Isaac Newton
*Biography*
The great English physicist, mathematician and astronomer.
The author of the fundamental work "Mathematical Principles of Natural Philosophy" (Latin: Philosophiae Naturalis Principia Mathematica), in which he described the law of universal gravitation and the so called Newton's Laws, which laid the foundations of classical mechanics.
He developed differential and integral calculus, color theory, and many other mathematical and physical theories.
Isaac Newton, the son of a small but well to do farmer, was born in the village of Woolsthorpe (Lincolnshire), in the year of Galileo's death and on the eve of the Civil War.
Newton's father did not live to see the birth of his son.
The boy was born sickly, prematurely, but still survived and lived for 84 years.
The fact of being born on Christmas Eve, Newton considered a special sign of fate.
The boy's patron was his maternal uncle, William Ayscough.
After graduating from school (1661), Newton entered Trinity College (College of the Holy Trinity), Cambridge University.
Even then, his powerful character was formed — scientific meticulousness, the desire to get to the point, intolerance of deception and oppression, indifference to public fame.
As a child, Newton, according to contemporaries, was closed and isolated, loved to read and make technical toys: a clock, a mill, etc.
Apparently, the physicists: Galileo, Descartes and Kepler were the most scientific support and inspirers of Newton's work.
Newton completed their works by combining them into a universal system of the world.
Other mathematicians and physicists had a smaller but significant influence: Euclid, Fermat, Huygens, Mercator, Wallis.
Of course, the enormous influence of his direct teacher Barrow should not be underestimated.
It seems that Newton made a significant part of his mathematical discoveries as a student, in the "plague years" of 1664-1666.
At the age of 23, he was already fluent in the methods of differential and integral calculus, including the decomposition of functions into series and what was later called Newton's Leibniz formula.
At the same time, according to him, he discovered the law of universal gravitation, or rather, he was convinced that this law follows from Kepler's third law.
In addition, during these years, Newton proved that white is a mixture of colors, derived the formula "Newton's binomial" for an arbitrary rational indicator (including negative ones), etc.
All these epoch making discoveries were published 20-40 years later than they were made.
Newton was not chasing fame.
The desire to discover the truth was his main goal.
1667: the plague epidemic recedes, and Newton returns to Cambridge.
He was elected a fellow of Trinity College, and in 1668 became a master.
In 1669, Newton was elected professor of mathematics, Barrow's successor.
Barrow sends to London Newton's essay "Analysis by means of equations with an infinite number of terms", which contained a concise summary of some of his most important discoveries in analysis.
It has gained some fame in England and abroad.
Newton is preparing a full version of this work, but it is not possible to find a publisher.
It was published only in 1711.
Experiments on optics and color theory are continuing.
Newton investigates spherical and chromatic aberrations.
To minimize them, he builds a mixed telescope reflector (a lens and a concave spherical mirror that he polishes himself).
He is seriously interested in alchemy, conducts a lot of chemical experiments.
1672: demonstration of the reflector in London — universal rave reviews.
Newton becomes famous and is elected a member of the Royal Society (British Academy of Sciences).
Later, improved reflectors of this design became the main tools of astronomers, with their help other galaxies, redshift, etc. were discovered.
There is a controversy about the nature of light with Hooke, Huygens and others.
Newton makes a vow for the future: do not get involved in scientific disputes.
1680: Newton receives a letter from Hooke with the formulation of the law of universal gravitation, which, according to the former, served as the reason for his work on determining planetary movements (although later postponed for some time), which formed the subject of "Principles".
Subsequently, Newton, for some reason, perhaps suspecting Hooke of illegally borrowing some earlier results of Newton himself, does not want to recognize any merits of Hooke here, but then agrees to do so, although rather reluctantly and not completely.
1684-1686: work on the "Mathematical Principles of Natural Philosophy" (the entire three volume book was published in 1687).
World fame and fierce criticism of the Cartesians come: the law of universal gravitation introduces a long range action that is incompatible with the principles of Descartes.
1696: By Royal Decree, Newton was appointed caretaker of the Mint (since 1699 — director).
He is vigorously pursuing monetary reform, restoring confidence in the thoroughly launched British monetary system by his predecessors.
1699: the beginning of an open priority dispute with Leibniz, in which even the reigning personages were involved.
This absurd feud between the two geniuses cost science dearly — the English mathematical school soon withered for a whole century, and the European school ignored many of Newton's outstanding ideas, rediscovering them much later.
On the continent, Newton was accused of stealing the results of Hooke, Leibniz and the astronomer Flamsteed, as well as of heresy.
The conflict was not extinguished even by the death of Leibniz (1716).
1703: Newton is elected president of the Royal Society, which he ruled for twenty years.
1705: Queen Anne raises Newton to knighthood.
He is now Sir Isaac Newton.
For the first time in English history, the title of knight was awarded for scientific merits.
Newton devoted the last years of his life to writing the "Chronology of the Ancient Kingdoms", which he was engaged in for about 40 years, and preparing the third edition of the "Beginnings".
In 1725, Newton's health began to deteriorate noticeably (stone disease), and he moved to Kensington near London, where he died at night, in his sleep, on March 20 (31), 1727.
The inscription on his grave reads:
Here lies Sir Isaac Newton, a nobleman who, with an almost divine mind, was the first to prove with the torch of mathematics the motion of the planets, the paths of comets and the tides of the oceans.
He investigated the difference in light rays and the different properties of colors that appear at the same time, which no one had previously suspected.
A diligent, wise and faithful interpreter of nature, antiquity and Holy Scripture, he affirmed the greatness of Almighty God with his philosophy, and expressed the simplicity of the Gospel with his disposition.
Let mortals rejoice that there was such an ornament of the human race.
In honor of Newton, they are named:
craters on the Moon and on Mars;
the unit of force in the SI system.
On the statue erected to Newton in 1755 at Trinity College, verses from Lucretius are carved:
Qui genus humanum ingenio superavit (He surpassed the human race in intelligence)
Scientific activity
A new era in physics and mathematics is connected with the works of Newton.
Powerful analytical methods appear in mathematics, there is an outbreak in the development of analysis and mathematical physics.
In physics, the main method of studying nature is the construction of adequate mathematical models of natural processes and the intensive study of these models with the systematic involvement of all the power of the new mathematical apparatus.
Subsequent centuries have proved the exceptional fruitfulness of this approach.
According to A. Einstein, "Newton was the first who tried to formulate elementary laws that determine the time course of a wide class of processes in nature with a high degree of completeness and accuracy" and "... had a deep and strong influence on the whole worldview through his works".
Mathematical analysis
Newton developed differential and integral calculus simultaneously with G. Leibniz (a little earlier) and independently of him.
Before Newton, actions with infinitesimals were not linked into a single theory and had the character of scattered ingenious techniques (see the Method of Indivisible Ones), at least there was no published systematic formulation and the power of analytical techniques for solving such complex problems as the problems of celestial mechanics in their entirety was not sufficiently revealed.
The creation of mathematical analysis reduces the solution of the corresponding problems, to a large extent, to the technical level.
A complex of concepts, operations and symbols appeared, which became the starting point for the further development of mathematics.
The next, the XVIII century, became the century of rapid and extremely successful development of analytical methods.
Apparently, Newton came to the idea of analysis through difference methods, which he studied a lot and deeply.
True, in his" Principles " Newton almost did not use infinitesimals, adhering to the ancient (geometric) methods of proof, but in other works he used them freely.
The starting point for differential and integral calculus was the work of Cavalieri and especially Fermat, who was already able (for algebraic curves) to draw tangents, find extremes, inflection points and curvature of a curve, calculate the area of its segment.
Among other predecessors, Newton himself named Wallis, Barrow and the Scottish astronomer James Gregory.
There was no concept of a function yet, he interpreted all curves kinematically as the trajectories of a moving point.
Even as a student, Newton realized that differentiation and integration are mutually inverse operations (apparently, the first published work containing this result in the form of a detailed analysis of the duality of the area problem and the tangent problem belongs to Newton's teacher Barrow).
For almost 30 years, Newton did not bother to publish his version of the analysis, although in letters (in particular, to Leibniz) he willingly shares many of the achievements.
Meanwhile, Leibniz's version has been widely and openly distributed throughout Europe since 1676.
It was only in 1693 that the first exposition of Newton's version appeared — in the form of an appendix to Wallis '"Treatise on Algebra".
We have to admit that the terminology and symbols of Newton compared leibnizens quite clumsy: fluxion (the derivative), fluent (primitive), the moment magnitude (differential), etc.
Preserved only in mathematics, the Newtonian symbol "o" for an infinitesimal dt (however, this letter in the same sense used previously Gregory), and even dot above the letter as a symbol of a time derivative.
Newton published a fairly complete statement of the principles of analysis only in the work "On the quadrature of curves" (1704), an appendix to his monograph "Optics".
Almost all of the material presented was ready back in the 1670s and 1680s, but only now Gregory and Halley persuaded Newton to publish a work that, 40 years late, became Newton's first printed work on analysis.
Here, Newton's derivatives of higher orders appear, the values of integrals of various rational and irrational functions are found, examples of solving differential equations of the 1st order are given.
1711: finally published, after 40 years, "Analysis using equations with an infinite number of terms".
Newton explores both algebraic and "mechanical" curves (cycloid, quadrature) with equal ease.
Partial derivatives appear, but for some reason there is no rule for differentiating fractions and complex functions, although Newton knew them; however, Leibniz had already published them at that time.
In the same year, the "Method of Differences" was published, where Newton proposed an interpolation formula for drawing through (n + 1) data points with equally spaced or unequally spaced abscissas of a parabolic curve of the nth order.
This is the difference analogue of the Taylor formula.
1736: the final work "The Method of fluxes and infinite Series" is published posthumously, significantly advanced compared to "Analysis using equations".
Numerous examples of finding extremums, tangents and normals, calculating radii and centers of curvature in Cartesian and polar coordinates, finding inflection points, etc. are given.
In the same work, quadratures and straightening of various curves are made.
It should be noted that Newton not only developed the analysis quite fully, but also made an attempt to strictly substantiate its principles.
If Leibniz was inclined to the idea of actual infinitesimals, then Newton proposed (in the "Principles") the general theory of limit transitions, which he somewhat ornately called "the method of first and last relations".
It is the modern term "limes" that is used, although there is no clear description of the essence of this term, implying an intuitive understanding.
The theory of limits is set out in 11 lemmas of Book I of the Principles; there is also one lemma in book II.
There is no arithmetic of limits, there is no proof of the uniqueness of the limit, its connection with infinitesimals is not revealed.
However, Newton rightly points to bo?the greater rigor of this approach compared to the "rough" method of indivisible ones.
Nevertheless, in book II, by introducing moments (differentials), Newton again confuses the matter, in fact considering them as actual infinitesimals.
Other mathematical achievements
Newton made his first mathematical discoveries while still a student: the classification of algebraic curves of the 3rd order (Fermat studied curves of the 2nd order) and the binomial decomposition of an arbitrary (not necessarily integer) degree, from which the Newtonian theory of infinite series begins — a new and powerful tool for analysis.
Newton considered series expansion to be the main and general method of analyzing functions, and in this case he reached the heights of mastery.
He used series to calculate tables, solve equations (including differential ones), and study the behavior of functions.
Newton was able to obtain a decomposition for all the standard functions at that time.
In 1707, the book "Universal Arithmetic"was published.
It presents a variety of numerical methods.
Newton always paid great attention to the approximate solution of equations.
The famous Newton's method made it possible to find the roots of equations with previously unthinkable speed and accuracy (published in Wallis ' Algebra, 1685).
The modern form of Newton's iterative method was given by Joseph Raphson (1690).
It is noteworthy that Newton was not interested in number theory at all.
Apparently, physics was much closer to mathematics to him.
The theory of gravity
The very idea of the universal force of gravity was repeatedly expressed before Newton.
Earlier, Epicurus, Kepler, Descartes, Huygens, Hooke and others thought about it.
Kepler believed that gravity is inversely proportional to the distance to the Sun and propagates only in the plane of the ecliptic; Descartes considered it the result of vortices in the ether.
There were, however, guesses with the correct formula (Bulliald, Rehn, Hooke), and even quite seriously justified (by correlating the Huygens centrifugal force formula and Kepler's third law for circular orbits).
But before Newton, no one was able to clearly and mathematically prove the law of gravitation (si lu, inversely proportional to the square of the distance) and the laws of planetary motion (Kepler's laws).
It is important to note that Newton published not just a supposed formula for the law of universal gravitation, but actually proposed a complete mathematical model in the context of a well developed, complete, explicitly formulated and systematically stated approach to mechanics:
the law of gravity;
the law of motion (Newton's 2nd law);
a system of methods for mathematical research (mathematical analysis).
Together, this triad is sufficient for a complete study of the most complex movements of celestial bodies, thereby creating the foundations of celestial mechanics.
Before Einstein, no fundamental amendments to this model were needed, although the mathematical apparatus was very much developed.
The Newtonian theory of gravity has caused many years of debate and criticism of the concept of long range action.
The first argument in favor of the Newtonian model was the strict conclusion of Kepler's empirical laws on its basis.
The next step was the theory of the motion of comets and the Moon, set out in the"Principles".
Later, with the help of Newtonian gravity, all the observed movements of celestial bodies were explained with high accuracy; this is a great merit of Clareau and Laplace.
The first observed corrections to Newton's theory in astronomy (explained by GR) were discovered only more than 200 years later (the displacement of the perihelion of Mercury).
However, they are also very small within the Solar system.
Newton also discovered the cause of tides: the attraction of the Moon (even Galileo considered tides to be a centrifugal effect).
Moreover, after processing long term data on the height of the tides, he calculated the mass of the Moon with good accuracy.
Another consequence of gravity was the precession of the Earth's axis.
Newton found out that due to the flatness of the Earth at the poles, the Earth's axis under the influence of the attraction of the Moon and the Sun performs a constant slow displacement with a period of 26,000 years.
Thus, the ancient problem of "pre equinoxes" (first noted by Hipparchus) has found a scientific explanation.
Optics and theory of light
Newton made fundamental discoveries in optics.
He built the first mirror telescope (reflector), in which, unlike purely lens telescopes, there was no chromatic aberration.
He also discovered the dispersion of light, showed that white light decomposes into rainbow colors due to the different refraction of rays of different colors when passing through a prism, and laid the foundations of a correct color theory.
During this period, there were many speculative theories of light and chromaticity; mainly the point of view of Aristotle ("different colors are a mixture of light and darkness in different proportions") and Descartes ("different colors are created when light particles rotate at different speeds") fought.
Hooke in his" Micrography " (1665) offered a variant of Aristotelian views.
Many believed that color is an attribute not of light, but of an illuminated object.
The general discord was aggravated by a cascade of discoveries of the XVII century: diffraction (1665, Grimaldi), interference (1665, Hooke), double refraction (1670, Erasmus Bartholin, studied by Huygens), estimation of the speed of light (1675, Roemer), significant improvement of telescopes.
There was no theory of light compatible with all these facts.
In his speech to the Royal Society, Newton refuted both Aristotle and Descartes, and convincingly proved that white light is not primary, but consists of colored components with different angles of refraction.
These components are the primary ones — Newton could not change their color by any tricks.
Thus, the subjective sense of color received a solid objective base — the refractive index.
Newton created a mathematical theory of interference rings discovered by Hooke, which have since been called "Newton's Rings".
In 1689, Newton stopped research in the field of optics — according to a common legend, he swore not to print anything in this field during the life of Hooke, who constantly pestered Newton with the latter's painfully perceived criticism.
In any case, in 1704, the year after Hooke's death, the monograph "Optics"was published.
During the life of the author, "Optics", like" Beginnings", went through three editions and many translations.
The first book of the monograph contained the principles of geometric optics, the doctrine of the dispersion of light and the composition of white color with various applications.
Book two: Interference of light in thin plates.
Book three: Diffraction and polarization of light.
Newton explained the polarization at double refraction closer to the truth than Huygens (a supporter of the wave nature of light), although the explanation of the phenomenon itself is unsuccessful, in the spirit of the emission theory of light.
Newton is often considered a proponent of the corpuscular theory of light; in fact, he, as usual, "did not invent hypotheses" and readily admitted that light could also be associated with waves in the ether.
In his monograph, Newton described in detail the mathematical model of light phenomena, leaving aside the question of the physical carrier of light.
Other works in physics
Newton is the author of the first derivation of the speed of sound in a gas, based on Boyle Marriott's law.
He predicted the flatness of the Earth at the poles, approximately 1:230.
At the same time, Newton used a model of a homogeneous liquid to describe the Earth, applied the law of universal gravitation and took into account the centrifugal force.
At the same time, Huygens performed similar calculations on similar grounds, considered gravity as if its source was located in the center of the planet, since, apparently, he did not believe in the universal nature of the gravitational force, that is, in the end, he did not take into account the gravity of the deformed surface layer of the planet.
Accordingly, Huygens predicted more than half the compression than Newton, 1:576.
Moreover, Cassini and other Cartesians proved that the Earth is not compressed, but convex at the poles like a lemon.
Subsequently, although not immediately (the first measurements were inaccurate), direct measurements (Clerault, 1743) confirmed Newton's correctness; the real compression is 1:298.
The reason for the difference between this value and the Huygens value proposed by Newton is that the model of a homogeneous liquid is still not completely accurate (the density increases noticeably with depth).
A more precise theory, which explicitly takes into account the dependence of density on depth, was developed only in the XIX century.
Other works
In parallel with the research that laid the foundation of the current scientific (physical and mathematical) tradition, Newton devoted a lot of time to alchemy, as well as theology.
He did not publish any works on alchemy, and the only known result of this long term hobby was the serious poisoning of Newton in 1691.
It is paradoxical that Newton, who worked for many years at the College of the Holy Trinity, apparently did not believe in the Trinity himself.
Researchers of his theological works, such as L. Mohr, believe that Newton's religious views were close to Arianism.
Newton proposed his own version of the biblical chronology, leaving behind a significant number of manuscripts on these issues.
He also wrote a commentary on the Apocalypse.
Newton's theological manuscripts are now kept in the National Library in Jerusalem.
The Secret Works of Isaac Newton
As you know, shortly before the end of his life, Isaac refuted all the theories put forward by himself and burned the documents that contained the secret of their refutation: some did not doubt that everything was exactly like that, while others believe that such actions would be simply absurd and claim that the archive with the documents is intact, but only belongs to the chosen ones...
