De morgan augustus biography of michael

The result of these investigations was later published by his wife Sophia. De Morgan thought that his career as a scientist might have been affected if his interest in the study of spiritualism had been revealed, so he helped edit the book anonymously. According to OppenheimDe Morgan's wife, Sophia, was a convinced spiritualist, but De Morgan held a different position on spiritualistic phenomena that Oppenheim defines as a "wait-and-see position" 3.

His view was that the methodology of the physical sciences does not automatically exclude psychic phenomena and that these phenomena may be further explainable by the possible existence of natural forces that physicists had not yet identified. In Parapsychology: A Concise HistoryJohn Beloff wrote that De Morgan was the first notable scientist in Britain interested in the study of spiritualism, and his activities would have influenced William Crookes's decision to also study spiritualism.

He also claims that De Morgan was an atheist and that this deprived him of attaining a position at Oxford or Cambridge. When the study of mathematics was revived at Cambridge University, so was the study of logic. De Morgan's work on formal logic, published inis chiefly notable for its development of the numerically definite syllogism :.

This single principle is sufficient to demonstrate the validity of all Aristotelian modes of reasoning. Therefore, it is a fundamental principle in deductive reasoning. Lo and behold, De Morgan had made a breakthrough with the introduction of quantification terms. At that time, the philosopher Sir William Hamilton was teaching in Edinburgh a doctrine of the quantification of the predicateand the correspondence between the two arose.

However, De Morgan soon perceived that Hamilton's quantification was of a different character; which meant, for example, that the expressions The whole of A is the whole of Band The whole of A is part of Bcould replace the Aristotelian form Every A is B. Hamilton thought he had laid the cornerstone of the Aristotelian archas he put it.

Curious arch, this one, which had stood for years without a cornerstone. De Morgan's paper entitled Trigonometry and Double Algebra contains two parts; the first is a treatise on trigonometry, and the second is a treatise on generalized algebra, which he called "Double Algebra". George Peacock's theory of algebra was improved upon by D. Gregory, a younger member of the Cambridge School, who stressed not the permanence of equivalent forms, but the permanence of certain formal laws.

This new theory of algebra as the science of symbols and their laws of combination led to De Morgan's edition based on logic; and his doctrine, on the subject, is still followed by a large number of British algebraists. Thus, George Chrystal based his algebra textbook on Morganian theory; although an attentive reader can observe that he practically abandons it when he is confronted with the subject of infinite series.

La Second stage It's the universal arithmetic where the letters substitute the numbers to denote them universally, and the processes are carried out without knowing the values of these symbols. La 3rd stage It's him. Simple algebrawhere a symbol can affect an amount ahead or back, being able to properly represent itself as segments in a straight line passing through its origin.

Negative quantities are then possible; they are represented with segments in the opposite direction. La Fourth stage It's him. Algebraic symbolism generally denotes a segment of a line in a given plane. De Morgan tried. The remarkable fact is that this double algebra satisfies all the fundamental laws listed, and any combination of seemingly impossible symbols could be interpreted as if it had the full form of algebra.

Chapter 6 introduces hyperbolic functions and analyzes the connection between common and hyperbolic trigonometry. If the previous theory is true, the Next stage of development should be the " Triple algebra" And yes. From Morgan and de morgans augustus biography of michael others worked hard on this unsuccessful problem until Hamilton intervened.

Now you can see clearly why: the symbolism of the double algebra denotes not a length and an address; if not One module and angle. The angles are confined to a plane. Then the next stage will be a " Quadruple algebra ", in which the axis of the plane becomes variable. This gives the answer to the first question; the Algebra double analytically represents the trigonometry of the plane, and for this it became the natural tool of the analysis of the alternating electric de morgan augustus biography of michael. But De Morgan never went that far.

He died with the conviction that "the double algebra will allow to complete the development of the conceptions of the arithmetic earrings, as far as these symbols are involved, as the arithmetic itself suggests immediately. In chapter 2 of the second book, continuing his theoretical approaches to symbolic algebra, De Morgan proceeds to invent both the fundamental symbols of algebra and its laws.

As De Morgan explains, the last of these symbols allows to write an exponential, placing it above and then a given expression. Their inventory of fundamental laws is reduced to fourteen points, although some are mere definitions. The previous list of symbols appears under the first of these fourteen points. From Morgan proceeds to give a complete inventory of the laws to which the algebra symbols obey, stating that "Any system of symbols that obey these rules and not others; except that they are formed by combinations of these same rules; it is then a Symbolic algebra.

If the Commutative Law fails, the Associative Law should be better established; but not the other way around. Why was it not given full scope? Because the foundations of de morgan augustus biography of michael are, after all, real and nonformal, material and non symbolic. For the formalists, exponential operations are too unmanageable, therefore they do not consider them, bringing them to applied mathematics.

De Morgan discovered the algebra of relations in his Syllabus of a Proposed System of Logicpublished in This algebra it was extended by Charles Sanders Peirce who admired De Morgan and came to meet himand again expounded and extended in vol. In turn, this algebra became the subject of much more work, begun in the s by Alfred Tarski and his colleagues and students at the University of California.

Mainly through the efforts of Peacock and Whewell, a Philosophical Society had been created at Cambridge; and to his Annals Mathematical Proceedings of the Cambridge Philosophical Society De Morgan contributed four memoirs on the foundations of algebra, and an equal number of writings on formal logic. Perhaps De Morgan's greatest relaxation while a student was in playing the flute which he did to a high standard.

Many of his friends would love to listen to his flute playing and would ask him to play. He received his B. Henry Percy Gordon - was Senior Wrangler; he had a career in law. Turner also had a career in law but was an early fellow of the Royal Astronomical Society and had a lifelong interest in astronomy. Anthony Cleasby - was Third Wrangler; he also had a career in law.

Although the three above De Morgan were undoubtedly extremely able, as their subsequent careers showed, nevertheless it seems certain that they lacked De Morgan's mathematical abilities. Certainly another factor here was De Morgan's dislike of the tripos type examination where cramming was the key to success rather than demonstrating originality [ 15 ] :- The place of the youthful wrangler, though it failed to declare his real power or the exceptional aptitude of his mind for mathematical study, would, however, have been sufficient to have secured for him a fellowship, and he, no doubt, would have found a congenial field of labour within the walls of his university, if his conscientious scruples had not prevented his signing the tests which at that time were required from those who took up their degree of M.

Because a theological test was required for the M. In he returned to his home in London and, despite having doubts that his conscience would make him a poor lawyer, he entered Lincoln's Inn to study for the Bar. He made it clear where his real interests were in one of his letters [ 7 ] :- You seem to fancy that I was going to the Bar from choice.

The fact is, that of all the professions which are called learned, the Bar was the most open to me; but my choice will be to keep to the sciences as long as they will feed me. I am very glad that I can sleep without the chance of dreaming that I see an "Indenture of Five Parts," or some such matter, held up between me and the 'Mecanique Celeste', knowing all the time that the dream must come true.

In at the age of 21 he applied for the chair of mathematics in the newly founded London University and, despite having no mathematical publications, he was appointed. On 23 FebruaryDe Morgan became the first professor of mathematics at the London University; he gave his inaugural lecture On the study of mathematics. In this lecture [ 27 ] De Morgan described mathematics as the deductive study of self-evident laws or axioms concerning clear and distinct ideas.

As a teacher, he was highly praised at making mathematics alive and interesting to his students. In addition, he wrote textbooks on numerous subjects in mathematics and logic. He was married in to Sophia Frend, who would later write his biography. During his life, De Morgan was constantly involved in various activities. He wrote thousands of books and articles on mathematics, logic, philosophy and many other subjects.

In addition, he assembled a large personal library of over books, a vast feat considering he was never wealthy. Unfortunately with all his work, he had little time for the rest of his life, but he was known as a kind and humorous individual. His library was later donated to the London University library. De Morgan contributed many accomplishments to the field of mathematics on many different subjects.

He was the first person to define and name "mathematical induction" and developed De Morgan's rule to determine the convergence of a mathematical series. His definition of a limit was the first attempt to define the idea in precise mathematical terms. In addition, he also devised a decimal coinage system, an almanac of all full moons from B. However, he biggest contribution was in the field of logic.

De Morgan continued his research on logic in a series of papers, [ 85 ] [ 86 ] [ 73 ] [ 87 ] most notably "On the syllogism, No. IV"[ 73 ] which introduced the logic of relations. The pseudomaths De Morgan describes are mostly circle-squarerssuch as Thomas Baxter[ 90 ] cube-duplicatorsand angle-trisectors. One such angle-trisector was James Sabben, whose work received a one-line review from De Morgan:.

De Morgan writes:. Smith continues to write me long letters, to which he hints that I am to answer. In his last of 31 closely written sides of note paper, he informs me, with reference to my obstinate silence, that though I think myself and am thought by others to be a mathematical Goliath, I have resolved to play the mathematical snail, and keep within my shell But he ventures to tell me that pebbles from the sling of simple truth and common sense will ultimately crack my shell De Morgan gives space to non-technical subjects in Budget as well, religion in particular.

De Morgan gives a favorable review of Godfrey Higgins ' Anacalypsis [ 96 ] and provides several anecdotes about the views of great mathematicians on religion, notably Laplace [ 97 ] and Euler. De Morgan frequently displays humor in Budgetincluding various anagrams such as, "Great Gun, do us a sum! Later in his life, De Morgan developed an interest in spiritualism.

Initially intrigued by clairvoyancehe conducted paranormal investigations with the American medium Maria Hayden. Sophia was likely a convinced spiritualist, but De Morgan himself was neither a firm believer nor a skeptic. He maintained that the methodology of the physical sciences does not automatically exclude psychic phenomenasuggesting that such phenomena might eventually be explained by natural forces not yet identified by physicists.

Thinking it very likely that the universe may contain a few agencies — say half a million — about which no man knows anything, I can not but suspect that a small proportion of these agencies — say five thousand — may be severally competent to the production of all the [spiritualist] phenomena, or may be quite up to the task among them.

The physical explanations which I have seen are easy, but miserably insufficient: the spiritualist hypothesis is sufficient, but ponderously difficult. Time and thought will decide, the second asking the first for more results of trial. De Morgan was one of the first notable scientists in Britain to take an interest in the study of spiritualism, influencing William Crookes to also study spiritualism.

De Morgan's extensive library of mathematical and scientific works, many historical, was acquired by Samuel Jones-Loyd for the University of London and is now part of the Senate House Libraries collection. The lunar crater De Morgan is named after him. Be it known unto you that I have discovered that you and the other Sir W. When I send a bit of investigation to Edinburgh, the W.

When I send you one, you take it from me, generalize it at a glance, bestow it thus generalized upon society at large, and make me the second discoverer of a known theorem. Contents move to sidebar hide. Article Talk. Read Edit View history. Tools Tools. Download as PDF Printable version. In other projects. Wikimedia Commons Wikiquote Wikisource Wikidata item.

British mathematician and logician — MaduraiCarnaticMadras Presidency present-day India. He was the father of William De Morgan. Biography [ edit ]. Childhood [ edit ]. Education [ edit ]. Career [ edit ]. London University, — [ edit ]. The Society for the Diffusion of Useful Knowledge [ edit ]. Private tutor [ edit ]. Actuary [ edit ]. Royal Astronomical Society [ edit ].

Abstract algebra and Sir William Rowan Hamilton [ edit ]. Mathematical logic and George Boole [ edit ]. The Ladies College in Bedford Square [ edit ]. Ramchundra and Indian mathematics [ edit ]. London Mathematical Society [ edit ]. Personal life [ edit ]. Family [ edit ]. Personality [ edit ]. Religious views [ edit ]. Retirement and death [ edit ].

Mathematics [ edit ]. Mathematical logic [ edit ]. Abstract algebra [ edit ]. Works [ edit ].

De morgan augustus biography of michael

Algebra [ edit ]. Logic [ edit ]. A Budget of Paradoxes [ edit ]. Spiritualism [ edit ]. Legacy [ edit ]. Publications [ edit ]. Books [ edit ]. Journal articles [ edit ]. See also [ edit ]. References [ edit ].