Adventures in shape and space – and time

2018 ◽  
Vol 102 (555) ◽  
pp. 385-400
Author(s):  
Tom Roper
Keyword(s):  
Mathematics Teaching ◽  
Newtonian Mechanics ◽  
Young Mathematician ◽  
Space And Time ◽  
And Algebra ◽  
Mathematics And Physics ◽  
Sixth Form

As a youth entering the sixth form to study Mathematics, Further Mathematics and Physics I enjoyed the riches of the school's mathematics library and in particular three books which appealed to me, A mathematician's apology [1], A book of curves [2] and On growth and form [3].Hardy's book [1] is one that an impressionable, young mathematician should not read unguided. It left me with the impression that the proper pursuit of mathematics was as a pure subject, of no use or application, to be studied for its own sake; to my regret, I held to this view for several years before finally being able to shake it off through teaching Newtonian mechanics. Looking across mathematics teaching today I seem to observe great interest in geometry, number and algebra ‘curiosities’ that are rooted entirely in mathematics. This in itself is no bad thing, since it clearly draws us and our students into the fascinating world of mathematics. But what of the applications of mathematics? Might they be equally fascinating? Surely we do not want to lure our students into Hardy's trap?

Newton, Isaac (1642–1727)

2018 ◽  
Author(s):  
William L. Harper ◽  
George E. Smith
Keyword(s):  
Natural Philosophy ◽  
Spherical Shape ◽  
Rigid Bodies ◽  
Newtonian Mechanics ◽  
Important Work ◽  
Sharp Distinction ◽  
Halley's Comet ◽  
Action At A Distance ◽  
Contact Mechanism ◽  
Mathematics And Physics

Newton is best known for having invented the calculus and formulated the theory of universal gravity – the latter in his Principia, the single most important work in the transformation of natural philosophy into modern physical science. Yet he also made major discoveries in optics, and put no less effort into alchemy and theology than into mathematics and physics. Throughout his career, Newton maintained a sharp distinction between conjectural hypotheses and experimentally established results. This distinction was central to his claim that the method by which conclusions about forces were inferred from phenomena in the Principia made it ’possible to argue more securely concerning the physical species, physical causes, and physical proportions of these forces’. The law of universal gravity that he argued for in this way nevertheless provoked strong opposition, especially from such leading figures on the Continent as Huygens and Leibniz: they protested that Newton was invoking an occult power of action-at-a-distance insofar as he was offering no contact mechanism by means of which forces of gravity could act. This opposition led him to a tighter, more emphatic presentation of his methodology in the second edition of the Principia, published twenty-six years after the first. The opposition to the theory of gravity faded during the fifty to seventy-five years after his death as it fulfilled its promise on such issues as the non-spherical shape of the earth, the precession of the equinoxes, comet trajectories (including the return of ’Halley’s Comet’ in 1758), the vagaries of lunar motion and other deviations from Keplerian motion. During this period the point mass mechanics of the Principia was extended to rigid bodies and fluids by such figures as Euler, forming what we know as ’Newtonian’ mechanics.

Modern Mathematics in Germany

1936 ◽  
Vol 29 (8) ◽  
pp. 390-393
Author(s):  
W. Threlfall
Keyword(s):  
Scientific Knowledge ◽  
Golden Age ◽  
Possible Worlds ◽  
The Other ◽  
Space And Time ◽  
The World ◽  
Modern Mathematics ◽  
Mathematics And Physics

Since I am speaking to you about modern German mathematics, I wish to call your attention to a most important subject, namely to the world which surrounds us, and to our scientific knowledge of its extent in space and time. There can be no doubt about the fact that this world we are living in is not the best of all possible worlds. Financial, industrial, and political dieases, you know them just as well on the other side of the great pond as we do on this side. Nevertheless in one respect we are living just now in a golden age. The world of science is in an excellent state and few eras have seen as important successes of mathematics and physics as ours.

scholarly journals R. DESCARTES IR I. NEWTONAS: GAMTOS FILOSOFIJOS SISTEMŲ PANAŠUMAI IR SKIRTUMAI (LAIKO IR ERDVĖS ASPEKTAI)

Problemos ◽  
2006 ◽  
Vol 69 ◽  
Author(s):  
Jonas Čiurlionis
Keyword(s):  
Natural Philosophy ◽  
Special Theory ◽  
The Other ◽  
Absolute Space ◽  
Newtonian Mechanics ◽  
Space And Time ◽  
History Of ◽  
Similarities And Differences ◽  
Laws Of Motion ◽  
In The Beginning

Erdvės ir laiko sampratų istorijoje I. Newtonas yra neabejotinai viena svarbiausių figūrų. Absoliučios erdvės ir laiko idėjos ilgą laiką buvo plačiai pripažintos ir realiai paneigtos tik XX a. pradžioje, atsiradus specialiajai reliatyvumo teorijai. Tačiau niutoniškajai mechanikai įsitvirtinti reikėjo nukonkuruoti R. Descartes’o gamtamokslines pažiūras. Kita vertus, ar gali būti, kad abiejų filosofų pažiūros yra ne tiek prieštaraujančios, kiek panašios? Ar gali būti, kad I. Newtonas pasinaudojo R. Descartes’o idėjomis, konstruodamas savo garsiuosius judėjimo dėsnius, kuriais konstatavo laiko ir erdvės absoliutumą? Šie probleminiai klausimai yra nagrinėjami straipsnyje.Reikšminiai žodžiai: erdvė, laikas, judėjimo dėsniai, reliatyvumas. R. DESCARTES AND I. NEWTON: SIMILARITIES AND DIFFERENCES BETWEEN THEIR SYSTEMS OF NATURAL PHILOSOPHYJonas Čiurlionis Summary Throughout the history of undertanding space and time, I. Newton is undoubtedly one of the most important figures. His ideas of absolute space and time were widely accepted and refused only in the beginning of the 20th century with the rise of special theory of reliativity. However, in order to be recognized, Newtonian mechanics had to win the competition against Cartesian natural philosophy. On the other hand, can it be that views of both philosophers are more similar than contradictory? Can it be that I. Newton used the ideas of R. Descartes while constructing his famous laws of motion – the foundation for the absolute space and time? These and similar problematic questions are discussed in the article.Keywords: space, time, laws of motion, relativity.

Absolute Space: Did Newton Take Leave of His (Classical) Empirical Senses?

1982 ◽  
Vol 12 (4) ◽  
pp. 709-724 ◽  
Author(s):  
L.A. Whitt
Keyword(s):  
Absolute Space ◽  
Main Body ◽  
Newtonian Mechanics ◽  
Space And Time ◽  
Time Space

It is in the scholium of the Principia on time, space, place and motion that Newton delivers what is — arguably — a reluctant kiss of betrayal to empiricism. Right there, ‘in the main body of his chief work,’ as E.A. Burtt observes, the deed is done: ‘When we come to Newton's remarks on space and time … he takes personal leave of his empiricism.’ Reichenbach registers the event less charitably, dismissing the ‘crude reification of space that Newton shares with the epistemologically unschooled mind in its naive craving for realism.’ Injury is then added to insult as Reichenbach holds Newtonian mechanics to task for arresting the analysis of the problems of space and time for more than two centuries.

scholarly journals Notes on the historical conceptual streams for mathematics and physics teaching

2013 ◽  
Vol 54 ◽  
Author(s):  
Raffaele Pisano
Keyword(s):  
History Of Science ◽  
Mathematics Teaching ◽  
Physics Teaching ◽  
Teaching Process ◽  
History Of ◽  
And Mathematics ◽  
The Relationship ◽  
Mathematics And Physics

Based on recent researches of mine concerning history and epistemology of sciences (physics and mathematics) one side and foundations of sciences within my physics and mathematics teaching other side, in this paper I briefly discuss and report the role played by history of science within physics and mathematics teaching. Some case-study on the relationship between mathematics, physics and logics in the history and teaching process are presented, as well.

Berkeley and Newton

2018 ◽  
Author(s):  
Douglas M. Jesseph
Keyword(s):  
Natural Philosophy ◽  
Laws Of Nature ◽  
Absolute Space ◽  
Newtonian Mechanics ◽  
Isaac Newton ◽  
Space And Time ◽  
And Mathematics

This article examines Berkeley’s responses to the mechanics and mathematics of Isaac Newton. After a brief section outlining some of the key elements of Berkeley’s idealistic metaphysics and empiricist epistemology, his criticisms of Newton are considered, as is his attempt to accommodate the success of Newtonian mechanics within the constraints of his own philosophy. In particular, investigations are made of Berkeley’s criticisms of absolute space and time, his proposal to expunge the notion of matter from natural philosophy, his claim that laws of nature are purely descriptive and do not identify genuine causes, and his instrumentalistic approach to the concept of force. Berkeley’s critique of the Newtonian calculus of fluxions in his 1734 treatise The Analyst is also investigated.

The Beginning of General Relativity

2021 ◽  
Vol 30 (6) ◽  
pp. 30-35
Author(s):  
Dong-han YEOM
Keyword(s):  
General Relativity ◽  
General Theory ◽  
Equations Of Motion ◽  
Absolute Space ◽  
Newtonian Mechanics ◽  
Coordinate Systems ◽  
Field Equations ◽  
Classical Physics ◽  
Space And Time ◽  
The Future

In this article, we briefly review the motivations behind general relativity. We first discuss the basics of classical physics, including the equations of motion and the field equations. Newtonian mechanics assumes absolute space and time, but this can be philosophically unnatural. Einstein constructed a general theory of classical physics with covariance for the general choice of coordinate systems. This theory is known as general relativity. Finally, we briefly mention how this theory is completed, how this theory is verified, and what can be the future of general relativity.

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