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.Motion is essentially a relation between some object of nature and the onetimeless space of a time-system.An instantaneous space is static, being relatedto the static nature at an instant.In perception when we see things moving in anapproximation to an instantaneous space, the future lines of motion asimmediately perceived are rects which are never traversed.These approximaterects are composed of small events, namely approximate routes andevent-particles, which are passed away before the moving objects reach them.Assuming that our forecasts of rectilinear motion are correct, these rects occupythe straight lines in timeless space which are traversed.Thus the rects aresymbols in immediate sense-awareness of a future which can only be expressed interms of timeless space.We are now in a position to explore the fundamental character ofperpendicularity.Consider the two time-systems and , each with its own timelessspace and its own family of instantaneous moments with their instantaneousspaces.Let M and N be respectively a(118) moment of and a moment of.In M there is the direction of and in N thereis the direction of.But M and N, being moments of different time-systems,intersect in a level.Call this level.Then is an instantaneous plane in theinstantaneous space of M and also in the instantaneous space of N.It is thelocus of all the event-particles which lie both in M and in N.In the instantaneous space of M the level is perpendicular to the direction ofin M, and in the instantaneous space of N the level is perpendicular to thedirection of in N.This is the fundamental property which forms the definitionof perpendicularity.The symmetry of perpendicularity is a particular instance ofthe symmetry of the mutual relations between two time-systems.We shall find inthe next lecture that it is from this symmetry that the theory of congruence isdeduced.The theory of perpendicularity in the timeless space of any time-system followsimmediately from this theory of perpendicularity in each of its instantaneousspaces.Let be any rect in the moment M of and let be a level in M which isperpendicular to.The locus of those points of the space of which intersect Min event-particles on is the straight line r of space , and the locus of thosepoints of the space of which intersect M in event-particles on is the plane lPage 43Easy PDF Creator is professional software to create PDF.If you wish to remove this line, buy it now. Alfred North Whitehead - The Concept Of Nature.txtof space.Then the plane l is perpendicular to the line r.In this way we have pointed out unique and definite properties in nature whichcorrespond to perpendicularity.We shall find that this discovery of definiteunique properties defining perpendicularity is of critical importance in thetheory of congruence which is the topic for the next lecture.(119)I regret that it has been necessary for me in this lecture to administer such alarge dose of four-dimensional geometry.I do not apologise, because I am reallynot responsible for the fact that nature in its most fundamental aspect isfour-dimensional.Things are what they are; and it is useless to disguise thefact that 'what things are' is often very difficult for our intellects to follow.It is a mere evasion of the ultimate problems to shirk such obstacles.Copyright © 1996, 1997, 1998, 1999, 2000, 2001 The Mead Project.All rightsreserved.The text of the document presented here is in the public domain.The hypertextversion is copyrighted and represents an official communication of The MeadProject.While scholars are permitted to reproduce these materials for the own privateneeds, no part of this publication may be reproduced or transmitted in any formor by any means, electronic or mechanical, including photocopy, recording or anyinformation storage or retrieval system, for the purpose of profit or personalbenefit, without written permission from the Department of Sociology at BrockUniversity.Permission is granted for inclusion of the electronic text of thesepages, and their related images in any index that provides free access to itslisted documents.Lloyd Gordon Ward and Robert ThroopThe Mead Project, Department of Sociology, Brock University, St.Catharines,Ontario, Canada L2S 3A1(905) 688-5550 x 3455Please direct written communications toDr.Lloyd Gordon Ward4501 - 44 Charles Street WestToronto Ontario Canada M4Y 1R8Phone: (416) 964-6799George's Page is a winner of the Britannica.com Internet Guide Award January2000Last revision: 11/01/02 12:16:31 PMAlfred North Whitehead'sThe Concept of Nature6: CongruenceCitation: Alfred North Whitehead."Congruence".6 in The Concept of Nature.Cambridge: Cambridge University Press (1920): 120-142.CONGRUENCETHE aim of this lecture is to establish a theory of congruence.You mustunderstand at once that congruence is a controversial question.It is the theoryof measurement in space and in time.The question seems simple.In fact it issimple enough for a standard procedure to have been settled by act of parliament;Page 44Easy PDF Creator is professional software to create PDF.If you wish to remove this line, buy it now. Alfred North Whitehead - The Concept Of Nature.txtand devotion to metaphysical subtleties is almost the only crime which has neverbeen imputed to any English parliament.But the procedure is one thing and itsmeaning is another.First let us fix attention on the purely mathematical question.When the segmentbetween two points A and B is congruent to that between the two points C and D,the quantitative measurements of the two segments are equal.The equality of thenumerical measures and the congruence of the two segments are not always clearlydiscriminated, and are lumped together under the term equality.But the procedureof measurement presupposes congruence.For example, a yard measure is appliedsuccessively to measure two distances between two pairs of points on the floor ofa room [ Pobierz caÅ‚ość w formacie PDF ]
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.Motion is essentially a relation between some object of nature and the onetimeless space of a time-system.An instantaneous space is static, being relatedto the static nature at an instant.In perception when we see things moving in anapproximation to an instantaneous space, the future lines of motion asimmediately perceived are rects which are never traversed.These approximaterects are composed of small events, namely approximate routes andevent-particles, which are passed away before the moving objects reach them.Assuming that our forecasts of rectilinear motion are correct, these rects occupythe straight lines in timeless space which are traversed.Thus the rects aresymbols in immediate sense-awareness of a future which can only be expressed interms of timeless space.We are now in a position to explore the fundamental character ofperpendicularity.Consider the two time-systems and , each with its own timelessspace and its own family of instantaneous moments with their instantaneousspaces.Let M and N be respectively a(118) moment of and a moment of.In M there is the direction of and in N thereis the direction of.But M and N, being moments of different time-systems,intersect in a level.Call this level.Then is an instantaneous plane in theinstantaneous space of M and also in the instantaneous space of N.It is thelocus of all the event-particles which lie both in M and in N.In the instantaneous space of M the level is perpendicular to the direction ofin M, and in the instantaneous space of N the level is perpendicular to thedirection of in N.This is the fundamental property which forms the definitionof perpendicularity.The symmetry of perpendicularity is a particular instance ofthe symmetry of the mutual relations between two time-systems.We shall find inthe next lecture that it is from this symmetry that the theory of congruence isdeduced.The theory of perpendicularity in the timeless space of any time-system followsimmediately from this theory of perpendicularity in each of its instantaneousspaces.Let be any rect in the moment M of and let be a level in M which isperpendicular to.The locus of those points of the space of which intersect Min event-particles on is the straight line r of space , and the locus of thosepoints of the space of which intersect M in event-particles on is the plane lPage 43Easy PDF Creator is professional software to create PDF.If you wish to remove this line, buy it now. Alfred North Whitehead - The Concept Of Nature.txtof space.Then the plane l is perpendicular to the line r.In this way we have pointed out unique and definite properties in nature whichcorrespond to perpendicularity.We shall find that this discovery of definiteunique properties defining perpendicularity is of critical importance in thetheory of congruence which is the topic for the next lecture.(119)I regret that it has been necessary for me in this lecture to administer such alarge dose of four-dimensional geometry.I do not apologise, because I am reallynot responsible for the fact that nature in its most fundamental aspect isfour-dimensional.Things are what they are; and it is useless to disguise thefact that 'what things are' is often very difficult for our intellects to follow.It is a mere evasion of the ultimate problems to shirk such obstacles.Copyright © 1996, 1997, 1998, 1999, 2000, 2001 The Mead Project.All rightsreserved.The text of the document presented here is in the public domain.The hypertextversion is copyrighted and represents an official communication of The MeadProject.While scholars are permitted to reproduce these materials for the own privateneeds, no part of this publication may be reproduced or transmitted in any formor by any means, electronic or mechanical, including photocopy, recording or anyinformation storage or retrieval system, for the purpose of profit or personalbenefit, without written permission from the Department of Sociology at BrockUniversity.Permission is granted for inclusion of the electronic text of thesepages, and their related images in any index that provides free access to itslisted documents.Lloyd Gordon Ward and Robert ThroopThe Mead Project, Department of Sociology, Brock University, St.Catharines,Ontario, Canada L2S 3A1(905) 688-5550 x 3455Please direct written communications toDr.Lloyd Gordon Ward4501 - 44 Charles Street WestToronto Ontario Canada M4Y 1R8Phone: (416) 964-6799George's Page is a winner of the Britannica.com Internet Guide Award January2000Last revision: 11/01/02 12:16:31 PMAlfred North Whitehead'sThe Concept of Nature6: CongruenceCitation: Alfred North Whitehead."Congruence".6 in The Concept of Nature.Cambridge: Cambridge University Press (1920): 120-142.CONGRUENCETHE aim of this lecture is to establish a theory of congruence.You mustunderstand at once that congruence is a controversial question.It is the theoryof measurement in space and in time.The question seems simple.In fact it issimple enough for a standard procedure to have been settled by act of parliament;Page 44Easy PDF Creator is professional software to create PDF.If you wish to remove this line, buy it now. Alfred North Whitehead - The Concept Of Nature.txtand devotion to metaphysical subtleties is almost the only crime which has neverbeen imputed to any English parliament.But the procedure is one thing and itsmeaning is another.First let us fix attention on the purely mathematical question.When the segmentbetween two points A and B is congruent to that between the two points C and D,the quantitative measurements of the two segments are equal.The equality of thenumerical measures and the congruence of the two segments are not always clearlydiscriminated, and are lumped together under the term equality.But the procedureof measurement presupposes congruence.For example, a yard measure is appliedsuccessively to measure two distances between two pairs of points on the floor ofa room [ Pobierz caÅ‚ość w formacie PDF ]