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William Kingdon Clifford

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side of a jelly-fish, the elements of mind-stuff which go along with them are so combined as to form the faint beginnings of Sentience. When the molecules are so combined as to form the brain and nervous system of a vertebrate, the corresponding elements of mind-stuff are so combined as to form some kind of consciousness; that is to say, changes in the complex which take place at the same time get so linked together that the repetition of one implies the repetition of the other. When matter takes the complex form of a living human brain, the corresponding mind-stuff takes the form of a human consciousness, having intelligence and volition.
880:, Clifford argues that it is immoral to believe things for which one lacks evidence. He describes a ship-owner who planned to send to sea an old and not well-built ship full of passengers. The ship-owner had doubts suggested to him that the ship might not be seaworthy: "These doubts preyed upon his mind, and made him unhappy." He considered having the ship refitted even though it would be expensive. At last, "he succeeded in overcoming these melancholy reflections." He watched the ship depart, "with a light heart…and he got his insurance money when she went down in mid-ocean and told no tales." 493: 1263: 1279: 1247: 1304: 1231: 4303: 406: 887:." Moreover, he contends that even in the case where the ship successfully reaches the destination, the decision remains immoral, because the morality of the choice is defined forever once the choice is made, and actual outcome, defined by blind chance, doesn't matter. The ship-owner would be no less guilty: his wrongdoing would never be discovered, but he still had no right to make that decision given the information available to him at the time. 4293: 2579: 47: 2824: 1383:"If a man, holding a belief which he was taught in childhood or persuaded of afterwards, keeps down and pushes away any doubts which arise about it in his mind, purposely avoids the reading of books and the company of men that call in question or discuss it, and regards as impious those questions which cannot easily be asked without disturbing it—the life of that man is one long sin against mankind." 421: 1084:
and Christopher Knee examined the record on acknowledgement of Clifford's foresight. They conclude that "it was Clifford, not Riemann, who anticipated some of the conceptual ideas of General Relativity." To explain the lack of recognition of Clifford's prescience, they point out that he was an expert
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Bolder even than Riemann, Clifford confessed his belief (1870) that matter is only a manifestation of curvature in a space-time manifold. This embryonic divination has been acclaimed as an anticipation of Einstein's (1915–16) relativistic theory of the gravitational field. The actual theory, however,
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That element of which, as we have seen, even the simplest feeling is a complex, I shall call Mind-stuff. A moving molecule of inorganic matter does not possess mind or consciousness; but it possesses a small piece of mind-stuff. When molecules are so combined together as to form the film on the under
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Combining the two brought the operation of division into play. This greatly expanded our qualitative understanding of how objects interact in space. Crucially, it also provided the means for quantitatively calculating the spatial consequences of those interactions. The resulting geometric algebra, as
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In 1876, Clifford suffered a breakdown, probably brought on by overwork. He taught and administered by day, and wrote by night. A half-year holiday in Algeria and Spain allowed him to resume his duties for 18 months, after which he collapsed again. He went to the island of Madeira to recover, but
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with great ingenuity foresaw in a qualitative fashion that physical matter might be conceived as a curved ripple on a generally flat plane. Many of his ingenious hunches were later realized in Einstein's gravitational theory. Such speculations were automatically premature and could not lead to
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named in his honour. The operations of geometric algebra have the effect of mirroring, rotating, translating, and mapping the geometric objects that are being modelled to new positions. Clifford algebras in general and geometric algebra in particular have been of ever increasing importance to
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Briefly put, the conception is that mind is the one ultimate reality; not mind as we know it in the complex forms of conscious feeling and thought, but the simpler elements out of which thought and feeling are built up. The hypothetical ultimate element of mind, or
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anything constructive without an intermediate link which demanded the extension of 3-dimensional geometry to the inclusion of time. The theory of curved spaces had to be preceded by the realization that space and time form a single four-dimensional entity.
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of mind-stuff, precisely corresponds to the hypothetical atom of matter, being the ultimate fact of which the material atom is the phenomenon. Matter and the sensible universe are the relations between particular organisms, that is, mind organized into
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hold that once tensors had been used in the theory of general relativity, the framework existed in which a geometrical perspective in physics could be developed and allowed the challenging geometrical conceptions of Riemann and Clifford to be
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bears but slight resemblance to Clifford's rather detailed creed. As a rule, those mathematical prophets who never descend to particulars make the top scores. Almost anyone can hit the side of a barn at forty yards with a charge of buckshot.
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Riemann, and more specifically Clifford, conjectured that forces and matter might be local irregularities in the curvature of space, and in this they were strikingly prophetic, though for their pains they were dismissed at the time as
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Moreover, Clifford's algebraic schema extends to higher dimensions. The algebraic operations have the same symbolic form as they do in 2 or 3-dimensions. The importance of general Clifford algebras has grown over time, while their
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in his book on parallelism: "The boldness of this speculation is surely unexcelled in the history of thought. Up to the present, however, it presents the appearance of an Icarian flight." Years later, after
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As such, he is arguing in direct opposition to religious thinkers for whom 'blind faith' (i.e. belief in things in spite of the lack of evidence for them) was a virtue. This paper was famously attacked by
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Clifford's contemporaries considered him acute and original, witty and warm. He often worked late into the night, which may have hastened his death. He published papers on a range of topics including
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The geometry of rotors and motors…forms the basis of the whole modern theory of the relative rest (Static) and the relative motion (Kinematic and Kinetic) of invariable systems.
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in metric geometry, and "metric geometry was too challenging to orthodox epistemology to be pursued." In 1992, Farwell and Knee continued their study of Clifford and Riemann:
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on the curved space concepts of Riemann, and included speculation on the bending of space by gravity. Clifford's translation of Riemann's paper was published in
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he called it, eventually realized the long sought goal of creating an algebra that mirrors the movements and projections of objects in 3-dimensional space.
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This passage is immediately followed by a section on "The bending of space." However, according to the preface (p.vii), this section was written by
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in quaternions facilitate representation of rotation. Clifford laid the foundation for a geometric product, composed of the sum of the
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Clifford argues that the ship-owner was guilty of the deaths of the passengers even though he sincerely believed the ship was sound: "
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on 7 April 1875, with whom he had two children. Clifford enjoyed entertaining children and wrote a collection of fairy stories,
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Farwell, Ruth; Knee, Christopher (1990). "The End of the Absolute: a nineteenth century contribution to General Relativity".
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In 1878, Clifford published a seminal work, building on Grassmann's extensive algebra. He had succeeded in unifying the
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Dechant, Pierre-Philippe (March 2014). "A Clifford algebraic framework for Coxeter group theoretic computations".
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classes - as real algebras - have been identified in other mathematical systems beyond simply the quaternions.
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as his independent development. The book continues with a chapter "On the bending of space", the substance of
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and Grassmann's outer product. The geometric product was eventually formalized by the Hungarian mathematician
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might be a manifestation of an underlying geometry. In his philosophical writings he coined the expression
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into an encyclopedic article, rather than a list of quotations, please do so and remove this message.
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in 1867 and second Smith's prizeman. In 1870, he was part of an expedition to Italy to observe the
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Space Through the Ages: The Evolution of Geometrical Ideas from Pythagoras to Hilbert and Einstein
452:’s 1854 essay "On the hypotheses which lie at the bases of geometry". In 1870, he reported to the 4139: 3854: 3794: 3786: 3483: 3478: 3265: 3250: 3115: 2566: 2358: 2071: 1420: 1368:"It is wrong always, everywhere, and for anyone, to believe anything upon insufficient evidence." 1118: 891: 845: 139: 2159:. 1962 . "Curved empty space as the building material of the physical world: an assessment." In 868:
The grave in Highgate Cemetery - East - of William Kingdon Clifford, just north of the grave of
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Elements of Dynamic: An Introduction to the Study of Motion And Rest In Solid And Fluid Bodies
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Elements of Dynamic: An Introduction to the Study of Motion And Rest In Solid And Fluid Bodies
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of 22 December 1870. During that voyage he survived a shipwreck along the Sicilian coast.
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As a philosopher, Clifford's name is chiefly associated with two phrases of his coining,
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itself as well as to curved lines and surfaces. Clifford was very much impressed by
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Clifford, William K. 1873. "On the hypotheses which lie at the bases of geometry."
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theory, be reckoned on the idealist side. To speak technically, it is an idealist
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opened new possibilities in geometry in Clifford's era. The field of intrinsic
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Clifford, William K. 1878. "Applications of Grassmann's Extensive Algebra."
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Clifford, William (1878). "Applications of Grassmann's extensive algebra".
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In Mathematical Circles: A Selection of Mathematical Stories and Anecdotes
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formulation of general relativity by crediting Clifford as the initiator.
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Such Silver Currents - The Story of William and Lucy Clifford, 1845-1929
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Clifford, William K. 2007 . "On the Space-Theory of Matter." P. 71 in
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From Kant to Hilbert: A Source Book in the Foundations of Mathematics
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of known algebras, and proposed instead two other tensor products of
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Clifford, William K. 1878. "On the Nature of Things-in-Themselves."
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recalls Clifford's prescience, quoting him in order to describe the
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In 1871, he was appointed professor of mathematics and mechanics at
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Biggs, Norman L.; Lloyd, Edward Keith; Wilson, Robin James (1976).
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Volumes 1 (1878) and 2 (1887) containing books I-IV of Clifford's "
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Title page of Volume 1 (1878) containing books I-III of Clifford's
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This article incorporates text from a publication now in the
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Clifford, William Kingdon, William James, and A.J. Burger (Ed.),
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The Road to Reality: A Complete Guide to the Laws of the Universe
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Lectures on Ten British Mathematicians of the Nineteenth Century.
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Lectures on Ten British Mathematicians of the Nineteenth Century
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Lectures and Essays by the Late William Kingdon Clifford, F.R.S.
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Lectures and Essays by the Late William Kingdon Clifford, F.R.S
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Lectures and Essays by the Late William Kingdon Clifford, F.R.S
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Lectures and Essays by the Late William Kingdon Clifford, F.R.S
1557:. Cambridge, England: Cambridge University Press. p. 592. 818: 610:, which inhabit this 3-sphere, provide a representation of the 607: 564: 70: 1907:"On the Evolution of Geometric Algebra and Geometric Calculus" 1798:), translated by W. K. Clifford. – via School of Mathematics, 890:
Clifford famously concludes with what has come to be known as
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e had no right to believe on such evidence as was before him
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Congress for Logic, Methodology, and Philosophy of Science
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Cambridge Scholars Press, Cambridge, UK 978-1847-18503-7.
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Clifford, William K. 1996 . "Elements of Dynamic" 2. In
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Beyond Geometry: Classic Papers from Riemann to Einstein
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1878. "Applications of Grassmann's Extensive Algebra."
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after a few months, leaving a widow with two children.
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On the hypotheses which lie at the bases of geometry
651:: Clifford argued that the "scalars" taken from the 1826:Clifford, William K. 1882. "Paper #9." P. 55–71 in 934:Though Clifford never constructed a full theory of 393:"Clifford was above all and before all a geometer." 294:, where he was elected fellow in 1868, after being 2718: 2310:Proceedings of the Cambridge Philosophical Society 2268:, edited by L. Boi, D. Flament, and J. Salanskis. 720: 690: 639: 286:and showed great promise at school. He went on to 2783: 1102:On the aims and instruments of scientific thought 1002:, anticipated the geometric ideas of relativity. 743:William Kingdon Clifford (1901), as shown on the 606:embedded in a four-dimensional space. Quaternion 16:British mathematician and philosopher (1845–1879) 4319: 1838: 1723:. Cambridge: The Lutterworth Press. p. 26. 2758:. Vol. 2. New York: Macmillan and Company. 2747:. Vol. 1. New York: Macmillan and Company. 1587:From Past to Future: GraĂźmann's Work in Context 772:conception, suggested to him by his reading of 2751: 2740: 1743: 1589:. Basel, Germany: Springer. pp. 243–260. 981:In 1910, William Barrett Frankland quoted the 786:"On the Nature of Things-in-Themselves" (1878) 2861: 2161:Logic, Methodology, and Philosophy of Science 348:Clifford and his wife are buried in London's 2752:Stephen, Leslie; Pollock, Frederick (1879). 2741:Stephen, Leslie; Pollock, Frederick (1879). 2668:Studies in History and Philosophy of Science 2249:Studies in History and Philosophy of Science 1744:Stephen, Leslie; Pollock, Frederick (1901). 1550: 1268:Table of contents page for an 1885 copy of " 929: 776:, which Clifford (1878) defined as follows: 2665: 2495:. Science and Technology Library. FR 14652. 1058:(1970) summarizes Clifford's premonitions: 2875: 2868: 2854: 2806:Works by or about William Kingdon Clifford 2694: 1050:Friedmann–LemaĂ®tre–Robertson–Walker metric 602:of quaternions, thanks to its notion of a 45: 4267:Relationship between religion and science 2779:William and Lucy Clifford (with pictures) 1933: 1700: 1621:Geometric Algebra for Computer Scientists 1158:—includes four popular science lectures: 262:. Clifford was the first to suggest that 19:For other people with the same name, see 2651:. Cambridge, UK: The Lutterworth Press. 2646: 2614: 2589: 1869: 1718: 1688: 1577: 863: 738: 491: 419: 404: 2795:MacTutor History of Mathematics Archive 2716: 2711:W.K. Clifford and "The Ethics of Belief 1919: 1702:"Clifford, William Kingdon (CLFT863WK)" 1551:Doran, Chris; Lasenby, Anthony (2007). 972:. Clifford also discussed his views in 598:have been expanded through the algebra 466:", was published in 1876, anticipating 4383:Academics of University College London 4320: 3193:Proper basis and Reformed epistemology 2538:The Common Sense of the Exact Sciences 1648: 1286:The Common Sense of the Exact Sciences 1270:The Common Sense of the Exact Sciences 1254:The Common Sense of the Exact Sciences 1238:The Common Sense of the Exact Sciences 1210:The Common Sense of the Exact Sciences 4373:Fellows of Trinity College, Cambridge 4338:19th-century deaths from tuberculosis 2849: 2622:Advances in Applied Clifford Algebras 2239: 2237: 2054: 2052: 2050: 2048: 1922:Advances in Applied Clifford Algebras 1617: 373:Advances in Applied Clifford Algebras 309:, and in 1874 became a fellow of the 4368:Alumni of Trinity College, Cambridge 1904: 1772: 1297: 1179:I & II, with an introduction by 1094: 51:William Kingdon Clifford (1845–1879) 4348:19th-century English mathematicians 462:in 1873. His report at Cambridge, " 335: 241:, he introduced what is now termed 13: 2608: 2234: 2225:Dictionary of the History of Ideas 2103:Frankland, William Barrett. 1910. 2087:Common Sense of the Exact Sciences 2045: 964:, though Clifford made these into 736:, a common mapping in kinematics. 376:publishes on Clifford's legacy in 14: 4429: 4343:19th-century British philosophers 2815:Works by William Kingdon Clifford 2770:Works by William Kingdon Clifford 2763: 2701:. New York: John Wiley and Sons. 614:. Clifford noted that Hamilton's 474:by 40 years. Clifford elaborated 21:William Clifford (disambiguation) 4302: 4301: 4291: 2822: 2577: 2266:1830–1930: A Century of Geometry 1554:Geometric Algebra for Physicists 1519:The italics are in the original. 1504:Philosophical Papers and Letters 1302: 1277: 1261: 1245: 1229: 1186:1881. "Mathematical fragments" ( 1025:, during the 1960 International 960:This passage makes reference to 4413:Tuberculosis deaths in Portugal 4378:Alumni of King's College London 2551: 2529: 2498: 2477: 2450: 2432: 2418:American Journal of Mathematics 2409: 2389: 2364: 2349:, edited by P. Pesic. Mineola: 2339: 2297: 2255: 2214: 2194: 2174: 2150: 2134: 2114: 2097: 2078: 2010: 1979: 1966: 1913: 1898: 1872:American Journal of Mathematics 1863: 1832: 1820: 1805: 1781: 1522: 1513: 1488: 1284:First page of an 1885 copy of " 1252:Title page of an 1885 copy of " 1148:American Journal of Mathematics 672:. In terms of tensor products, 454:Cambridge Philosophical Society 313:. He was also a member of the 2695:Macfarlane, Alexander (1916). 2246:, and Christopher Knee. 1990. 2189:The Natural Philosophy of Time 2187:(1st ed.). pp. 246–47.—1980 . 2185:The Natural Philosophy of Time 2145:The Development of Mathematics 1766: 1737: 1712: 1694: 1653:. Phillimore. pp. 64–66. 1642: 1611: 1571: 1544: 1116:1877. "The Ethics of Belief." 1042:The Natural Philosophy of Time 1011:The Development of Mathematics 791:Regarding Clifford's concept, 440:was born, with the concept of 387: 1: 2370:Clifford, William K. 1886 . " 2305:On the Space-Theory of Matter 2303:Clifford, William K. 1876 . " 1476: 1293: 1110:On the Space-Theory of Matter 975:On the Space-Theory of Matter 755: 464:On the Space-Theory of Matter 360:, just north of the grave of 4393:Burials at Highgate Cemetery 4388:Fellows of the Royal Society 4363:British relativity theorists 4232:Desacralization of knowledge 2709:Madigan, Timothy J. (2010). 2706:(See especially pages 78–91) 2688:10.1016/0039-3681(90)90016-2 2547:Kegan, Paul, Trench, and Co. 2483:Clifford, William K. 1881. " 2456:Clifford, William K. 1901 . 2386:. – via A. J. Burger (2008). 2058:Clifford, William K. 1877. " 1595:10.1007/978-3-0346-0405-5_22 1538: 840:was still unreconciled with 813:. But the theory must, as a 768:. The former symbolizes his 658:might instead be taken from 273: 7: 3644:Best of all possible worlds 3601:Eschatological verification 3158:Fine-tuning of the universe 2821:(public domain audiobooks) 2737:(See especially Chapter 11) 2535:Clifford, William K. 1885. 2504:Clifford, William K. 1882. 2438:Clifford, William K. 1879. 2395:Clifford, William K. 1878. 2084:Clifford, William K. 1885. 1845:. Oxford University Press. 1706:A Cambridge Alumni Database 1409: 1321:using the Transwiki process 950:parametrized unit hyperbola 538: 315:London Mathematical Society 10: 4434: 2790:"William Kingdon Clifford" 2276:Springer Berlin Heidelberg 2109:Cambridge University Press 2092:Kegan Paul, Trench and Co. 2032:10.1177/0957154x0001104305 1708:. University of Cambridge. 1201:, with an introduction by 1170:"Of Boundaries in General" 850:psychophysical parallelism 721:{\displaystyle H\otimes N} 691:{\displaystyle H\otimes D} 640:{\displaystyle H\otimes C} 292:Trinity College, Cambridge 237:. Building on the work of 128:Clifford's circle theorems 114:Trinity College, Cambridge 18: 4287: 4219: 4123: 4008: 3928: 3863: 3785: 3692: 3677: 3629: 3591: 3303: 3228: 3103: 3094: 3024: 2961: 2952: 2883: 2595:Clifford, William Kingdon 2331:proceedingscamb06socigoog 2169:Stanford University Press 2020:. 2000. "Body and Mind." 1952:10.1007/s00006-013-0422-4 930:Premonition of relativity 859: 307:University College London 215: 205: 200:University College London 195: 181: 174: 163: 119: 105: 82: 56: 44: 30: 3873:Friedrich Schleiermacher 3459:Theories about religions 3261:Inconsistent revelations 2840:William Kingdon Clifford 2800:University of St Andrews 2487:" (facsimile). London: 2292:10.1007/3-540-55408-4_56 2271:Lecture Notes in Physics 1773:Eves, Howard W. (1969). 1578:Hestenes, David (2011). 1502:(8 September 1679)." In 1481: 1471:Will to Believe Doctrine 1416:Bessel–Clifford function 1167:"The Brain and Thinking" 604:three-dimensional sphere 399:Henry John Stephen Smith 245:, a special case of the 222:William Kingdon Clifford 148:Bessel–Clifford function 4418:British epistemologists 2717:Penrose, Roger (2004). 2629:: 27–41. Archived from 2600:Encyclopædia Britannica 2567:Oxford University Press 2462:I (3rd ed.), edited by 2406:– via Internet Archive. 2229:Charles Scribner's Sons 2157:Wheeler, John Archibald 2105:Theories of Parallelism 2065:23 January 2014 at the 1842:Graph Theory: 1736-1936 1161:"The Eye and the Brain" 476:elliptic space geometry 4408:Scientists from Exeter 3737:Gaunilo of Marmoutiers 2877:Philosophy of religion 2493:University of Bordeaux 2485:Mathematical Fragments 2223:. 1973. "Relativity." 1997:10.1093/mind/os-3.9.57 1800:Trinity College Dublin 1649:Harvey, Hazel (1996). 1406: 1394: 1379: 1364: 1349: 1134:Book I: "Translations" 1092: 1023:John Archibald Wheeler 983:Space-Theory of Matter 873: 854:John Hughlings Jackson 823: 789: 752: 722: 692: 641: 549:William Rowan Hamilton 502: 434:non-Euclidean geometry 429: 417: 403: 4272:Faith and rationality 4227:Criticism of religion 4165:Robert Merrihew Adams 4155:Nicholas Wolterstorff 3358:Divine command theory 2647:Chisholm, M. (2002). 2615:Chisholm, M. (1997). 2472:The Macmillan Company 2378:(2nd ed.), edited by 2181:Whitrow, Gerald James 2023:History of Psychiatry 2016:Clifford, C. K., and 1719:Chisholm, M. (2002). 1396: 1381: 1366: 1351: 1336: 1181:Sir Frederick Pollock 1137:Book II: "Rotations" 1087: 990:had been advanced by 867: 797: 793:Sir Frederick Pollock 778: 742: 723: 693: 660:split-complex numbers 642: 519:. His application of 495: 438:differential geometry 423: 408: 391: 352:, near the graves of 288:King's College London 110:King's College London 4262:Religious philosophy 3742:Pico della Mirandola 3707:Anselm of Canterbury 3639:Augustinian theodicy 3551:Religious skepticism 2884:Concepts in religion 2832:The Ethics of Belief 2786:Robertson, Edmund F. 2372:The Ethics of Belief 2060:The Ethics of Belief 1828:Mathematical Papers. 1796:Habilitationsschrift 1721:Such Silver Currents 1580:"Grassmann's legacy" 1498:. 1976 . "Letter to 1421:Clifford's principle 1389:The Ethics of Belief 1374:The Ethics of Belief 1164:"The Eye and Seeing" 1046:Gerald James Whitrow 914:for the debate over 892:Clifford's principle 878:The Ethics of Belief 706: 676: 625: 612:rotation group SO(3) 529:William Spottiswoode 319:Metaphysical Society 252:mathematical physics 4247:History of religion 3948:Friedrich Nietzsche 3825:Gottfried W Leibniz 3820:Nicolas Malebranche 3752:King James VI and I 3032:Abrahamic religions 2784:O'Connor, John J.; 2725:. Alfred A. Knopf. 2680:1990SHPSA..21...91F 2507:Mathematical Papers 2459:Lectures and Essays 2441:Seeing and Thinking 2376:Lectures and Essays 2359:2007bgcp.book...71K 2191:(2nd ed.). pp. 291. 2072:Contemporary Review 1944:2012arXiv1207.5005D 1618:Dorst, Leo (2009). 1344:Mathematical Papers 1325:If the page can be 1313:is a candidate for 1221:Elements of Dynamic 1195:Mathematical Papers 1177:Lectures and Essays 1156:Seeing and Thinking 1140:Book III: "Strains" 1119:Contemporary Review 966:split-biquaternions 945:Elements of Dynamic 876:In his 1877 essay, 749:Lectures and Essays 700:split-biquaternions 551:, with Grassmann's 527:was followed up by 516:Elements of Dynamic 511:projective geometry 444:broadly applied to 426:Elements of Dynamic 413:Elements of Dynamic 157:Elements of Dynamic 140:Clifford–Klein form 4257:Religious language 4237:Ethics in religion 4195:William Lane Craig 4070:Charles Hartshorne 3810:Desiderius Erasmus 3712:Augustine of Hippo 3654:Inconsistent triad 3616:Apophatic theology 3611:Logical positivism 3593:Religious language 3213:Watchmaker analogy 3178:Necessary existent 2954:Conceptions of God 2914:Intelligent design 2514:, introduction by 2351:Dover Publications 2201:Lanczos, Cornelius 1496:Leibniz, Gottfried 1466:Split-biquaternion 988:general relativity 970:general relativity 874: 753: 734:screw displacement 718: 688: 637: 503: 487:Clifford parallels 472:general relativity 430: 418: 132:Clifford's theorem 4315: 4314: 4215: 4214: 4175:Peter van Inwagen 4160:Richard Swinburne 4105:George I Mavrodes 3965:Vladimir Solovyov 3905:Søren Kierkegaard 3830:William Wollaston 3777:William of Ockham 3757:Marcion of Sinope 3659:Irenaean theodicy 3649:Euthyphro dilemma 3576:Transcendentalism 3405:Womanist theology 3395:Feminist theology 3299: 3298: 3090: 3089: 2976:Divine simplicity 2896:Euthyphro dilemma 2774:Project Gutenberg 2658:978-0-7188-3017-5 2489:Macmillan Company 2446:Macmillan and Co. 2404:MacMillan and Co. 2284:978-3-540-47058-8 2141:Bell, Eric Temple 2125:Raum Zeit Materie 1905:Hestenes, David. 1856:978-0-19-853916-2 1788:Riemann, Bernhard 1730:978-0-7188-3017-5 1604:978-3-0346-0404-8 1500:Christian Huygens 1426:Clifford analysis 1360:Royal Institution 1335: 1334: 1203:Henry J. S. Smith 1095:Selected writings 1056:Cornelius Lanczos 1033:, introduced his 513:and the textbook 432:The discovery of 350:Highgate Cemetery 330:The Little People 324:Clifford married 243:geometric algebra 239:Hermann Grassmann 219: 218: 206:Doctoral students 176:Scientific career 144:Clifford parallel 4425: 4398:Second Wranglers 4353:English atheists 4305: 4304: 4295: 4200:Ali Akbar Rashad 4063:Reinhold Niebuhr 4023:Bertrand Russell 4018:George Santayana 3915:Albrecht Ritschl 3900:Ludwig Feuerbach 3690: 3689: 3686:(by date active) 3546:Process theology 3291:Russell's teapot 3101: 3100: 3096:Existence of God 3006:Process theology 2959: 2958: 2944:Theological veto 2907:religious belief 2870: 2863: 2856: 2847: 2846: 2826: 2825: 2810:Internet Archive 2802: 2759: 2748: 2736: 2724: 2705: 2691: 2662: 2642: 2640: 2638: 2633:on 3 August 2020 2604: 2583: 2581: 2580: 2570: 2555: 2549: 2533: 2527: 2524:Internet Archive 2520:MacMillan and Co 2502: 2496: 2481: 2475: 2454: 2448: 2436: 2430: 2413: 2407: 2400:I, II, & III 2393: 2387: 2384:Macmillan and Co 2382:and F. Pollock. 2368: 2362: 2343: 2337: 2335:Internet Archive 2301: 2295: 2259: 2253: 2241: 2232: 2221:Hoffmann, Banesh 2218: 2212: 2198: 2192: 2178: 2172: 2154: 2148: 2138: 2132: 2118: 2112: 2101: 2095: 2082: 2076: 2056: 2043: 2014: 2008: 1983: 1977: 1972:Frontispiece of 1970: 1964: 1963: 1937: 1917: 1911: 1910: 1902: 1896: 1895: 1867: 1861: 1860: 1836: 1830: 1824: 1818: 1809: 1803: 1785: 1779: 1778: 1770: 1764: 1763: 1761: 1759: 1741: 1735: 1734: 1716: 1710: 1709: 1698: 1692: 1686: 1665: 1664: 1646: 1640: 1639: 1615: 1609: 1608: 1584: 1575: 1569: 1568: 1548: 1532: 1526: 1520: 1517: 1511: 1492: 1404: 1392: 1377: 1362: 1347: 1330: 1306: 1298: 1281: 1265: 1249: 1233: 1035:geometrodynamics 1007:Eric Temple Bell 1000:Bernhard Riemann 787: 730:dual quaternions 727: 725: 724: 719: 697: 695: 694: 689: 646: 644: 643: 638: 596:complex analysis 560:exterior product 525:invariant theory 450:Bernhard Riemann 401: 382:abstract algebra 369:academic journal 336:Death and legacy 290:(at age 15) and 247:Clifford algebra 228: 124:Clifford algebra 93: 91: 67: 65: 49: 39: 32:William Clifford 28: 27: 4433: 4432: 4428: 4427: 4426: 4424: 4423: 4422: 4318: 4317: 4316: 4311: 4283: 4211: 4207:Alexander Pruss 4190:Jean-Luc Marion 4145:Alvin Plantinga 4140:Dewi Z Phillips 4127: 4125: 4119: 4090:Walter Kaufmann 4080:Frithjof Schuon 4053:Rudolf Bultmann 4010: 4004: 4000:Joseph MarĂ©chal 3990:Pavel Florensky 3985:Sergei Bulgakov 3970:Ernst Troeltsch 3953:Harald Høffding 3930: 3924: 3895:William Whewell 3883:Georg W F Hegel 3878:Karl C F Krause 3865: 3859: 3855:Johann G Herder 3845:Baron d'Holbach 3795:Augustin Calmet 3781: 3697: 3685: 3684: 3681: 3673: 3631:Problem of evil 3625: 3621:Verificationism 3587: 3295: 3241:Atheist's Wager 3224: 3086: 3020: 2948: 2924:Problem of evil 2879: 2874: 2823: 2766: 2733: 2659: 2636: 2634: 2611: 2609:Further reading 2593:, ed. (1911). " 2578: 2576: 2573: 2556: 2552: 2541:, completed by 2534: 2530: 2503: 2499: 2482: 2478: 2455: 2451: 2437: 2433: 2427:10.2307/2369379 2414: 2410: 2394: 2390: 2374:" (full text). 2369: 2365: 2344: 2340: 2302: 2298: 2260: 2256: 2242: 2235: 2219: 2215: 2199: 2195: 2179: 2175: 2155: 2151: 2139: 2135: 2129:Springer-Verlag 2119: 2115: 2102: 2098: 2083: 2079: 2067:Wayback Machine 2057: 2046: 2026:11(43):311–38. 2015: 2011: 1984: 1980: 1971: 1967: 1918: 1914: 1903: 1899: 1884:10.2307/2369379 1868: 1864: 1857: 1837: 1833: 1825: 1821: 1817:8:14–17, 36–37. 1810: 1806: 1786: 1782: 1771: 1767: 1757: 1755: 1754:on 3 March 2008 1742: 1738: 1731: 1717: 1713: 1699: 1695: 1687: 1668: 1661: 1647: 1643: 1636: 1628:. p. 664. 1626:Morgan Kaufmann 1616: 1612: 1605: 1582: 1576: 1572: 1565: 1549: 1545: 1541: 1536: 1535: 1527: 1523: 1518: 1514: 1493: 1489: 1484: 1479: 1446:Clifford number 1441:Clifford module 1436:Clifford bundle 1412: 1407: 1405: 1402: 1395: 1393: 1387: 1380: 1378: 1372: 1365: 1363: 1357: 1350: 1348: 1342: 1331: 1324: 1307: 1296: 1289: 1282: 1273: 1266: 1257: 1250: 1241: 1234: 1212:, completed by 1097: 1071:(1973) writes: 1069:Banesh Hoffmann 992:Albert Einstein 932: 908:Will to Believe 862: 788: 785: 758: 707: 704: 703: 677: 674: 673: 653:complex numbers 626: 623: 622: 547:, developed by 541: 507:algebraic forms 501: 468:Albert Einstein 402: 397: 390: 358:Herbert Spencer 338: 296:Second Wrangler 276: 224: 188: 154: 152:Dual quaternion 150: 146: 142: 138: 134: 130: 126: 112: 106:Alma mater 101: 95: 89: 87: 78: 68: 63: 61: 52: 40: 35: 33: 24: 17: 12: 11: 5: 4431: 4421: 4420: 4415: 4410: 4405: 4400: 4395: 4390: 4385: 4380: 4375: 4370: 4365: 4360: 4355: 4350: 4345: 4340: 4335: 4330: 4313: 4312: 4310: 4309: 4299: 4288: 4285: 4284: 4282: 4281: 4274: 4269: 4264: 4259: 4254: 4249: 4244: 4239: 4234: 4229: 4223: 4221: 4220:Related topics 4217: 4216: 4213: 4212: 4210: 4209: 4203: 4202: 4197: 4192: 4187: 4182: 4180:Daniel Dennett 4177: 4172: 4170:Ravi Zacharias 4167: 4162: 4157: 4152: 4147: 4142: 4137: 4135:William L Rowe 4131: 4129: 4121: 4120: 4118: 4117: 4112: 4110:William Alston 4107: 4102: 4097: 4092: 4087: 4082: 4077: 4072: 4066: 4065: 4060: 4058:Gabriel Marcel 4055: 4050: 4045: 4040: 4035: 4030: 4025: 4020: 4014: 4012: 4006: 4005: 4003: 4002: 3997: 3995:Ernst Cassirer 3992: 3987: 3982: 3977: 3972: 3967: 3961: 3960: 3955: 3950: 3945: 3940: 3934: 3932: 3926: 3925: 3923: 3922: 3917: 3912: 3907: 3902: 3897: 3892: 3890:Thomas Carlyle 3886: 3885: 3880: 3875: 3869: 3867: 3861: 3860: 3858: 3857: 3852: 3847: 3842: 3837: 3832: 3827: 3822: 3817: 3815:Baruch Spinoza 3812: 3807: 3802: 3800:RenĂ© Descartes 3797: 3791: 3789: 3783: 3782: 3780: 3779: 3774: 3772:Thomas Aquinas 3769: 3764: 3759: 3754: 3749: 3744: 3739: 3734: 3729: 3724: 3719: 3714: 3709: 3703: 3701: 3687: 3678: 3675: 3674: 3672: 3671: 3666: 3661: 3656: 3651: 3646: 3641: 3635: 3633: 3627: 3626: 3624: 3623: 3618: 3613: 3608: 3603: 3597: 3595: 3589: 3588: 3586: 3585: 3578: 3573: 3568: 3563: 3558: 3553: 3548: 3543: 3541:Possibilianism 3538: 3533: 3528: 3523: 3518: 3513: 3508: 3503: 3498: 3497: 3496: 3491: 3486: 3476: 3471: 3466: 3461: 3456: 3451: 3450: 3449: 3444: 3439: 3429: 3424: 3419: 3417:Fundamentalism 3414: 3409: 3408: 3407: 3402: 3392: 3391: 3390: 3385: 3378:Existentialism 3375: 3370: 3365: 3360: 3355: 3350: 3345: 3340: 3335: 3330: 3325: 3320: 3315: 3309: 3307: 3301: 3300: 3297: 3296: 3294: 3293: 3288: 3283: 3278: 3273: 3271:Noncognitivism 3268: 3263: 3258: 3253: 3248: 3243: 3238: 3232: 3230: 3226: 3225: 3223: 3222: 3220:Transcendental 3217: 3216: 3215: 3210: 3200: 3195: 3190: 3188:Pascal's wager 3185: 3180: 3175: 3170: 3165: 3160: 3155: 3150: 3145: 3140: 3139: 3138: 3133: 3123: 3118: 3116:Christological 3113: 3107: 3105: 3098: 3092: 3091: 3088: 3087: 3085: 3084: 3079: 3074: 3069: 3064: 3059: 3054: 3049: 3044: 3039: 3034: 3028: 3026: 3022: 3021: 3019: 3018: 3013: 3008: 3003: 2998: 2993: 2988: 2983: 2978: 2973: 2968: 2962: 2956: 2950: 2949: 2947: 2946: 2941: 2936: 2931: 2926: 2921: 2916: 2911: 2910: 2909: 2898: 2893: 2887: 2885: 2881: 2880: 2873: 2872: 2865: 2858: 2850: 2844: 2843: 2836: 2827: 2812: 2803: 2781: 2776: 2765: 2764:External links 2762: 2761: 2760: 2749: 2738: 2731: 2714: 2707: 2692: 2663: 2657: 2644: 2610: 2607: 2606: 2605: 2591:Chisholm, Hugh 2572: 2571: 2550: 2528: 2516:H. J. S. Smith 2497: 2476: 2449: 2431: 2408: 2388: 2363: 2338: 2296: 2254: 2233: 2213: 2209:Academic Press 2193: 2173: 2149: 2133: 2113: 2096: 2077: 2044: 2009: 1978: 1965: 1912: 1897: 1878:(4): 350–358. 1862: 1855: 1831: 1819: 1804: 1780: 1765: 1736: 1729: 1711: 1693: 1691:, p. 506. 1666: 1659: 1641: 1634: 1610: 1603: 1570: 1563: 1542: 1540: 1537: 1534: 1533: 1521: 1512: 1486: 1485: 1483: 1480: 1478: 1475: 1474: 1473: 1468: 1463: 1458: 1453: 1448: 1443: 1438: 1433: 1431:Clifford gates 1428: 1423: 1418: 1411: 1408: 1400: 1385: 1370: 1355: 1340: 1333: 1332: 1310: 1308: 1301: 1295: 1292: 1291: 1290: 1283: 1276: 1274: 1267: 1260: 1258: 1251: 1244: 1242: 1236:1885 copy of " 1235: 1228: 1225: 1224: 1217: 1206: 1191: 1184: 1173: 1172: 1171: 1168: 1165: 1162: 1152: 1143: 1142: 1141: 1138: 1135: 1123: 1114: 1105: 1096: 1093: 1078: 1077: 1065: 1064: 1052:in cosmology. 1020: 1019: 958: 957: 931: 928: 861: 858: 783: 774:Baruch Spinoza 757: 754: 717: 714: 711: 687: 684: 681: 636: 633: 630: 620:tensor product 590:The realms of 540: 537: 496: 395: 389: 386: 341:died there of 337: 334: 284:Bedford Circus 275: 272: 217: 216: 213: 212: 207: 203: 202: 197: 193: 192: 183: 179: 178: 172: 171: 165: 161: 160: 136:Clifford torus 121: 120:Known for 117: 116: 107: 103: 102: 96: 84: 80: 79: 69: 58: 54: 53: 50: 42: 41: 34: 31: 15: 9: 6: 4: 3: 2: 4430: 4419: 4416: 4414: 4411: 4409: 4406: 4404: 4401: 4399: 4396: 4394: 4391: 4389: 4386: 4384: 4381: 4379: 4376: 4374: 4371: 4369: 4366: 4364: 4361: 4359: 4356: 4354: 4351: 4349: 4346: 4344: 4341: 4339: 4336: 4334: 4331: 4329: 4326: 4325: 4323: 4308: 4300: 4298: 4294: 4290: 4289: 4286: 4280: 4279: 4275: 4273: 4270: 4268: 4265: 4263: 4260: 4258: 4255: 4253: 4250: 4248: 4245: 4243: 4240: 4238: 4235: 4233: 4230: 4228: 4225: 4224: 4222: 4218: 4208: 4205: 4204: 4201: 4198: 4196: 4193: 4191: 4188: 4186: 4183: 4181: 4178: 4176: 4173: 4171: 4168: 4166: 4163: 4161: 4158: 4156: 4153: 4151: 4150:Anthony Kenny 4148: 4146: 4143: 4141: 4138: 4136: 4133: 4132: 4130: 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3292: 3289: 3287: 3284: 3282: 3279: 3277: 3276:Occam's razor 3274: 3272: 3269: 3267: 3264: 3262: 3259: 3257: 3254: 3252: 3249: 3247: 3244: 3242: 3239: 3237: 3234: 3233: 3231: 3227: 3221: 3218: 3214: 3211: 3209: 3206: 3205: 3204: 3201: 3199: 3196: 3194: 3191: 3189: 3186: 3184: 3181: 3179: 3176: 3174: 3171: 3169: 3166: 3164: 3161: 3159: 3156: 3154: 3151: 3149: 3146: 3144: 3141: 3137: 3134: 3132: 3129: 3128: 3127: 3124: 3122: 3121:Consciousness 3119: 3117: 3114: 3112: 3109: 3108: 3106: 3102: 3099: 3097: 3093: 3083: 3080: 3078: 3075: 3073: 3070: 3068: 3065: 3063: 3060: 3058: 3055: 3053: 3050: 3048: 3045: 3043: 3040: 3038: 3035: 3033: 3030: 3029: 3027: 3023: 3017: 3016:Unmoved mover 3014: 3012: 3011:Supreme Being 3009: 3007: 3004: 3002: 2999: 2997: 2994: 2992: 2989: 2987: 2984: 2982: 2979: 2977: 2974: 2972: 2969: 2967: 2964: 2963: 2960: 2957: 2955: 2951: 2945: 2942: 2940: 2937: 2935: 2932: 2930: 2927: 2925: 2922: 2920: 2917: 2915: 2912: 2908: 2904: 2903: 2902: 2899: 2897: 2894: 2892: 2889: 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Located at 2490: 2486: 2480: 2473: 2469: 2465: 2461: 2460: 2453: 2447: 2443: 2442: 2435: 2428: 2424: 2420: 2419: 2412: 2405: 2401: 2399: 2392: 2385: 2381: 2377: 2373: 2367: 2360: 2356: 2352: 2348: 2342: 2336: 2333: at the 2332: 2328: 2324: 2320: 2316: 2312: 2311: 2306: 2300: 2293: 2289: 2285: 2281: 2277: 2273: 2272: 2267: 2263: 2262:Farwell, Ruth 2258: 2251: 2250: 2245: 2244:Farwell, Ruth 2240: 2238: 2230: 2226: 2222: 2217: 2210: 2206: 2202: 2197: 2190: 2186: 2182: 2177: 2170: 2166: 2162: 2158: 2153: 2147:. pp. 359–60. 2146: 2142: 2137: 2130: 2126: 2122: 2121:Weyl, Hermann 2117: 2110: 2107:. Cambridge: 2106: 2100: 2093: 2089: 2088: 2081: 2074: 2073: 2068: 2064: 2061: 2055: 2053: 2051: 2049: 2041: 2037: 2033: 2029: 2025: 2024: 2019: 2018:G. E. 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Index

William Clifford (disambiguation)
FRS

Exeter
Devon
Madeira
King's College London
Trinity College, Cambridge
Clifford algebra
Clifford's circle theorems
Clifford's theorem
Clifford torus
Clifford–Klein form
Clifford parallel
Bessel–Clifford function
Dual quaternion
Elements of Dynamic
Lucy Clifford
Mathematics
Philosophy
University College London
Arthur Black
FRS
mathematician
philosopher
Hermann Grassmann
geometric algebra
Clifford algebra
mathematical physics
geometry

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