on March 22, 2015
As always, Steven Weinberg writes well and explains things clearly. His thesis is that the scientific revolution was very real and that it was a very real change in the way people went about trying to understand the world. Although he discusses possible reasons for the change, he does not claim to have reached a definitive conclusion. He concentrates on physics and astronomy and on the transition from the Ancient Greek approach - applying pure reason with only a nod to observation of phenomena - to the modern approach based on an essential combination of experiments, observation, and theory. This is not a full fledged history of science (or even of physics and astronomy) but a refutation of the viewpoint the science is merely a social construct, no more valid than any other viewpoint (e.g., religious mysticism). I think he makes a strong case, but then I am a practicing physicist, so I am probably biased. If you are interested in the historical discontinuity between pre-scientific thinking ("philosophizing") and modern scientific thinking, then I highly recommend this book.
A note on the eBook version. While the footnote links work pretty well, the links to the Technical notes all take you to the first such note so you have to page through all the earlier notes before you get to the one you wanted to read. I found that annoying.
A note on the eBook version. While the footnote links work pretty well, the links to the Technical notes all take you to the first such note so you have to page through all the earlier notes before you get to the one you wanted to read. I found that annoying.
on April 4, 2015
I am reviewing this book with the understanding that it is written by an extraordinarily talented physicist, a person who has devoted his life in the pursuit of scientific truth. It is not often that a prominent physicist takes the time to share his/her perspective of the early history of modern science. It was a great oppertunity to see the history of modern science from a person who has made his own contributions. Unfortunately, I don't think it worked as he intended. It fell short for several reasons. The author's perspective on the history of science is too narrow. He judges the success of contributors to the making of modern science by how close they were to our current understanding of science. This is much too narrow and simplistic a view. The author's selection of the making of modern science is biased and he makes little apology for leaving out contributors to the biological sciences, and chemistry. He also has trouble understanding the importance of the tension between philosophy and science in the making of modern science.
The text is nearly flawless, but very dry and sterile and I could not find one instance where a hint of humor entered the text.
While his unique perspective did get me to rethink the extent of the contributions made by the great luminaries of science, the last third of the book (Technical Notes) is a treasure trove. He makes 2,500 years of mathematical reasoning in support of explaining the world so easy to understand. I get the sense that Dr. Weinberg is a walking enclyopedia of physics! I suspect he did most of these derivations off the top of his head.
The editing of this book was exceptional. I believe there is an error on page 242 regarding his interpretation of Newton's theory of the tides. The author states the tidal bulge on the opposite side of the Earth is created by the Moon's gravity pulling the Earth away from the water. The tidal bulge on the opposite side of the Earth is the result of centrifugal forces produced by the revolution of the earth and moon (and to a lesser extent by the earth and sun) around their common center of gravity (mass) or barycenter. This is a minor quibble.
One can only admire the author's understanding of physics. I suspect he did not have to even check the correctness of his physics. The majority of his time in writing this book was probably spent getting the history right. He did a scholarly job and gives the Islamic contributions their due.
The author has a strong respect for precision in his writing. If you have read other books of similar ilk you will find this one a very worthwhile read (for his unique perspective alone).
The book has now been added to my bookcase among Dr. Weinberg's other books.
The text is nearly flawless, but very dry and sterile and I could not find one instance where a hint of humor entered the text.
While his unique perspective did get me to rethink the extent of the contributions made by the great luminaries of science, the last third of the book (Technical Notes) is a treasure trove. He makes 2,500 years of mathematical reasoning in support of explaining the world so easy to understand. I get the sense that Dr. Weinberg is a walking enclyopedia of physics! I suspect he did most of these derivations off the top of his head.
The editing of this book was exceptional. I believe there is an error on page 242 regarding his interpretation of Newton's theory of the tides. The author states the tidal bulge on the opposite side of the Earth is created by the Moon's gravity pulling the Earth away from the water. The tidal bulge on the opposite side of the Earth is the result of centrifugal forces produced by the revolution of the earth and moon (and to a lesser extent by the earth and sun) around their common center of gravity (mass) or barycenter. This is a minor quibble.
One can only admire the author's understanding of physics. I suspect he did not have to even check the correctness of his physics. The majority of his time in writing this book was probably spent getting the history right. He did a scholarly job and gives the Islamic contributions their due.
The author has a strong respect for precision in his writing. If you have read other books of similar ilk you will find this one a very worthwhile read (for his unique perspective alone).
The book has now been added to my bookcase among Dr. Weinberg's other books.
on February 26, 2015
Did you know that Dr. Steven Weinberg, the author of this book, along with getting the Nobel Prize, also received the Lewis Thomas Prize for Scientist as Poet? He did.
Reading some of Dr. Weinberg’s earlier writing left me with the impression that he is an intelligent fellow who is capable of looking at more than one side of an issue and is likely to arrive at conclusions that are reasonable, if not necessarily likely to garner universal agreement. Reading an excerpt from this book, I was struck by the line “As great as is the progress that has been made in the methods of science, we may today be repeating some of the errors of the past.” Uh-oh, I thought, better find out about that, I don’t want to be going all Ptolemy on anybody without realizing it.
Dr. Weinberg starts off by considering what the ancient Greeks had to say about the natural world. He begins with Thales, who said “Everything is water,” which is remembered as the first physical Theory of Everything. Dr. Weinberg seems to think that this theory wasn’t too bad for a first try, but, personally, I think Heraclitus’s “Everything is fire” has more pizzazz. We then visit with Socrates, Plato, Aristotle, Democritus, all bright fellows, to be sure, but, when they turned to science, “none of them attempted to verify or even . . . seriously to justify their speculations.” This point seems a bit exaggerated. Aristotle’s argument that if the Earth moved, then a ball thrown straight up in the air would not come straight down to where it was thrown, sounds to me like an attempt to support a conclusion. A kindergarten–level experiment would have sufficed to cast doubt on Aristotle’s thinking, but the classical philosophers’ method of investigation was not experimentation but discussion and argument. Philosophy was compared to a wrestling match, with the expectation that shaky ideas would be beaten down and the strongest and therefore best philosophy would come out on top.
The successors to the classical Greeks, the technicians, mathematicians and scientists of the Hellenistic era, had a better handle on things. Dr. Weinberg admires Hero and thinks the world of Archimedes, but he devotes more pages to Ptolemy’s “Almagest,” which was a standard astronomy text for more than a thousand years, but today is seen as THE science botch of all time, and a lesson to us all.
Dr. Weinberg then discusses Arab and European scholarship in the Middle Ages. Much of the sophistication of Greece and Rome was gone, and religious leaders felt that, if there was to be such a thing as thinking, every bit of it should be concerned with holy writ and the wisdom of the saints. Questioning was out. But there was still astronomy, needed to make the calendars that told you when it was a holy day, and astronomy kept men thinking about the natural order. And there was Aristotle, and Aristotle, for all Dr. Weinberg’s critical opinion of him, got men to thinking about thinking, and logical thinking at that.
Dr. Weinberg then comes to the Scientific Revolution, which he considers as beginning with Copernicus. Galileo’s experiments on falling bodies – which demonstrated that Aristotle’s not-experiment-based ideas in this area were wrong - are Dr. Weinberg’s starting point for modern experimental science. The book that Galileo wrote about these experiments had to be smuggled out of Italy and published in London, since, by that time, the Church had arrested and tortured Galileo, forcing him to recant his teaching that the Earth moves (which, it was argued, was in conflict with a few sentences in the Old Testament that talk about the sun moving across the sky and do not say that it was the spinning of the Earth that made it appear that the sun was moving in the heavens) and sentenced him to permanent house arrest, and banned his books, and forbade him to publish anything ever again. As Darwin also could have told you, being a scientist is not for wimps.
The idea of experimental science took hold: “No longer were natural philosophers relying on nature to reveal its principles to casual observers.” Experimental science was rolling along pretty well by the time Isaac Newton arrived on the scene. “Newton’s achievements provided the paradigm that all subsequent science has followed.” Newton was The Man.
Dr. Weinberg’s short-list of the greatest scientists of all time reads “Galileo, Newton, Darwin, Einstein,” all world changers and earth shakers.
Dr. Weinberg points out that while it is perfectly possible for a person to be both very religious and very scientific (Newton was such a one), “It was essential for the discovery of science that religious ideas be divorced from the study of nature. Once one invokes the supernatural, anything can be explained, and no explanation can be verified.” So, scientists run into trouble with established religions. Along with the church’s pounding down of Galileo, we are told about Anaxagoras, who had to flee Athens after teaching that the sun is not a god but a physical object, and Hypatia, who was literally torn to pieces by a mob of good Christians for the unforgivable crimes of being a scientist, a mathematician, and, at the same time, a woman, a pagan, and hot. Dr. Weinberg also mentions fellow Nobel Prize winner Abdus Salaam, a devout Moslem, who, when he attempted to promote scientific research in the Islamic Middle East, was told that, for the Faithful, the study of science would be “culturally corrosive.” Whether Islam would benefit from cultural corrosion of this sort I will leave to the internet’s “comment” pages.
Particular pleasures:
Philosophers, natural and un-, have, figuratively speaking, been beating each other over the head with inflated pig bladders since day one. It’s a tradition that Dr. Weinberg gleefully joins in this book. Aristotle takes a drubbing throughout, but the chapter in which Dr. Weinberg disrespects Francis Bacon and Rene Descartes, was, by itself, worth the price of admission.
Disappointments:
Dr. Weinberg never does say which errors of the past are the ones that we might be repeating today. I guess we will just have to keep our guard up and hope for the best.
I had a half-formed hope that Dr. Weinberg, in this book subtitled “The Discovery of Modern Science,” would spell out just what was achieved, providing an explicit, concise, lucid, perhaps even poetic, description of, and users guide for, the scientific method, preferably one suitable for copying and pasting into every single internet discussion of evolution and global warming.
Dr. Weinberg did not do this. He seems happiest with a description of science as a rudderless chaos that sometimes manages to produce results in spite of itself, or as “a tangle of deduction, induction, and guesswork.” “We learn how to do science, not by making rules about how to do science, but from the experience of doing science.”
I have a tiny little small suspicion that Dr. Weinberg talks about science in this way in order to allow string theory to be classified as “science” rather than as “mathematical pastime.” But his description allows the most uninformed cranks in the universe to have as much right as anyone to claim that their conclusions are scientific, “Oh, yeah, we got a HUGE tangle of induction, deduction, reduction, convection and guesswork going on here ALL the time.”
No one should be led to suppose that science is whatever you happen to think, or something indefinable and unteachable. Putting it into practice requires discipline, desire and effort, but, despite all the long ages it took to formulate, the scientific method is not conceptually difficult. The basics can be explained, in detail, in an hour or two, after which the reasonably bright and attentive listener can perform a good approximation of thinking and acting like a scientist (Readers who feel they may need more information before saying “aye,” “nay,” or “eh” on this point are invited to read the technical footnote, below).
Ah, well, even if Dr. Weinberg had included a most excellent Junior Woodchuck’s guide to the scientific method in his book, I probably would have found myself disagreeing with him on several points. I will give his book 4.5 stars, to show that there are no hard feelings. End of book review.
Technical footnote:
The last third of To Explain the World is headed “Technical Notes.” This section is all math, designed to give the reader an idea of how the investigators mentioned in the book arrived at their results. It is not actually necessary to read this section in order to appreciate the book, but don’t let it scare you. When it is time to put, say, a cosine, to work, Dr. Weinberg explains what a cosine is, rather than assuming, as most writers will, that you took trig in high school, and, due to being some sort of mutant or something, actually remember it.
In a similar spirit, for the benefit of readers who had the proper response (“show me”) to the apparently controversial claim that the process of doing science can be defined and taught, for discussion I offer this sketch/outline of a description of that method by which science is done. The complete description would include consideration of:
Observation
Wonder or Puzzlement
Speculation - Here it is pointed out that no one needs to teach you how to speculate, speculation is a built-in feature of the human brain. Let it rip, let your brain make up its little stories that explain what you observed or suggest what might be done. Do not mistake any one of these stories for the truth, or anything like it, until it is supported by a considerable amount of reproducible physical evidence and can be shown to conflict with none,
Literature Search - Meant to be exhaustive. If you are investigating, say, the emerald ash borer, then, before you start making scientific pronouncements about the emerald ash borer you should know as much about the emerald ash borer as anyone in the world, including the emerald ash borer’s mom. If, on the other hand, your goal is to make pseudoscientific statements about the emerald ash borer on the internet or in congress, then you are free to remain utterly ignorant,
Hypothesis
Investigation – If you are doing experimental science you may be designing and doing experiments to obtain reproducible physical evidence relevant to the viability of a hypothesis, or you may be doing things to see if they work, or you may be trying things to see what happens. If you are doing descriptive science you may be doing dissections, going on an expedition or spending time with a telescope. If you are doing theoretical science you may be doing calculations that, if they look promising, will require experimental and observational support.
Conclusion - in the case of experimental science the likely conclusions are “the evidence supports the hypothesis” or “the evidence does not support the hypothesis” but “Wow, didn’t expect THAT!” is also possible.
Publication
Confrontation - All of your colleagues who are competent in your area are required to point out every weakness in your knowledge, method, results, reasoning and conclusions. You are not allowed to reply “Bite me.” It’s all for the good. If you don’t have an appreciable number of exceptionally bright and well-informed people telling the world where you went wrong, then probably no one is paying any attention to you. Remember that every scientific conclusion, even one that won the Nobel Prize, comes with the unspoken qualifier “until we know better,”
followed by
More Research – of course
All of this is carried on in the presence of a strong, continuous, conscious awareness that your basic tool is a limited, fallible, delusion-prone human brain, and, at any stage, from observation and speculation onward, you are most probably wrong. The goal is reliable inference, reliable conclusions, reliable description, with the hope that we will know things tomorrow that we don’t know today, we will understand things tomorrow that we don’t understand today, and we will be able to do things tomorrow that we can’t do today. Some people think it is fun.
Reading some of Dr. Weinberg’s earlier writing left me with the impression that he is an intelligent fellow who is capable of looking at more than one side of an issue and is likely to arrive at conclusions that are reasonable, if not necessarily likely to garner universal agreement. Reading an excerpt from this book, I was struck by the line “As great as is the progress that has been made in the methods of science, we may today be repeating some of the errors of the past.” Uh-oh, I thought, better find out about that, I don’t want to be going all Ptolemy on anybody without realizing it.
Dr. Weinberg starts off by considering what the ancient Greeks had to say about the natural world. He begins with Thales, who said “Everything is water,” which is remembered as the first physical Theory of Everything. Dr. Weinberg seems to think that this theory wasn’t too bad for a first try, but, personally, I think Heraclitus’s “Everything is fire” has more pizzazz. We then visit with Socrates, Plato, Aristotle, Democritus, all bright fellows, to be sure, but, when they turned to science, “none of them attempted to verify or even . . . seriously to justify their speculations.” This point seems a bit exaggerated. Aristotle’s argument that if the Earth moved, then a ball thrown straight up in the air would not come straight down to where it was thrown, sounds to me like an attempt to support a conclusion. A kindergarten–level experiment would have sufficed to cast doubt on Aristotle’s thinking, but the classical philosophers’ method of investigation was not experimentation but discussion and argument. Philosophy was compared to a wrestling match, with the expectation that shaky ideas would be beaten down and the strongest and therefore best philosophy would come out on top.
The successors to the classical Greeks, the technicians, mathematicians and scientists of the Hellenistic era, had a better handle on things. Dr. Weinberg admires Hero and thinks the world of Archimedes, but he devotes more pages to Ptolemy’s “Almagest,” which was a standard astronomy text for more than a thousand years, but today is seen as THE science botch of all time, and a lesson to us all.
Dr. Weinberg then discusses Arab and European scholarship in the Middle Ages. Much of the sophistication of Greece and Rome was gone, and religious leaders felt that, if there was to be such a thing as thinking, every bit of it should be concerned with holy writ and the wisdom of the saints. Questioning was out. But there was still astronomy, needed to make the calendars that told you when it was a holy day, and astronomy kept men thinking about the natural order. And there was Aristotle, and Aristotle, for all Dr. Weinberg’s critical opinion of him, got men to thinking about thinking, and logical thinking at that.
Dr. Weinberg then comes to the Scientific Revolution, which he considers as beginning with Copernicus. Galileo’s experiments on falling bodies – which demonstrated that Aristotle’s not-experiment-based ideas in this area were wrong - are Dr. Weinberg’s starting point for modern experimental science. The book that Galileo wrote about these experiments had to be smuggled out of Italy and published in London, since, by that time, the Church had arrested and tortured Galileo, forcing him to recant his teaching that the Earth moves (which, it was argued, was in conflict with a few sentences in the Old Testament that talk about the sun moving across the sky and do not say that it was the spinning of the Earth that made it appear that the sun was moving in the heavens) and sentenced him to permanent house arrest, and banned his books, and forbade him to publish anything ever again. As Darwin also could have told you, being a scientist is not for wimps.
The idea of experimental science took hold: “No longer were natural philosophers relying on nature to reveal its principles to casual observers.” Experimental science was rolling along pretty well by the time Isaac Newton arrived on the scene. “Newton’s achievements provided the paradigm that all subsequent science has followed.” Newton was The Man.
Dr. Weinberg’s short-list of the greatest scientists of all time reads “Galileo, Newton, Darwin, Einstein,” all world changers and earth shakers.
Dr. Weinberg points out that while it is perfectly possible for a person to be both very religious and very scientific (Newton was such a one), “It was essential for the discovery of science that religious ideas be divorced from the study of nature. Once one invokes the supernatural, anything can be explained, and no explanation can be verified.” So, scientists run into trouble with established religions. Along with the church’s pounding down of Galileo, we are told about Anaxagoras, who had to flee Athens after teaching that the sun is not a god but a physical object, and Hypatia, who was literally torn to pieces by a mob of good Christians for the unforgivable crimes of being a scientist, a mathematician, and, at the same time, a woman, a pagan, and hot. Dr. Weinberg also mentions fellow Nobel Prize winner Abdus Salaam, a devout Moslem, who, when he attempted to promote scientific research in the Islamic Middle East, was told that, for the Faithful, the study of science would be “culturally corrosive.” Whether Islam would benefit from cultural corrosion of this sort I will leave to the internet’s “comment” pages.
Particular pleasures:
Philosophers, natural and un-, have, figuratively speaking, been beating each other over the head with inflated pig bladders since day one. It’s a tradition that Dr. Weinberg gleefully joins in this book. Aristotle takes a drubbing throughout, but the chapter in which Dr. Weinberg disrespects Francis Bacon and Rene Descartes, was, by itself, worth the price of admission.
Disappointments:
Dr. Weinberg never does say which errors of the past are the ones that we might be repeating today. I guess we will just have to keep our guard up and hope for the best.
I had a half-formed hope that Dr. Weinberg, in this book subtitled “The Discovery of Modern Science,” would spell out just what was achieved, providing an explicit, concise, lucid, perhaps even poetic, description of, and users guide for, the scientific method, preferably one suitable for copying and pasting into every single internet discussion of evolution and global warming.
Dr. Weinberg did not do this. He seems happiest with a description of science as a rudderless chaos that sometimes manages to produce results in spite of itself, or as “a tangle of deduction, induction, and guesswork.” “We learn how to do science, not by making rules about how to do science, but from the experience of doing science.”
I have a tiny little small suspicion that Dr. Weinberg talks about science in this way in order to allow string theory to be classified as “science” rather than as “mathematical pastime.” But his description allows the most uninformed cranks in the universe to have as much right as anyone to claim that their conclusions are scientific, “Oh, yeah, we got a HUGE tangle of induction, deduction, reduction, convection and guesswork going on here ALL the time.”
No one should be led to suppose that science is whatever you happen to think, or something indefinable and unteachable. Putting it into practice requires discipline, desire and effort, but, despite all the long ages it took to formulate, the scientific method is not conceptually difficult. The basics can be explained, in detail, in an hour or two, after which the reasonably bright and attentive listener can perform a good approximation of thinking and acting like a scientist (Readers who feel they may need more information before saying “aye,” “nay,” or “eh” on this point are invited to read the technical footnote, below).
Ah, well, even if Dr. Weinberg had included a most excellent Junior Woodchuck’s guide to the scientific method in his book, I probably would have found myself disagreeing with him on several points. I will give his book 4.5 stars, to show that there are no hard feelings. End of book review.
Technical footnote:
The last third of To Explain the World is headed “Technical Notes.” This section is all math, designed to give the reader an idea of how the investigators mentioned in the book arrived at their results. It is not actually necessary to read this section in order to appreciate the book, but don’t let it scare you. When it is time to put, say, a cosine, to work, Dr. Weinberg explains what a cosine is, rather than assuming, as most writers will, that you took trig in high school, and, due to being some sort of mutant or something, actually remember it.
In a similar spirit, for the benefit of readers who had the proper response (“show me”) to the apparently controversial claim that the process of doing science can be defined and taught, for discussion I offer this sketch/outline of a description of that method by which science is done. The complete description would include consideration of:
Observation
Wonder or Puzzlement
Speculation - Here it is pointed out that no one needs to teach you how to speculate, speculation is a built-in feature of the human brain. Let it rip, let your brain make up its little stories that explain what you observed or suggest what might be done. Do not mistake any one of these stories for the truth, or anything like it, until it is supported by a considerable amount of reproducible physical evidence and can be shown to conflict with none,
Literature Search - Meant to be exhaustive. If you are investigating, say, the emerald ash borer, then, before you start making scientific pronouncements about the emerald ash borer you should know as much about the emerald ash borer as anyone in the world, including the emerald ash borer’s mom. If, on the other hand, your goal is to make pseudoscientific statements about the emerald ash borer on the internet or in congress, then you are free to remain utterly ignorant,
Hypothesis
Investigation – If you are doing experimental science you may be designing and doing experiments to obtain reproducible physical evidence relevant to the viability of a hypothesis, or you may be doing things to see if they work, or you may be trying things to see what happens. If you are doing descriptive science you may be doing dissections, going on an expedition or spending time with a telescope. If you are doing theoretical science you may be doing calculations that, if they look promising, will require experimental and observational support.
Conclusion - in the case of experimental science the likely conclusions are “the evidence supports the hypothesis” or “the evidence does not support the hypothesis” but “Wow, didn’t expect THAT!” is also possible.
Publication
Confrontation - All of your colleagues who are competent in your area are required to point out every weakness in your knowledge, method, results, reasoning and conclusions. You are not allowed to reply “Bite me.” It’s all for the good. If you don’t have an appreciable number of exceptionally bright and well-informed people telling the world where you went wrong, then probably no one is paying any attention to you. Remember that every scientific conclusion, even one that won the Nobel Prize, comes with the unspoken qualifier “until we know better,”
followed by
More Research – of course
All of this is carried on in the presence of a strong, continuous, conscious awareness that your basic tool is a limited, fallible, delusion-prone human brain, and, at any stage, from observation and speculation onward, you are most probably wrong. The goal is reliable inference, reliable conclusions, reliable description, with the hope that we will know things tomorrow that we don’t know today, we will understand things tomorrow that we don’t understand today, and we will be able to do things tomorrow that we can’t do today. Some people think it is fun.
on February 19, 2015
Author Steven Weinberg provides a comprehensive history of astronomy and physics from ancient times up to the time of Isaac Newton. Weinberg writes in a conversational tone, but nonetheless can be overly technical even though there are technical notes. On the positive side, the book covers the ancient times and middle ages quite well. On the downside, although this book is on the history of science, there was nothing on biology. And readers interested only in astronomy might be better off reading Recentering the Universe: The Radical Theories of Copernicus, Kepler, Galileo, and Newton by Ron Miller and Stargazers by Alan Chapman. Nonetheless, I recommend this book for readers interested in the history of physics and astronomy.
on April 22, 2015
I’m a bit of a pragmatist. My wife has probably heard me utter the words “form follows function” a million times. Something doesn’t have to be pretty for me to find it useful though I do appreciate good aesthetics. In fact, if something works well AND is nice looking then I’d say that pretty much rocks. But even if it’s “dog ugly” I won’t mind so long as it serves its purpose.
I think my love for science can be explained by this pragmatic outlook. Science works and it works pretty darn well. Whereas religion has tried (and failed) to explain the workings of the natural world, science has given us answers to many of the most perplexing questions we could ever ask. And those questions that we don’t quite have answers to yet, science is diligently working on.
This is the crux of Steve Weinberg’s latest book subtitled “The Discovery of Modern Science.” Within its pages, TO EXPLAIN THE WORLD seeks to paint a picture of how science has advanced in the last twenty-five hundred years. “Science is not now what it was at its start,” writes Weinberg. (xiii) Much of early science was philosophical and mathematical, relying more on abstract thinking than on empirical observation. Science rises and falls on data and as technology progressed so did science. (Or perhaps there is a tautology there!)
Weinberg begins with the ancient Greeks and tells, what he calls, an irreverent history that seeks to laud the successes of past thinkers and to correct them where they were wrong. (xii) Isaac Newton, the famed British scientist, is of particular interest in Weinberg’s work, taking up a significant portion of it (see chapter 14 – “The Newtonian Synthesis”). In all of this story telling, Weinberg points us to how science operates:
“We learn how to do science, not by making rules about how to do science, but from the experience of doing science, driven by desire for the pleasure we get when our methods succeed in explaining something.” (214)
Indeed, there is a rush when your model’s predictions come to pass like the prediction of left over heat from the Big Bang is found in the Cosmic Microwave Background or when the prediction of quantum tunneling becomes useful to see the subatomic world. Science’s success is a worthy tale to tell.
My favorite section of the book was a chapter focusing on the contributions of Arab scientists in the Middle Ages. Men like al-Biruni, an astronomer living during the Abbasid era, despised astrology and made attempts to calculate the radius of the Earth. Others like Ibn Sahl and al-Haitam made contributions to optics that Weinberg considers to be the greatest contribution the Arabs made in the field of physics. (110) Many of these men were Islamic in culture only, paying lip service to the religious leaders of their day. “Arab scientists in their golden age were not doing Islamic science. They were doing science.” (123)
This book is in no sense a definitive history of science. That isn’t its aim. But what this book does do is to give us an outline of the significant contributions that many have made from the pre-Socratics to the dawn of the Scientific Revolution and beyond. Of all the things humans have done, science ranks among the greatest. Weinberg’s book is a testament to that fact.
“So the world acts on us like a teaching machine, reinforcing our good ideas with moments of satisfaction. After centuries we learn what kinds of understanding are possible, and how to find them. We learn not to worry about purpose, because such worries never lead to the sort of delight we seek. We learn to abandon the search for certainty, because the explanations that make us happy never are certain. We learn to do experiments, not worrying about the artificiality of our arrangements. We develop an aesthetic sense that gives us clues to what theories will work, and that adds to our pleasure when they do work. Our understandings accumulate. It is all unplanned and unpredictable, but it leads to reliable knowledge, and gives us joy along the way.” (255)
So maybe I’m about more than just pragmatism. Maybe science gives a satisfaction few other enterprises can offer. Perhaps there is a direct relationship between our increase in knowledge and our increase in joy.
Perhaps science does give us joy along the way.
I think my love for science can be explained by this pragmatic outlook. Science works and it works pretty darn well. Whereas religion has tried (and failed) to explain the workings of the natural world, science has given us answers to many of the most perplexing questions we could ever ask. And those questions that we don’t quite have answers to yet, science is diligently working on.
This is the crux of Steve Weinberg’s latest book subtitled “The Discovery of Modern Science.” Within its pages, TO EXPLAIN THE WORLD seeks to paint a picture of how science has advanced in the last twenty-five hundred years. “Science is not now what it was at its start,” writes Weinberg. (xiii) Much of early science was philosophical and mathematical, relying more on abstract thinking than on empirical observation. Science rises and falls on data and as technology progressed so did science. (Or perhaps there is a tautology there!)
Weinberg begins with the ancient Greeks and tells, what he calls, an irreverent history that seeks to laud the successes of past thinkers and to correct them where they were wrong. (xii) Isaac Newton, the famed British scientist, is of particular interest in Weinberg’s work, taking up a significant portion of it (see chapter 14 – “The Newtonian Synthesis”). In all of this story telling, Weinberg points us to how science operates:
“We learn how to do science, not by making rules about how to do science, but from the experience of doing science, driven by desire for the pleasure we get when our methods succeed in explaining something.” (214)
Indeed, there is a rush when your model’s predictions come to pass like the prediction of left over heat from the Big Bang is found in the Cosmic Microwave Background or when the prediction of quantum tunneling becomes useful to see the subatomic world. Science’s success is a worthy tale to tell.
My favorite section of the book was a chapter focusing on the contributions of Arab scientists in the Middle Ages. Men like al-Biruni, an astronomer living during the Abbasid era, despised astrology and made attempts to calculate the radius of the Earth. Others like Ibn Sahl and al-Haitam made contributions to optics that Weinberg considers to be the greatest contribution the Arabs made in the field of physics. (110) Many of these men were Islamic in culture only, paying lip service to the religious leaders of their day. “Arab scientists in their golden age were not doing Islamic science. They were doing science.” (123)
This book is in no sense a definitive history of science. That isn’t its aim. But what this book does do is to give us an outline of the significant contributions that many have made from the pre-Socratics to the dawn of the Scientific Revolution and beyond. Of all the things humans have done, science ranks among the greatest. Weinberg’s book is a testament to that fact.
“So the world acts on us like a teaching machine, reinforcing our good ideas with moments of satisfaction. After centuries we learn what kinds of understanding are possible, and how to find them. We learn not to worry about purpose, because such worries never lead to the sort of delight we seek. We learn to abandon the search for certainty, because the explanations that make us happy never are certain. We learn to do experiments, not worrying about the artificiality of our arrangements. We develop an aesthetic sense that gives us clues to what theories will work, and that adds to our pleasure when they do work. Our understandings accumulate. It is all unplanned and unpredictable, but it leads to reliable knowledge, and gives us joy along the way.” (255)
So maybe I’m about more than just pragmatism. Maybe science gives a satisfaction few other enterprises can offer. Perhaps there is a direct relationship between our increase in knowledge and our increase in joy.
Perhaps science does give us joy along the way.
on March 5, 2015
What a privilege it was to spend time with Steven Weinberg as he explained the world in which we live. It was so much fun to visit with so many of the contributors of scientific thought. I feel that I have visited with Aristotle,Copernicus, Galileo , Kepler,and Newton to mention a few. This book is a treasure. Jack Kushner
on April 12, 2015
This is an excellent account not only of the history of the development of modern science but also of the discovery of how to do modern science, by one of the world’s outstanding living scientists. The book should be accessible to the reader without scientific training, but is also fascinating for those of us who are familiar with the basic concepts discussed but not with the details nor the societal context within which they were developed.
As with so many other things, the first people reasoning about the nature of things (beyond the primitive mythologies) were the Greeks of 600-500 BC. According to legend, Thales knew of geometry from Egypt and believed that the world is animate and full of divinities, and that water was the universal primary substance. Empedocles by the mid 400s BC had generalized this to four elements—water, air, earth and fire—and by the late 400s BC Democritus believed that matter consisted of tiny indivisible particles called atoms. Democritus’ teacher, Leucippus, believed “No thing happens in vain, but everything for a reason and by necessity”. Plato brought these four elements and atoms together, associating the atoms of each with a geometric shape, and Aristotle later added a fifth element, the ether that filled space above the moon.
Aristotle believed that terrestrial motion was determined by a body moving immediately to its proper location—earth below, then water, then air and finally fire above. He reasoned that there was a first cause for this terrestrial motion or change to enable things to be in their proper place and serve their proper purpose, whereas heavenly bodies move on spheres centered on the earth because a sphere was the most perfect shape, and the earth of course must be the center of everything.
This was the age of philosophy, and truth was found by reasoning—the idea of looking up to see if the heavenly bodies actually did circle around the earth or do an experiment to find out how something moves terrestrially certainly did not occur to anyone.
Aristotle said that the heavenly bodies must move on circles centered on the earth, and this became doctrine of the Roman catholic church, which from the fall of the Roman empire until the Reformation was the last word in all matters temporal as well as spiritual, in Europe. Small epi-circles on the larger spheres and even smaller epi-epi-circles on the epi-circles, with rotation at different speeds and in different directions, were allowed in order to fit the accumulating data by Eudoxus, Ptolemy and others. Ptolemy (150 AD) encapsulated this model of the solar system within an elaborate framework described in the Almagest in which the various spheresand “offsets” for the center of the sphere on which the body rotated about another larger body from the actual center of the body in question (planet, moon, etc.) were taken as free parameters to be adjusted to fit the heavenly observations, a practice scorned by the philosophers of the day as being “data-fitting” (to match observation) not “physics” (from reason alone in order to satisfy the body’s preordained “purpose”, and therefore to be preferred).
With the fall of the Roman Empire, midieval Europe indeed entered a dark age, and the philosophy and science of the Greeks was preserved, if not much advanced, in the countries of Islam, where it ultimately became viewed as dangerous to religious belief.
The author credits Copernicus (b 1473 AD in Poland) with beginning the scientific revolution, in Europe. Copernicus published an anonymous Commentariolus in about 1510 (only published in his name after his death) putting forward a belief that the sun, rather than the earth, was the center about which all the heavenly bodies except the moon rotated, and only the moon rotated about the earth. From this it followed that the apparent daily motion of stars around the earth was entirely due to the earth’s motion, and that the apparent motion of the sun and planets arose jointly from the earth’s revolution about its axis and partly from the earth’s revolution about the sun, like that of the other planets. In other words, men (at least the few of those looking) were viewing the heavens from a moving, revolving point, not a fixed point. This was indeed a revolutionary viewpoint, and one with which Copernicus wisely did not associate himself publically, given the fate of burning at the stake imposed a few years later on the Italian philosopher Giordano Bruno by the Roman Inquisition for holding such views. Copernicus published the details of his system in De Revolutionibus only as he lay on his deathbed in 1543.
Although vigorously opposed by the Catholic church and opposed less venomously by the Protestant church, Copernicus’ system was much simpler than Ptolemy’s and quickly gained acceptance among astronomers and mathematicians who set about devising mathematical transformations of the theory of Copernicus to one in which the earth rather than the sun is stationary, most prominent of whom was the Dane Tycho Brahe, an extraordinarily proficient astronomical observer. The Austrian mathematician Johannes Kepler, who was influenced by Copernicus, conjectured that each of the heavenly spheres just fits inside one of the five regular polyhedrons, but after trying for years to reconcile this with Brahe’s huge collection of planetary observations, abandoned this heavenly spheres assumption of Plato, Aristotle, Ptolemy, Copernicus and Brahe that planets move on circles and concluded from the observations that planets move on ellipses. Kepler then went on to pose three laws for planetary motion based on application of mathematics to Brahe’s observations.
The work of Copernicus and Kepler made the case for a sun-centered solar system rather than the Ptolemaic earth-centered system on the basis of mathematicsl simplicity, not on the ability to obtain a better match with observation—with enough adjustable parameters either system could be made to fit the data. The first observational evidence favoring the heliocentric (sun-centered) over the Ptolemiac (earth-centered) system was provided by the telescopic observations of Galileo Galilei, an Italian mathematician and astronomer born in 1564. Galileo made six historical astronomical discoveries that confirmed the Copernican earth-centered solar system: i) the light of the moon is sunlight reflected from the earth; ii) there were an inconceivable number of stars visible to the telescope that had never been visible before to the naked eye; iii) the stars, which could only be seen indistinctly, were much further away than the planets, which appeared as spheres; iv) the four moons of Jupiter that seem to revolve about it; v) the lunar-like phases of darkness and brightness of Venus; and vi) dark spots apparently moving across the sun are indications of its revolving.
In the meantime the Copernican solar system model was submitted to a panel of Catholic theologians by the Pope, which concluded that it was “foolish and absurd in Philosophy, and formally heretical inasmuch as it contradicts the express position of Holy Scripture in many places”, and Galileo was summoned to the Inquisition and received confidential orders not to hold or teach Copernicanism in any way.
Aristotle believed that terrestrial motion was determined by a body moving immediately to its proper location—earth below, then water, then air and finally fire above—and here the matter was left until the experimental study of terrestrial motion began with Galileo by timing the motion of balls down inclined planes since timing devices were not available to time bodies allowed to fall vertically. In 1656 Christian Huygens, a Dutch mathematician, invented the pendulum clock, based on Galileo’s observation that the time a pendulum takes for each swing is independent of the amplitude of the swing, which enabled him to calculate the acceleration of gravity and, presumably by observing the impact of swinging pendulums, to infer the laws of conservation of momentum and kinetic energy and to calculate the acceleration associated with motion on a curved path. Huygens thus refuted Aristotle and set the stage for Newton to bring the Scientific Revolution to its climax.
Isaac Newton, an Englishman born in 1642, crossed the boundary between the natural philosophers, mathematicians and astronomical observers who had gone before and the modern scientist of today. His early work was on optics and demonstrated experimentally that white light is made up of light of all colors, each of which is bent a different amount when crossing an interface between different media. Newton also made a major advance in astronomy by inventing the reflecting telescope, but his great contribution was the synthesis from observation and mathematical calculation (he also invented the math—calculus) of a common theory of motion for celestial and terrestrial bodies as published in his Principia. A great contribution of the present book is to explain the Principia, which was written in Latin, translated into the English of several centuries ago, and argued mainly in geometry. Eventually Newton’s concept of scientific method prevailed because it provided universal principals, based on experimental observation and mathematical analysis, that allowed successful calculation of a great deal that was observed, not because it satisfied a pre-existing metaphysical criterion for a scientific theory.
The author provides very interesting Technical Notes explaining how all these people from Aristotle to Newton actually calculated such things as the distance to the sun, the acceleration of gravity, etc. He treats later developments in science—electromagnetic theory, quantum mechanics, nuclear and elementary particle theory—in a brief epilogue. We can only hope that he decides to make it into a second volume at some point in the future.
As with so many other things, the first people reasoning about the nature of things (beyond the primitive mythologies) were the Greeks of 600-500 BC. According to legend, Thales knew of geometry from Egypt and believed that the world is animate and full of divinities, and that water was the universal primary substance. Empedocles by the mid 400s BC had generalized this to four elements—water, air, earth and fire—and by the late 400s BC Democritus believed that matter consisted of tiny indivisible particles called atoms. Democritus’ teacher, Leucippus, believed “No thing happens in vain, but everything for a reason and by necessity”. Plato brought these four elements and atoms together, associating the atoms of each with a geometric shape, and Aristotle later added a fifth element, the ether that filled space above the moon.
Aristotle believed that terrestrial motion was determined by a body moving immediately to its proper location—earth below, then water, then air and finally fire above. He reasoned that there was a first cause for this terrestrial motion or change to enable things to be in their proper place and serve their proper purpose, whereas heavenly bodies move on spheres centered on the earth because a sphere was the most perfect shape, and the earth of course must be the center of everything.
This was the age of philosophy, and truth was found by reasoning—the idea of looking up to see if the heavenly bodies actually did circle around the earth or do an experiment to find out how something moves terrestrially certainly did not occur to anyone.
Aristotle said that the heavenly bodies must move on circles centered on the earth, and this became doctrine of the Roman catholic church, which from the fall of the Roman empire until the Reformation was the last word in all matters temporal as well as spiritual, in Europe. Small epi-circles on the larger spheres and even smaller epi-epi-circles on the epi-circles, with rotation at different speeds and in different directions, were allowed in order to fit the accumulating data by Eudoxus, Ptolemy and others. Ptolemy (150 AD) encapsulated this model of the solar system within an elaborate framework described in the Almagest in which the various spheresand “offsets” for the center of the sphere on which the body rotated about another larger body from the actual center of the body in question (planet, moon, etc.) were taken as free parameters to be adjusted to fit the heavenly observations, a practice scorned by the philosophers of the day as being “data-fitting” (to match observation) not “physics” (from reason alone in order to satisfy the body’s preordained “purpose”, and therefore to be preferred).
With the fall of the Roman Empire, midieval Europe indeed entered a dark age, and the philosophy and science of the Greeks was preserved, if not much advanced, in the countries of Islam, where it ultimately became viewed as dangerous to religious belief.
The author credits Copernicus (b 1473 AD in Poland) with beginning the scientific revolution, in Europe. Copernicus published an anonymous Commentariolus in about 1510 (only published in his name after his death) putting forward a belief that the sun, rather than the earth, was the center about which all the heavenly bodies except the moon rotated, and only the moon rotated about the earth. From this it followed that the apparent daily motion of stars around the earth was entirely due to the earth’s motion, and that the apparent motion of the sun and planets arose jointly from the earth’s revolution about its axis and partly from the earth’s revolution about the sun, like that of the other planets. In other words, men (at least the few of those looking) were viewing the heavens from a moving, revolving point, not a fixed point. This was indeed a revolutionary viewpoint, and one with which Copernicus wisely did not associate himself publically, given the fate of burning at the stake imposed a few years later on the Italian philosopher Giordano Bruno by the Roman Inquisition for holding such views. Copernicus published the details of his system in De Revolutionibus only as he lay on his deathbed in 1543.
Although vigorously opposed by the Catholic church and opposed less venomously by the Protestant church, Copernicus’ system was much simpler than Ptolemy’s and quickly gained acceptance among astronomers and mathematicians who set about devising mathematical transformations of the theory of Copernicus to one in which the earth rather than the sun is stationary, most prominent of whom was the Dane Tycho Brahe, an extraordinarily proficient astronomical observer. The Austrian mathematician Johannes Kepler, who was influenced by Copernicus, conjectured that each of the heavenly spheres just fits inside one of the five regular polyhedrons, but after trying for years to reconcile this with Brahe’s huge collection of planetary observations, abandoned this heavenly spheres assumption of Plato, Aristotle, Ptolemy, Copernicus and Brahe that planets move on circles and concluded from the observations that planets move on ellipses. Kepler then went on to pose three laws for planetary motion based on application of mathematics to Brahe’s observations.
The work of Copernicus and Kepler made the case for a sun-centered solar system rather than the Ptolemaic earth-centered system on the basis of mathematicsl simplicity, not on the ability to obtain a better match with observation—with enough adjustable parameters either system could be made to fit the data. The first observational evidence favoring the heliocentric (sun-centered) over the Ptolemiac (earth-centered) system was provided by the telescopic observations of Galileo Galilei, an Italian mathematician and astronomer born in 1564. Galileo made six historical astronomical discoveries that confirmed the Copernican earth-centered solar system: i) the light of the moon is sunlight reflected from the earth; ii) there were an inconceivable number of stars visible to the telescope that had never been visible before to the naked eye; iii) the stars, which could only be seen indistinctly, were much further away than the planets, which appeared as spheres; iv) the four moons of Jupiter that seem to revolve about it; v) the lunar-like phases of darkness and brightness of Venus; and vi) dark spots apparently moving across the sun are indications of its revolving.
In the meantime the Copernican solar system model was submitted to a panel of Catholic theologians by the Pope, which concluded that it was “foolish and absurd in Philosophy, and formally heretical inasmuch as it contradicts the express position of Holy Scripture in many places”, and Galileo was summoned to the Inquisition and received confidential orders not to hold or teach Copernicanism in any way.
Aristotle believed that terrestrial motion was determined by a body moving immediately to its proper location—earth below, then water, then air and finally fire above—and here the matter was left until the experimental study of terrestrial motion began with Galileo by timing the motion of balls down inclined planes since timing devices were not available to time bodies allowed to fall vertically. In 1656 Christian Huygens, a Dutch mathematician, invented the pendulum clock, based on Galileo’s observation that the time a pendulum takes for each swing is independent of the amplitude of the swing, which enabled him to calculate the acceleration of gravity and, presumably by observing the impact of swinging pendulums, to infer the laws of conservation of momentum and kinetic energy and to calculate the acceleration associated with motion on a curved path. Huygens thus refuted Aristotle and set the stage for Newton to bring the Scientific Revolution to its climax.
Isaac Newton, an Englishman born in 1642, crossed the boundary between the natural philosophers, mathematicians and astronomical observers who had gone before and the modern scientist of today. His early work was on optics and demonstrated experimentally that white light is made up of light of all colors, each of which is bent a different amount when crossing an interface between different media. Newton also made a major advance in astronomy by inventing the reflecting telescope, but his great contribution was the synthesis from observation and mathematical calculation (he also invented the math—calculus) of a common theory of motion for celestial and terrestrial bodies as published in his Principia. A great contribution of the present book is to explain the Principia, which was written in Latin, translated into the English of several centuries ago, and argued mainly in geometry. Eventually Newton’s concept of scientific method prevailed because it provided universal principals, based on experimental observation and mathematical analysis, that allowed successful calculation of a great deal that was observed, not because it satisfied a pre-existing metaphysical criterion for a scientific theory.
The author provides very interesting Technical Notes explaining how all these people from Aristotle to Newton actually calculated such things as the distance to the sun, the acceleration of gravity, etc. He treats later developments in science—electromagnetic theory, quantum mechanics, nuclear and elementary particle theory—in a brief epilogue. We can only hope that he decides to make it into a second volume at some point in the future.
on March 14, 2015
This book is written for two levels of interest. First is for people such as I who are interested in general. Second is for those who want and understand the maths behind the history. Either will be pleased.
on August 7, 2015
Through some inexcusable oversight at summer camp, I saw Blues Brothers the very year it came out. I was not even a teenager. I thought it was the best car chase movie ever.
And I saw it again a couple years later, when my English was better and I was a little bit more mature (with the emphasis on “a little bit”) and I thought it was the best comedy ever.
And I saw it again in college and I realised it was a musical. A damn good musical at that.
I’m 47 now and things are the other way round. I’m probably a bit too old to be reading “To Explain the World.” But it’s three books in one, alright.
So what we have here is a truly FANTASTIC introduction to history of science and mechanics in particular. If your fifteen year old / sixteen year old thinks physics is boring, this book truly brings the subject alive. I remember, for example, how much I was bored by optics as a teenager, but Steven Weinberg had me hanging at the edge of my seat, because I needed to know how Galileo got around to looking at the stars. Honest!
Second, the book is a self-study guide. There’s a series of worked-out problems here that take you from the area of a circle (think of it as a bunch of triangles, basically, whose base is around the circumference) all the way to considering the moon as a falling object. If I’m 100% honest, this is the weaker part of the book, it’s only 4 stars in my opinion, but it’s all there as supporting evidence for the narrative and the problems are selected extremely carefully. It’s six stars in terms of how the problems were selected and three for how they were worked out.
Finally, this is a philosophy book with a twist in the tail!
Throughout the book there’s this recurring discussion about the “pure” Aristotelean view that the planets circle around the earth in spheres versus the “dirty” Ptolemaic view that employed epicycles to correctly predict the apparent motion of the heavens around the earth; you, the reader, are constantly reminded that neither’s right and the center of the solar system is the Sun. The entire book, basically feels like a setup, waiting for Kepler, Copernicus and Galileo to come in and set things straight.
But then comes the surprise, and stop reading now if you don’t want me to spoil it for you.
Weinberg never states it in so many words, but comes out batting for Ptolemy, the man whose theory actually EXPLAINED the world as he saw it. The fact that others came around later who explained the world better is a story to be discussed as and when they did so, and Weinberg tells it superbly. But of course the sun is not the center of the universe either, so score one for the guy who explained things best in his own times!
And I saw it again a couple years later, when my English was better and I was a little bit more mature (with the emphasis on “a little bit”) and I thought it was the best comedy ever.
And I saw it again in college and I realised it was a musical. A damn good musical at that.
I’m 47 now and things are the other way round. I’m probably a bit too old to be reading “To Explain the World.” But it’s three books in one, alright.
So what we have here is a truly FANTASTIC introduction to history of science and mechanics in particular. If your fifteen year old / sixteen year old thinks physics is boring, this book truly brings the subject alive. I remember, for example, how much I was bored by optics as a teenager, but Steven Weinberg had me hanging at the edge of my seat, because I needed to know how Galileo got around to looking at the stars. Honest!
Second, the book is a self-study guide. There’s a series of worked-out problems here that take you from the area of a circle (think of it as a bunch of triangles, basically, whose base is around the circumference) all the way to considering the moon as a falling object. If I’m 100% honest, this is the weaker part of the book, it’s only 4 stars in my opinion, but it’s all there as supporting evidence for the narrative and the problems are selected extremely carefully. It’s six stars in terms of how the problems were selected and three for how they were worked out.
Finally, this is a philosophy book with a twist in the tail!
Throughout the book there’s this recurring discussion about the “pure” Aristotelean view that the planets circle around the earth in spheres versus the “dirty” Ptolemaic view that employed epicycles to correctly predict the apparent motion of the heavens around the earth; you, the reader, are constantly reminded that neither’s right and the center of the solar system is the Sun. The entire book, basically feels like a setup, waiting for Kepler, Copernicus and Galileo to come in and set things straight.
But then comes the surprise, and stop reading now if you don’t want me to spoil it for you.
Weinberg never states it in so many words, but comes out batting for Ptolemy, the man whose theory actually EXPLAINED the world as he saw it. The fact that others came around later who explained the world better is a story to be discussed as and when they did so, and Weinberg tells it superbly. But of course the sun is not the center of the universe either, so score one for the guy who explained things best in his own times!
on May 3, 2015
To Explain The World is a decent but unspectacular review of the history of science by Steven Weinberg, a Nobel Prize Laureate in physics (1979). The book does not go into as much depth as many readers will expect from someone with such prolific scientific credentials. As another reviewer put it, a little harshly, this is basically a long Wikipedia entry.
The best part of the book was Weinberg's somewhat more technical description (p.271) which ran about 100 pages long. A useful book, but primarily to those with a limted scientific background.
The best part of the book was Weinberg's somewhat more technical description (p.271) which ran about 100 pages long. A useful book, but primarily to those with a limted scientific background.
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