he adopts an "axiom"
which predetermines conclusions forced by that "axiom."
For Rabinowitz there is no question whether
his statement is true or not – he simply claims it to be true, thus effectively
closing ways to an impartial discussion of any real problem of the universe's
and intelligent life's existence.
as could have been expected from the proclaimed "creation axiom," the rest of
Rabinowitz's article contains little more than categorically proclaimed
statements for which he does not offer a substantiation beyond his original
sole merit I found in Rabinowitz's paper is its relative brevity.
the section titled The Common Ground of Science and Genesis, Rabinowitz
correctly states that "Science does not deal with that which cannot be
objectively and universally observed by scientists, and so does not deal with
the soul." Besides this obviously
correct statement, the rest of the section offers nothing more than completely
arbitrary suggestions regarding the "G-d's infusion of a soul – and perhaps a
mind as well – into a humanoid emerging from the 'the dust of the earth,' as
detailed by evolutionary theory, in a universe which developed from a big bang
created by G-d."
Rabinowitz's acceptance of the evolutionary theory is fine, it can be noted
that if by "evolutionary theory" he means either Darwin's theory or the
Neo-Darwinian synthesis, neither is really about the origin of life. Both are
theories of the development of the variety of species from a common ancestor by
means of descent with modification, led by natural selection. As to the origin of life, there are various
hypotheses regarding the natural emergence of the first living replicators, but
these hypotheses are not part of the theory of descent with modification. The main objection to the quoted statement
by Rabinowitz is, though, related to his contention that the big bang was
created by God. What is the source of Rabinowitz's confidence that the big bang
was indeed created by God? A skeptic would search Rabinowitz's article in vain for
any arguments in favor of his categorical assertion. If Rabinowitz wishes to
believe that the big bang was "created by God" it is his privilege. Likewise,
if he wishes he may believe that the moon is made of green cheese, and it is
nobody's business what his beliefs are. But for a skeptic who is not inclined
to simply take Rabinowitz's word without supporting evidence, his claim is
rest of Rabinowitz's paper is in the same vein – unsubstantiated assertions not
supported by evidence but simply evincing his beliefs. Some of his statements are plainly
misleading. For example, in the section titled Designing the Big Bang: G-d's
Choice, we read, "According to scientific origin theory, in order to
produce our universe, at some point a big bang would have to be created."
seems to be Rabinowitz's secret which scientific theory he has in mind. No scientific
theory asserts anything of the sort. The most widely accepted theory of the hot
big bang (including its prevalent form - the inflationary theory by Guth – see Alan
Guth, The Inflationary Universe: The Quest For a New Theory of Cosmic
Origins, Addison-Wesley, Reading, MA, 1997) does not at all assert that the
big bang "would have to be created." Such an assertion would require derivation of the necessity of the big
bang from certain underlying concepts. No such concepts are known. The big bang
theory interprets the observed facts and concludes that they are best explained
by the assumption of the big bang occurrence some 12 to 15 billion years
ago. This is a far cry from the
assertion, based on some more fundamental scientific concepts, that the big
bang must have occurred to create our universe. The big bang theory says nothing at all
about the "creation" of the big bang. The cause of the big bang is beyond
science and is not discussed in science at all, leaving its discussion to
philosophy, theology, and religion.
continues, "Since a central purpose of the created being is its exercise of
free-willed moral choice, the universe would have to be designed to contain
morally meaningful situations and dilemmas." Of course Rabinowitz is free to believe in anything his imagination may
offer, including any wild hypotheses about the "central purpose of the created
being," but for a mind not encumbered by a priori notions, his suppositions
have no evidentiary value.
subsequent sections of his paper Rabinowitz continues to offer arbitrary
assertions, never making the slightest attempt to substantiate them, but only
referring to his self-published books, where he supposedly elaborates on the
article in question.
the end of his paper Rabinowitz turns to the question of the "collapse of the
wave function" referred to on the journal's cover. His idea is close to what is discussed in more detail in the
article by Poltorak which immediately follows Rabinowitz's. Since Poltorak's discourse about this topic is more
detailed, I will discuss the "collapse of the wave function" when reviewing
The article by Dr.
Alexander Poltorak is titled On The Age Of the Universe (pages 19-37). It is evident both from the article's text and from the biographical note that
Poltorak is a highly qualified theoretical physicist, an expert in the General
Theory of Relativity. The main thesis of article in question is, however, in an
area different from Poltorak's scientific expertise. He tries to show that the
biblical story, according to which the universe was created about 6,000 years
ago, and the theories of the modern cosmology which hold that the universe
exists for about 12 to 15 billion years can be reconciled by using certain
concepts of quantum physics.
writers as Schroeder (see, for example,
Not a Very Big Bang About Genesis who suggested alternative
explanations for the same discrepancy based on blatantly fallacious assumptions,
Poltorak indeed knows his subject (in this case quantum-mechanical concepts)
quite well. Nevertheless his explanation is also based on an arbitrary
overextension of quantum-mechanical theory into the area where its application
is at best doubtful and at worst plainly absurd. As I will show, in his endeavor
Poltorak not only interprets concepts of the physical science in an illegitimate
way, but offers ideas logically incompatible with the Torah story as well.
is preceded by the following sentence: "Readers with no physics background can
skip equations and still follow the discussion."
reasonable to ask, if the equations are not really necessary for understanding
Poltorak's discussion, why are they shown in his article? Let us try to find
the answer to that question in the text of Poltorak's article.
those equations reveals several things:
(a) If all those equations were removed from the article,
it would in no way affect Poltorak's thesis (which will be discussed later).
They play no role in Poltorak's discourse except, perhaps, for
demonstrating Poltorak's bona fide credentials as a well-educated
physicist. But there is no reason to doubt Poltorak's qualifications and no
reason for him to cite equations which can be found in multiple textbooks and
monographs and to which he could simply refer if need be (although there seems
to be no need for such references either, because these equations do not seem to
be relevant to Poltorak's main thesis).
(b) My opinion as expressed in item (a) seems to be even
more justified if we note that the equations in question all are printed in
Poltorak's article in an unrecognizable form, with typos piled one upon another.
Both subscripts and superscripts all are printed on the base line rather than
above or under it, so they are indistinguishable from characters which are
legitimately printed on the base line. Even a reader with a background in
physics needs to decipher those formula based on his prior knowledge of those
formulas. Therefore they play no useful role. It does not matter
whether those typos are attributed to Poltorak, or to the editors, or to whoever
else they may be; they make the formulas a meaningless addition to the article
entire first part (titled Cosmological Models) of Poltorak's paper
is nothing more than a synopsis-like tale about the data and theories related to
the age of the universe and has no relation to his main thesis (which I'll
idea is the subject of the second part of the paper, titled The Torah View
and the Role of the Observer. If the first part were completely excised
from the paper, it would lose nothing of its essential content.
In Part 2 Poltorak
still could not resist the temptation to write equations incomprehensible for
ordinary readers and serving no useful role. Moreover, he devotes many words to
the discussion of certain concepts of quantum physics wherein he offers no new
ideas or interpretations but simply repeats the points which have been discussed
many times before in much more detail, on various levels of sophistication. For
example, he resurrects the worn-out discussion of the so-called Schroedinger cat
gedanken experiment. Schroedinger was a brilliant theoretical physicist
who contributed mightily to quantum theory. His famous example of a cat in a
box was discussed an endless number of times in the literature. Since, however,
Poltorak uses the Schroedinger cat gedanken experiment as a tool for his
subsequent far-reaching conclusions, I have no choice but to briefly review that
experiment here as well
Imagine a box
wherein a cat and a glass vial with a potent poison are placed. Above the vial a
hammer hovers, supported by a hook. The hook is part of a simple mechanism that
holds the hammer suspended. The hammer would be released, thus breaking the vial
and killing the cat, if a pulse of electric voltage passed through the
hook-holding mechanism. The voltage pulse is generated if a particle emanated
from a lump of radioactive material passes a Geiger counter. This event - a
particle passing through the counter - is unpredictable. Hence, the life or
death of the cat depends on a random event. The probability of the Geiger
counter triggering the breakdown of the vial can be calculated. Assume that it
is 1/2 (or 50%).
Here is a quote
from Poltorak's article: "Prior to measurement, the state vector of the first
atom to decay is a linear superposition of two possibilities, a decayed and a
non-decayed atom. Accordingly, the state vector of the cat is also a linear
superposition of two physical possibilities: a live cat and a dead cat. In other
words, before a human being makes a measurement by looking into the box, the cat
is simultaneously alive and dead at the same time! To be more precise, the cat
is neither alive or dead but in a peculiar state of blurred combination of both
I have no
intention of delving into the discussion of Schroedinger's famous example to
which scores of articles and books have been devoted. I will say, though, that
although Poltorak more or less faithfully repeats here notions offered more than
once before by some prominent scientists, I dare submit that the suggestion of a
cat that is both alive and dead or in the "blurred combination of both possible
states" is void of meaning. The conclusion of the cat both alive and dead is
the result of an unsubstantiated extension of certain formal mathematical
concepts of quantum mechanics beyond their limitations. Regardless of whether or
not an observer looks at the cat, the cat is either alive or dead at any moment
of time. If the interpretation of quantum mechanical concepts says otherwise,
it means that those concepts are either faulty or misinterpreted or misapplied.
The only statement legitimately applicable to the situation at hand is that
until an observer has looked into the box, it is unknown whether the cat is
alive or dead. The same can be said about thousands of other cats, within or
without any boxes anywhere in the world.
Nothing in science, including quantum mechanics, is
absolute. Science is a creation of human endeavors, and reflects reality only in
an approximate way and always within certain limits, beyond which its
application is just free play of the mind. The theoretical construct of the
state vector as a linear superposition of several possibilities is a way we try
to describe events in the subatomic world. Applying this concept to such
situations as that with a cat in a box means inflating the meaning of the
concept beyond its legitimate boundaries and leads to absurd conclusions like
that of a cat being both alive and dead. Actually Schroedinger himself
viewed the conclusion of a cat being both dead and alive as absurd, so that, in
his opinion, testified to the incompleteness of quantum mechanics (an opinion
shared also by many other scientists including Einstein).
uncritically repeating the meaningless inflation of quantum mechanical concepts
to a cat in a box, inflates them even further, applying them to the universe as
a whole and trying to connect them to the story told in the book of Genesis.
thesis is that the physical existence of our universe actually started at the
moment when the first human (Adam) "looked at the universe" which occurred about
6,000 years ago. Until that moment the universe existed (for about 12 to 15
billion years) only "in a superposition of all possible states, including the
states of existence and non-existence" (page 33).
To explain the
meaning of the above statement, Poltorak turns to the concept of the wave
function and of its "collapse" - concepts which have been discussed extensively
in the literature on quantum mechanics. In order to analyze Poltorak's
argument, we need to make a few preliminary comments.
(traditionally denoted ψ) is a fundamental concept of quantum mechanics. It can
be calculated by solving the famous Schroedinger equation for given boundary
conditions. Since this review is for an ordinary reader, who may not have
the background necessary to discuss the problem of the collapse of the wave
function in a rigorously mathematical way, I will not delve into the discussion
of the intricacies of quantum mechanics or its mathematical apparatus.
The name "wave
function" is due to the fact that ψ, which is a function of coordinates (and
time), from a formally mathematical viewpoint represents a wave. Of
course the concept of a wave was well known long before the advent of quantum
mechanics. For example, a widely known wave is that propagating in water (if a
stone has been dropped into water, a wave will propagate radially away from the
location of the stone's fall). The simplest definition of a wave says that a
wave is the propagation of a disturbance without the propagation of matter.
suggested his equation, its solution - the function ψ - turned out to be
mathematically analogous to a function representing the previously known waves,
such as waves in water, in air (sound waves), and electromagnetic waves
(including visible light).
If we see a wave
propagating in water, we realize that we observe the propagation of the
oscillatory motion of water's molecules. In the sound wave, what propagates is
the alternating compressed and rarified clusters of the molecules of air (or any
other medium wherein sound propagates). In an electromagnetic wave it is a
combination of oscillating electric and magnetic fields that propagates. In all
these cases it is an oscillatory motion of a certain entity which propagates
from the source of disturbance. What is the entity whose oscillations are
carried by function ψ?
of ψ-function views it as describing the distribution of a particle's mass (and
charge) over a certain volume. For example, for an electron in an atom the
function ψ2 , according to that interpretation, represents the
distribution of the electron's mass and charge over the atom's volume. This
interpretation can be followed in a formally consistent way and tied to a
classic Newtonian dynamic via the Ehrenfest theorem (see, for example, G. Marx,
Quantum Mechanics, Academiai Kiado pubslishers, Budapest, Hungary, 1962), whose
discussion is beyond the scope of this essay. However, while formally
consistent, this interpretation of ψ-function, as I'll show in a few lines,
contradicts empirical evidence which shows beyond a doubt that an electron is an
indivisible ("elementary") particle.
Attempts by the
most prominent scientists, including Schroedinger himself, to interpret
ψ-function as a real field analogous to electromagnetic or gravitational fields
were rapidly realized to lead nowhere (as is correctly mentioned by Poltorak in
As was first
realized by Max Born in the late twenties, function ψ, although formally
represented by the same mathematical expression for a wave as in all mentioned
cases, does not represent oscillations of any material substance or any real
field. Born's interpretation, promptly supported by Niels Bohr and Pascual Jordan, was
rapidly and overwhelmingly accepted as best fitting all the experimental
evidence. According to Born's idea, function ψ is just a mathematical tool
reflecting the behavior of particles in a probabilistic way. For example,
consider an electron about which we know that it is within a certain volume.
However, we don't know where exactly in that volume it is located. If we solve
Schroedinger's equation for that electron we obtain ψ as a function of different
locations within the volume in question. If we square ψ, the quantity ψ 2dV
(where dV is an element of volume calculated for every location within the
volume in question), represents the probability that electron is within
the element dV of volume at a given location. What distinguishes the
quantum-mechanical solution from the Newtonian solution (which is excellent in
the macroscopic world but fails in the microscopic one) is that in the Newtonian
macroscopic world the location of a body can be calculated precisely,
while the required precision of the calculation has in principle no theoretical
limitations. In the subatomic world, where we can't directly observe the
behavior of particles, we are limited to a probabilistic approach wherein we
obtain function ψ2 for every location within the volume in question.
Any location where ψ2 is not zero is possible for the electron in
question, albeit not with the same probability.
earlier, the described situation led to an interpretation of the wave function
according to which ψ2 represents not the probability of the particle
being materially at a certain location. but rather the distribution of the
particle's "density" over the volume in question. According to that
interpretation, the particle is actually "spread" all over the volume, "more of
it" being where ψ2 has larger value and "less of it" where the
squared wave function has a smaller value. While formally that interpretation
seems as consistent and valid as Born's probabilistic interpretation, it
actually has no foundation in any empirical data. Moreover, such an
interpretation leads to absurd conclusions.
following simple experiment which can easily be conducted. Generate a beam of
electrons of a very small density, such that electrons are emitted from an
electron gun and pass, one by one, through a tube leading to a box with walls
impervious for electrons. The tube is equipped with a shutter. Open the shutter
for a short time and close it immediately after a single electron has passed
into the box. At the moment the electron was entering the box, its location was
known with a precision determined by the diameter of the ingress aperture of the
box. Upon entering the box, electron can happen to be anywhere in the box, and
we don't know its exact location except for the certainty that it is in the box.
(In the often used quantum-mechanical terms, it is said that the electron is a
"wave packet" which, upon entering the box, spreads over the width of the box).
Let us provisionally accept the model of the particle's matter being "spread"
all over the box, wherein the squared wave function ψ2 represents the
distribution of the density of electron's mass and charge over the volume of the
box. Now imagine that we insert into the box a partition which separates the two
halves of the box. If the electron were "spread" over the box's volume, then
each half of the box would now hold 1/2 of the electron's mass and charge. This is
an obvious impossibility because an electron (as is every lepton) is a real
elementary particle. In no experiment has a fraction of an electron ever been
observed. It is always observed only as a whole. (For certain situations the
last statement requires a subtle clarification, for example for an electron in a
crystal lattice of solids, but although the electron's behavior in crystals has
some peculiar features, it does not negate the notion that electrons are
Therefore the only
consistent interpretation of the wave function is that it describes the behavior
of particles in probabilistic terms. There is neither a material substance nor a
real field represented by function ψ.
interpretation of ψ2 as the spatial distribution of a particle's mass
and or charge, formally legitimate but contradicting empirical evidence, paved
the way to viewing wave function as representing oscillations of some material
entity, and this in turn led to the concept of the "collapse" of the wave
function as of some real event in physical reality.
One more comment
is in order. As the Ehrenfest theorem shows, quantum mechanics (at least for
slowly changing fields) contains all classical mechanics as an approximation. In
other words, equations of quantum mechanics are valid not only for subatomic
particles, but also for every macroscopic body as well. For masses substantially
exceeding those of subatomic particles, equations of quantum mechanics convert
into equations of classical Newtonian mechanics. The peculiarities of the
behavior of subatomic articles revealed by quantum mechanics become less and
less noticeable as the mass of the bodies increases. The wave function is in
principle a valid tool for the description of the behavior of not only subatomic
particle, but also of whole atoms and even molecules, although for the molecules
the uncertainty in their location as determined by the wave function becomes
negligible. With the amazing advances in tunnel electron microscopy, scientists
are nowadays able to see (and even manipulate) individual atoms. What we see is
entities which have a definite shape and distinctively occupying a definite
volume each, by no means being spread over a large volume with a variable
density. This provides another piece of strong evidence in favor of Born's
probabilistic interpretation of the wave function. There is practically no doubt
that ψ does not represent any real material quantity or a real field. It is a
mathematical construct reflecting, besides the objective behavior of subatomic
particles, our inability to visualize subatomic particles which are unlike
anything we interact with in our macroscopic world.
When we say that a
particle possesses wave properties, this does not at all mean that an individual
particle is indeed a wave. If particles pass one by one through the slits in a
partition, no single particle ever generates a diffraction pattern. Each
particle hits the screen at a definite location which can be identified,
although with limited precision, but quite unequivocally. However, the location
where the particle hits the screen is not arbitrary. For each location on the
screen there is a definite probability of being hit by a particle. For some
locations this probability is zero. No particle ever hits the screen at such
locations. Wherever the probability is higher, more particles will hit such
locations. The distribution of probabilities is such that when a large number of
particles has hit the screen, either as high-density beam or one by one, all the
points of encounters of the particles with the screen form a diffraction pattern
which depends on the number of the open slits and follows the rules of
diffraction for a wave mathematically described by the ψ 2 function.
pattern appears only as a result of many particles hitting the screen, either in
a high density beam, or one by one. What then is the meaning of the term "wave
properties of particles" or "wave behavior of particles?" It means that each
particle, when hitting the screen, never does it at a location where the
corresponding wave would have a distractive interference. The behavior
of each electron, although it moves through the slits individually and itself
creates no diffraction pattern, follows (in a probabilistic way) only such
paths which, when the entire collective of electrons hits the screen, would
result in a diffraction pattern corresponding to a wave passing the given number
of open slits.
Hence, while we
definitely know that subatomic particles possess certain properties which make
them follow the pattern of wave behavior, there is no way to visualize these
particles. All we can do is to describe the particles' behavior using a
mathematical construct, and the ψ-function fits the bill very well.
seems to be a difference between leptons and hadrons. Leptons (for example,
electrons) are viewed as genuinely elementary particles having no constituent
structural elements, so they can be viewed as having no volume at all ("material
points") while hadrons (for examples, protons and neutrons) are believed to
contain quarks as their structural components, thus occupying certain volumes
(which is definitely true for atoms). It is possible (although there is no
empirical evidence for this) that the volume occupied by a particle is not
constant but varies depending on its interaction with other particles and
However, the above
notions have no bearing on my thesis. When we say that a particle is at a
definite location, this statement should be construed within the limitations
imposed by the uncertainty principle, valid both for leptons and hadrons. The
point is that wave function reflects the indeterminacy in the "precise" location
of a particle ("precise" to the extent limited by the uncertainty principle)
rather than reflecting a "spread" of matter constituting a particle over the
volume where ψ is not zero.
With this in mind,
we can now discuss the fallacy of the interpretation of the "collapse of the
wave function" as exemplified by Poltorak's article. Although Poltorak refers
to von Neumann (John von Neumann, Mathematical Foundations of Quantum
Mechanics, Princeton University Press, Princeton, NJ, 1955) and other
prominent scientists who discussed various interpretations of the wave function
and its "collapse," my task in this paper is not the overall discussion of this
difficult and important problem, but only a critical review of Poltorak's
presentation of the wave function collapse in the "light of the Torah."
The notion of the
collapse of the wave function can be explained as follows:
example, an electron beam directed toward a wall in which there are two narrow
slits located close to each other. If the aperture of each slit and the distance
between the slits are in a certain range, a diffraction pattern appears on a
screen behind the wall. If one of the slits is closed, the diffraction pattern
changes. If the closed slit is opened again, the original diffraction pattern
reappears. This phenomenon is observed even if the electrons pass the slits one
by one. It looks like an electron which is passing one of the slits somehow
"knows" whether the second slit is open or closed. The explanation of this
phenomenon is usually given by referring to the wave properties of the
electron. If a wave passes through slits in a wall, it is always going through
all opened slits simultaneously. For example, a wave front of sea water coming
through opening in a breakwater passes through all openings simultaneously and
generates a diffraction pattern which depends on the number of openings.
Now enter the wave
function again. Its square value tells us the probability of the electron being,
at this or that moment of time, at this or that location. Until the electron
hits the screen its whereabouts are known only in terms of probabilities and are
reflected in the wave function. At the moment the electron hits the screen its
location immediately becomes determined by the spark of light on the screen. No
probabilities any more, now the electron's whereabouts become determined (albeit
within certain limits of precision). This phenomenon of an instant revelation of
the particle's whereabouts is referred to as the "collapse of the wave
This term is
interpreted in quantum theory as the result of the interaction of the subatomic
particle with a macroscopic device (a screen in the above example).
shares the view that the described collapse of the wave function happened only
because the event was observed by a conscious observer. This idea was offered by
some scientists but is by no means commonly accepted. In particular, proponents
of that idea routinely refer to the prominent physicist John Archibald Wheeler
as being allegedly one of the originators and a strong supporter of that idea.
In fact, however, such references misuse a statement made by Wheeler in 1982,
wherein he wrote, "No elementary quantum phenomenon is a phenomenon until it is
a registered phenomenon... In some strange sense, this is a participatory
universe." (In the collection Mind in Nature, edited by R. Q. Elvee, San
Francisco, Harper and Row, 1982, page 17). Adherents of the idea of a
participatory universe usually ignore other statements by Wheeler showing that
he himself did not at all mean it in the sense supporting the concept of
consciousness being a necessary component of quantum phenomena. In particular,
Wheeler has also said, "Consciousness, we have been forced to recognize, has
nothing whatsoever to do with quantum process." (In the same collection,
page 21). Anyway, appeal to authority is not really a compelling argument.
Since Poltorak promotes the idea of consciousness as a necessary condition for
the collapse of a wave function, a few words regarding that idea are in
that the wave function is a mathematical construct reflecting the impossibility
of describing the behavior of subatomic particles in a visually comprehensible
way, limiting us to a probabilistic approach. We just cannot in principle
visualize an elementary particle and therefore can't really describe what it
means for a particle to be at a certain location in terms of our mundane
Function ψ does not represent any material entity but only a mathematical phantom
whose variations in space and time reflect the probabilities of a particle being
in a certain state (in particular at a certain location). When the wave function
"collapses," nothing material does.(This notion can actually be traced to
Bohr, and to Copenhagen interpretation in general.) All that collapses is
phantom, the way of description of the particle's behavior. From the "viewpoint"
of the particle itself, nothing "collapses."
The collapse of
the wave function would mean a collapse of a material entity only if the
ψ-function indeed represented the physical "spread" of a particle's density over
a given volume. Although formally consistent, such a model contradicts empirical
evidence, so the only proper interpretation of the "collapse" is that this term
is only applicable to a mathematical construct, to such an event where the
whereabouts of a particle (which before the "collapse" could only be determined
in probabilistic terms) become revealed because of the interaction of the
particle with a macroscopic device.
Although we do not
really understand what the meaning of a particle being "located" here or there
is, in a certain sense we may state that before the wave function collapsed, the
particle was still actually "located" somewhere, rather than having its density
distributed all over the volume in question according to the values of the
squared wave function. We simply did not know its "whereabouts";
we knew only the probability of its being here or there. (It may be noted
that there is still no consensus among scientists regarding what the precise
meaning of the concept of a particle's whereabouts is.) All that happens
when the particle hits the screen, is that its whereabouts become revealed
to us. As always with probabilities, as soon as the event whose probability was
estimated has actually taken place, all estimates of probability cease to be
meaningful, being replaced by a certainty. The term "collapse" is an unfortunate
one. All that "collapses" (if we choose at all to use such a term) is our
mathematical construct, our best available tool for the description of
imperfectly known reality. It is not needed any more because the location of the
particle is revealed with a certain precision, which, although limited, is
satisfactory from the cognitive viewpoint corresponding to our conventional
macroscopic experience. No probabilistic approach is needed any longer.
Is a conscious
observer necessary for the "collapse" of the wave function? Let us see. Imagine
that we set up our experiment with an electron beam passing through slits and
hitting a screen. Let us use a screen with a long afterglow, or a photographic
plate instead of a screen. We turn on the setup and leave the lab until the next
day. When, the next day, we come in we discover the photographic plate wherein
the diffraction pattern has been recorded. The device was automatically turned
off before we arrived, so no electrons are hitting the screen in our presence,
but the photographic emulsion holds the diffraction pattern which formed in our
absence. If we believe that a conscious observer is necessary for the wave
function to collapse, then in our absence no diffraction pattern could have
formed. This is an absurd supposition. We know that the pattern on the photo
plate will be exactly the same regardless of whether a conscious observer was
present or not in the lab during the experiment. The wave function which is just
a mathematical construct would "collapse" (which simply means that the
electrons' whereabouts would be revealed for a potential future observer) as a
result of their interaction with a macroscopic device (photographic emulsion) in
our absence as well as if we were present in the lab. This "collapse" of the
wave function would have nothing to do with any intervention by a conscious
observer. So, quoting again the prominent physicist Wheeler,
"consciousness has nothing whatsoever to do with quantum process."
Poltorak's reference to Wheeler seems to be ill-conceived.
the wave function does not represent any material entity, formally it can be
handled as though it indeed were such a material entity. The mathematical
treatment of the subatomic event is the same regardless of whether we interpret
ψ as representing a material entity or a real field or just as reflecting the
apparatus of quantum mechanics is very sophisticated, what with its Hermite's
operators, Hamiltonians, and other esoteric mathematical concepts which are
incomprehensible to ordinary folks but are a source of enjoyment for the
cognoscenti. The experts, enchanted by the mathematical beauty of their
equations, are sometimes prone to forget the material reality which the
equations so beautifully represent, and tend to view the mathematical
abstraction as the reality itself. In this vein, the "collapse" of the wave
function which actually occurs only on the formal mathematical plane, is
sometimes attributed to the physical reality (while most often such an
interpretation is done by philosophers rather than by scientists). In particular, the events which
take place in von Neumann's magnificent mathematical description of quantum
sometimes viewed as though they take place in the real physical world. In that,
Poltorak goes much further than
von Neumann himself suggested.
Poltorak's interpretation is not limited even to viewing the
"collapse" of the wave function as though it happens in the real physical world
rather than in its abstract mathematical, probabilistic reflection. He extends
the application of the wave function well beyond its legitimate bounds.
The wave function
which is found by solving Schroedinger's equation describes in probabilistic
terms the behavior of subatomic particles. As the mass of the articles
increases, the indeterminacy in their behavior decreases; although
Schroedinger's equation may be formally written, say, even for a planet, it
becomes of little meaning already on the molecular level.
The wavelength of
the wave represented by the ψ-function is inversely proportional to
the particle's momentum, i.e. to its mass and velocity. When the mass of an
object is on the order of a mass of a molecule, the wavelength becomes so
miniscule that the wave behavior is practically beyond any observable limits. A
billiard ball has a very definite location and simultaneously a very definite
momentum, not because Schroedinger's equation is principally inapplicable to the
ball (it is) but because the mass of the ball is so large that the corresponding
wave has an exceedingly small length, so the ball does not display any
measurable wave behavior. The concept of location acquires a very definite
meaning for bodies whose mass is much larger than it is for subatomic particles,
and the use of the wave function for such relatively large bodies makes no
sense. If this is true for bodies of a molecular size, it is much truer for
When we deal with
macroscopic bodies, the very concept of the wave function and hence of its
collapse deteriorates to a pure game of the mind with no practical content.
Poltorak, however, applies the concept of the wave function and its collapse to
the universe as a whole, which is an immensely exaggerated inflation of
the concept's reasonable applicability.
interpretation, which has no factual basis, the universe materialized only 6,000
years ago, when the first conscious observer, Adam, caused "the world wave
function" to collapse.
"Prior to the first human, the universe existed in a superposition of all
possible states, including the states of existence and non-existence. When the
first human looked for the first time at the universe, the world wave function
immediately collapsed and the world came into physical existence."
The abject absent
of elementary logic is coupled in that statement with an equally abject
extension of the wave function concept far beyond its meaningful limits.
If the first human
"looked the first time at the universe," this means the universe he could look
at must have already existed. Moreover, the first human himself must have been a
part of an existent universe. Or did he exist by himself without anything else
If we believe the
Torah, upon which Poltorak supposedly based his ideas, it tells us that the
first human was created (according to Genesis 1) or formed (according to Genesis
2) on the last of the six days of creation, after everything else - the sun, the
moon, the earth, water and firmament, etc., had been already in place. Hence,
the first human, according to the Torah but contrary to Poltorak's model,
already had a universe available to look at, so this human hardly could cause
the alleged "collapse of the world wave function" thus calling the universe into
existence out of "both existence and non-existence."
Either the universe existed before the first human or it did not.
There is no tertiary quid. If the universe could have been called into existence
only by the first human looking at it and thus causing the "collapse of the
world wave function," this means the first human existed before the universe and
therefore could not "look" at the yet non-existent universe.
If, though, a
universe existed before the first human could look at it, then its existence
could not be caused by the as yet non-existent human looking at it.
makes no sense both from the viewpoint of the Torah and that of science.
Poltorak's is a
model based on groundless suppositions having nothing to do either with quantum
mechanics or any other science or with the Torah's story. It seems to stem from
an overriding desire to reconcile, by
whatever means, the biblical legendary narrative with the achievements of
entitled to believe whatever he likes. However, his attempts to substantiate his
beliefs by using the concepts of quantum theory which have no relation to
Poltorak's theological exercise is far from convincing.
article by Professors Ruvin Ferber and Herman Branover (from now on to be
referred as FB) is titled The Observer and the System of Reference: A
presentation consists of two very different parts. The second part, titled The Changing Views of Science,
could be a separate article written on a good (although popular) scientific
level, wherein the main thesis, although it could be disputed (and I intend to
dispute it in this review) is a legitimate subject of discussion wherein FB are
entitled to their interpretation of the relativity of motion. I believe his interpretation is wrong, but
it is far cry from unsubstantiated ruminations we find in the articles by
Poltorak, Rabinowitz, or some other authors. At least FB talk in that part of their
article only about subjects relevant to their topic - the interpretation of
relativity of motion.
the first part of the article looks like ransom paid to a religious agenda. Take,
for example, the sections titled The Rebbe's view and The Wager
wherein FB refer to the opinion of the seventh Lubavitcher Rebbe Menachem
Mendel Schneerson in regard to relativity of motion and the alleged equivalence
of Ptolemy's and Copernicus's models of the solar system.
the esteemed late Rebbe as an authority on scientific problems sounds
like a joke. Schneerson never took part in any scientific activity and did not
even have sufficient education in any area of science, but apparently liked to
indulge in discussing scientific questions in all areas of knowledge. The
amateurish level of his judgments was, for example, illustrated at Challenging the Challenge
is hard to comprehend how a well qualified physicist like Professor Ferber
could feel proper to lend his signature to these ridiculous sections of the
article in question.
us talk now about the real thesis of FB's presentation.
page 45 we read, "One of the conclusions of the theory of relativity is that
when there are two systems, or planets, in motion relative to each other - such
as the sun and the earth in our case - either view, namely the sun rotating
around the earth, or the earth rotating around the sun, has equal validity."
Ferber and Branover, you should know better.
when you mention the theory of relativity, it is advisable to specify whether
you mean the special theory of relativity (STR) or the general theory of
whichever theory of relativity you have in mind, neither asserts the "equal
validity" of the two mentioned models of the solar system. FB's statement is nothing more than their
personal interpretation of both STR and GTR rather than a straight conclusion
of either of the two theories.
discussing in detail FB's arguments, let us briefly review in layman's terms
what STR and GTR indeed say about the problem at hand.
show that from the viewpoint of STR Ferber-Branover's position is wrong. From
the viewpoint of GTR, while not plainly wrong, their position is just their
preferred interpretation of the GTR rather than an uncontroversial conclusion.
with STR. This theory asserts that all inertial frames of reference are
equivalent. The term inertial denotes such systems (i.e. physical
bodies) which move without acceleration (i.e. with a constant velocity; velocity
itself has no absolute value-it depends on which frame of reference is chosen
as being "at rest"-so the velocity of the system in question is measured
relative to the chosen frame of reference). The choice of the frame of reference (i.e. of a body which is agreed to
be viewed as being at rest) is arbitrary. Hence, within the framework of STR
only inertial systems are equivalent, while systems (i.e. bodies) which have
acceleration (i.e. are non-inertial) are not equivalent and can be
distinguished unequivocally from inertial systems and from each other by
detecting their accelerations. Acceleration, unlike velocity, is, within the
framework of STR, absolute and does not depend on the frame of reference.
the above to the solar system. The central body (the sun) has no acceleration.
Every planet moves on an elliptic orbit wherein it has acceleration. The main
component of the acceleration is the centripetal acceleration caused by the
gravitational attraction of the planet to the sun. This component of
acceleration makes the planet's velocity turn toward the sun, thus forcing the
planet to circle the sun on an elliptical path. Planets also have a
longitudinal acceleration due to the deviation of their elliptical orbits from
a perfect circle. Hence planets are not inertial systems and therefore not
equivalent to the central body-the sun. Therefore, if we limit ourselves to
the tenets of STR, there is no equivalence between Ptolemy's and Copernicus's
models. The sun is the only body in the solar system which has no acceleration,
all planets do have one. The sun occupies a unique position in the solar
system. Copernicus was right and Ptolemy (and with him the Judaic, Christian, and
Muslim religions) was wrong.
from the viewpoint of STR the question about the alleged equal validity of two
models is answered unequivocally and easily in favor of Copernicus's
the standpoint of GTR, however, the answer is not that simple and plain and FB
take advantage of the complexity of the position based on GTR to offer their
interpretation according to which the two models are, after all, equally valid.
Let us see if their argument is
convincing enough to assert that the model of the sun rotating around the earth
is as valid as the heliocentric model is.
is a complex scientific theory which can be rendered in various forms. For the
purpose of this discussion (and having in mind that it is for an ordinary
reader rather than for the mathematically sophisticate) it seems convenient to
present the main point of GTR as follows:
STR is the mechanics of inertial systems, GTR is the mechanics of non-inertial
systems. This is, though, only one aspect of GTR. It also is a theory of
gravitation and as such it asserts equivalence of gravitational and inertial
forces. Based on that concept, FB announce
the equivalence of heliocentric and geocentric models of the solar system,
which serves their purpose of substantiating the Torah's assertion that the
earth is the center of the universe and the sun (and the rest of the universe)
is rotating around the earth. To be
sure, FB only suggest that the heliocentric system is no more reasonable from a
scientific viewpoint than the geocentric system of the Torah, so there are no
scientific reasons to reject the Torah's model. They do not insist that science
directly supports the Torah's model.
it can be shown that GTR actually provides reason to prefer Copernicus's
heliocentric system to Ptolemy's geocentric one (supported by the Torah). To
this end let us consider another rendition of GTR which can be offered without
resorting to mathematical equations. One of the easily visualized renditions of
GTR tells us that space does not exist by itself but must be viewed as an
attribute of matter. Wherever there is
a clump of matter it makes space around it curved. The sun makes space around
it curved, and so does the earth. However, since the sun has an immensely
larger mass than the earth (or than any other planet in the solar system) the
curvature of space caused by the sun is immensely stronger than the curvature
caused by the earth. There is no equivalence between the effects of space
curving caused by the sun and by the earth. The model according to which the
planets move on elliptical orbits, their path determined by the curvature of
space caused by the immense mass of the sun, is plainly preferable to the model
in which the sun, with its much larger mass moves on a path curved by the much
smaller mass of the earth (or of the other planets).
if we consider the motion of the sun and of the earth relative to the rest of our
galaxy, it is much more reasonable to view the solar system as a whole as such
wherein there is a central body (the sun) and a family of planets orbiting the
sun on simple elliptical paths rather than the earth as the center of that
system and everything else rotating around the earth on fancy convoluted paths.
theory of relativity, either special or general, provides no support whatsoever
for the Torah's geocentric picture, regardless of how strongly FB and their
co-believers would like us to believe.
their main thesis of the equivalence of Ptolemy's and Copernicus's models, the
article contains a number of sections dealing with quantum mechanical theory of
measurement including von Neumann's ideas of the role of an observer, as well
as their further discussion by Wheeler and Wigner; the Copenhagen interpretation
of the quantum mechanics; Mach's principle attributing the inertial forces to
the overall effect of the galaxies, etc. All this material, interesting in
itself, would be appropriate for a semi-popular article for laymen interested in
learning about some theories discussed in modern science, or for a teaching aid
for a freshman class in physics, but it does not offer any material which would
be the authors' original contribution to the subject. It is not clear why such
a brief narrative about well known problems of science was thought to be a
proper contribution to a conference where the relation between science and the
Torah was to be discussed. The only point which went beyond just one more
rendition of the stuff elucidated many times before was FB's assertion of the
equal validity of Ptolemy's and Copernicus's models of the solar system wherein
the two professors strived to show that the Torah's story does not contradict
article by professor of physics Nathan Aviezer is titled Richard Dawkins and
very title of that article portends its highly polemical and controversial
nature. Everybody familiar with the real situation in contemporary biological
science knows that there is no such thing as Darwinian fundamentalism
(although individual scientists may sometimes feel reluctant to subject the
established theories to a major overhaul). This derogatory term implies a dogmatic
adherence to a set of preconceived notions impervious to reason and critique.
It may be justifiably applied to the position of the authors and editors of the
B'Ohr Ha'Torah journal who base all of their arguments and opinions on an
unshakeable belief in the Torah's inerrancy, a belief indeed impervious to
reason and seeking no reason. Biological science is a different matter.
Although the overwhelming majority of biologists are firmly convinced of the
validity of the principal tenets of the Neo-Darwinian synthesis, there are constantly
lively discussions and disputes among biologists regarding various aspects of
their science, and no subject or principle, however fundamental to Darwinism,
is immune to rebuttals and modifications. It is sufficient to point out the
heated dispute between the proponents of the "punctuated equilibrium" concept
and its detractors (discussed in more detail below), with both sides adhering
to Darwin's evolution theory but fervently disputing its various details and
interpretations. There are no sacred cows in biology. Aviezer's application of the term fundamentalism to the
Darwinian theory (as well as his use of another pejorative term,
"ultra-Darwinism") betrays his prejudice.
punctuated equilibrium theory was suggested by the late Stephen Jay Gould and
Niles Eldredge (see for example S. J. Gould and N. Eldredge, Punctuated
Equilibrium Comes of Age, Nature, v. 366, p. 223, 1993). Since the
prominent writers and biologists Richard Dawkins and Daniel Dennet were among
the most outspoken detractors of the "punctuated equilibrium" hypothesis, Gould
(whose acerbic style of dispute, often displaying arrogant self-confidence, was
his trademark) singled out these two colleagues cum adversaries for his most
energetic rebuttals. However, while
Gould and Eldredge on the one side, and Dawkins, Dennet, and some other
biologists on the other side, vigorously defended their respective position in
regard to "punctuated equilibrium," both sides adhered to the Neo-Darwinian
synthesis in general.
position is different. His goal in the article in question is to smear his
targets – three prominent writers and scientists, Richard Dawkins, Daniel
Dennet, and Peter Atkins, who happened not to share Aviezer's religious
of discussing the substance of the arguments offered by Dawkins, Dennet, and
Atkins, Aviezer resorts to ad hominem remarks and innuendos, accusing these
three writers of various kinds of misconduct, dishonesty, and other shameful
acts. In doing so, Aviezer does not shy away from quoting out of context and
misrepresenting the views of his targets thus himself committing those untoward
actions he attributes to the subjects of his assault.
main thrust of Aviezer's attack is against Richard Dawkins.
to Dawkins's popular book The Blind Watchmaker (Norton, NY, 1986)
Aviezer exaggerates the animosity between Dawkins and Gould as it is allegedly
expressed in Dawkins's book. Contrary to Aviezer's story, Dawkins does not
depict Gould as a "villain." Dawkins
offers arguments against Gould's "punctuated equilibrium" hypothesis, which is
a normal occurrence in scientific disputes.
his acclaimed essay Nonoverlapping Magisteria (Natural History, March
1997, p. 16) Gould, while professing his respect for religious faiths, clearly
indicated that he himself did not share any such faith. Aviezer's attempt to
enroll Gould for his attack on Dawkins is obviously caused by the abject
paucity of allies having a reasonable scientific status to whom Aviezer could
refer in his crusade. Therefore Aviezer resorted to exploiting the dispute
between Dawkins and Gould which was about a certain specific hypothesis and not
about the fundamentals of the Neo-Darwinian synthesis, as if it provided an
indication of the deep rift within the scientific community and wherein Dawkins
allegedly committed grievous sins.
entire section in Aviezer's paper titled Ultra-Darwinian Tactics is a
bunch of innuendos, ad hominem remarks and inventions aimed at smearing Dawkins
and distorting Dawkins's position to the extent of making it unrecognizable.
Although Aviezer derides Dawkins's assertion of passionately caring "about what
is true," what is clear for an unbiased reader familiar both with
Dawkins's and Aviezer's writing is that
it is Aviezer who is ready, willing, and able to distort the plain meaning of
Dawkins's words to suit his agenda.
devotes two whole sections of his paper to the discussion of Gould and
Eldredge's "punctuated equilibrium" hypothesis. His goal is to show that this hypothesis is really a firmly
established theory which cardinally undermines Darwinian evolution theory. In
fact, this is far from true.
in the course of several years after Gould and Eldredge suggested their
hypothesis their original concept underwent substantial modifications. Some of
Gould's and Eldredge's notions became a part of Neo-Darwinian theory, while
some other parts were rejected by mainstream biology, as often happen with
scientific theories. It is a common situation that the authors of an original
theory tend to overextend its supposed area of applicability and the theory in
its initial form contains both valid elements and excessive generalizations.
The critique by biologists such as Dawkins, Miller, and others played a
constructive role in defining the limits of the theory's applicability. Within these limits, the original notions of
the theory's authors were clarified. In particular, the consensus among the
scientist is that "punctuated equilibrium" theory, as it is legitimately
interpreted, is perfectly compatible with the foundations of Darwin's evolution
theory. The "rapid" evolution of new
species between the long period of "stasis" is actually not really "rapid" since,
according to the paleontological data used by Gould and Eldredge, this "rapid"
evolution took millions of years and looks "rapid" only on the background of
the much longer periods of time paleontology usually deals with. There are many
other fine arguments partially rejecting certain elements of Gould-Eldredge's
original theory and partially interpreting them in a way compatible with the
Darwinian position. Aviezer, using selective quotations, paints a distorted
to Aviezer's assertions, the Darwinian gradualism can be reconciled with
properly interpreted punctuated equilibrium, and the majority of biologists are
comfortable with such a reconciliation.
for example, how Aviezer distorts the exchange of views between Gould and
Dawkins regarding the evolution of the eye. He quotes both Gould and Dawkins,
wherein Gould used the expression "What good is 5 percent of an eye?" Dawkins, however, used instead an expression
"Vision that is 5 percent as good as yours or mine is very much worth having in
comparison with no vision at all."
Aviezer's presentation, Dawkins's statement means "ridiculing" Gould. To an
unbiased reader it is obvious that there is not even a shadow of ridicule in
Dawkins's sentence but only the expression of a legitimate disagreement on some
nuances of the matter, on whose principal features Gould agrees with Dawkins to
a much larger extent than Gould could ever support Aviezer's general position.
Aviezer continues, he misrepresents the gist of the disagreement between
Dawkins and Gould by making the unsubstantiated claim that Dawkins
"transformed" Gould's statement about "5 percent of an eye... into a statement
about '5 percent vision.'" However,
reading both Gould's and Dawkins's texts reveals that no distortion has taken place. The expressions "part of an
eye" and "part of vision" were used to refer to exactly the same thing. To see
that it is indeed so, it is sufficient to look at Dawkins's example of a
light-sensitive cell which is both "a small percentage of an eye" and provides
"a small percentage of vision." Dawkins did not distort Gould's notions. It is
Aviezer who misused the inconsequential variations in the language used by
Dawkins and Gould. In doing so, it is Aviezer who actually ridicules Dawkins
and thus creates deception aimed at misrepresenting the gist of the Dawkins vs.
Gould discussion, for the sake of Aviezer's agenda.
is little doubt that were Gould still alive, he would reject the dubious "help"
from Aviezer in his dispute with Dawkins. Gould used to be a powerful defender
of the evolution theory and simultaneously an iconoclast in the interpretation
of some of its features. In that he had
many detractors within the ranks of his fellow evolutionists. However,
Aviezer's attempt to enroll Gould as an ally in his fight against the so-called
"ultra-Darwinists" is an insult both to Gould and to the idea of objectivity in
a similar way, Aviezer refers to other renowned scientists who allegedly share
his views regarding the "ultra-Darwinists." When assaulting Daniel Dennet,
Aviezer again tries to create the impression that Gould and another respected
biologist, Allen Orr, share Aviezer's position. The actual situation is
different. H. Allen Orr is as firm a Darwinist as they come. His position has
nothing in common with that of Aviezer. To see that this is indeed so, it is
sufficient to read Orr's critical reviews of the books by latter-day
creationists Behe (H. Allen Orr Responds, Boston Review, Feb-March 1997,
p. 35) and Dembski (Boston Review,
Summer 2002; also available at Boston Review),
as well as his essay (H. Allen Orr, The Descent of Gould: How a
paleontologist sought to revolutionize evolution. The New Yorker, Sept. 30,
2002, p. 132) on life and work of Gould. In the latter essay Orr demonstrates
that according to the overwhelming consensus among the biologists the original
form of Gould's and Eldredge's punctuation equilibrium theory did not survive
the test of impartial verification; while some elements of punctuated
equilibrium theory have been successfully incorporated into Darwinian evolution
theory, its many other features have been rejected as contrary to evidence. The
efforts of Gould's opponents like Dawkins have served as catalyzing agents in
defining the limits of that theory's applicability. Despite the sometimes
acrimonious tenor of the dispute (not at all uncommon in science) it did not
trespass the boundaries of a normal process of refining a good (but never
perfect) theory as the Darwinian theory of evolution is.
Gould nor Orr are Aviezer's allies, all his attempts to prove otherwise
the end of his article Aviezer shows his disregard for plain logic. Discussing
the book by British chemist Peter Atkins, Aviezer writes, "Note the striking
difference between Atkins's assertion that it is undeniable that the evolution
of human beings was inevitable, and the exactly opposite opinion expressed by
world class scientists like Alvarez and Gould. It follows, of course, that if
Atkins's scientific assertions are incorrect, then his conclusions about
religion based on them are equally erroneous."
Is this indeed so?
First, if Atkins on the one hand and Gould or Alvarez on the other hand, have
different opinion on whatever subject, this does not mean that Atkins is
necessarily wrong. Although Gould and
Alvarez are both fine scientists and their view deserves respect, they have no
monopoly on truth. The greatest scientists all have made mistakes, sometimes
very serious ones. Regarding the particular point Aviezer addresses, there is
no consensus among the scientists regarding the question of whether life's
emergence was inevitable or it was a random occurrence which may never occur again
anywhere in the universe. Both views have their proponents. However, whatever side one takes in that
discussion has little to do with Atkins's views on religion. Atkins's views on
religion have been shared by scientists both agreeing and disagreeing with him
in regard to the inevitability of life's spontaneous emergence; in particular,
Gould's view of religion was certainly closer to that of Atkins than that of
Aviezer, although Gould disagreed with Atkins on the inevitability of life's
emergence. There are other scientists
who disagree with Atkins's view of religion but share his view regarding the
spontaneous emergence of life. Therefore Aviezer's "conclusion" that Atkins's
views on religion are erroneous is nothing more than Aviezer's personal opinion,
not supported by objective arguments. Aviezer's attempt to enroll prominent
scientists as allegedly sharing his worldview is hardly convincing.
Aviezer's article is a misleading piece by a religious propagandist who does
not shy away from using whatever means available to drive his beliefs into the
minds of his readers and using for this end some not quite kosher means.
pages 108-111 we find an article by Professor Edward Simon wherein he reviews
Dr. Lee Spetner's book Not By Chance: Shattering the Modern Theory of
Evolution. Spetner's book
(published in 1998 by the Judaica Press) has been reviewed many times,
including a very critical and well substantiated review by Dr. C. Feit in Jewish
Action magazine (Spring 1999 issue). This magazine serves the Orthodox
Jewish community and Dr. Feit criticizes Spetner from the position of an
his co-believer Feit, Professor Simon has a very positive opinion of Spetner's
book. Although in Simon's view Spetner's alternative to Neo-Darwinism is not
substantiated well enough, he asserts that Spetner has successfully debunked
the Neo-Darwinian paradigm. In Simon's
words, Spetner did an "excellent job in pointing out the problems associated
with attributing evolution to random mutations and selection (the new Darwinian
theory)." Continuing, Simon writes that
Darwinian evolution, "for all its strengths and attractiveness, fails to
explain how life arose and developed."
put it mildly, this is a rather odd statement for a professor of biology. It
does not take an expert to know that evolution theory is not about "how life
arose." Evolution theory is about the evolution of the variety of living
organisms from a common ancestor. As to the origin of that common ancestor, the
first replicator, this question is beyond evolution theory. Since
Spetner discusses only the mechanism of evolution, his assault on Neo-Darwinism
has little to do with the question of "how life arose."
critique of Neo-Darwinian theory is based on three points: (1) Estimates of
probabilities; (2) Discussion of randomness; and (3) Discussion of information.
Professor Simon is a biologist. Perhaps this is the reason he does not address
the above three points in his review. However, without addressing the validity
of Spetner's treatment of these three concepts no proper evaluation of
Spetner's arguments can be done.
his review in Jewish Action Dr. Feit (who also is a biologist) does not
write about probabilities or information, but he rejects Spetner's treatment of
randomness, and this point alone makes Feit's review much more reasonable than
that of Simon. Feit, though, criticizes Spetner's treatment of randomness not
as much from a mathematical as from a religious viewpoint.
consistent critical review of all three main points of Spetner's assault on
Neo-Darwinism is given in an article on this site (A Lost Chance).
As shown in that article, Spetner's treatment of probabilities, randomness, and
information is largely fallacious. Simon does not seem to be familiar with that
critique. However, without answering the mentioned critique, assertions of an
"excellent job" allegedly done by Spetner sound hollow. Simon's opinion that
Spetner's book indeed shattered the Neo-Darwinian evolution theory is nothing
more than attributing to the desired the status of the actual.
detailed and substantial critique of Spetner's book from a biological viewpoint
is found in a number of publications at talkorigins.org. Simon does not seem to be familiar with this critique either, although as a
biologist he should be expected to be aware of it. Another critical discussion of Spetner's book which is much
better substantiated than Simon's, is found at Gert Korthof's website (Was Darwin Wrong? ).
The conclusion made in all the listed sources is different from the one suggested by Simon. All the mentioned
reviewers from Feit to Perakh to a number of authors on talkorigins.org and to
Korthof, find many faults and fallacies in Spetner's book which Simon seems to
miss and which show that Spetner's opus makes no real contribution to biology.
Neo-Darwinian synthesis is nowadays as strong as ever and is supported by an
ever growing and ever better body of evidence. Spetner's book is a feeble (albeit popular) attempt to overturn a solid
theory, strongly supported by an immense amount of evidence, by using poorly
to Simon's assertion at the end of his review, the critique of Spetner's book
in the mentioned sources was by no means offered in a dogmatic way. In fact,
this critique pointed to specific weaknesses and errors in Spetner's work and
that is why, contrary to professor Simon's view, the overwhelming majority of
both biologists and mathematicians rejected Spetner's critique of Neo-Darwinism
Simon's evaluation of Spetner's book is without merit as it leaves without real
analysis the actual weaknesses of Spetner's book.
paper by Dr. Tsvi Victor Saks is titled Different Levels of Infinity in
Torah and Mathematics.
an obligatory reference to the Lubavitcher Rebbe Menahem M. Schneerson, as to
an allegedly great thinker of our time with the status of a prophet, Saks
offers a brief explanation of the concept of mathematical infinity, limiting
his discourse mainly to the ideas of the prominent German mathematician Georg
Cantor (1845-1918). Saks emphasizes that Cantor was Jewish, "had an intimate
relationship with G-d" (page 118), and received his concepts of infinite sets
directly from God. Saks does not share
with readers the source of his uncanny knowledge of how Cantor received such a
revelation from God except for mentioning (without a specific reference)
Mittag-Leffler to whom Cantor reportedly revealed that he received a direct
message from God. Similar statements are heard day in and day out by physicians
in mental hospitals as well.
the story of Cantor's mathematical work as told by Saks is more or less
factually accurate, it is not the whole story. Cantor was indeed a brilliant
mathematician and his contribution to the set theory in general and to the
concept of mathematical infinity in particular was very significant. However,
Cantor was not alone in the development of the above mentioned concepts. As
Saks remarks, Galileo Galilei (1564-1642) (in his famous Dialogue Concerning
the Two Chief World Systems (1632)) had already discussed certain ideas
related to infinite sets. A substantial contribution was also made by the
German mathematician Richard Dedekind (1831-1916), the already mentioned
Swedish mathematician Gösta Mittag-Leffler (1846-1927), British mathematicians
Augustus de Morgan (1806-1871), and Bertrand Russel (1872-1970) and others. I
don't know whether or not any of them had an "intimate relationship with God"
(Russel was known as a militant atheist) but none of them was Jewish.
Furthermore, if God had indeed revealed to Cantor the esoteric essence of
mathematical infinity, why did he not go all the way? Why did he instead
abandon Cantor halfway to the completion of his theory? Indeed, Cantor tried hard to prove the
so-called continuum hypothesis, which would be a real crowning
achievement for his set theory. (For
the sake of the most curious readers, briefly, the continuum hypothesis
asserts that an infinite set of real numbers either is denumerable, that
is, in one-to-one correspondence with the set of natural numbers, or can be put
in one-to-one correspondence with the set that contains all real numbers
between 0 and 1; the meaning of the terms in this definition can be found in
textbooks on mathematics; an excellent semi-popular explanation is given in Mathematics
From the Birth Of Numbers by Jan Gullberg, W.W. Norton, New York, 1997.) Despite Cantor's persistent effort and his
alleged direct communication with God, he failed to prove his hypothesis. In
1940, German-American mathematician Kurt Gödel showed that Cantor's hypothesis
cannot be disproved. In 1963, American mathematician Paul Cohen showed that the
continuum hypothesis is undecidable. Although Cohen's surname probably
indicates his Jewish (or at least partly Jewish) origin, as far as I know he
never claimed to have received a revelation about the continuum hypothesis
directly from God.
view of the above, it seems evident that Saks's paper is largely irrelevant to
the question of the Torah vs. science relationship. Its mathematical part belongs in an introductory mathematical
textbook, and its non-mathematical parts in a semi-philosophical treatise
designed to give vent to Saks's personal views and religious preferences. This
paper is of little interest to readers who would like to gain even a modest
insight into the Torah vs. science controversy.
article by Professor Shimon Silman is titled A System of Logic for Messianic
Phenomena. As are many other articles in the same issue, this paper is long
on explanation of matters which are irrelevant to the relationship between the
Torah and science, in this case certain concepts of mathematical logic. The
sole reason for that detailed excursion into the esoteric depths of modern
mathematics seems to be the author's desire to demonstrate his erudition and
intelligence (as is also the case with the articles by Belenkiy, Poltorak,
Farber & Branover, Rabinowitz and others). Since Silman's credentials are provided in the summary preceding the article,
and they are impressive, readers do not need an additional proof of Silman's
qualifications to be given by the way of explaining the 3-valued logic which,
in such a brief rendition, will anyway remain largely mysterious for a lay
The level of the
essential part of Silman's discourse can perhaps be demonstrated by referring
to just two assertions found in his paper.
is a secondary, albeit telltale point found on page 127. Silman discusses here
a question which used to be a topic of discourse in the late twenties and early
thirties of the last century, but later practically disappeared from scientific
publications, probably because of its more philosophical rather than scientific
character – why the volume occupied by an atom is so immensely larger than the
volume of the particles which are the atom's constituent parts, so the
overwhelming part of the atom's volume is empty. Mentioning the famous Danish physicist Niels Bohr, Silman
irrelevantly refers to him as a "Jewish physicist."
Silman wanted to stress the disproportional contribution to 20th
century physics by scientists who happened to be Jews, either observant or not,
thus providing an outlet for his pride in belonging to the same ancient tribe.
However, while such a desire may be understood, the way Silman indulged in it
can only cause derision, and the editors did not do their job as they failed to
excise that ridiculous epithet from Silman's text.
Niels Bohr did indeed have some fraction of "Jewish blood," if such a concept
has any meaning to reasonable people and not only to visceral anti-Semites.
However, he was not of the Jewish faith, never expressed any interest in
specifically Jewish affairs or religion, was reportedly inclined to share
religious concepts of Hinduism, so to characterize him as a "Jewish physicist"
is a display of a non-scientifically biased attitude by Silman.
point speaking volumes about Silman's far-from-scientific position is found on
page 135. Silman writes, "In 1966, a
team of physicists working with Dr. C. Monroe at the National Institute of
Standards and Technology in Boulder, Colorado, succeeded in getting an entire
atom to exist simultaneously in two widely separated places." Silman does not provide a direct reference
to Monroe's publications, referring instead to a report in New York Times.
should have been a little more cautious in his references. Note first that if Monroe's assertion were
true, it would drastically contradict the assertions by Silman's colleagues in the same issue such as
Branover, Poltorak, Rabinowitz, and Ferber, who all wrote a lot about the
"collapse of the wave function" which occurs in the act of measurement by a
conscious observer. Monroe and his
collaborators were certainly conscious observers. Their measurement of the
atom's location, according to the statements by Silman's colleagues, must have
resulted in a collapse of the wave function of the atom, and as soon as the
wave function collapses, the atom's whereabouts become instantly determined;
upon the measurement such an atom is located at a certain point. If, though, the atom is indeed
simultaneously in more than one location, the wave function has not collapsed.
You can't have it both ways, gentlemen of B'Ohr Ha'Torah.
course we know that the collapse of a wave function does not occur in the
material sense; only a mathematical construct reflecting the probabilities of
the atom's whereabouts "collapses" in the sense that probability is replaced
amazing development of the tunnel electron microscopy nowadays enables
physicists to see atoms. What they see are entities which have a definite
shape, each at a definite location, not at two or more locations at the same
time. Physicists (for example, at the IBM Research Center) can move individual
atoms from location to location as whole entities. Of course, atoms have a
complex structure, so their constituent parts (such as electrons, nuclei, and
constituent particles of the nucleus such as protons and neutrons), can be
separated and thus turn out to be at different locations. This has been known
for a century and has nothing to do with the reported sensational discovery by
Monroe et al.
than six years have elapsed since the report in New York Times of May 28, 1996.
If Monroe's finding were true, no doubt the sensation would not have died as it
did–practically without further development.
story reported by Silman belongs to the genre loved by journalists, although
sometimes scientists in pursuit of fame give journalists a perfect alibi by
acclaiming and interpreting their data beyond their legitimate boundaries. Here is an example.
July 2002 the prestigious peer-reviewed journal Physical Review Letters
printed an article by a group of Australian scientists (G.M. Wang, E.M. Sevick,
Emil Mittag, Debra J. Searles, and Denis J. Evans) titled "Experimental
Demonstration of Violation of the Second Law of Thermodynamics for Small
Systems and Short Time Scale."
soon a popular journal, New Scientist, printed a brief report about the article by the five Aussies. This
report did not describe the Australians' experiment in detail and may have
created in the minds of gullible readers an impression that the Second Law of
thermodynamics has been shown to be not as universal a law as it was meant to
be. A couple of weeks later some websites (for example Compulenta) announced the sensational news: the Second Law has been overturned!
of the sort actually happened. The five Australians had conducted a
sophisticated and ingenious experiment. Their results do not cause doubts
(although, as always in science, the final acceptance of these data can occur
only after other researchers reproduce these data). However, they did not discover anything sensational or
contradicting the Second Law of thermodynamics. On the contrary, their data,
albeit interesting, were fully expected based on the fundamentals of
statistical thermodynamics known since
the last quarter of the 19th century. The crucial words in the title
of their article were "For Small Systems and Short Time Scale." The Second Law
of thermodynamics has been formulated only for macroscopic systems. Even in
macroscopic systems the laws of thermodynamics are realized via fluctuations
around the most probable state. For small systems and short periods of time
fluctuations are expected to occur as local and temporary deviations from the
general trend which is the subject of the statistically valid law. The
Australians' ingenious experiment confirmed the prediction of statistical
thermodynamics, as they probably realized themselves. Unfortunately, they did
not withstand the temptation of giving their report a sensational sounding and
easily misconstrued title. This provided journalists, and along with them
people like Silman who apparently are prone to use any source if it seems to
support their preconceived position, with a pretext to publicize an allegedly
The article by Dr. Menachem Kovacs
is titled Finding G-d in the Study of the Sociology of Religion. This paper is full of imprecise statements
making Kovacs's entire exercise
largely irrelevant. Here are a few examples.
page 164 we read that "the typical treatment of religion in the introductory
sociology texts today is usually cursory and highly critical. It is often based
on the Marxist view that religion is an illusion, a deception to comfort the
ignorant masses with the promise of a better life in a non-existent afterlife."
indeed entails an anti-religious trend. However, there are scores of thinkers
who reject Marxism but also reject religious beliefs. The negative view of
religions is by no means a monopoly of Marxism. In fact, Marxism is itself a
form of religion, since like any religion it is based not on evidence but on a
hypothetical theory utilizing only a limited subset of data out of the much
larger entirety of all data. Like religions Marxism is dogmatic as it requires
from its faithful an uncritical acceptance of every word uttered by its
prophets Marx and Engels, and in its most tested (and failed) form also by
Lenin and/or Stalin. Marxism's
hostility to other religions is akin to the mutual hostility among various
religions which led to mass murders committed by Chrisitan on Mulsims, by
Muslims on Christians, by both Muslims and Christians on Jews, by Catholics on
Protestants and vice versa, exactly as the followers of Marxism did to their
alleged enemies, who were believed to be all those who did not share the
page 165 Kovacs provides a classification of religions. The very first point in
that classification lists theistic religions in the following words: "(1)
theism – religions that believe in G-d, such as Judaism (monotheism),
Christianity and Islam; or in gods, such as Hinduism (polytheism)."
the odd wording of a passage which asserts that "religions believe" in this or
that (actually it is people who believe or disbelieve this or that; religions
are systems of beliefs and as such cannot be said to believe in anything), the
gist of that item is not quite accurate.
it sounds strange that among the three monotheistic religions only Judaism is
accorded by Kovacs the status of monotheism. Furthermore, the difference
between the monotheistic religions on the one hand and the polytheistic on the
other, however great in many respects, is not really in what Kovacs says. Take,
for example, Hinduism. Yes, in that religion there are scores of deities known
under various names – Shiva, Krishna,
Vishnu, Mahesvara, Shakti, etc. However, one of the most fundamental principles
of Hinduism is that in their essence all these deities are just different forms
assumed by one and only one real God (see, for example, Louis Renou, ed., Hinduism,
George Brazilier publ., New York 1962).
Judaism, Islam, and Christianity all entail similar beliefs. In Catholicism and
in the Russian and Greek Orthodox religions the concept of Trinity is paramount
and is just another, truncated version of polytheistic beliefs. In Judaism,
Islam and Christianity belief in angels is very similar to the Hindus' belief
in the scores of lesser gods subordinated to the "God of gods," the supreme
being whose attributes are similar in all of these religions, although with a
number of variations. Therefore the classification suggested by Kovacs seems to
be rather shallow and not really very useful for the proclaimed goal of his
Kovacs's article has little relation to the proclaimed subject of the
conference in Miami and of issue 13 of B'Ohr Ha'Torah.
article by professor of mechanical engineering and mathematical sciences Isaac
Elishakoff is titled Probabilistic Analysis of the 'Torah Codes': A False
Premise? The main thesis of that article is that both proponents and
opponents of the Torah "codes" are in error in that both base their argument on
a false premise. This false premise, according to Elishakoff, is the assumption
that the appearance of the equidistant letter sequences (ELS) in the
text of Genesis can be analyzed using calculations of probabilities. This,
maintains Elishakoff, implies that there are (or may be) multiple "Torahs" in
existence rather than the unique Torah revealed to Moses on Sinai. In the
abstract preceding his paper, Elishakof writes, "... in order to apply
probabilistic methods the existence of multiple 'Torahs' would have to be
assumed – inadvertently or deliberately." Elishakoff asks, "Can one randomize Torah, as the supporters of the Torah
'codes' in effect suggest, and to which the opponents of the Torah 'codes'
seemingly do not object?"
the above thesis, a comment which immediately comes to mind is that Elishakoff
has mingled two different questions, to wit: (a) Is it legitimate to apply a
probabilistic estimate to a unique object (in this case the Torah)? (b) Is it
legitimate to randomize the text of the Torah for the sake of probabilistic
answers to the above questions are different, which is contrary to Elishakoff's
assertion denying the legitimacy of both (a) and (b).
regard to (a), the answer is that it is indeed illegitimate to calculate the
probability when only a single (unique) event is available for analysis.
However, asserting that both codes proponents and opponents erroneously agree
that a probabilistic analysis is legitimate in the case in question, Elishakoff
seems to show a lack of sufficient familiarity with the literature in question.
This sounds especially odd since Elishakoff refers to several publications by a
prominent expert in mathematical
statistics and an opponent of the Torah "codes", professor A. Michael Hasofer.
In a paper which, for example, can be seen at A Statistical Critique of the Witztum et al Paper, Hasofer has addressed that point. Unlike the nebulous assertion by Elishakoff,
Hasofer's statement is very clear when he writes that a probabilistic estimate
in the case of a unique event "has no frequentist interpretation." To my
knowledge, the code proponents have never responded to Hasofer's critique of
answer to (b) is, however, different. There is nothing illegitimate in randomizing
the text of Genesis thus generating a multitude of texts, the overwhelming
majority of them meaningless, in order to compare the behavior of clusters of
ELSs in the original text of Genesis with their behavior in randomized texts.
Contrary to Elishakoff's contention, such randomization (for example, by
randomly permuting the letters of the text of Genesis) is not tantamount to
creating multiple Torah's. The permuted texts each contain the same set of
letters as the original text of Genesis, but this does not make them
alternatives Torah's but only alternative strings of characters mostly lacking
the described randomization is a legitimate procedure for the sake of a
probabilistic analysis, this does not mean such a method will be a reliable way
to discriminate between chance and design as a source of the ELS clusters in
texts. A detailed analysis of the pitfalls such a method entails is given in
the appendix to a paper at Some remarks in regard to D.Witztum's writings concerning the "code" in the Book of Genesis.
The main shortcoming of the text randomization method stems from the substantial
degree of order which characterizes meaningful texts. Indeed, the specific types of order have been shown to distinguish
meaningful texts from strings of gibberish (see Statistical Properties of Meaningful Texts as Compared to Randomized Conglomerates of Letters).
Among the variety of texts obtained by permuting the letters (or words) of a
meaningful text, the original non-permuted text has a lower entropy than the
overwhelming majority of permuted texts. On the other hand, any mathematical
function reflecting properties of a text is necessarily tied in this or that
way to the text's entropy. Therefore any such function calculated for the
original meaningful text is expected to have a value close to either minimum or
maximum. The function used by the original proponents of the "codes," Witzum,
Rips and Rosenberg (WRR), which estimates the "distance" between any two ELSs
in the text is no exception. Hence, if the "distance" between any two
semantically related ELSs is found to be close to a minimal value in the
original text of Genesis as compared with permuted texts, this does not point
to design as the source of the "code" but quite reasonably may be attributed
simply to the existence of order (i.e. of low entropy) in semantically
this said, the main fault in Elishakoff's discourse is, however, that it is
irrelevant to the dispute between proponents and opponents of the "code."
Indeed, contrary to Elishakoff's apparent impression, in their work published
in Statistical Science, WRR did not apply randomization to the Genesis text.
Their method (reportedly suggested by Professor Persi Diaconis who served as a
referee for Statistical Science) was different. They randomized not the
text of the Torah, as Elishakoff erroneously thought, but the list containing
the appellations of 66 "famous rabbis" and the dates of birth and/or deaths of
these rabbis which happened to be found as ELSs in the text of Genesis. This procedure did not entail an assumption
of the existence of multiple "Torahs." WRR's procedure was strongly criticized by a number of authors, who
pointed to various faults in WRR's procedure, but none of this critique required
any assumption of multiple Torahs either (references to most of the
publications critical of WRR's work can be found either at In Search of Mathematical Miracles
or at B-Codes Page).
discourse, even we ignore its inconsistencies, is simply irrelevant to the
dispute in question.
the articles reviewed in the preceding sections of this paper, issue 13 of B'Ohr Ha'Torah contains several more
articles which I am not going to discuss in detail, mainly because most of them
have little relation to the main topic of that issue – the relationship between
science and the Torah (for example, a paper about "lending without interest in
a Jewish state" by Raphael Yehezkiel or a paper titled "Lactational Amenorrhea
and Mesuleket Damim – a Medical Halakhic Analysis" by Dr. Deena R. Zimmerman). Some other articles deal with the main thesis but in a largely
theological or philosophical way (for example, a paper titled "Creation and the
Symbiosis of Science and Judaism" by Professor Norbert Samuelson or a paper
titled "Genesis 1 Speaks about the Creation of Prophecy, Not the Creation of
World" by Dr. Russell Jay Hendel). One paper titled "Mathematical Drash" by Dr.
Ari Belenkiy, contains a number of topological diagrams hardly comprehensible
to an ordinary reader, whose relevance to the theme of the issue is at best
fuzzy. For example, Belenkiy asserts (page 152) that "whether the Jewish sages
thought the surface of the Earth to be like a plane or like a sphere" is
unimportant, "because in both cases the fundamental group is trivial." Such application of abstract mathematical
concepts to a simple question of whether the Earth is flat or it is a sphere
seems to me a display of a prejudice forcing its author to perform mental
acrobatics in order to support his irrational beliefs.
the reviewed issue of the B'Ohr Ha'Torah with its seeming sophistication and a
list of authors with advanced scientific degrees, strikes an unbiased reader as
a collection of quasi-scientific exercises by a bunch of people for whom a
blind faith in the Torah's inerrancy precludes a rational discussion of
objective arguments because in each case the conclusion is reached before the
discussion starts. Overall, this journal seems to be an example of a wasted
effort by a number of intelligent and educated people who should have known
better and directed their effort to a more useful end.