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Mark Perakh's Web Site

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Challenging the Challenge

By Mark Perakh

Posted on April 17, 2000

Discussion

Contents

  1. General remarks

  2. Brief overview of Section 1

  3. Review of Section 2

  4. Review of Section 2 - continued

  5. Review of Section 3

  6. Brief review of Section 4

  7. Conclusion

  8. 1. General remarks

    The collection of articles titled "Challenge" with the subtitle "Torah Views on Science and its Problems," edited by Aryeh Carmell and Cyril Domb, was published by the Association of Orthodox Jewish Scientists (via Feldheim Publishers of NY and Jerusalem) in 1976 and again in 1978.

    Moreover, many of the articles in this collection originally appeared even earlier, in the fifties and sixties.

    A natural question seems to be: why review a collection more than twenty years after its publication?

    The answer is that the articles of that collection offer many arguments in favor of the compatibility of the Torah with science which have been repeated time and time again in numerous subsequent publications, the latter often adding little new to the ideas and views already expressed more than twenty, thirty, and forty years ago. If one wishes to trace the origin and development of the modern popular trend aimed at proving the invincibility of the religious view of the world as it faces its obvious contradictions to scientific theories, the collection in question is a good source of pertinent information.

    Despite the obvious fact that the collection in question had covered the Torah vs. science problem quite extensively from a variety of viewpoints, it is rare to find any references to that collection in subsequent publications, often repeating the same notions. It is not surprising that writers approaching the problem from a Christian perspective omit references to the collection in question. Indeed, Christian writers generally avoid any references to Jewish sources, even when using the same sets of arguments, and often making the same or similar errors in their discourse. However, the writers approaching the problem from the vantage point of Judaism, strangely, also omit references to this collection, even when repeating the arguments already offered more than twenty to forty years ago. I leave it to readers to guess the reasons for the described situation.

    There is no mention in the book in question of such concepts as "intelligent design" or "irreducible complexity" of biochemical systems. These concepts emerged many years after the publication of the "Challenge" collection. This can hardly be viewed as a shortcoming of the book if we account for the emptiness of the two mentioned concepts, illustrated, for example, in some articles in this web site (for example, Irreducible contradiction). Actually, twenty plus years after its appearance, the collection in question is still among the most sophisticated for the genre in question.

    The authors of the 23 articles gathered in the book in question, by and large have impressive credentials. Most of them have advanced degrees in physics, chemistry, biology, or engineering. Many of them are also Rabbis. The overall level of discourse is characterized by ingenuity of argumentation.

    Of course, not all the papers in that book are on the same level. There are a few articles characterized by an elementary misunderstanding of science (like the paper by M. Schneerson) or by an improper use of mathematics to allegedly prove God's existence the same way the laws of physics have been "proven" (the paper by G. Schlesinger). A detailed review of the two mentioned articles will follow. Some other papers are just short notes lacking elaborate argumentation. Most of the material, though, can be viewed as being among the most powerful pieces of argumentation in favor of the compatibility of the Torah with science.

    However, despite that sophistication, the collection in question has failed to prove its point as far as skeptics are concerned.

    Indeed, all of the authors in this collection are firm believers in the Torah's inerrancy. There is no question for them of whether the Torah tells the truth or not. They take it for granted that the Torah is the depository of the ultimate truth. Of course, from such a position it follows automatically that whatever science has established or may establish in the future, must necessarily be compatible with the Torah. If such a notion is adopted as the premise for all the following discourse, there remains nothing to prove as the proof is already contained in the premise.

    Of course, the described attitude is unsatisfactory for skeptics who approach the problem without a pre-conceived opinion but are looking for arguments in favor of either science or the Torah in those cases where there is an obvious contradiction between them. The collection "Challenge" provides no arguments which would satisfy skeptics, as it caters to believers only and is designed to explain to the latter why they should not be puzzled by the seeming contradictions between their beliefs and the facts of science.

    The collection in question consists of four parts, to wit: 1. Areas of Interaction; 2. Creation and Evolution; 3. The Secular Bias; 4. Ethical Problems.

    2. Brief overview of Section 1

    The first section contains papers designed mainly to prove the principal compatibility of the Torah and science. The passages quoted a few lines below express this idea in various words. If the discourse were limited to the notion that science can neither prove nor disprove the existence of the Creator, it would be very hard to dispute the authors' assertions. Unfortunately, the authors of the papers in that section go much further and assert, without even trying to provide any supporting arguments, that whatever science says, automatically is in tune with the word of the Torah. To the authors' credit none of them resorts to a hard sale. The style of these articles is restrained, but the essence is uncompromising and categorical. They conduct their discourse mostly in general terms, avoiding the discussion of any particular points of controversy between the Torah and science. Of course, unless one blindly believes in the Torah's inerrancy, all the sophistication and ingenuity of arguments displayed in the papers in question remains dissatisfying and unconvincing. I don't believe a single skeptic could be swayed by the papers in question.

    Here are some quotations illustrating the position of the collection's authors.

    William Etkin, in his paper titled "Religious Meaning of Science" writes (page 38): "When we learn to comprehend a new geometry, a new chemical concept of gene structure, a new statistical analysis of the evolutionary process, a new theory of instinct, or any other of the great theoretic triumphs of contemporary science, we recognize that somehow we are in tune with the Creator and His creation." Aaron Vecht, in a paper titled "Genesis and Geology" writes (page 177): "Science is but the description of nature, and since both nature and Torah are the work of the one God there can be no basic incompatibility between them." Harry Marcell in a paper titled "Evolution Theory or Faith?" writes (page 195): "Whatever scientific theories are eventually held to account for the way things came about in the world, they will always only suggest how God created: they can never supplant the recognition of creation itself." Similar views have also been expressed by many other authors in the collection.

    3. Review of Section 2

    The second section contains papers which deal more specifically with the controversy between the Genesis, geology and evolution. It opens with a paper by Rabbi M. Schneerson which in a certain sense stands alone, for its level of discourse is well below the majority of articles in the collection. Since, however, the author of that paper was acclaimed as a great thinker of this century, let us take a closer look at his article.

    The article by Rabbi M. Schneerson

    Rabbi Menachem M. Schneerson, the seventh Lubavitcher Rebbe, is characterized in the collection as "one of the outstanding Torah personalities of the present generation." (The quoted characterization was printed in 1978; since then Rabbi Schneerson has passed away). The authority M. Schneerson enjoyed in his lifetime among his followers was enormous. Many of them viewed him as a modern Moses or even as a Messiah. Here is a telltale detail. When a magnificent synagogue was built in Miami Beach, Florida, stones were brought to be put into its foundation from two places one was the Kotel Hamaaravi, the western wall of the destroyed Temple in Jerusalem, and the other was the house in Brooklyn, NY where the seventh Lubavitcher Rebbe lived. Of course, I know of no arguments which would cast doubt on Rabbi Schneerson's reputation as a great man of the Torah. I would never try to dispute the above characterization of the esteemed Rabbi. Neither would I ever try to argue with Rabbi Schneerson about any question relating, say, to the Talmud, Halakha, or the like.

    However, in the paper published in the collection Challenge Schneerson endeavored to discuss science, and this is an area where I, having been a practicing experimental physicist for fifty years, may legitimately argue against Schneerson's notions.

    When I recently attended a conference where the relationship between science and the Torah was discussed, I accidentally overheard professor Herman Branover (who is a very active figure in the organized activities aimed at proving the supremacy of the Torah over science) say that the Lubavitcher Rebbe was beyond doubt not only a great man of the Torah but also one of the greatest scientists in the world, and the utmost authority in every field of science.

    From the collection Challenge we learn that M. M. Schneerson studied at the university of Berlin, Germany and at the Sorbonne in Paris. Unfortunately, the biographical segment in the collection in question does not tell us either which subjects Rabbi Schneerson studied in the mentioned universities or for how long. There is no information available regarding any possible contribution by Schneerson to any specific field of science. It seems safe to assume that he never performed any scientific work in any field of science. It seems safe to assume he had no personal experience in conducting scientific experiments, sorting out and interpreting experimental data, developing any scientific theories, participating in discussions of any specific scientific ideas and generally being involved in any real scientific activity, which is the only way a person acquires a real understanding of what a work of science is all about.

    Reading Schneerson's article leads to the conclusion that he had no real understanding of the scientific method and of the essence of the scientific exploration of reality. His paper is an odd mix of platitudes and misrepresentations of science.

    Among the platitudes in question is his assertion that "at best science can only speak in terms of theories inferred from certain known facts..." How true! Why, though, this situation, which is not being disputed by any scientist, should be viewed as a weakness, as Rabbi Schneerson seems to imply, remains his secret. Yes, science speaks in terms of theories inferred from known facts. How much more credible the Torah would be if it also spoke in terms of theories inferred from known facts! If, as Rabbi Schneerson indicated, using theories inferred from known facts is a limitation of science, what about the Torah whose statements are not inferred from any known facts but are simply unsubstantiated assertions without any factual basis?

    Among Rabbi Schneerson's misrepresentations of science was his alleged explanation of two methods utilized by science, one being extrapolation and the other, interpolation. The explanation in question was primitive in the extreme. It reduced the scientific method to only two possible variations, which of course is a gross simplification. Moreover, he distorted the essence of the two methods in question. .

    Interpolation, Rabbi Schneerson taught us, is a method "whereby, knowing the reaction under two extremes, we attempt to infer what the reaction might be at any point between the two." If we replaced the word "reaction" with the word "value," the above definition would be an adequate one for a mathematical operation of interpolation. However, it falls short of being a proper definition of any legitimate procedure employed in science. In physics, chemistry, biology, the simplistic inference of what the "reaction" might be at an intermediary point between two extreme" points where the reaction has been studied is not a proper way to develop a theory. Any interpolation, if it takes place at all, is never a bare guess but is always based on certain information enabling the researcher to reasonably predict the behavior of a system under study between the two known "extremes."

    That such interpolations are legitimate and not at all arbitrary is seen from the great successes of science which have led to the enormous progress of technology we all witness. The very picture presented by Schneerson, whereby there is information available at some two points, say A and B, and from that, information related to a point C located between A and B is inferred, is in itself a distortion of the scientific procedure. If an interpolation (which is a legitimate course of action in experimental science) is employed it is not normally based on the information related to just two extreme points.

    Let us discuss the question of a legitimate interpolation by using a specific example. Since Schneerson used the term "reaction" it seems appropriate to consider an example from chemistry. Imagine that a study is conducted whereby the dependence of the rate of an electrochemical reaction on parameters such as temperature, current density, solution composition, etc., is investigated. One of the common methods of experimental study is to gradually change one of the parameters (for example, temperature) while keeping all the rest of the parameters constant (within a certain range). The researcher chooses a discrete set of values of temperature, for example, 300 K, 320 K, 340 K, 360 K, 380 K, 400 K. (K stands for Kelvin, which is the thermodynamic unit of temperature; 1 K equals one degree Celsius). The researcher makes an effort to keep the variations of current density, solution composition and all other parameters as small as possible, and measures the reaction rate at the listed six values of temperature. She necessarily repeats the measurements many times, thus determining the margin of error. When she is satisfied that the repetition of measurements generates values which all are within the same margin of error, she applies some mathematical treatment to her data, for example, the least square fit. The result of the described meticulous procedure is some curve reflecting the dependence of the reaction rate on temperature, corresponding to the fixed values of current density, solution composition etc. Then the entire procedure is repeated for another value of current density, or for another value of concentration of solution components, etc. After many such measurements have been completed, the researcher has a family of curves, each showing the dependence of the reaction rate on temperature, but for various current densities or various concentrations of the solution components. This procedure is very far from the simplistic picture given by Schneerson, whereby the data for two extremes are used to infer the data for an intermediate point. The rate of reaction for, say, a temperature of 310 K, which is between the actually measured points at 300 K and 320 K, is estimated not just from the two values at 300 K and 320 K but from the entire consistent combination of multiple experimental points. The necessary next step is to form an explanation of the experimental curves in question. Such an explanation is never arbitrary, but is based on the enormous body of knowledge accumulated in science. Since the theory must explain a multitude of experimental data rather than just two values at some two points, as Schneerson naively suggested, there are usually not too many choices which would reasonably fit all the experimental points. Finally, when a theory is developed which seems to account for the entire set of experimental data, it is used to predict the outcome of other experiments. If, in the course of the further studies by various researchers the predictions of the theory are reasonably confirmed, the theory becomes a part of the scientific arsenal, as a reasonably plausible interpretation of facts. It is never viewed as the absolute truth, but usually every good scientific theory contains at least a grain of truth in it. This example illustrates that Schneerson's description of interpolation falls short of being an adequate presentation of a scientific method.

    Then Schneerson spoke about extrapolation, which, he asserted, is inferior to interpolation. He gave the following definition and an example: "The method of extrapolation, whereby inferences are made beyond a known range, on the basis of certain variables within the known range. For example, suppose we know the variables of a certain element within a temperature range of 00 and 1000 , and on the basis of this we estimate what the reaction might be at 1010 , 2000 , or 20000 ... Of the two methods, the second (extrapolation) is clearly the more uncertain. Moreover, the uncertainty increases with the distance away from the known range."

    Like in the case of interpolation, Schneerson's description is a gross simplification and hence a distortion of a real scientific procedure. No scientist would ever simply guess what "the reaction" would be at 1010 or 20000 based on the data for 1000 alone. Any extrapolation, if employed in genuine scientific research, is based on a multitude of data which establish a well-documented trend. Besides the particular set of data at the scientist's disposal, she always bases her extrapolation also on the enormous wealth of multifaceted knowledge accumulated in science about the "reaction" in question.

    Scientific theories are not built upon either simple interpolation or simple extrapolation, but rather on a combination of various mutually controlling methods and firmly established trends. The power and fruitfulness of the scientific method are obvious. It is impossible to deny the amazing achievements of science and the technology based upon scientific discoveries.

    Schneerson continued: "... a generalization inferred from a known consequent to an unknown antecedent is more speculative than an inference from an antecedent to consequent." To illustrate that assertion, Schneerson offers an example: " Four divided by two equals two. Here the antecedent is represented by the dividend and the divisor, and the consequent by the quotient (2) ...However, if we know only the end result, namely the number, 2, and we ask ourselves, how can we arrive at the number 2, the answer permits several possibilities, arrived at by means of different methods: 1)1 plus 1 equals 2; 2) 4-2 equals 2, 3) 4/2 equals 2..." This arithmetic platitude, contrary to Schneerson's view, is utterly irrelevant to the question of the validity of scientific theories. It is arithmetically correct that the number 2 can be obtained by an endless number of arithmetic procedures. However, in scientific research the inference from a consequent to an antecedent is never made simply based on some number alone. If a researcher obtains, as a result of a measurement, a certain individual number, be it 2 or anything else, he never tries to draw any conclusion as to what caused this number by limiting his discussion to that number alone. Any conclusion "from consequent to antecedent" is offered on the basis of a multitude of data, which show a distinctive trend, and taking into account the large body of information accumulated by science about the reaction in question and other similar reactions.

    Furthermore, Schneerson's assertion that "a generalization inferred from a known consequent to an unknown antecedent is more speculative than an inference from an antecedent to consequent" is factually wrong. The procedure Schneerson refers to as an inference from a consequent to antecedent is the most common one in science, and boils down to developing a theory explaining a set of known facts. On the other hand the procedure he refers to as inference from antecedent to consequent is actually using a theory to predict the outcome of experiments yet to be performed. More often than not, the former is less speculative than the latter, which is contrary to Scheersohn's dilettantish assertion. If a set of experimental data is sufficiently large, a theory explaining it can be reasonably substantiated. On the other hand, predicting the results of future experiments is a more speculative endeavor. Therefore the actual occurrence of events predicted by a theory is normally viewed as a more convincing argument in favor of that theory than simply an explanation by a theory of the already available data.

    Of course, scientific theories can be wrong. If that is the case, they usually have a very short life. Every theory, even if it explains a certain set of data very well, is always subjected to multiple unmerciful tests, probing the limits of its applicability. The process of establishing an accepted scientific theory is very complex and quite different from the simplistic picture painted by Schneerson. This process includes many facets, starting with measurements, followed by offering some hypothetical explanation of experimental data which is aimed at forming a logically consistent concept accounting for every experimental fact, then followed by designing additional experiments whose outcome can be predicted on the base of the hypothesis in question, testing the prediction, then amending the hypothesis, etc.

    Contrary to Schneerson's view, this elaborate procedure ensures the high reliability of scientific theories, although none of them, unlike the Torah, is viewed as the absolute truth.

    Schneerson continued his attack on the validity of science by listing a number of weaknesses plaguing scientific theories. Among those weaknesses is, for example, that scientific theories "have been advanced on the basis of observable data during a relatively short period of time." Since Schneerson's thesis is that the Torah provides more reliable information than science, a legitimate question is, what are those "observable data" which form the foundation of the Torah's story? There are no such data for either long or short period of time. Why then should we prefer the Torah's story to scientific theories?

    Another weakness of science is, according to Schneerson, that "on the basis of such a relatively small range of known (though by no means perfectly) data scientists venture to build theories by the weak method of extrapolation, and from the consequent to the antecedent, extending to many thousands (according to them, to millions and billions) of years!" This quotation shows once again Schneerson's primitive level of understanding of scientific theories. The age of the universe has been estimated in science through many different methods, all providing fairly consistent numbers. All these estimates are based on firmly established regularities with no indications whatsoever that any such regularity could not have been at work at any time in the past. Of course, there is no way to conduct a direct experiment to test if a certain regularity (for example, the constant rate of a radioactive decay of certain elements) indeed had been at work, say, a billion years ago. However, the large body of experimental evidence provides a reasonable foundation to believe that the regularity in question indeed was a feature of the world a billion years ago as it is now. Rabbi Schneerson might believe, if he was so inclined, that, for example, the rate of the radioactive decay was not constant in the course of millennia. By the same token, I may believe that the moon is made of green cheese. Those who do not share such a belief, may ask me: "What about the reports by American astronauts who landed on the moon and brought samples of its material back to the earth?" I can answer: "Well, Armstrong and the other astronauts may have lied. And, generally, all those TV images of people on the moon were made in Hollywood, and also there is a government's conspiracy to hide the truth about the moon, which is actually made of green cheese. This is my belief and nothing will convince me otherwise."

    Maybe it is the proper time to give an example of how science deals with hypothesizing an antecedent from a consequent. I take the liberty to give that example from my own experience.

    In the late fifties I encountered a phenomenon whereby thin metallic films deposited by various means, including electrodeposition, always grew in the state of strong mechanical stress. At that time, there existed no good theory which would explain the origin of stress in such films. Having conducted numerous measurements of stress, and accumulated piles of experimental data, mostly obtained in specifically designed experiments, I set out to develop a theory of the stress origin. I cannot explain why and how the idea of the theory in question emerged in my mind, but my guess, based on the multitude of results, was to attribute the emergence of tensile stress in films to the egress of a specific type of defects in the crystals forming the film, the so called dislocations, to the surface of crystals.

    At that time, the concept of dislocations was purely theoretical. In the early years of the 20th century, a German physicist Madelung calculated theoretically the strength of crystals. Madelung's theory was based on the well-established concepts of forces between atoms, ions, and molecules. Nobody could find any error in Madelung's calculations. However, the strength of crystals according to his calculation turned out to be about 100,000 times larger than the actually measured strength of real crystals. Very soon scientists realized that the discrepancy was due to Madelung's theory being valid for ideal (i.e. defectless) crystals, while the measurements were conducted with real crystals, where multiple imperfections of structure were inevitably present. The experimental technique of that time was not capable of observing those microscopic defects directly. While the presence of various defects could be inferred from indirect evidence, their precise character was not known. To explain the drastic difference between the theoretical and actually measured strength of crystals, three scientists (in England, Russia and Japan) simultaneously and independently suggested a hypothesis of a specific type of defects, to be named dislocations, being responsible for the drastic drop in crystal's strength. In the course of the next decades, a detailed theory of dislocations was developed, with an extensive mathematical apparatus.

    Using Schneerson's classification, it was a theory belonging to the pure "from consequent to antecedent" type. Various phenomena had been explained by the properties and behavior of dislocations which nobody has ever actually observed. Nevertheless, despite objections by a few dissenters, most physicists believed in the validity of the theory of dislocation simply because it could consistently and logically explain a multitude of facts.

    By the beginning of the fifties, the advances in electron microscopy allowed to observe certain microscopic features of crystals which were interpreted as the experimental manifestation of the presence of dislocations. This gave considerable support to the theory which until then was based only on pure logic and mental ingenuity.

    When I came up with the idea of the dislocations' egress, it was not based on any direct evidence, since the dislocations themselves have not yet been directly observed. My idea of their egress was based on a pure imagination, as it very logically and consistently seemed to explain a wide variety of experimental data I'd accumulated. Of course, my theory was also of the "consequent to antecedent" type, according to Schneerson's classification. Its foundation was in pure logic and consistency, as it was based not on some single number, as in Schneerson's example, but on a multitude of facts and on the observed trends. In this form, the theory was published. There were some scientists who disagreed with my explanation, but they did not come up with a good alternative. Several years later, new advances in electron microscopy enabled scientists to see the dislocations directly. This fully vindicated the creators of the dislocation theory, once again demonstrating the power of scientific inference. Soon afterwards, some English physicists observed directly the egress of dislocations to the crystals' surface, which I surmised several ears earlier to be the reason for the tensile stress in films, based on the logical analysis of a multitude of experimental data. Of course, before the direct observation of the dislocations' egress, people like Schneerson could argue that my theory was based on the use of a weak method "from consequent to antecedent," that it was based on data obtained for a limited range of conditions, etc. However, the entire history of science proves the power of scientific inference, and the high plausibility of good scientific theories.

    Several years later I set out to develop a theory which would explain the anisotropy of stress I observed in certain magnetic films. Again, my tools were logic and the plethora of experimental facts I accumulated. I suggested a theory which explained the observed anisotropy through the magnetic properties of dislocations at play in the course of their egress. The theory neatly explained in a fairly plausible way the entirety of the observed phenomena. However, nobody has yet been able to directly verify the assumed behavior of the moving dislocations, hence that theory has so far no direct experimental proof. Therefore I can't assert that the theory in question is true, as I could with the earlier theory of the stress origin. I tend to view, though, the theory of anisotropy as being plausible due to its ability to logically explain a multitude of facts.

    These two cases exemplify two types of scientific theories. To one type belong the theories which have a direct experimental confirmation. Of course, there is always a possibility that new experimental evidence may contradict the theory. More often than not, though, it means not that the theory is necessarily wrong, but rather that the new data reveal the boundaries of the theory's validity. To the second type belong theories which have no direct experimental confirmation. The plausibility of such theories is based, first, on their logical consistency and the ability to reasonably account for all known facts, and, second, on the fact that other scientific theories which have been confirmed by direct experiments were developed by the same process of scientific inference which therefore is known to usually provide a plausible insight into reality.

    How far is the real scientific method from the jejune picture painted by Rabbi Schneerson!

    Schneerson specifically argued against the theory of evolution. One of his categorical statements was: "If you are still troubled by the theory of evolution, I can tell you without fear of contradiction that it is not a shred of evidence to support it." Wow! What enviable self-confidence! Rabbi Schneerson obviously had a very limited knowledge of the subject he dared to discuss. While the theory of evolution has many yet unanswered questions, to insist that there is no evidence supporting it was a display of monumental ignorance on the matter. There is an enormous amount of evidence supporting the theory of evolution, even though some of that evidence is incomplete.

    Continuing his discussion, Schneerson displayed his position as an adherent of the so-called "young earth creationism." The defenders of that position maintain that the age of the universe is exactly as the Bible tells us, namely less than 6,000 years, and all the evidence pointing to the much older Earth (a few billion years) or the universe (about 15 billion years) are simply an illusion. He says: "Even assuming that the period of time the Torah allows for the age of the world is definitely too short for fossilization (although I do not see how one can be so categorical) we can still readily accept the possibility that God created ready fossils, bones or skeletons (for reasons best known to Him), just as He could create ready living organisms, a complete man, and such ready products as oil, coal, or diamonds, without any evolutionary process."

    I can readily accept that the moon is made of green cheese, and you can readily accept that in Australia people walk with their bodies hanging upside down, and your friend can readily accept that sunset occurs when a sorcerer who dwells beyond the horizon grabs the sun ands pulls it into a cave. If such suppositions were viewed as legitimate and reasonably explaining the facts, maybe Schneerson's "readily accepted" assumption could also be considered seriously. Otherwise the idea offered by the "young earth creationists" and shared by Schneerson, of God having created, for unknown reasons, ready fossils, bones, or skeletons, etc, remains in the realm of fairly tales, and hardly deserves serious discussion, since it lacks any semblance of substantiation and is a preposterously arbitrary explanation aimed at saving blind faith.

    Schneerson provided no arguments in favor of the Torah's story.All his argumentation was of a negative character whereby he tried to cast doubt on scientific theories. The essence of his argumentation was that since no scientific theory can be viewed as the absolute truth, there is no reason to doubt the Torah's story. Even if one disbelieves scientific theories, how does it prove the veracity of the Torah' story? What Schneerson left without discussion is what is (if any) substantiation for the Torah's story. If, as Schneerson asserted, science does not provide the absolute truth (which is true) scientific theories are at least based on facts and their logical interpretation, and survive a stringent process of verifications and tests. The Torah's story is not corroborated by any other reasonably reliable source. There is no reason to view it as anything more than a collection of ancient manuscripts on par with the Mahabharata or Greek mythology.

    4. Review of Section 2 -- continued

    Other papers in section 2 of the collection differ substantially from that by Schneerson, most of them displaying a level of sophistication well exceeding that of Schneerson's article. For example, the paper by Harry Marcell "Evolution theory or faith?" discusses in detail various difficulties encountered by the theory of evolution. These difficulties are real. For example, Marcell describes in detail the "design" of the apparatus enabling some snakes to produce an extremely potent poison and inject it into the bodies of their victims. The apparatus in question is very complex and looks like the product of a very ingenious design. The theory of evolution does not offer a detailed explanation of how exactly the apparatus in question developed via a natural unguided process. To Marcell's credit, he does not categorically assert that the natural development of the apparatus in question was impossible. He hints though at the utter improbability of such a natural development by pointing to its high complexity, and invites readers to make their own conclusion. His obvious implication is that attributing the development of the snake poisoning apparatus to a natural unguided process is implausible. While the mechanism of snake poison production and use is indeed fascinatingly complex and finely tuned, evolutionary biologists have suggested quite reasonable explanations of how such biological mechanisms could have naturally developed. Therefore Marcell's discourse, with all of its ingenuity and eloquence, remains just that an interesting story lacking evidentiary significance.

    One of the sections in Marcell's article is titled "Science and pseudo-science."

    In this section, Marcell says that his article is "not directed against the true scientist who holds his theories tentatively and knows that they are always subject to revision as facts accumulate." It is hard not to fully agree with Marcell on that point. A few lines further he continues: "Our thrust is directed against the exponents of 'scientism' who inflate biological theories into cosmic philosophies."

    Should we then interpret Marcell's attitude as not trying to disprove scientific theories when they are not "inflated into cosmic philosophies" but still contradict the Torah? What about the theory of evolution which in itself is not a "cosmic philosophy" but a powerful theory in biology, supported by a wealth of empirical evidence? Marcell's critique of the difficulties of the theory of evolution exemplified by his reference to the snake poison apparatus, is directed not against any inflation of the theory of evolution to a cosmic philosophy, but against the very essence of that biological theory itself. So much for the consistency of Marcell's discourse.

    The paper by Morris Goldman in the same section is a full-fledged denial of Darwinism as being incompatible with the Torah. This is how Goldman explains the essence of Darwinism: "The living things change from one form to another as a result of accidental events, and not as a result of deliberate purpose on the part of the Divine power... God is irrelevant in the Darwinian evolutionary scheme, and that is what is wrong with it for a Jew." Of course, other interpretations of Darwinism, some of them asserting its compatibility with religious beliefs have also been suggested. However, let us accept Goldman's definition. If we accept it, a natural question is how to reconcile Goldman's view with the statements we quoted in the preceding sections according to which there cannot be any contradiction between the Torah and science?

    While the assertion that no scientific discovery can in principle contradict the Torah obviously stems only from a strong desire by the proponents of such a view to reconcile their faith with the facts of science rather than being based on evidence, Goldman's view (shared also by some other authors in the collection) seems to reflect the actual situation. Unfortunately for the defenders of the compatibility of science (in this particular case the theory of evolution) with the Torah, the incompatibility of the Torah's story with science is quite obvious.

    Having pointed, as quoted, to the principal contradiction which in his view exists between theory of evolution and Judaism, Goldman unequivocally asserts that this contradiction in itself is sufficient reason to conclude that the theory of evolution must be wrong. He sees his task as "how to demonstrate even to the non-believer the falseness of the secularist beliefs" (page 218). The main argument used by Goldman to refute Darwinism boils down to the assertion that "Darwinian reasoning is completely beyond testing..." (page 221). This argument, regardless of its being right or wrong (and actually it is far from being right) sounds very strange coming from somebody who wants us to accept his beliefs as if the Torah's story is not "completely beyond testing."

    No article in section 2 provides any fact-based argumentation which would show the plausibility of the Genesis story thus making it reasonable at least equally with scientific theories, not to mention its being better substantiated than the evolution theory.

    Evolutionary scientists freely admit that the evolution theory has not answered all questions about the origin of species and related problems. Nevertheless, the theory of evolution has successfully and consistently explained a vast variety of empirical observations. Therefore denials of the theory of evolution based only on stressing its weak points, as has been practiced by the authors of the articles in section 2, fail to be convincing to an unbiased reader.

    5. Review of Section 3

    The article by Carl Klahr opening this section is titled "Science versus Scientism." It seems to present the program for all the papers in this section and purports to be supportive of genuine science while refuting what is referred to as "scientism." The latter term has been defined by Klahr as follows (page 289): "It is a conviction on the part of many scientists and teachers of science that the only valid answers to almost all the questions of fact or philosophy must come from extrapolation of science." Klahr does not provide references to any scientists or teachers of science who have ever suggested the above view. Isn't this a typical example of arguing with a straw man?

    I cannot recall any scientist saying that "philosophy must come from extrapolation of science."

    Klahr then suggests a long list of statements which allegedly evince the views of that mysterious never observed breed he calls "scientologists." This list is a funny mix of various unrelated claims, some of them a reasonable reflection of facts, and others unsubstantiated suppositions. For example, all "scientologists," according to Klahr, adhere, among other views, to the following two statements: statement 6 says that "Growing up in Samoa and growing up in New York are essentially identical; only the artifacts are somehow different. The human animal is only superficially different in various cultures." Statement 12 says: "There are billions of planets in the universe with intelligent forms of life living in some of them."

    In would be interesting to know, would a person qualify to be a "scientologist" rather than a scientist if she thinks that growing up in Samoa is different from growing up in New York, but on the other hand believes that there are billions of planets with life existing on some of them?

    Klahr seems to claim that he has a superior knowledge of all that variety of topics covered by the list of statements in question, from sociology to biology and from history to physics. For example, he seems to claim that he knows for a fact that there are no planets in the universe on some of which there exists life. And if somebody thinks otherwise, then, according to Klahr, this somebody cannot be viewed as a scientist but, by definition, must be referred to by the pejorative term "scientologist."

    However odd Klahr's assertions sound, his article may be viewed just as a not very serious attempt to remove the halo of respectability from some forms of scientific method, those where science (legitimately) deviates from a mere collecting of facts and embarks on hypothesizing their explanation. Another article in section 3, that by G. Schlesinger, presents a much worse case of blithely erroneous arguments suggested to allegedly prove the rationality of faith.

    Article by G.N. Schlesinger

    The paper by G.N. Schlesinger is titled "The empirical basis for belief in God" (pages 400-411).

    Schlesinger, according to the information provided on page 400 in the above collection, is a professor of philosophy of science, and a Rabbi.< His credentials include two books on the philosophy of science. Hence, we see in him a highly qualified participant in the dispute regarding the existence of God, combining knowledge of science (at least in some general sense, as he seems not to have contributed to any particular branch of science, but only to the philosophy thereof) with training in convoluted discourse using intricate argumentation, as practiced in the Torah and talmudic studies.

    Indeed, the paper in question amply illustrates that our expectations are fully met. In that paper, Schlesinger sets out to mathematically prove the existence of God, at least to the same extent and in the same sense as the laws of physics can be viewed as "proven."

    Of course, no law of physics has been "proven." All those laws are postulates based on the interpretation and generalization of experimental and observational data. All those laws are necessarily subject to revisions as new experimental evidence emerges. However, despite all the limitations of the scientific approach, we all are witnesses to the enormous success of scientific exploration of the world. Within legitimate limits, laws of physics work very well, despite each of them being just a reasonably plausible approximation of the real laws of nature, assuming that the latter indeed exist objectively. Because of the great successes of science, the laws accepted in physics and related disciplines are justifiably viewed as great achievements of the human mind.

    Schlesinger maintains that the existence of God can be justified to the same extent of plausibility as are justified the best scientific laws. To prove his point he indicates that every law of science is accepted only because we have first adopted some underlying presuppositions. These presuppositions, according to Schlesinger, are usually taken for granted, but are actually unsupported by evidence, and, moreover, are unsupportable.

    As an example, Schlesinger discusses the discovery of planet Neptune, which was predicted before its actual observation. The prediction in question was made based on the application of Newton's laws. However, says Schlesinger, the theory developed by Newton is by no means the only one possible describing the motion of celestial bodies. There can be an endless number of laws governing the motion of celestial bodies, and, in particular, one can imagine any number of theories other than that by Newton which would equally well predict the existence of Neptune in a particular area of the solar system. To substantiate his claim, Schlesinger suggests an example of a law which, while differing from that by Newton, would provide the same prediction in regard to Neptune.

    Let us see how Schlesinger constructs his example. The well known 2nd law of Newton can be (for the particular case of a constant mass) written as follows:

    acceleration = force/mass.

    Let us assume, says Schlesinger, that some scientist named Whewton suggested a different law instead of the above 2nd law of Newton. The supposed Whewton's law would add one more term to the expression of Newton's. Let us denote the additional term W. Then Whewton's law of mechanics would look as follows:

    Schlesinger suggested choosing the following form for W:

    where A is an arbitrary constant, T is the temperature at the center of the earth, expressed as an integer, n is the value of T at a particular date (Schlesinger chose that date to be January 1, 2001, midnight; his paper was published in 1976). He further assumed that at any time before January 1, 2001, T>>n, while T gradually decreases. With all these arbitrary assumptions, at any time before January 1, 2001, T!/n=I is an integer, and since

    is zero if I is an integer, hence W=0. Therefore, at least until January 1, 2001, the additional term W remains equal to zero, and both 2nd law of Newton and the alternative law by Whewton give identical results. Many other forms of W could be chosen, and an endless number of values can be assigned to A, and all those alternative laws would equally well predict the existence of Neptune. However, all those alternative laws are quite different from 2nd law of Newton. In the discussed example, if Whewton's law were true, then, after January 1, 2001, all celestial bodies would drastically change their behavior.

    Of course, says Schlesinger, scientists take it for granted that 2nd law of Newton is much more trustworthy than the law of Whewton. "This is a matter of prior judgment which is not and could not be, based on evidence available to anyone before the year 2001," says Schlesinger. All that discourse, maintained Schlesinger, demonstrates, that whatever statement is accepted in science, is necessarily built upon presuppositions which are taken for granted. In his further discussion Schlesinger proceeded to show that the acceptance of God's existence can be justified as reasonably as any of the scientific laws are.

    Before reviewing the next part of Schlesinger's discourse, let us go back to the above discussion of the alleged arbitrariness of scientific laws.

    Schlesinger's view seems to be that the 2nd law of Newton and what he calls Whewton's law, but what more properly should be called Schlesinger's law, have the same status. Since, until January 2001, no evidence could be obtained disproving Schlesinger's law, then, according to Schlesinger, his law was as good as the 2nd law of Newton or as any other of an endless variations of alternative laws all of which equally would predict the existence of Neptune.

    I just can't believe that an expert in philosophy of science, trained also in talmudic studies, is serious in that statement. A much more plausible assumption is that Schlesinger is perfectly aware of the fallacy of his argument, but uses it nevertheless, enjoying the convoluted twists of his thoughts on the way to an alleged proof of his thesis. Ingeniousness of an argument seems to be more attractive to Schlesinger than the pursuit of truth.

    The difference between the meanings of the 2nd law of Newton and of Schlesinger's law is too obvious not to be noticed by a man of Schlesinger's intellect and education. Newton's law, as every law of physics, is a postulate. But it is a postulate which is by no means arbitrary. On the contrary, its plausibility is well founded in an enormous amount of consistent evidence, whose interpretation in the form of the 2nd law of Newton is also highly logical. It enables scientists to make numerous predictions regarding the behavior of moving bodies, and so far these predictions have been fulfilled with an amazing accuracy. In the beginning of the 20th century certain limitations of the 2nd law of Newton were discovered which led to the establishment of its area of validity, and this area, despite the newly discovered limitations, remained amazingly large.

    The additional term suggested, as a possible example, by Schlesinger, was also a postulate. However, that is the only feature which is common for the two laws in question. Schlesinger's law, unlike that of Newton, was not based on any evidence whatsoever, but artificially contrived in such a way, so as not to add any non-zero values to the results following from Newton's law, at least until January 1, 2001. Since this added term, until January 2001, was zero, then, until the date in question it not only could not be disproved, but also was unverifiable and hence was not a law of science. Moreover, even if, on January 1, 2001, all laws of mechanics abruptly changed, this still would not constitute a proof of Schlesinger's concocted law, because its mathematical representation contains a quantity (the temperature at the center of the earth) which must be measured with a reasonable accuracy at the precisely predetermined moment of time. Schlesinger does not offer any method enabling one to conduct such a direct measurement. Moreover, every data which serve as a basis for a scientific theory must be reproducible. However, as soon as midnight of January 1, 2001 passed, there is no way to repeat the measurement. In other words, the additional term added by Schlesinger had only an appearance of a meaningful formula, but actually was a meaningless concoction designed as an example of an imaginary situation which actually did not and will not exist. Either before January 2001, or after that date, it has no meaning in scientific sense and there is no reason whatsoever to discuss this absolutely unsubstantiated addition. Scientists do not take for granted the 2nd law of Newton, and Schlesinger knows it. The 2nd law of Newton has been accepted for reasons. Nobody suggests that it is the absolute truth. But, based on an enormous amount of available evidence, 2nd law of Newton is a very reasonable approximation of reality, and we have all the reasons to base our predictions and conclusion on that law, as long as it is applied within the limits of its validity.

    The question of the possible validity of the artificially contrived law of Schlesinger is essentially a different question. The actual question is whether the laws of nature, which, as we believe, are reasonably approximated by laws of physics, as we know them, will remain the same in the future, or at some moment they will be changed. Schlesinger may argue that at any moment in the future the laws of nature may abruptly change. Such an assertion cannot be either confirmed or rejected by any means available to science. This question lies beyond science. Therefore the entire discourse by Schlesinger, employing his contrived alternative law, has no relation to science and is irrelevant even in regard to the philosophy of science, not to mention any practical implications of his discourse.

    Schlesinger's further argument, attempting to show equivalency between scientific theories and the belief in the existence of God, is actually only as good as his example with a contrived meaningless alternative law of mechanics. The alternative law was contrived to meet certain requirements, but was not based on any evidence, and, either before or after January 1, 2001 cannot be verified by any scientific method. Likewise, the hypothesis of God's existence has no more validity than the mentioned artificially contrived alternative law of mechanics, both, unlike scientific laws, lacking any supporting evidence. Moreover, there were no reasons whatsoever to expect that on January 1, 2001 all laws of mechanics would abruptly and drastically change. Therefore the entire discourse by Schlesinger which purported to demonstrate that any scientific statement is based on some presuppositions that cannot be substantiated and are taken for granted was simply a meaningless exercise in casuistry.

    Let us now review another approach by Schlesinger, in which he uses an estimation of probability for God's existence.

    To discuss Schlesinger's discourse, we have to follow rather closely his entire line of argument. He starts with a discussion of the reasons a scientific hypothesis can be believed to be plausible. To this end he uses the following mathematical relationship: if p(A) is the probability of event A, and p(B) is the probability of event B, and p(A|B) is the probability of event A provided event B has actually occurred, and p(B|A) is the probability of event B provided event A has actually occurred, then

    P(A|B)/p(A)=p(B|A)/p(B)................................................................................................[1]

    Schlesinger first applies that relationship (which is actually a simplified version of Bayes's theorem) to the prediction of the discovery of Neptune, based on Newton's mechanics. He refers to Bertrand Russell, as the source of his discussion of the probability of Newton's mechanics being true. Since I have no access to the referenced work by Russell, I have to rely on Schlesinger's presentation of Russell's discourse.

    Schlesinger's reasoning, apparently reproducing that by Russsell, is as follows: Let p(N) be the probability that Newton's mechanics is true. Let p(P) be the probability that in a specific part of the solar system there is a hitherto undiscovered planet to be named Neptune. Let p(N|P) be the probability of Newton's mechanics being correct provided a hitherto unknown planet named Neptune has indeed been discovered in a specific part of the solar system, as predicted based on Newton's mechanics, and let p(P|N) be the probability of discovering a new planet in a specific part of the solar system, provided Newton's mechanics is correct. Then, as per equation [1] we can write:

    p(N|P)/p(N)=p(P|N)/p(P).................................................................................................[2]

    The value of p(P|N), says Schlesinger, is obviously much larger than p(P). Indeed, p(P) is the probability of discovering a new planet in a specific part of the solar system. Such discoveries have been extremely rare (during the last couple of thousands of years, before the discovery of Neptune, only one new planet, Uranus, was ever discovered, hence the probability of discovering one more unknown planet must be very small). On the other hand, if Newton's mechanics is true, then Neptune must necessarily exist in a specific part of the solar system, hence p(P|N)=1. Hence, says Schlesinger, the right side of eq. 2 is a very large number, and therefore the left side must also be a very large number. This means that p(N|P)>>p(N). In other words, the discovery of Neptune increases very much the probability of Newton's mechanics being true.

    With all its seeming logic, the above discourse is rather feeble. If we believed that eq. 2 has indeed such power of enhancing the plausibility of Newton's mechanics, we would simply attach too much significance to that effect. Indeed, p(P) is a very small number. So the right side of the equation is a very large number (even though there is no way to assign to it any definite value). From that seems to follow that the discovery of Neptune has immensely enhanced the plausibility of Newton's mechanics. Actually such a suggestion is rather far from reality. In fact, even before the discovery of Neptune, Newton's mechanics was so firmly established as an extremely plausible and useful theory, that the discovery of Neptune had little effect on that theory's acceptance in science. As soon as Leverrier and Adams published their calculations predicting the existence of Neptune in a specific part of the solar system, the probability of that prediction being true was immediately accepted as being 1, as Newton's mechanics has been confirmed as a good theory by such an enormous amount of evidence, that its veracity was not the subject of any doubts. It was believed, even before Neptune's discovery, that p(N) = 1. (The limitations of Newton's mechanics were discovered later, but that did not diminish p(N), having only defined its area of validity).

    Having demonstrated the alleged way a scientific theory acquires plausibility, Schlesinger proceeds to apply an identical method to religious beliefs. For the sake of discussion, let us accept the procedure suggested by Schlesinger (or by Russell), and see if the same method, as Schlesinger wants us to believe, may also work in regard to religious beliefs.

    As his first example, Schlesinger discusses the well known Bible's story about the destruction of the walls of Jericho at precisely that moment when the Israelites, led by Yehoshua Bin-Nun completed their march around the city.

    Let p(D) be the probability that God exists, and p(J) the probability that the walls of Jericho would collapse at the mentioned moment of time. Let, further, p(D/J) be the probability that God exists provided the walls of Jericho have indeed collapsed at the precisely defined moment of time, and p(J/D) the probability that the walls of Jericho would collapse at the mentioned moment of time provided God indeed exists. As per eq.1, we can write, says Schlesinger, the following relationship:

    p(D|J)/p(D)=p(J|D)/p(J).................................................................................................[3]

    Schlesinger then maintains that p(J/D) is "obviously" much larger than p(J) because, in his view, if God exists, then it "is quite likely that He should listen when He is called upon by His true followers..." In other words, Schlesinger says that the probability of Jericho's walls collapsing at a precisely defined moment, which is a very unlikely event, is quite small, but if God exists, then the same event must become much more probable. From that he concludes that, by virtue of eq.3, also p(D/J) is much larger than p(D). The conclusion: the collapse of Jericho's walls makes the probability of God's existence immensely more probable. If we compare this discussion with that related to the case of Neptune's discovery, we see that p(D) in eq. 3 is analog of p(N) in eq. 2 and p(J) in eq. 3 is an analog of p(P) in eq. 2, while p(D|J) in eq. 3 is an analog of p(N|P) in eq. 2 and, finally, that p(J|D) in eq. 3 is an analog of p(P|N) in eq. 2. It is easy to see, however, that there is no actual analogy between the listed probabilities. The main difference is between p(N|P) in eq. 2 and p(D|J) in eq. 3. In eq. 2, p(N|P) was the probability that Newton's theory is true, provided a new planet is discovered precisely in a specific part of the solar system, as predicted on the basis of Newton's theory. Event P, that is the discovery of a new planet, as predicted, has actually occurred. In eq.3, though, p(D|J) is the probability of God's existence provided the walls of Jericho did indeed collapsed at a defined moment of time. Unlike event P in eq. 1, which has actually occurred, there is no evidence whatsoever, that event J in eq. 3 has ever occurred. If one believes in the veracity of the Bible's account, most commonly one also believes that God exists. However, as an alleged proof that God's existence is highly probable, eq. 3 is illegitimate, since it is used to verify a hypothesis, on the basis of another hypothesis, the latter not being supported by any evidence. Many contemporary Israeli archeologists came to the conclusion that there is no archeological evidence of the destruction of Jericho's walls at the time of Joshusa's conquest of Canaan (although some other archeologists dispute such a conclusion). The story of Jericho's walls cannot be viewed as fact. Hence, even if we were to accept the scheme suggested by Schlesinger (or by Russell?) it would not be helpful for the case of estimating the probability of God's existence.

    Schlesinger seems to realize the weakness of his example, so, for his ultimate argument he discusses another example, again using the same scheme of symmetric probabilities. It is as follows.

    Let p(D) again be the probability that God exists, and p(M) the probability that the laws governing the universe and making possible the existence of man, do exist. Let, further p(D|M) be the probability that God exists, provided that indeed the mentioned laws, and, hence, man, indeed exist. Finally, let p(M|D) be the probability that the mentioned laws and hence man exist, provided that God indeed exists. Now, again, Schlesinger uses the equation of symmetric probabilities:

    p(D|M)/p(D)=p(M|D)/p(M)...........................................................................................[4]

    According to Schlesinger, the right side of eq. 4 is a very large number. The reason for that, according to Schlesinger, is that the probability p(M) of the existence of laws of nature enabling the existence of man is extremely low. However, if God exists, then that probability, which is now p(M|D), becomes immensely larger. Hence, says Schlesinger, the left side of eq. 4 must also be a very large number. Hence, the mere existence of the laws of nature which enable the existence of man immensely increases the probability of God's existence. That, according to Schelsinger, is exactly the same reasoning that has been used in science to establish the laws of science.

    It is easy, though, to see illogical links in Schlesinger's chain of notions. The quantity p(M|D) in eq. 4 is supposed to be an analog of p(P|N) in eq. 2. Recall that p(P|N) in eq. 2 was the probability of discovering a planet provided Newton's theory is correct. On the other hand, p(M|D) in eq. 4 is the probability that the laws of nature enabling the existence of man do exist, provided God exists.There is an obvious drastic difference between these two probabilities. Probability p(P|N) in eq. 2 relates to the following events: a) event P is the discovery of Neptune, and b) event N is Newton's theory being true. It is not an arbitrary supposition, that if Newton's theory is true, then a new planet necessarily exists where the theory predicts it to be. It is an expectation based on an abundance of firmly established evidence. On the other hand, probability p(M/D) in eq. 4 relates to the following two events; a) M, actual existence of man, and b) D, actual existence of God. In order for p(D|M) to be much larger than p(D), we must assume that God must have wished to create conditions for man's existence. Unlike in the case of Newton's theory and the discovery of Neptune, there exists no evidence that God, if he exists, must necessarily have wished to provide conditions for man's existence. Schlesinger may think he knows what God must or must not do, but this supposed information is nothing more than Schlesinger's private opinion, which has no evidentiary value. Hence, Schlesinger's alleged proof that God's existence can be proven with the same degree of certainty as scientific theories are, is not convincing.

    6. Brief review of Section 4

    In the six papers constituting this section, a topic is discussed which seems to be quite apart from the rest of the collection. While in sections 1 through 3, various aspects of the relationship between science and the Torah are discussed, the papers in section 4 deal with ethical problems from the Torah's viewpoint rather than with the science vs Torah controversy. However, in some of the papers in this section their authors still cannot leave behind them the controversy in question and return to its discussion in various forms.

    The section in question opens with a rather lengthy article by one of the two editors of the collection, Cyril Domb, titled "Biology and Ethics." On page 16 of the book in question we find biographical information on Domb. He used to be a professor of theoretical physics at the King College in England, specializing in statistical mechanics, phase transitions and critical phenomena. He also held positions as a professor of physics at Bar-Ilan University and at the Weizman Institute in Israel and at several other universities. Cyril Domb, according to that information, is a fellow of the Royal Society. These are indeed very impressive credentials.

    Domb starts his article by listing the names of a number of scientists who have achieved prominence in their field of research while also being devoted Orthodox Jews, many of them also ordained Rabbis. The second section of Domb's paper is titled "Philosophic outlook." Here is a quotation from that section: "The fundamental assumption of all sciences that there is a regular pattern in nature so that experiments performed under identical conditions will lead to identical results is very much in accord with religious tradition." A few words later, Domb continues: "God who is responsible for these "natural" laws can revoke them on any particular occasion."

    There is an obvious contradiction between the two quoted sentences. If we accept the second statement, then a scientist can never be sure that identical conditions will necessarily lead to identical results, because at any moment God can intervene and revoke the "natural" law which makes a certain outcome an unavoidable result of given conditions. Professor Domb, you can't have it both ways. I have very serious doubts that professor Domb would resort to such type of logic in his work on statistical physics or phase transitions. However, when he wants to assert his religious beliefs, elementary logic must give way to an odd combination of two incompatible statements.

    In the other articles of that section we find a discussion of such problems as the ethical aspect of organs transplantation from the viewpoint of Judaism, the Jewish view on the population control, etc. Since these topics are beyond the main theme of this review, which relates to the science vs the Torah controversy I leave the rest of that section without further discussion

    7. Conclusion

    As it was said at the beginning of this review, the main idea evinced by the authors of the collection "Challenge" was to assert that the Torah in no way contradicts the achievements of modern science. Unfortunately, to prove that assertion, the authors of the collection did not offer anything beyond unsubstantiated statements, often contradicting each other and avoiding the discussion of the obvious inconsistencies so abundant in the Torah's story. Some of the authors, though, could not constrain themselves to following the above main idea, and fell into a pit of denying certain scientifically established facts. Overall, despite the impressive credentials of many of the authors in that collection, and despite the often seemingly considerable sophistication of their discourse, a skeptic would not be moved at all to abandon his skepticism and to accept the statements of these believers with scientific degrees on the base of the discourse presented.

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