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The Magic of Numbers (Dover Books on Mathematics) by Bell, Eric Temple (2011) Paperback
In this stimulating, thought-provoking book, one of the foremost interpreters for laymen of the history and meaning of mathematics invites readers to join him in probing the origins of mathematical thought to the modern era. Eric Temple Bell (1883-1960), a former professor of mathematics at California Institute of Technology and prolific author, combines a fascinating history of ideas with an engaging series of life stories of the brilliant thinkers who forged mathematical history.
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First published January 1, 1946
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About the author
Eric Temple Bell
54 books41 followersEric Temple Bell (February 7, 1883 – December 21, 1960) was a mathematician and science fiction author born in Scotland who lived in the U.S. for most of his life. He published his non-fiction under his given name and his fiction as John Taine.
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Displaying 1 - 8 of 8 reviews
October 27, 2022
This is not a great book, and it is not a very good book either, but at least it's an interesting book. Bell seems willing to put up with a lot of divergent ideas but boy oh boy he hates the Gnostics for some reason. So much that the book kind of stops for a page or two while he gets really insulting.
Anyhow, I know more about Pythagoras than I did before.
Anyhow, I know more about Pythagoras than I did before.
September 7, 2022
The historian of mathematics Eric Temple Bell achieved notoriety in 1937 with his somewhat cavalier though not particularly erudite popular staple, entitled Men of Mathematics. By the time of writing of the present work, The Magic of Numbers, he had acquired maturity and a perspective of his own on intellectual things – the man himself is very much in evidence here. But one should not allow oneself to be bowled over by his uncommonly crisp yet fluent prose, just as with the skeptical philosopher David Hume. All the latter manages in his Enquiries concerning human understanding and The principles of morals of 1777, over the genial work of his youth, A treatise of human nature (1739-1740), is to trot out a bevy of more polished sneers against traditional Christianity (as his editor of the standard edition from the Oxford University Press, L.A. Selby-Bigge, acknowledges). The same, however, cannot be alleged of Eric Temple Bell.
Bell’s view of the matter can be stated succinctly: Pythagoras’ greatest innovation was the very idea of quantitative experimentation; at the same time, his greatest failing was to succumb to religious nonsense – what Bell styles ‘the magic of numbers’ or ‘numerology’; e.g. coincidences, gematria etc. Indeed, he asseverates:
If only Pythagoras has not gone numerological, Greek science might have developed from such promising origins more rapidly than it did, and quite possibly would have accomplished much of lasting value. (p. 70) NB implying it didn’t in fact! Why? Even Archimedes never got to dynamics.
For the author, then, the disparity between the scientific and putative religious mindsets issues in a cosmic cataclysm:
Both science and numerology continue to thrive after twenty-five centuries of fighting each other, and neither as yet shows any evidence of being strong enough to destroy its hated rival. If numerical superiority counts for anything, active or potential believers in numerology outnumber believers in science thousands to one. In western civilization the numerology is not necessarily of the sorry fortune-telling variety, though in even the most advanced civilizations this prostituted arithmetic is common enough. It assures anyone who will adjust his conduct to his true Pythagorean number health and prosperity [vide etymology] in this life, to be followed by everlasting joy and felicity in the next. But in general, modern Pythagorean numerology is much more refined, and it may be an unintended slur to call it numerology at all. The more subtle manifestations of the ancient doctrine are disguised and occluded in those monumental philosophies that incorporated fragments of the Pythagorean ‘everything’ into their foundations. (pp. 75-76)
So numerology = accursed religion = including esp. the monotheistic faiths; its modern variety = what? = scientific cranks, as we see in following passage:
In science also the creed that everything is number has been successively refined to accommodate advancing sophistication. Today no reputable scientist would risk asserting that everything is number lest his colleagues think him queer. If he did have a secret hankering to restore number to its Pythagorean universality, he would not phrase his declaration of servitude to the past so bluntly. It would suffice – as it already has – to go back no farther than Plato, who is said to have asserted that ‘the deity ever geometrizes’. Without jeopardizing their scientific reputations, the modern Pythagoreans might profitably announce – as indeed Sir James Jeans did in 1930 – that ‘the Great Architect of the Universe now begins to appear as a pure mathematician’. This is a step ahead of ‘everything is number’, but only a step, for the mathematics applied to the architecture of the universe is based on numbers. Pythagoras would have understood this modernized version of his creed. He might even have certified the sublime truth it mayt express. (p. 76)
If he were around today, Bell would surely name inter alia Michio Kaku, Brian Greene, David Deutsch and above all Max Tegmark. Yet, cranks aside, Bell in a certain Baconian mode does identify a serious shortcoming associated with all human thought, viz., our cognitive biases that induce us to fasten upon stratagems by which to shirk hard mental effort:
The most enduring residue of Pythagorean numerology is only remotely connected with arithmetic. Briefly, it is the very human desire to find easy shortcuts to positive knowledge. (p. 77)
Numerology is the faith that the universe can be summed up and compressed through a single grand formula to a unified whole comprehensible by human beings. Thorough understanding of the one supreme generalization will make all the secrets of nature plain. The tyranny of time will then be overthrown, and man will become the undisputed master of his future….By the twentieth century ‘everything’ for Sir Arthur Eddington and his school had shrunk to mean only all the laws of the astronomical and physical sciences. But in its earlier forms the vision of knowledge included literally everything, from the heavens to the human emotions. When Pythagoras announced that everything is number he meant exactly that. (p. 77)
Indeed, Descartes, string theorists, virtually all western atheists subscribe to the creed so described. Now, has Bell discovered anything essentially new that was not, for instance, well known among the Jena circle of early German Romantics after circa 1794? For their immediate context [Anliegen] was an anti-foundationalist critique of Fichte’s Wissenschaftslehre. Hard to say, for Bell omits to engage his theme very philosophically at all. All the same, he will blare forth an edict of the following kind:
Probably no scientist today hopes to include this universal everything under the rubric of number. Others, the orthodox and immovable adherents of the ancient wisdom, do not need to hope. They are as certain as ever Pythagoras himself was that everything is number. (p. 77)
So, despite our low rating of Bell’s present work, there will be an occasional nugget to prompt reflection on the part of the attentive reader. Another would the following: if, for Bell, not everything is number, what else is there? Sorcery buttressed by relativism, as we shall see.
First off, Bell is an anti-Platonist and a dialectician with respect to the development of mathematical science. The determinative peripety in the entire history of western mathematics he locates in the celebrated discovery of the incommensurability of the diagonal of a square with its sides. For the sake of brevity, let us spell out the implications with a series of quotations
If a diagonal of a square whose side is one unit in length is not measureable by a ‘number’ – rational number that is – what ‘is’ it? The Greek geometers called it a ‘magnitude’, and constructed a theory of the ‘measurement’ of magnitudes in which, instead of appealing to the familiar natural numbers for sanction, they invoked spacial [sic] intuition. Rather than the Pythagorean declaration that ‘space is number’, the new creed might have asserted that ‘number is space’. (pp. 213-214)
The theory of measurement and comparison of magnitudes was capable – with certain amplifications – of giving a rational account of continuous motion. But, as often has been observed, the Greek genius was unsympathetic to the fluent and dynamic, preferring to impress itself on sharply distinct objects, each marked off from all the others by its finite completeness and perfection. In their geometry this predilection for the static as opposed to the dynamic produced a multitude of special theorems with no hint of a general principle unifying any considerable number of them in one synthesis [q.v. Descartes’ problematical methodology in his Geometry]. Modern geometry is only passively interested in individual theorems. What it seeks and finds are comprehensive generalizations from which any desired number of special theorems can be obtained by uniform processes. The distinction between the ancient approach and the modern has been compared to the difference between chiseling away a granite boulder a chip at a time and blasting it to fragments with a charge of dynamite. Another common simile likens Greek mathematics to the Parthenon and modern mathematics to a Gothic cathedral. The temple is an end of everything it represents, the cathedral suggests no cramped finality. (p. 217)
Before glancing at the kind of paradox which stopped the Greeks on the very threshold of modern mathematics we may note how Plato attempted to unify all numbers. The Pythagoreans had generated all natural numbers from the One or the Monad by the mystical union of the Odd and the Even, or what was numerologically equivalent, by the marriage of the Limited with the Unlimited. With the discovery of the irrationals the Pythagorean categories of the Odd and Even, Limited and Unlimited were no longer adequate to specify either ‘number’ or ‘space’. Instead of Number being in essence discrete, like a handful of pebbles, it was now essentially a continuum, like the atmosphere as reported by the senses. In this inseparable and uncountable whole the natural numbers and all other rational numbers were more sparsely scattered than the stars against the black of midnight. Desiring a unified substrate for the beautiful simplicity of the Pythagorean ‘Everything is number’, Plato sought an extended definition of Number which would comprehend both rationals and irrationals and which, moreover, would include them as numbers with no reliance on spacial intuition as in the ‘magnitudes’ of the mathematicians. Had he succeeded he might have anticipated at least a part of the modern theory of the continuum. (p. 218)
Zusammenfassung
For sure, Bell is not for beginners. His style tends to be quite viewy, as when he blames Zeno for the failure of the ancients to develop a calculus of the continuum and transfinitum (p. 224) and when he regales the reader with breezy summaries of history which unreflectingly presuppose his own prejudices: no rational argumentation anywhere, just bare assertion.
Now Bell’s approach (not so different, say from Nietzsche’s in Also sprach Zarathustra) might work if he were (like Nietzsche) at all original, but hardly any real mathematics or discussion of theorems, definitions, proofs etc. is to be found here. Bell is manifestly more an ideologist than a mathematician, as the student of intellectual history may gather from his analysis of Plato’s concept of the idea, which is not after all particularly deep, apart from an aside to the effect that the late Plato identifies his ideas with ideal numbers (p. 268-271). Here is what he tells us,
Plato’s theory of Ideas was completed in the fourth century BC. Why, the indifferent scientist may ask, should anyone in the twentieth century AD take it seriously?….Whether or not they are [long-defunct], no scientific mind of the reactionary twentieth century can dismiss the doctrine of Ideas as a negligible error of the past. The inveterate and implacable enemy of science is not dogmatic theology, as some scientists have supposed, but realism in the Platonic sense. (pp. 274-275)
Medieval realism does in fact strike this reviewer as a fascinating subject, revolving around differing modern versus ancient conceptions of the connection between epistemology and ontology. Unfortunate that Bell himself declines to explore it, after having so sententiously dismissed it. A promissory note: we shall return to medieval realism in future reviews! Again, p. 297: the mediaeval fraction of [Roger] Bacon’s mind bowed to astrology, the rest was free: a pithy contention but the actual situation was scarcely so simplistic [see David C. Lindberg, The Beginnings of Western Science: The European Scientific Tradition in Philosophical, Religious and Institutional Context, Prehistory to AD 1450, 2nd ed., University of Chicago Press (2007)]. In the same vein, Bell’s treatment of Galileo, Bruno and Newton descends into the increasingly shoddy, assertions without any documentation. In general, the present work may be faulted for fixating too much on biography and too little on philosophy. As a result, the quality of his thesis can only suffer and is to be adjudged nowhere near as insightful as what may readily be found in popular writings by Weyl, Poincaré etc.
What had been unthinkable before Saccheri constructed his geometries was to become the working creed of thousands whose business it is to think in order that others may act: the truths of mathematics and the mathematical formulations of the principle of science are of purely human origin; they are not eternal necessities but matters of human convenience. Neither in mathematics nor in science are there any absolutes. (p. 355)
The source of Lobachevsky’s total success was his ability to disbelieve something that seemed to be necessarily true and his capacity for implementing his disbelief. This flair for constructively doubting the traditionally obvious seems to be the rarest of all intellectual gifts. Whoever has it, and exercises his talent, usually achieves a revolution. (p. 359)
Bell’s greatest weakness is that he offers no arguments whatsoever against numerology, only invective. His fears of a return to Pythagoreanism (which is to be deplored) make little sense because his target is the astronomer Arthur Eddington, not greats such as Heisenberg, Schrödinger etc.; how could he have been taken in by the vogue of such a second rater? (Q.v. pp. 404-407-418.) Neither are the contemporary physicists with whom he engages towards the end of the book very memorable.
Therefore, a rating of 2 out of 5. The real evil faction among us comprises not those who, though professedly upholding science adhere to possibly false premises or theories, but those who reject science [scientia] and truth altogether. Etymology of truth: ME trewthe, treuthe, from OE trēowth, trīewth, akin to OHG getriuwida = fidelity, ON tryggth = faith, trustiness, derivative from the Indo-European root *h1sónt = the participial of *h1es- = to be, with certain connotations such as OE sōðian = to bear witness, prove true (as also NE soothsayer). Therefore, that which is true gives evidence of itself by causing knowledge of itself to exist, or in other words, knowledge is possible only on the basis of truth, metaphysical and theological. Hence, Bell contradicts himself; he wants, as it were, to be a relativist who denies truth yet also one who upholds science. How could we have a science of the non-existent? But the existent, as real, is knowable and so a potential subject of science.
Closing critical comment. Bell nevertheless raises a crucial question: what if Newton’s celebrated method of analysis and synthesis – not Pappus’ – were to fail? For Pappus’ method involves an ascent in the space of possible principles to the ideal summit and therefrom descent down to their exemplifications, while Newton’s, merely resolution of a given thing into small pieces followed by their re-aggregation. The former, thus, is conceptual in nature and cannot fail whereas the latter is merely quantitative. But – supposing the latter method equally valid in all cases, how then could we explain phenomena such as cohesion, entropy and hysteresis?
Bell’s view of the matter can be stated succinctly: Pythagoras’ greatest innovation was the very idea of quantitative experimentation; at the same time, his greatest failing was to succumb to religious nonsense – what Bell styles ‘the magic of numbers’ or ‘numerology’; e.g. coincidences, gematria etc. Indeed, he asseverates:
If only Pythagoras has not gone numerological, Greek science might have developed from such promising origins more rapidly than it did, and quite possibly would have accomplished much of lasting value. (p. 70) NB implying it didn’t in fact! Why? Even Archimedes never got to dynamics.
For the author, then, the disparity between the scientific and putative religious mindsets issues in a cosmic cataclysm:
Both science and numerology continue to thrive after twenty-five centuries of fighting each other, and neither as yet shows any evidence of being strong enough to destroy its hated rival. If numerical superiority counts for anything, active or potential believers in numerology outnumber believers in science thousands to one. In western civilization the numerology is not necessarily of the sorry fortune-telling variety, though in even the most advanced civilizations this prostituted arithmetic is common enough. It assures anyone who will adjust his conduct to his true Pythagorean number health and prosperity [vide etymology] in this life, to be followed by everlasting joy and felicity in the next. But in general, modern Pythagorean numerology is much more refined, and it may be an unintended slur to call it numerology at all. The more subtle manifestations of the ancient doctrine are disguised and occluded in those monumental philosophies that incorporated fragments of the Pythagorean ‘everything’ into their foundations. (pp. 75-76)
So numerology = accursed religion = including esp. the monotheistic faiths; its modern variety = what? = scientific cranks, as we see in following passage:
In science also the creed that everything is number has been successively refined to accommodate advancing sophistication. Today no reputable scientist would risk asserting that everything is number lest his colleagues think him queer. If he did have a secret hankering to restore number to its Pythagorean universality, he would not phrase his declaration of servitude to the past so bluntly. It would suffice – as it already has – to go back no farther than Plato, who is said to have asserted that ‘the deity ever geometrizes’. Without jeopardizing their scientific reputations, the modern Pythagoreans might profitably announce – as indeed Sir James Jeans did in 1930 – that ‘the Great Architect of the Universe now begins to appear as a pure mathematician’. This is a step ahead of ‘everything is number’, but only a step, for the mathematics applied to the architecture of the universe is based on numbers. Pythagoras would have understood this modernized version of his creed. He might even have certified the sublime truth it mayt express. (p. 76)
If he were around today, Bell would surely name inter alia Michio Kaku, Brian Greene, David Deutsch and above all Max Tegmark. Yet, cranks aside, Bell in a certain Baconian mode does identify a serious shortcoming associated with all human thought, viz., our cognitive biases that induce us to fasten upon stratagems by which to shirk hard mental effort:
The most enduring residue of Pythagorean numerology is only remotely connected with arithmetic. Briefly, it is the very human desire to find easy shortcuts to positive knowledge. (p. 77)
Numerology is the faith that the universe can be summed up and compressed through a single grand formula to a unified whole comprehensible by human beings. Thorough understanding of the one supreme generalization will make all the secrets of nature plain. The tyranny of time will then be overthrown, and man will become the undisputed master of his future….By the twentieth century ‘everything’ for Sir Arthur Eddington and his school had shrunk to mean only all the laws of the astronomical and physical sciences. But in its earlier forms the vision of knowledge included literally everything, from the heavens to the human emotions. When Pythagoras announced that everything is number he meant exactly that. (p. 77)
Indeed, Descartes, string theorists, virtually all western atheists subscribe to the creed so described. Now, has Bell discovered anything essentially new that was not, for instance, well known among the Jena circle of early German Romantics after circa 1794? For their immediate context [Anliegen] was an anti-foundationalist critique of Fichte’s Wissenschaftslehre. Hard to say, for Bell omits to engage his theme very philosophically at all. All the same, he will blare forth an edict of the following kind:
Probably no scientist today hopes to include this universal everything under the rubric of number. Others, the orthodox and immovable adherents of the ancient wisdom, do not need to hope. They are as certain as ever Pythagoras himself was that everything is number. (p. 77)
So, despite our low rating of Bell’s present work, there will be an occasional nugget to prompt reflection on the part of the attentive reader. Another would the following: if, for Bell, not everything is number, what else is there? Sorcery buttressed by relativism, as we shall see.
First off, Bell is an anti-Platonist and a dialectician with respect to the development of mathematical science. The determinative peripety in the entire history of western mathematics he locates in the celebrated discovery of the incommensurability of the diagonal of a square with its sides. For the sake of brevity, let us spell out the implications with a series of quotations
If a diagonal of a square whose side is one unit in length is not measureable by a ‘number’ – rational number that is – what ‘is’ it? The Greek geometers called it a ‘magnitude’, and constructed a theory of the ‘measurement’ of magnitudes in which, instead of appealing to the familiar natural numbers for sanction, they invoked spacial [sic] intuition. Rather than the Pythagorean declaration that ‘space is number’, the new creed might have asserted that ‘number is space’. (pp. 213-214)
The theory of measurement and comparison of magnitudes was capable – with certain amplifications – of giving a rational account of continuous motion. But, as often has been observed, the Greek genius was unsympathetic to the fluent and dynamic, preferring to impress itself on sharply distinct objects, each marked off from all the others by its finite completeness and perfection. In their geometry this predilection for the static as opposed to the dynamic produced a multitude of special theorems with no hint of a general principle unifying any considerable number of them in one synthesis [q.v. Descartes’ problematical methodology in his Geometry]. Modern geometry is only passively interested in individual theorems. What it seeks and finds are comprehensive generalizations from which any desired number of special theorems can be obtained by uniform processes. The distinction between the ancient approach and the modern has been compared to the difference between chiseling away a granite boulder a chip at a time and blasting it to fragments with a charge of dynamite. Another common simile likens Greek mathematics to the Parthenon and modern mathematics to a Gothic cathedral. The temple is an end of everything it represents, the cathedral suggests no cramped finality. (p. 217)
Before glancing at the kind of paradox which stopped the Greeks on the very threshold of modern mathematics we may note how Plato attempted to unify all numbers. The Pythagoreans had generated all natural numbers from the One or the Monad by the mystical union of the Odd and the Even, or what was numerologically equivalent, by the marriage of the Limited with the Unlimited. With the discovery of the irrationals the Pythagorean categories of the Odd and Even, Limited and Unlimited were no longer adequate to specify either ‘number’ or ‘space’. Instead of Number being in essence discrete, like a handful of pebbles, it was now essentially a continuum, like the atmosphere as reported by the senses. In this inseparable and uncountable whole the natural numbers and all other rational numbers were more sparsely scattered than the stars against the black of midnight. Desiring a unified substrate for the beautiful simplicity of the Pythagorean ‘Everything is number’, Plato sought an extended definition of Number which would comprehend both rationals and irrationals and which, moreover, would include them as numbers with no reliance on spacial intuition as in the ‘magnitudes’ of the mathematicians. Had he succeeded he might have anticipated at least a part of the modern theory of the continuum. (p. 218)
Zusammenfassung
For sure, Bell is not for beginners. His style tends to be quite viewy, as when he blames Zeno for the failure of the ancients to develop a calculus of the continuum and transfinitum (p. 224) and when he regales the reader with breezy summaries of history which unreflectingly presuppose his own prejudices: no rational argumentation anywhere, just bare assertion.
Now Bell’s approach (not so different, say from Nietzsche’s in Also sprach Zarathustra) might work if he were (like Nietzsche) at all original, but hardly any real mathematics or discussion of theorems, definitions, proofs etc. is to be found here. Bell is manifestly more an ideologist than a mathematician, as the student of intellectual history may gather from his analysis of Plato’s concept of the idea, which is not after all particularly deep, apart from an aside to the effect that the late Plato identifies his ideas with ideal numbers (p. 268-271). Here is what he tells us,
Plato’s theory of Ideas was completed in the fourth century BC. Why, the indifferent scientist may ask, should anyone in the twentieth century AD take it seriously?….Whether or not they are [long-defunct], no scientific mind of the reactionary twentieth century can dismiss the doctrine of Ideas as a negligible error of the past. The inveterate and implacable enemy of science is not dogmatic theology, as some scientists have supposed, but realism in the Platonic sense. (pp. 274-275)
Medieval realism does in fact strike this reviewer as a fascinating subject, revolving around differing modern versus ancient conceptions of the connection between epistemology and ontology. Unfortunate that Bell himself declines to explore it, after having so sententiously dismissed it. A promissory note: we shall return to medieval realism in future reviews! Again, p. 297: the mediaeval fraction of [Roger] Bacon’s mind bowed to astrology, the rest was free: a pithy contention but the actual situation was scarcely so simplistic [see David C. Lindberg, The Beginnings of Western Science: The European Scientific Tradition in Philosophical, Religious and Institutional Context, Prehistory to AD 1450, 2nd ed., University of Chicago Press (2007)]. In the same vein, Bell’s treatment of Galileo, Bruno and Newton descends into the increasingly shoddy, assertions without any documentation. In general, the present work may be faulted for fixating too much on biography and too little on philosophy. As a result, the quality of his thesis can only suffer and is to be adjudged nowhere near as insightful as what may readily be found in popular writings by Weyl, Poincaré etc.
What had been unthinkable before Saccheri constructed his geometries was to become the working creed of thousands whose business it is to think in order that others may act: the truths of mathematics and the mathematical formulations of the principle of science are of purely human origin; they are not eternal necessities but matters of human convenience. Neither in mathematics nor in science are there any absolutes. (p. 355)
The source of Lobachevsky’s total success was his ability to disbelieve something that seemed to be necessarily true and his capacity for implementing his disbelief. This flair for constructively doubting the traditionally obvious seems to be the rarest of all intellectual gifts. Whoever has it, and exercises his talent, usually achieves a revolution. (p. 359)
Bell’s greatest weakness is that he offers no arguments whatsoever against numerology, only invective. His fears of a return to Pythagoreanism (which is to be deplored) make little sense because his target is the astronomer Arthur Eddington, not greats such as Heisenberg, Schrödinger etc.; how could he have been taken in by the vogue of such a second rater? (Q.v. pp. 404-407-418.) Neither are the contemporary physicists with whom he engages towards the end of the book very memorable.
Therefore, a rating of 2 out of 5. The real evil faction among us comprises not those who, though professedly upholding science adhere to possibly false premises or theories, but those who reject science [scientia] and truth altogether. Etymology of truth: ME trewthe, treuthe, from OE trēowth, trīewth, akin to OHG getriuwida = fidelity, ON tryggth = faith, trustiness, derivative from the Indo-European root *h1sónt = the participial of *h1es- = to be, with certain connotations such as OE sōðian = to bear witness, prove true (as also NE soothsayer). Therefore, that which is true gives evidence of itself by causing knowledge of itself to exist, or in other words, knowledge is possible only on the basis of truth, metaphysical and theological. Hence, Bell contradicts himself; he wants, as it were, to be a relativist who denies truth yet also one who upholds science. How could we have a science of the non-existent? But the existent, as real, is knowable and so a potential subject of science.
Closing critical comment. Bell nevertheless raises a crucial question: what if Newton’s celebrated method of analysis and synthesis – not Pappus’ – were to fail? For Pappus’ method involves an ascent in the space of possible principles to the ideal summit and therefrom descent down to their exemplifications, while Newton’s, merely resolution of a given thing into small pieces followed by their re-aggregation. The former, thus, is conceptual in nature and cannot fail whereas the latter is merely quantitative. But – supposing the latter method equally valid in all cases, how then could we explain phenomena such as cohesion, entropy and hysteresis?
January 14, 2023
3-4-5
Not sure what to make of this book. Will have to re-read it again. Like a mystery thriller after reading, you have to read again to see the clues you missed the first time around.
It looks like some mixture of philosophy, religion, and science; all mixed up with numbers. Most of this hovers around Pythagoras who lived and died around 570–495 BCE. “ALL THINGS ARE NUMBER”
Not sure what to make of this book. Will have to re-read it again. Like a mystery thriller after reading, you have to read again to see the clues you missed the first time around.
It looks like some mixture of philosophy, religion, and science; all mixed up with numbers. Most of this hovers around Pythagoras who lived and died around 570–495 BCE. “ALL THINGS ARE NUMBER”
May 31, 2020
Тяжелая книга, видимо для понимания надо все таки иметь какой-то бекграунд.
Но были отдельные интересные места из жизни математиков и истории математики в целом.
Но были отдельные интересные места из жизни математиков и истории математики в целом.
July 28, 2024
Slow and fancy.
October 15, 2023
3-4-5
Not sure what to make of this book. Will have to re-read it again. Like a mystery thriller after reading, you have to read again to see the clues you missed the first time around.
It looks like some mixture of philosophy, religion, and science; all mixed up with numbers. Most of this hover around Pythagoras who lived and died around 570–495 BCE. “ALL THINGS ARE NUMBER”
Not sure what to make of this book. Will have to re-read it again. Like a mystery thriller after reading, you have to read again to see the clues you missed the first time around.
It looks like some mixture of philosophy, religion, and science; all mixed up with numbers. Most of this hover around Pythagoras who lived and died around 570–495 BCE. “ALL THINGS ARE NUMBER”
August 20, 2012
This is about Pythagarus and geometry with the bits of rumors and juicy tidbits of his "cult" in between. Think Euclidean vs non Euclidean thought patterns in regards to geometry and mathematics. e
December 24, 2024
The most interesting topics somehow explained in the most tedious, boring way possible. 3/5 stars for you !!!
Displaying 1 - 8 of 8 reviews