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P:4&0  B(    H\<   < 0   B<  0 < 0   B< R  < *_ (/_zmm`  B#<   < *_ (/_zmm`  H$1< <RY  < *_ (/_zmm`  HX:< < Y < *_ (/_zmm`<  c $޽h鳊 ? ̙3380___PPT10.HP|  `@(  @ @ N9#S?S? P  # ~*   zmm` @ NC#S?S?   # *   zmm` @ T,G#S?S? ;PY  # ~*   zmm` @ T,R#S?S? ; Y # *   zmm`H @ 0޽h鳊 ? 3380___PPT10.`. 0 LL(  Lr L S 54}g  5  L S 54W<$0 5  L <h5~_~_ ?WwF ,$D0 qIf one can have linear vibration, without anything to vibrate, Then Why cannot one have rotation, without anything to rotate?hhhh2D X  w @ L <5~_~_ ?+,$D0 ;The attempt to answer that question led to a 4-year research effort by KVK Nehru and Bruce Peret... and they discovered the answer. But the answer, itself, is not as important as the journey getting there...2D X  w @H L 0?rs ? 3f___PPT10.`2 +uWDn' 5= @B D)' = @BA?%,( < +O%,( < +Dl' =%(D' =%(D' =A@BB6BB0B%()?D' =1:Bvisible*o3>+B#style.visibility<*L %(D' =+4 8?fCB#ppt_w*0.05BCB#ppt_wB*Y3>B ppt_w<*L D' =+4 8?\CB#ppt_hBCB#ppt_hB*Y3>B ppt_h<*L D' =+4 8?bCB#ppt_x-.2BCB#ppt_xB*Y3>B ppt_x<*L D' =+4 8?\CB#ppt_yBCB#ppt_yB*Y3>B ppt_y<*L D' =-g6B fade*<3<*L Dr' =%(D' =%(D' ='@BB6B%()?))D' =1:Bvisible*o3>+B#style.visibility<*L%(D' =+4 8?fCB#ppt_w*0.05BCB#ppt_wB*Y3>B ppt_w<*LD' =+4 8?\CB#ppt_hBCB#ppt_hB*Y3>B ppt_h<*LD' =+4 8?bCB#ppt_x-.2BCB#ppt_xB*Y3>B ppt_x<*LD' =+4 8?\CB#ppt_yBCB#ppt_yB*Y3>B ppt_y<*LD' =-g6B fade*<3<*LDr' =%(D' =%(D' ='@BB6B%()?))D' =1:Bvisible*o3>+B#style.visibility<*L%(D' =+4 8?fCB#ppt_w*0.05BCB#ppt_wB*Y3>B ppt_w<*LD' =+4 8?\CB#ppt_hBCB#ppt_hB*Y3>B ppt_h<*LD' =+4 8?bCB#ppt_x-.2BCB#ppt_xB*Y3>B ppt_x<*LD' =+4 8?\CB#ppt_yBCB#ppt_yB*Y3>B ppt_y<*LD' =-g6B fade*<3<*L+8+0+L0 +;' 0 jbP(  Px P c $'(}w   R P s * ?@b l }  P} ,$D0 P Nee}X Larson s RS identifies 4 distinct  regions of speed, with 3 boundary conditions:R(2R R @ N   P  ) P # l ee?" 7   w Space 1/s     Dk ?`( P # lw<ee?" 7  vTime 1/t     Dk ?`. P # l b<ee?" 7  |Time/space t/s   Dk ?`.  P # lD5ee?" 7  |Space/time s/t   Dk ?`fB  P 6o ?`B  P 01 ?fB  P 6o ?  fB  P 6o ? `B P 01 ?7 7 fB P 6o ?  P N 5ee"`m H d Unit Space (2   @ P N|)ee"` mH c Unit Time (2   @ P Tee"` - m  d Unit Speed (2   @ P TZee  e Cosmic Sector  @ P T ee  gMaterial Sector  @@ P Hee( ,$0 Regions Space/time (Larson s time-space) Conventional reference frame. Time/space (Larson s space-time)  Anti-matter (cosmic) reference. Time Atomic configuration space. Space Anti-matter configuration space.(2 2 6 :#  @ P Hee- 7,$0 4jBoundaries Unit Speed Crossover point between material and cosmic sectors Unit Space Boundary between the conventional reference system and the region of material atomic configuration. Unit Time Boundary between the cosmic  anti-matter reference system and the region of cosmic atomic configuration. (2+ 2  6 g q 6 @H P 0?rs ? f;v3ffyq___PPT10Q.}+X{D'  = @B Dp' = @BA?%,( < +O%,( < +D' =%(D' =%(DG' =4@BBB B%(D' =1:Bvisible*o3>+B#style.visibility<*P%(D' =-6B'blinds(horizontal)*<3<*PDP' =%(D' =%(D' =A@BB/BB0B%()))D' =1:Bvisible*o3>+B#style.visibility<*P%(D' =-g6B fade*<3<*PD' =+4 8?\CB#ppt_xBCB#ppt_xB*Y3>B ppt_x<*PD' =+4 8?bCB#ppt_y-.1BCB#ppt_yB*Y3>B ppt_y<*PDP' =%(D' =%(D' =A@BB/BB0B%()))D' =1:Bvisible*o3>+B#style.visibility<*P%(D' =-g6B fade*<3<*PD' =+4 8?\CB#ppt_xBCB#ppt_xB*Y3>B ppt_x<*PD' =+4 8?bCB#ppt_y-.1BCB#ppt_yB*Y3>B ppt_y<*P+p+0+P0 ++0+P0 +_< 0 OG8\(  \r \ S '(}w   E \ HLeeM7 qFor now, only the material sector perspective will be considered, as that is the region of our common experience.r(2r r @  2\ #"<$D0 t \  `$ee  ? "Angle ( radians)B' &4    Dk ?` \ Z5ee ?G  o1   Dk ?` \ Z6ee ?G  o0   Dk ?`   \  ``)ee  ? tRotation     Dk ?`  \  `0ee  ?e {Linear distance   Dk ?`  \ ZRee ?G e "0&   Dk ?`  \ ZLee ?eG  o1   Dk ?`  \  `dee  ?e w Translation     Dk ?` \  ` nee  ?e Spatial Measurement   Dk ?` \  ` wee  ?G e ~Maximum Quantity   Dk ?` \  `dee  ?G e ~Minimum Quantity   Dk ?`  \  `ee  ?e tMotion   Dk ?`fB \ 6o ?`B \ 01 ?ee`B \ 01 ?fB \ 6o ?fB \ 6o ?`B \ 01 ?`B \ 01 ?G G `B \ 01 ?fB \ 6o ? *\ Hee ,$0 HTranslational motion has a minimum quantity of 1, because the natural datum of motion in the RS is unit speed. But there is no upper limit to that speed. The units of translational motion are the natural units of linear speed.& d2  @ 3\ 6ę),$0 lFrom the perspective of the space/time (Larson s time-space) region, linear motion must precede rotational motion.Ht d2F, t @ 4\ 6m ,$0 :The minimum quantity of motion will always occur. Thus, linear motion in space/time will always occur, which we observe as the outward progression of the natural reference system the  Hubble Expansion .h d2hh  @ 5\ 6p- J ,$0 vRotation has no minimum quantity, so it can only exist as a modifier to other motions. It has a maximum quantity of 1 (), because further increases move the angle back to its starting point of zero angle, where the rotation repeats.L d2wer&w r @H \ 0?rs ? f;v3ff___PPT10.\+|b1D' = @B D?' = @BA?%,( < +O%,( < +D' =%(D' =%(DG' =4@BBB B%(D' =1:Bvisible*o3>+B#style.visibility<*2\%(D' =-6B'blinds(horizontal)*<3<*2\DP' =%(D' =%(D' =A@BB/BB0B%()))D' =1:Bvisible*o3>+B#style.visibility<**\%(D' =-g6B fade*<3<**\D' =+4 8?\CB#ppt_xBCB#ppt_xB*Y3>B ppt_x<**\D' =+4 8?bCB#ppt_y-.1BCB#ppt_yB*Y3>B ppt_y<**\DP' =%(D' =%(D' =A@BB/BB0B%()))D' =1:Bvisible*o3>+B#style.visibility<*5\%(D' =-g6B fade*<3<*5\D' =+4 8?\CB#ppt_xBCB#ppt_xB*Y3>B ppt_x<*5\D' =+4 8?bCB#ppt_y-.1BCB#ppt_yB*Y3>B ppt_y<*5\DP' =%(D' =%(D' =A@BB/BB0B%()))D' =1:Bvisible*o3>+B#style.visibility<*4\%(D' =-g6B fade*<3<*4\D' =+4 8?\CB#ppt_xBCB#ppt_xB*Y3>B ppt_x<*4\D' =+4 8?bCB#ppt_y-.1BCB#ppt_yB*Y3>B ppt_y<*4\Do' =%(D' =%(D' =A@BB)BB0B@ A%()))D' =1:Bvisible*o3>+B#style.visibility<*3\%(DE' =+ 4 8?CB#ppt_xBCB#ppt_x+.1BCB#ppt_xB*Y3>B ppt_x<*3\D' =+4 8?\CB#ppt_yBCB#ppt_yB*Y3>B ppt_y<*3\DM' =+4 8?CB#ppt_h/10BCB#ppt_h+.01BCB#ppt_hB*Y3>B ppt_h<*3\DM' =+4 8?CB#ppt_w/10BCB#ppt_w+.01BCB#ppt_wB*Y3>B ppt_w<*3\D' =+B#0,0; .5, 1; 1, 1-g6B fade*<3<*3\++0+*\0 ++0+3\0 ++0+4\0 ++0+5\0 +C 0 x)h(  hr h S g'(}w    h Hxee,$0 IThe Unit Space boundary separates the Time Region from the space/time region, making everything within the inverse of the space/time region. Zero becomes Infinity; Infinity becomes Zero, and Unity stays Unity.8(2k`  @F   &h #" -% ,$D0 h Z,ee ?  qShift   Dk ?` h Zee ?7   o1   Dk ?` h Z@ee ?:7   o0   Dk ?`   h Zee ?:  w Translation     Dk ?`  h Zee ? pTurn   Dk ?`  h Z,ee ?7  "0&   Dk ?`  h Z #ee ?:7  o1   Dk ?`  h Z$-ee ?: tRotation     Dk ?` h Z5ee ? Counterspatial Measurement   Dk ?` h Z`?ee ?7  ~Maximum Quantity   Dk ?` h ZHee ?:7  ~Minimum Quantity   Dk ?` h ZQee ?: Motion in the Time Region   Dk ?`fB h 6o ?`B h 01 ?`B h 01 ?fB h 6o ?  fB h 6o ? `B h 01 ?:: `B h 01 ?7 7  `B h 01 ? fB h 6o ? f h H|UeeM  ,$0 6Rotational motion has a minimum quantity of 1, because the natural datum of motion in the RS is unit speed. But there is no upper limit to that speed, so the angle of this rotation can be infinite. This type of rotation, where it doesn t loop around back to zero, is called a  Turn .D d2 b  @w 'h 6<] ,$0 WFrom the perspective of the time region, rotational motion must precede linear motion.HX d2*, X @p (h 6l{],$0 0The minimum quantity of motion will always occur. Thus, rotational motion in the time region will always occur, which we observe as a  rotational base .h d2hho  @ )h 6@h :,$0 Linear motion has no minimum quantity and becomes  optional . When it does occur, upon reaching its maximum it turns back and heads towards zero, producing a vibration, measured as a  Shift between  Turns .8 d2  @H h 0?rs ? f;v3ff%$___PPT10$.@1+դ1D#' = @B DS#' = @BA?%,( < +O%,( < +Dl' =%(D' =%(D' =A@BB6BB0B%()?D' =1:Bvisible*o3>+B#style.visibility<*h%(D' =+4 8?fCB#ppt_w*0.05BCB#ppt_wB*Y3>B ppt_w<*hD' =+4 8?\CB#ppt_hBCB#ppt_hB*Y3>B ppt_h<*hD' =+4 8?bCB#ppt_x-.2BCB#ppt_xB*Y3>B ppt_x<*hD' =+4 8?\CB#ppt_yBCB#ppt_yB*Y3>B ppt_y<*hD' =-g6B fade*<3<*hD'' =%(D' =%(Dw' =4@BBB B%()))D' =1:Bvisible*o3>+B#style.visibility<*&h%(D' =-6B'blinds(horizontal)*<3<*&hDP' =%(D' =%(D' =A@BB/BB0B%()))D' =1:Bvisible*o3>+B#style.visibility<*h%(D' =-g6B fade*<3<*hD' =+4 8?\CB#ppt_xBCB#ppt_xB*Y3>B ppt_x<*hD' =+4 8?bCB#ppt_y-.1BCB#ppt_yB*Y3>B ppt_y<*hD ' =%(D' =%(Dp' =A@BB/BB0B%(D' =1:Bvisible*o3>+B#style.visibility<*)h%(D' =-g6B fade*<3<*)hD' =+4 8?\CB#ppt_xBCB#ppt_xB*Y3>B ppt_x<*)hD' =+4 8?bCB#ppt_y-.1BCB#ppt_yB*Y3>B ppt_y<*)hD ' =%(D' =%(Dp' =A@BB/BB0B%(D' =1:Bvisible*o3>+B#style.visibility<*(h%(D' =-g6B fade*<3<*(hD' =+4 8?\CB#ppt_xBCB#ppt_xB*Y3>B ppt_x<*(hD' =+4 8?bCB#ppt_y-.1BCB#ppt_yB*Y3>B ppt_y<*(hD?' =%(D' =%(D' =A@BB)BB0B@ A%(D' =1:Bvisible*o3>+B#style.visibility<*'h%(DE' =+ 4 8?CB#ppt_xBCB#ppt_x+.1BCB#ppt_xB*Y3>B ppt_x<*'hD' =+4 8?\CB#ppt_yBCB#ppt_yB*Y3>B ppt_y<*'hDM' =+4 8?CB#ppt_h/10BCB#ppt_h+.01BCB#ppt_hB*Y3>B ppt_h<*'hDM' =+4 8?CB#ppt_w/10BCB#ppt_w+.01BCB#ppt_wB*Y3>B ppt_w<*'hD' =+B#0,0; .5, 1; 1, 1-g6B fade*<3<*'h++0+h0 ++0+h0 ++0+'h0 ++0+(h0 ++0+)h0 +/7 0 '  (Ap(  pr p S 7'(}w   s   }T 7p #"gd  ,$D0 p  `ee ?T wRotational Base   Dk ?` p  `Pee ?T lTurn   Dk ?` p  `,ee ? T nTime   Dk ?`  p  `Dee ?6 s Progression     Dk ?`  p  `\ee ?6 nLinear   Dk ?`   p  `ee ? 6 t Space/time     Dk ?`   p  `ee ?}6 u Observed As     Dk ?`  p  `ee ?}6 xPrimary Motion   Dk ?`  p  `ee ? }6 pRegion   Dk ?``B p 0o ? }}ZB p s *1 ? 66ZB p s *1 ? `B p 0o ? TT`B p 0o ? } TZB p s *1 ?}TZB p s *1 ?}T`B p 0o ?}T p Hee ,$0 |Primary Motions Given a natural datum of Unity, the minimum quantity of motion must always occur. These are PRIMARY MOTIONS:b} 2? h } @2 p HH ee ,$0 Secondary Motions When there is no minimum quantity, the motion can act only as a modifier to a primary motion. These motions are always rhythmic in nature, because of the maximum quantity of 1 unit. These are SECONDARY MOTIONS:b 2wAh  @~   -  Ap #"eg-  ,$D0  p  ` ee ?_ q Vibration     Dk ?` p  `` ee ?_ mShift   Dk ?` p  `ee ? _ nTime   Dk ?` p  `2ee ? _ Oscillation as Rotation   Dk ?` p  `:ee ? _ pRotation     Dk ?`  p  `Dee ? _ t Space/time     Dk ?`  p  `Nee ?-   u Observed As     Dk ?`  p  `Hee ?-   zSecondary Motion   Dk ?` !p  `d`ee ? -   pRegion   Dk ?``B "p 0o ? - - ZB #p s *1 ?  ZB $p s *1 ? __`B %p 0o ? `B &p 0o ? -  ZB 'p s *1 ?- ZB (p s *1 ?- `B )p 0o ?- H p 0?rs ? f;v3ff___PPT10.Ю|:+x/D' f= @B D' = @BA?%,( < +O%,( < +Dl' =%(D' =%(D' =A@BB6BB0B%()?D' =1:Bvisible*o3>+B#style.visibility<*p%(D' =+4 8?fCB#ppt_w*0.05BCB#ppt_wB*Y3>B ppt_w<*pD' =+4 8?\CB#ppt_hBCB#ppt_hB*Y3>B ppt_h<*pD' =+4 8?bCB#ppt_x-.2BCB#ppt_xB*Y3>B ppt_x<*pD' =+4 8?\CB#ppt_yBCB#ppt_yB*Y3>B ppt_y<*pD' =-g6B fade*<3<*pD' =%(D' =%(DG' =4@BBB B%(D' =1:Bvisible*o3>+B#style.visibility<*7p%(D' =-6B'blinds(horizontal)*<3<*7pDl' =%(D' =%(D' =A@BB6BB0B%()?D' =1:Bvisible*o3>+B#style.visibility<*p%(D' =+4 8?fCB#ppt_w*0.05BCB#ppt_wB*Y3>B ppt_w<*pD' =+4 8?\CB#ppt_hBCB#ppt_hB*Y3>B ppt_h<*pD' =+4 8?bCB#ppt_x-.2BCB#ppt_xB*Y3>B ppt_x<*pD' =+4 8?\CB#ppt_yBCB#ppt_yB*Y3>B ppt_y<*pD' =-g6B fade*<3<*pD' =%(D' =%(DG' =4@BBB B%(D' =1:Bvisible*o3>+B#style.visibility<*Ap%(D' =-6B'blinds(horizontal)*<3<*Ap+p+0+p0 ++0+p0 +x* 0 [S(  r  S '(}w     w   # #"eYG ,$D0   `@ee ?   |POLAR GEOMETRY   Dk ?`   `ee ?w   RECTANGULAR GEOMETRY   Dk ?`n   `Lee ? q  jPrimary rotational motions producing a polar coordinate system of three, imaginary dimensions: iX, jY, kZ.kk k  Dk ?`h   `$ee ?wq  dPrimary linear motions producing a rectangular coordinate system of three, real dimensions: X, Y, Z.ee e  Dk ?`    `Hee ? q y Time Region     Dk ?`    `tee ?w  q Space/time Region   Dk ?``B   0o ?w  ZB   s *1 ?wqq`B   0o ?w  `B  0o ?w w ZB  s *1 ?   `B  0o ?  ZB  s *1 ?w    Hee};,$0 ,When we compare the characteristics of the time and space/time regions, it becomes obvious that the space/time region is represented by rectangular (linear) relationships, expressed by real numbers and the time region is represented by rotational (polar) relationships, expressed using imaginary numbers (aka  rotational operators).TM(2a & M @  H8ee= GZ,$0 Rectangular and Polar geometries are geometric inverses of each other, and thus abide by the reciprocal relationship that is the basis of the Reciprocal System of theory.& d2  @  6x}G,$0 #Each region must therefore have an underlying geometry attached to it, to properly determine the rules of perspective transformation to account for the influences of the observer principle.( d2  @H  0?rs ? f;v3ff___PPT10.¸n+1)D' = @B D' = @BA?%,( < +O%,( < +Dl' =%(D' =%(D' =A@BB6BB0B%()?D' =1:Bvisible*o3>+B#style.visibility<*%(D' =+4 8?fCB#ppt_w*0.05BCB#ppt_wB*Y3>B ppt_w<*D' =+4 8?\CB#ppt_hBCB#ppt_hB*Y3>B ppt_h<*D' =+4 8?bCB#ppt_x-.2BCB#ppt_xB*Y3>B ppt_x<*D' =+4 8?\CB#ppt_yBCB#ppt_yB*Y3>B ppt_y<*D' =-g6B fade*<3<*D' =%(D' =%(DG' =4@BBB B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-6B'blinds(horizontal)*<3<*D ' =%(D' =%(Dp' =A@BB/BB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-g6B fade*<3<*D' =+4 8?\CB#ppt_xBCB#ppt_xB*Y3>B ppt_x<*D' =+4 8?bCB#ppt_y-.1BCB#ppt_yB*Y3>B ppt_y<*D ' =%(D' =%(Dp' =A@BB/BB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-g6B fade*<3<*D' =+4 8?\CB#ppt_xBCB#ppt_xB*Y3>B ppt_x<*D' =+4 8?bCB#ppt_y-.1BCB#ppt_yB*Y3>B ppt_y<*++0+0 ++0+0 ++0+0 + & 0   @ xO (  xx x c $4}g   B x H"5ee,$0 2Two seemingly contradictory claims have been made:3 23 3 `pl 'm R  xm 'R,$D0 x Neem R tThe key word here being: perspective. Even with this simple reciprocal analysis across the unit space boundary, it becomes obvious that the location of the observer must be considered when analyzing the systems of motion, for without it, contradictions abound. With the advent of computer modeling, the techniques for creating perspective transformations have become well-defined and commonplace, known as the study of Projective Geometry.| 2 h  @Z  x C *Aj0195812'] 9  x 6=Z t$D0@8___PPT9 WFrom the perspective of the time region, rotational motion (turn) can occur without anything to rotate, but linear motion must have an underlying rotational motion to vibrate.`I d2 =hJ  @`p,  x 6p$0<4___PPT9 NFrom the perspective of the space/time region, linear motion can occur without anything moving, but rotational motion must have an underlying linear motion to rotate.`I d2/hI  @`pH x 0?rs ? f;v3ff___PPT10.:/+D$' != @B D' = @BA?%,( < +O%,( < +Dl' =%(D' =%(D' =A@BB6BB0B%()?D' =1:Bvisible*o3>+B#style.visibility<*x%(D' =+4 8?fCB#ppt_w*0.05BCB#ppt_wB*Y3>B ppt_w<*xD' =+4 8?\CB#ppt_hBCB#ppt_hB*Y3>B ppt_h<*xD' =+4 8?bCB#ppt_x-.2BCB#ppt_xB*Y3>B ppt_x<*xD' =+4 8?\CB#ppt_yBCB#ppt_yB*Y3>B ppt_y<*xD' =-g6B fade*<3<*xD ' =%(D' =%(Dp' =A@BB/BB0B%(D' =1:Bvisible*o3>+B#style.visibility<* x%(D' =-g6B fade*<3<* xD' =+4 8?\CB#ppt_xBCB#ppt_xB*Y3>B ppt_x<* xD' =+4 8?bCB#ppt_y-.1BCB#ppt_yB*Y3>B ppt_y<* xD' =%(D' =%(Dc' =4@BB/BB%(D' =1:Bvisible*o3>+B#style.visibility<* x%(D' =-g6B fade*<3<* xD' =+4 8?\CB#ppt_xBCB#ppt_xB*Y3>B ppt_x<* xD' =+4 8?bCB#ppt_y-.1BCB#ppt_yB*Y3>B ppt_y<* xD_' =%(D' =%(D' =4@BB6BB%()?D' =1:Bvisible*o3>+B#style.visibility<* x%(D' =+4 8?fCB#ppt_w*0.05BCB#ppt_wB*Y3>B ppt_w<* xD' =+4 8?\CB#ppt_hBCB#ppt_hB*Y3>B ppt_h<* xD' =+4 8?bCB#ppt_x-.2BCB#ppt_xB*Y3>B ppt_x<* xD' =+4 8?\CB#ppt_yBCB#ppt_yB*Y3>B ppt_y<* xD' =-g6B fade*<3<* x+p+0+x0 ++0+ x0 +S 0 BxB >BB(  r  S -4}g       #  S,$D0  Z3ee?J 0 nReal    DDkk   Ztee? J0 w Number System    DDkk  Z09ee?J0  q3 Axial    DDkk  Z,Oee?0J t Dimensions      DDkk   ZPee?J  Euclidean: Rectangular    DDkk   Z`ee? J  rGeometry      DDkk   Zbee?Jx  Oscillation as Rotation    DDkk    Zsee?x J  zSecondary Motion    DDkk   Z}ee?J x  |Linear Translation    DDkk   Zwee?Jx  xPrimary Motion    DDkk   Zee?=  ySpace/time Region    DDkk`B  0o ?= =ZB  s *1 ? ZB  s *1 ?x x ZB  s *1 ? ZB  s *1 ? `B  0o ? `B  0o ?=`B  0o ? = ZB  s *1 ?JJZB  s *1 ?0 0`  0=^o`"  0=oN   C  T  c $X99? `  0BCDEF;;V)v[D0'!<Q g~#0@ QpczWlK_AQ7C-4%&  Z 41MmpW#A\.!jx|@`: [ h  8BCNDEpFz\\MMMMMMM4MQMqNNNNN,NTN}NTx8"ItlI,:p   &9#L+`5r@KWft~wog^V N &4^D#Uh|w>e/ <Wud3w8J\uN@&i1M@`8    BC|DE,F6 dWK>.1=$M] m||d@`uZ8 ! BCDEFH ry#J=Wl~i(T&tKv"i]N=,pQ4Qi)S Z 3Z|wdQ=' " nYF4$a@?HR^ m$}7FORL>( )02Z0()vhbgttaRF=8BHBUBbBmBwBBAA5)  *9IZk{wwywlwZwDw,wwwwww^w2wwwwwzwTw/w wwwwwnwVwAw.w www wdFFwwn^N>- 9.8CqN`YPf?q0} Q}!dExT4UGHOY,fhv ;g4W|@` <    "#  S,$D0 # Zee?z 0 s Imaginary      DDkk  $ Zȧee? z0 w Number System    DDkk % Z԰ee?z0 r3 Planar      DDkk & Zee? 0z t Dimensions      DDkk  ' Zee?z   zEuclidean: Polar    DDkk ( ZHee? z  rGeometry      DDkk ) Zee?zx   oShift    DDkk  * Zee? x z  zSecondary Motion    DDkk + Zee?zx  nTurn    DDkk  , ZPee? zx  xPrimary Motion    DDkk - Zee? = s Time Region      DDkk`B . 0o ? ==ZB / s *1 ? ZB 0 s *1 ? x x ZB 1 s *1 ?  ZB 2 s *1 ?  `B 3 0o ? `B 4 0o ? = `B 5 0o ?=ZB 6 s *1 ?zzZB 7 s *1 ? 00`b 8 0'MJ`r 9 0MJT : c $X99? .` ; 0BCDEF;;V)v[D0$!9N d{#0@QpcuWgKZAL7?-0%" W 1 1MmpV#@\.!jx|@`[h < 8BCNDEpFz\\MMMMMMM0MMMlNNNNN%NNNvNyTx8AklI,/e   -#?+S5e@xKWftyqjbZRI A &4SDUh|n5^) <Wu_/t8G\tM@&i/M@` = BC|DE,F6 cVJ=.0=$M] m||c@`:u8 > BCDEF9 byJ,EZmiz(T&xtoKe"XK<,pQ4BYo)S Z 3Zw|gUB- " u`L9'a@2:EP _$o7FORL>( !#Z!(vhbgztfTE90+B:BHBUB_BjBrByA}A5)  *9IZk{~wwwlw^wMw7wwwwww{wSw'wwwwwqwKw&wwwwwwgwOw:w(wwwww_FFw~wm]M=- 9!+6qA`LPX?d0o |uD}dElH)U G=DN,[hk ;g'In@` .R B C *Aj0240719 H  0?rs ? 3f( ___PPT10.ĸEY+<|eD' = @B D' = @BA?%,( < +O%,( < +D_' =%(D' =%(D' =4@BB6BB%()?D' =1:Bvisible*o3>+B#style.visibility<*%(D' =+4 8?fCB#ppt_w*0.05BCB#ppt_wB*Y3>B ppt_w<*D' =+4 8?\CB#ppt_hBCB#ppt_hB*Y3>B ppt_h<*D' =+4 8?bCB#ppt_x-.2BCB#ppt_xB*Y3>B ppt_x<*D' =+4 8?\CB#ppt_yBCB#ppt_yB*Y3>B ppt_y<*D' =-g6B fade*<3<*D_' =%(D' =%(D' =4@BB6BB%()?D' =1:Bvisible*o3>+B#style.visibility<*"%(D' =+4 8?fCB#ppt_w*0.05BCB#ppt_wB*Y3>B ppt_w<*"D' =+4 8?\CB#ppt_hBCB#ppt_hB*Y3>B ppt_h<*"D' =+4 8?bCB#ppt_x-.2BCB#ppt_xB*Y3>B ppt_x<*"D' =+4 8?\CB#ppt_yBCB#ppt_yB*Y3>B ppt_y<*"D' =-g6B fade*<3<*"++ 0 ?7@N (  x  c $'(}w    ! 0,$0 RCounterspace is the inverse of  space ; the space of common understanding, and is nothing more than a name for a  polar time region . The cosmic equivalent to counterspace is  countertime , the inverse of time, and is the  polar space region ..8" dd2  @l 'z N'z,$D0- 5 Z?"0@NNN?N  z cShift  ={, 4 Zx ?"0@NNN?N  bTurn  ={@ 3 Z`,?"0@NNN?N'  vCounterspace (Polar)h  ={0 2 Z 5?"0@NNN?N  z  fRotation    ={3 1 Z&?"0@NNN?N   i Translation    ={? 0 ZG?"0@NNN?N'   uSpace (Rectangular)h  ={5 / ZP?"0@NNN?N z  k Secondary  h  ={3 . ZY?"0@NNN?N   iPrimaryh  ={8 - ZPc?"0@NNN?N'  nNames of Motions  ={B 6 No ?"0@NNN?N'zB 7 H1 ?"0@NNN?N' z B 8 H1 ?"0@NNN?N' z B 9 No ?"0@NNN?N'zB : No ?"0@NNN?N''B ; H1 ?"0@NNN?NB < H1 ?"0@NNN?N  B = No ?"0@NNN?Nzz @ T?"0@NNN?N n / 2 A  `HYI?"0@NNN?N -n 2 B T?"0@NNN?Nm  2 C Z3?"0@NNN?N-   D T?"0@NNN?N]" E T?"0@NNN?N}H  0?rs ? 3fme___PPT10E.͸wg+-D' h= @B D' = @BA?%,( < +O%,( < +Dl' =%(D' =%(D' =A@BB6BB0B%()?D' =1:Bvisible*o3>+B#style.visibility<*!%(D' =+4 8?fCB#ppt_w*0.05BCB#ppt_wB*Y3>B ppt_w<*!D' =+4 8?\CB#ppt_hBCB#ppt_hB*Y3>B ppt_h<*!D' =+4 8?bCB#ppt_x-.2BCB#ppt_xB*Y3>B ppt_x<*!D' =+4 8?\CB#ppt_yBCB#ppt_yB*Y3>B ppt_y<*!D' =-g6B fade*<3<*!D_' =%(D' =%(D' =4@BB6BB%()?D' =1:Bvisible*o3>+B#style.visibility<*N%(D' =+4 8?fCB#ppt_w*0.05BCB#ppt_wB*Y3>B ppt_w<*ND' =+4 8?\CB#ppt_hBCB#ppt_hB*Y3>B ppt_h<*ND' =+4 8?bCB#ppt_x-.2BCB#ppt_xB*Y3>B ppt_x<*ND' =+4 8?\CB#ppt_yBCB#ppt_yB*Y3>B ppt_y<*ND' =-g6B fade*<3<*N+8+0+!0 +;  0 #70 (  r  S P%5'(}w   l 7 ] -  4]7 - ,$D0ZB  s *D7 ]7   0y  Q  y Unit Boundary.8" dd2  @`B  0Dg   B  ND?"0@NNN?N7 = ' - l   7 ,$D0lB   <DlB   <Dmm| '  fH{v @?"6@ NNN?N-q  Point Origin PlaneP8" dd2  @~B   ND`B  0Dp  rB  BD8cm m B   TD?"0@NNN?NB # TD?"0@NNN?N-  l 7 m  2m7  ,$D0x &  `xv @?"6@`NNN?N-q  Plane Infinity PointP8" dd2   @4@    7 w n  0"`  n  0"`  `B  0DpmB  ND?"0@NNN?N}G]B $B ND?"0@NNN?N7- G= dl  7M  6 7M ,$D0B + ND?"0@NNN?N V (  fv @?"6@ NNN?N M 74  zParallel Lines.8" dd2  @B ) TD?"0@NNN?N  B * TD?"0@NNN?N  B ,B TD?"0@NNN?N = W B -B TD?"0@NNN?N= W B .B TD?"0@NNN?N= WM l g'T 5g'T,$D0: / B?"0@NNN?N Spatial (Euclidean) Geometry.8" dd2  @G 0 B?"0@NNN?Ngm'T )Counterspatial (Polar Euclidean) Geometry.*8" dd2* * @H  0?rs ? f;v3ff""___PPT10".Ѹp& +}0D]"' = @B D"' = @BA?%,( < +O%,( < +D_' =%(D' =%(D' =4@BB6BB%()?D' =1:Bvisible*o3>+B#style.visibility<*5%(D' =+4 8?fCB#ppt_w*0.05BCB#ppt_wB*Y3>B ppt_w<*5D' =+4 8?\CB#ppt_hBCB#ppt_hB*Y3>B ppt_h<*5D' =+4 8?bCB#ppt_x-.2BCB#ppt_xB*Y3>B ppt_x<*5D' =+4 8?\CB#ppt_yBCB#ppt_yB*Y3>B ppt_y<*5D' =-g6B fade*<3<*5D ' =%(D' =%(Dp' =4@BB1BB%()?D' =1:Bvisible*o3>+B#style.visibility<*7%(D' =+4 8?RCBBCB#ppt_wB*Y3>B ppt_w<*7D' =+4 8?RCBBCB#ppt_hB*Y3>B ppt_h<*7D' =+4 8?HCBCBCBB*k3>'Bstyle.rotation<*7D' =-g6B fade*<3<*7D ' =%(D' =%(Dp' =4@BB1BB%()?D' =1:Bvisible*o3>+B#style.visibility<*2%(D' =+4 8?RCBBCB#ppt_wB*Y3>B ppt_w<*2D' =+4 8?RCBBCB#ppt_hB*Y3>B ppt_h<*2D' =+4 8?HCBCBCBB*k3>'Bstyle.rotation<*2D' =-g6B fade*<3<*2D' =%(Dp' =%(D' =4@BB4BB%(D' =1:Bvisible*o3>+B#style.visibility<*4%(D' =0l9 BBzCzCBB*<3<*4%())?D' =.7 BBBBBM -0.46736 0.92887 C -0.37517 0.88508 -0.02552 0.75279 0.0908 0.66613 C 0.20747 0.57948 0.21649 0.50394 0.23177 0.40825 C 0.24705 0.31256 0.22118 0.15964 0.18264 0.09152 C 0.1441 0.02341 0.03802 0.0 0.0 0.0 *3>*B ppt_xB ppt_y=B0B<*4%())?D' =-g6B fade*<3<*4D' =%(Dp' =%(D' =4@BB4BB%(D' =1:Bvisible*o3>+B#style.visibility<*6%(D' =0l9 BBzCzCBB*<3<*6%())?D' =.7 BBBBBM -0.46736 0.92887 C -0.37517 0.88508 -0.02552 0.75279 0.0908 0.66613 C 0.20747 0.57948 0.21649 0.50394 0.23177 0.40825 C 0.24705 0.31256 0.22118 0.15964 0.18264 0.09152 C 0.1441 0.02341 0.03802 0.0 0.0 0.0 *3>*B ppt_xB ppt_y=B0B<*6%())?D' =-g6B fade*<3<*6+]  0 %%)7`K%(  r  S |'(}w   *l w T 2 wT,$D0B  ZD?"0@NNN?N  B  TDp?"0@NNN?N B   ZD?"0@NNN?N  2   N?"6@`NNN?N L   H?"0@NNN?Nw$ 0D8" dd2 @>  H?"0@NNN?N T P"D8" dd2$  @vl wm  0mw ,$D0B  TDp?"0@NNN?NmB B # lD?"0@NNN?N}}2  N?"6@`NNN?N]R   Ht?"0@NNN?Nw  "J8" dd2Go$ @<  H?"0@NNN?N]  P0D8" dd2  @` % H?"0@NNN?Nt,$0 |Outward in Space.8" dd2  @a & B(?"0@NNN?N w ,$0 Outward in Counterspace.8" dd2  @Tl g 3g,$D0B  HD?"0@NNN?NB  HD?"0@NNN?NB B ND?"0@NNN?N==  B ?"0@NNN?NGg m0.8" dd2  @  B( ?"0@NNN?Ng' m1.8" dd2  @  ) B ?"0@NNN?N'M4 nES.8" dd2  @4 + BH ?"0@NNN?N} ES: Equivalent Space08" dd2  @l  m  7 m ,$D0$ " BD% ?"0@NNN?NG 7  r"28" dd2'  @B  ND?"0@NNN?N m B  ND?"0@NNN?N m B   TD?"0@NNN?N  % # H@7 ?"0@NNN?N W  m1.8" dd2  @( ( H8 ?"0@NNN?N   pTime.8" dd2  @? , HlB ?"0@NNN?Nw   Time: Motion in Time Only08" dd2  @l =   6=  ,$D 0B  ND?"0@NNN?N   $ B,U ?"0@NNN?N= '$  m0.8" dd2  @- - BV ?"0@NNN?N7m wT  {Inward in Space.8" dd2  @l = 5=,$D0B B ND?"0@NNN?N==$ ! B+B#style.visibility<*0%(D' =+4 8?RCBBCB#ppt_wB*Y3>B ppt_w<*0D' =+4 8?RCBBCB#ppt_hB*Y3>B ppt_h<*0D' =+4 8?HCBCBCBB*k3>'Bstyle.rotation<*0D' =-g6B fade*<3<*0D ' =%(D' =%(Dp' =4@BB1BB%()?D' =1:Bvisible*o3>+B#style.visibility<*2%(D' =+4 8?RCBBCB#ppt_wB*Y3>B ppt_w<*2D' =+4 8?RCBBCB#ppt_hB*Y3>B ppt_h<*2D' =+4 8?HCBCBCBB*k3>'Bstyle.rotation<*2D' =-g6B fade*<3<*2Dl' =%(D' =%(D' =A@BB6BB0B%()?D' =1:Bvisible*o3>+B#style.visibility<*%%(D' =+4 8?fCB#ppt_w*0.05BCB#ppt_wB*Y3>B ppt_w<*%D' =+4 8?\CB#ppt_hBCB#ppt_hB*Y3>B ppt_h<*%D' =+4 8?bCB#ppt_x-.2BCB#ppt_xB*Y3>B ppt_x<*%D' =+4 8?\CB#ppt_yBCB#ppt_yB*Y3>B ppt_y<*%D' =-g6B fade*<3<*%Dl' =%(D' =%(D' =A@BB6BB0B%()?D' =1:Bvisible*o3>+B#style.visibility<*&%(D' =+4 8?fCB#ppt_w*0.05BCB#ppt_wB*Y3>B ppt_w<*&D' =+4 8?\CB#ppt_hBCB#ppt_hB*Y3>B ppt_h<*&D' =+4 8?bCB#ppt_x-.2BCB#ppt_xB*Y3>B ppt_x<*&D' =+4 8?\CB#ppt_yBCB#ppt_yB*Y3>B ppt_y<*&D' =-g6B fade*<3<*&D@' =%(D' =%(D' =4@BB1BB%())?)D' =1:Bvisible*o3>+B#style.visibility<*7%(D' =+4 8?RCBBCB#ppt_wB*Y3>B ppt_w<*7D' =+4 8?RCBBCB#ppt_hB*Y3>B ppt_h<*7D' =+4 8?HCBCBCBB*k3>'Bstyle.rotation<*7D' =-g6B fade*<3<*7D@' =%(D' =%(D' =4@BB1BB%())?)D' =1:Bvisible*o3>+B#style.visibility<*3%(D' =+4 8?RCBBCB#ppt_wB*Y3>B ppt_w<*3D' =+4 8?RCBBCB#ppt_hB*Y3>B ppt_h<*3D' =+4 8?HCBCBCBB*k3>'Bstyle.rotation<*3D' =-g6B fade*<3<*3D' =%(D' =%(DH' =4@BB4BB%()))D' =1:Bvisible*o3>+B#style.visibility<*5%(D' =0l9 BBzCzCBB*<3<*5%())?D' =.7 BBBBBM -0.46736 0.92887 C -0.37517 0.88508 -0.02552 0.75279 0.0908 0.66613 C 0.20747 0.57948 0.21649 0.50394 0.23177 0.40825 C 0.24705 0.31256 0.22118 0.15964 0.18264 0.09152 C 0.1441 0.02341 0.03802 0.0 0.0 0.0 *3>*B ppt_xB ppt_y=B0B<*5%())?D' =-g6B fade*<3<*5D' =%(Dp' =%(D' =4@BB4BB%(D' =1:Bvisible*o3>+B#style.visibility<*6%(D' =0l9 BBzCzCBB*<3<*6%())?D' =.7 BBBBBM -0.46736 0.92887 C -0.37517 0.88508 -0.02552 0.75279 0.0908 0.66613 C 0.20747 0.57948 0.21649 0.50394 0.23177 0.40825 C 0.24705 0.31256 0.22118 0.15964 0.18264 0.09152 C 0.1441 0.02341 0.03802 0.0 0.0 0.0 *3>*B ppt_xB ppt_y=B0B<*6%())?D' =-g6B fade*<3<*6+p+0+%0 ++0+&0 +z!  0 P(  r  S  '(}w     S  +(W><$0   H  0?rs ? f;v3ffbZ___PPT10:.ޮ+[W_D'  = @B D' = @BA?%,( < +O%,( < +Dl' =%(D' =%(D' =A@BB6BB0B%()?D' =1:Bvisible*o3>+B#style.visibility<*@%(D' =+4 8?fCB#ppt_w*0.05BCB#ppt_wB*Y3>B ppt_w<*@D' =+4 8?\CB#ppt_hBCB#ppt_hB*Y3>B ppt_h<*@D' =+4 8?bCB#ppt_x-.2BCB#ppt_xB*Y3>B ppt_x<*@D' =+4 8?\CB#ppt_yBCB#ppt_yB*Y3>B ppt_y<*@D' =-g6B fade*<3<*@Dl' =%(D' =%(D' =A@BB6BB0B%()?D' =1:Bvisible*o3>+B#style.visibility<*@%(D' =+4 8?fCB#ppt_w*0.05BCB#ppt_wB*Y3>B ppt_w<*@D' =+4 8?\CB#ppt_hBCB#ppt_hB*Y3>B ppt_h<*@D' =+4 8?bCB#ppt_x-.2BCB#ppt_xB*Y3>B ppt_x<*@D' =+4 8?\CB#ppt_yBCB#ppt_yB*Y3>B ppt_y<*@D' =-g6B fade*<3<*@Dl' =%(D' =%(D' =A@BB6BB0B%()?D' =1:Bvisible*o3>+B#style.visibility<*%(D' =+4 8?fCB#ppt_w*0.05BCB#ppt_wB*Y3>B ppt_w<*D' =+4 8?\CB#ppt_hBCB#ppt_hB*Y3>B ppt_h<*D' =+4 8?bCB#ppt_x-.2BCB#ppt_xB*Y3>B ppt_x<*D' =+4 8?\CB#ppt_yBCB#ppt_yB*Y3>B ppt_y<*D' =-g6B fade*<3<*Dl' =%(D' =%(D' =A@BB6BB0B%()?D' =1:Bvisible*o3>+B#style.visibility<*Y%(D' =+4 8?fCB#ppt_w*0.05BCB#ppt_wB*Y3>B ppt_w<*YD' =+4 8?\CB#ppt_hBCB#ppt_hB*Y3>B ppt_h<*YD' =+4 8?bCB#ppt_x-.2BCB#ppt_xB*Y3>B ppt_x<*YD' =+4 8?\CB#ppt_yBCB#ppt_yB*Y3>B ppt_y<*YD' =-g6B fade*<3<*Y+8+0+0 +z!  0 P(  r  S  '(}w     S  +(W><$0   H  0?rs ? f;v3ffbZ___PPT10:.-+[W_D'  = @B D' = @BA?%,( < +O%,( < +Dl' =%(D' =%(D' =A@BB6BB0B%()?D' =1:Bvisible*o3>+B#style.visibility<*=%(D' =+4 8?fCB#ppt_w*0.05BCB#ppt_wB*Y3>B ppt_w<*=D' =+4 8?\CB#ppt_hBCB#ppt_hB*Y3>B ppt_h<*=D' =+4 8?bCB#ppt_x-.2BCB#ppt_xB*Y3>B ppt_x<*=D' =+4 8?\CB#ppt_yBCB#ppt_yB*Y3>B ppt_y<*=D' =-g6B fade*<3<*=Dl' =%(D' =%(D' =A@BB6BB0B%()?D' =1:Bvisible*o3>+B#style.visibility<*=y%(D' =+4 8?fCB#ppt_w*0.05BCB#ppt_wB*Y3>B ppt_w<*=yD' =+4 8?\CB#ppt_hBCB#ppt_hB*Y3>B ppt_h<*=yD' =+4 8?bCB#ppt_x-.2BCB#ppt_xB*Y3>B ppt_x<*=yD' =+4 8?\CB#ppt_yBCB#ppt_yB*Y3>B ppt_y<*=yD' =-g6B fade*<3<*=yDl' =%(D' =%(D' =A@BB6BB0B%()?D' =1:Bvisible*o3>+B#style.visibility<*y%(D' =+4 8?fCB#ppt_w*0.05BCB#ppt_wB*Y3>B ppt_w<*yD' =+4 8?\CB#ppt_hBCB#ppt_hB*Y3>B ppt_h<*yD' =+4 8?bCB#ppt_x-.2BCB#ppt_xB*Y3>B ppt_x<*yD' =+4 8?\CB#ppt_yBCB#ppt_yB*Y3>B ppt_y<*yD' =-g6B fade*<3<*yDl' =%(D' =%(D' =A@BB6BB0B%()?D' =1:Bvisible*o3>+B#style.visibility<*%(D' =+4 8?fCB#ppt_w*0.05BCB#ppt_wB*Y3>B ppt_w<*D' =+4 8?\CB#ppt_hBCB#ppt_hB*Y3>B ppt_h<*D' =+4 8?bCB#ppt_x-.2BCB#ppt_xB*Y3>B ppt_x<*D' =+4 8?\CB#ppt_yBCB#ppt_yB*Y3>B ppt_y<*D' =-g6B fade*<3<*+8+0+0 +  0 P(  r  S  '(}w     S  +(W><$0   H  0?rs ? f;v3ff___PPT10. n+[W_Db'  = @B D' = @BA?%,( < +O%,( < +Dl' =%(D' =%(D' =A@BB6BB0B%()?D' =1:Bvisible*o3>+B#style.visibility<*n%(D' =+4 8?fCB#ppt_w*0.05BCB#ppt_wB*Y3>B ppt_w<*nD' =+4 8?\CB#ppt_hBCB#ppt_hB*Y3>B ppt_h<*nD' =+4 8?bCB#ppt_x-.2BCB#ppt_xB*Y3>B ppt_x<*nD' =+4 8?\CB#ppt_yBCB#ppt_yB*Y3>B ppt_y<*nD' =-g6B fade*<3<*nDl' =%(D' =%(D' =A@BB6BB0B%()?D' =1:Bvisible*o3>+B#style.visibility<*n%(D' =+4 8?fCB#ppt_w*0.05BCB#ppt_wB*Y3>B ppt_w<*nD' =+4 8?\CB#ppt_hBCB#ppt_hB*Y3>B ppt_h<*nD' =+4 8?bCB#ppt_x-.2BCB#ppt_xB*Y3>B ppt_x<*nD' =+4 8?\CB#ppt_yBCB#ppt_yB*Y3>B ppt_y<*nD' =-g6B fade*<3<*nDl' =%(D' =%(D' =A@BB6BB0B%()?D' =1:Bvisible*o3>+B#style.visibility<*%(D' =+4 8?fCB#ppt_w*0.05BCB#ppt_wB*Y3>B ppt_w<*D' =+4 8?\CB#ppt_hBCB#ppt_hB*Y3>B ppt_h<*D' =+4 8?bCB#ppt_x-.2BCB#ppt_xB*Y3>B ppt_x<*D' =+4 8?\CB#ppt_yBCB#ppt_yB*Y3>B ppt_y<*D' =-g6B fade*<3<*+8+0+0 + 0 P(  r  S  '(}w     S  +(W><$0   H  0?rs ? f;v3ff___PPT10.0+[W_Db'  = @B D' = @BA?%,( < +O%,( < +Dl' =%(D' =%(D' =A@BB6BB0B%()?D' =1:Bvisible*o3>+B#style.visibility<*[%(D' =+4 8?fCB#ppt_w*0.05BCB#ppt_wB*Y3>B ppt_w<*[D' =+4 8?\CB#ppt_hBCB#ppt_hB*Y3>B ppt_h<*[D' =+4 8?bCB#ppt_x-.2BCB#ppt_xB*Y3>B ppt_x<*[D' =+4 8?\CB#ppt_yBCB#ppt_yB*Y3>B ppt_y<*[D' =-g6B fade*<3<*[Dl' =%(D' =%(D' =A@BB6BB0B%()?D' =1:Bvisible*o3>+B#style.visibility<*[%(D' =+4 8?fCB#ppt_w*0.05BCB#ppt_wB*Y3>B ppt_w<*[D' =+4 8?\CB#ppt_hBCB#ppt_hB*Y3>B ppt_h<*[D' =+4 8?bCB#ppt_x-.2BCB#ppt_xB*Y3>B ppt_x<*[D' =+4 8?\CB#ppt_yBCB#ppt_yB*Y3>B ppt_y<*[D' =-g6B fade*<3<*[Dl' =%(D' =%(D' =A@BB6BB0B%()?D' =1:Bvisible*o3>+B#style.visibility<*'%(D' =+4 8?fCB#ppt_w*0.05BCB#ppt_wB*Y3>B ppt_w<*'D' =+4 8?\CB#ppt_hBCB#ppt_hB*Y3>B ppt_h<*'D' =+4 8?bCB#ppt_x-.2BCB#ppt_xB*Y3>B ppt_x<*'D' =+4 8?\CB#ppt_yBCB#ppt_yB*Y3>B ppt_y<*'D' =-g6B fade*<3<*'+8+0+0 +0 2*T(  T^ T S    <$ T c $Q< 0  < This is the primary question students of the Reciprocal System ask, after reading Larson s dissertation on how you can have linear vibration without anything to vibrate, yet he requires LV as a prerequisite to rotational motion. NOTE: conventional definitions of space/time and time/space are used in this presentation. Larson s  regions are backwards in that they are the other way around:  space/time is Larson s  time-space region and  time/space is Larson s  space-time region. They are distinguished by the connecting punctuation: dash for Larson and slash for conventional. I H T 0޽h鳊 ? ̙3380___PPT10.ZP 0 X`(  X^ X S    # X c $ȃ# 0d  #LD___PPT9& Regions of motion are separated by unit boundaries, of which there are two types, making three boundaries: The UNIT SPEED boundary, where the boundary is at s/t=1 or t/s=1, which separates the material and cosmic sectors. Two UNIT ASPECT boundaries, where motion occurs within a single unit of space or time (the numerator is fixed at unity, and only the denominator can increase speed). There is a fourth boundary, the one that separates material and cosmic atomic regions, but that was not within Larson s theory (it will be addressed later on, as a natural consequence of RS2).<k" " k E H X 0޽h鳊 ? ̙3380___PPT10.0@> 0 dN(  d^ d S    # d c $# 0  # DThis describes the normal, Euclidean setup that Larson uses, where linear motion is primary and is a prerequisite for rotation, which is simply a shear of two linear motions. The catch here is that the  linear motion is NOT  linear vibration , but the basic, outward translation of the natural reference system. To get linear vibration, Larson had to create a  direction reversal , but we will soon see that device is unnecessary, when the actual reciprocal relationships between space/time and the time region are clarified.  H d 0޽h鳊 ? ̙3380___PPT10.Y 0 80l(  l^ l S    >* l c $> 0  > jWith the scalar (min and max quantities) and geometric reciprocal relationships identified according to Region, it becomes apparent how Larson came to the conclusions that he did& The minimum motion within the Time Region is a rotation at unit speed the rotational equivalent of nothing, aka the  rotational base . Secondary motion is a the shift a linear vibration the  direction reversal . The motion characteristics of the Time Region thus give rise to both of Larson s base concepts of linear vibration and the rotational base but not necessarily in that order.$6  6 H l 0޽h鳊 ? ̙3380___PPT10.e 0 JB0t(  t^ t S    >< t c $.> 0  > Because Larson did not separate the space/time region and time region geometries, he ended up with 4 motions, all lumped together, without a clear distinction of what was primary and what was secondary. Those motions being: Linear outward (TSR primary), Rotational outward (TR primary), Linear vibration (TR secondary) and rotation (TSR secondary).  Oscillation as rotation is termed such because, unlike the Turn, it has a bounded angle with a range of 0 to pi, oscillating between 0 and pi in 2 dimensions. He then based his development on the incorrect assumption that all 4 of these motions were primary. KVK Nehru recognized this failing early on, and developed the bi-rotation model to compensate for the lack of a primary motion underlying the photon vibration. And as we have seen, it corrected virtually all of Larson s photon model problems. U H t 0޽h鳊 ? ̙3380___PPT10.K 0 (  ^  S    >  c $ A> 0  > 5We have been observing the Universe of Motion from the same reference region that the motion, itself, occurs in. Space/time region motion was observed from the space/time region; time region motion from the time region. The study of projective geometry allows us to move the observer to any region we wish, and to properly interpret the characteristics and geometries as they would appear to the observer. Since our microscopes and telescopes are firmly fixed in the space/time region, we can use the tool of projection to clearly see what could not be seen before.$6 / 6 H  0޽h鳊 ? ̙3380___PPT10.¸7{`0 p(  ^  S    >  c $M> 0  > f>By recognizing the geometric differences, we can now combine both geometries into a complex representation, including both the real numbers of rectangular coordinate systems and the imaginary numbers of the polar coordinate system, to get a clear and concise view of the entities that exist as combinations of motions. ? H  0޽h鳊 ? ̙3380___PPT10.ønf0 0v(  ^  S    >  c $8W> 0  > lDWith the mix of rectangular and polar geometries, a problem comes up with labels for motions. For example, a rotation in space/time is technically a 2-dimensional oscillation, because the rotation always moves from minimum to maximum, then back to minimum it oscillates though it appears to be one, continuous motion. However, rotation within the time region is unbounded as the Turn it can have an infinite angle and thus never turns back upon itself. The Counterspace terms of  turn and  shift provide a solution to this naming problem, introducing new terms which, at first, seem confusing, but in the long run aid in clarifying the types of motion one is dealing with.  H  0޽h鳊 ? ̙3380___PPT10.Ÿn*0 z(  ^  S    >t  c $j> 0  > Projective Geometry uses terms of  space and  counterspace to refer to regions of geometry. In RS terms, the PG  space is the space/time region, coupled to rectangular geometry. The PG  counterspace is the time region coupled with polar geometry. Of course, the cosmic equivalents of  time and  countertime would also exist within RS2, but are unknown within PG. q H  0޽h鳊 ? ̙3380___PPT10.ϸ@IP0 4,(  ^  S    >&  c $0o> 0  > XSpatial and counterspatial geometry are perfect inverses of each other, which one would expect in a theory known as the  Reciprocal System . A geometric inverse is called a  Dual and in a 3-dimensional system, points and planes are duals of each other, and the line is a dual of itself. When we take the  dual of rectangular, Euclidean geometry to find the counterspace equivalent, we exchange the points and planes: The Euclidean plane at infinity becomes a counterspatial point at infinity The Euclidean point at zero (the origin) becomes a counterspatial plane at zero (origin). This counterspace view then looks like a standard, vanishing-point perspective used by artists to render scenery on their canvas (the plane at zero), where parallel lines are drawn radially towards a vanishing point at infinity.2 "  " - - H  0޽h鳊 ? ̙3380___PPT10.ָk 0 RJ(  ^  S    >D  c $> 0  > Unity is the natural datum in a Universe of Motion, therefore the minimum quantity of motion, as we have seen is 1. All motion must, therefore, be composed of magnitudes greater than or equal to 1; 0 and infinity become reference points for direction. All motion is  outward in direction, proceeding from zero to infinity. From the spatial viewpoint, the center of a unit of space is zero. From the counterspatial viewpoint, that same point is infinity. If we retain the point of observation in the time-space region, the region of our microscopes, the time region will exhibit inverse behavior; what was  outward in time now becomes  inward in space, and this gives us Larson s concept of  inward motion.    H  0޽h鳊 ? ̙3380___PPT10.0  ,(  ^  S    >  c $r> 0  > " H  0޽h鳊 ? ̙3380___PPT10.]`0 2*0(  ^  S    >$  c $p> 0  > Linear translation in the space/time region always occurs, as progression. Linear vibration (the photon) cannot occur until a rotation occurs in the time region to create it as a secondary motion. Turning (unbounded rotation) in the time region always occurs, as the rotational base. Rotation cannot occur until a linear translation occurs in the space/time region to create it as a secondary motion.  H  0޽h鳊 ? ̙3380___PPT10.]ª0 @,(  ^  S    >  c $(> 0  > " H  0޽h鳊 ? ̙3380___PPT10.]P,0 P,(  ^  S    >  c $> 0  > " H  0޽h鳊 ? ̙3380___PPT10.]`3r"v\ Qg);4wA,Rt}~l: .p8 Zt8# :41Oh+'0  X` 4RS2: Re-evaluting the Reciprocal System of theoryRS2 Bruce PeretGlobe Bruce Peret115@ f@P՜.+,0|    Custom AntiquatisA' ArialArial Unicode MS StarSymbolTimes New RomanVerdana WingdingsTahomaGlobeOcean.Re-Evaluating the Reciprocal System of theoryRegions of MotionSpace/time Region SpeedsTime Region SpeedsPrimary and Secondary Motions GeometriesLearning from ContradictionsGeometric PerspectivesSpace and Counterspace"Spatial & Counterspatial GeometryDirections of MotionSummary of RegionsSummary of Motions ConclusionsEpilog  Fonts UsedDesign Template Slide Titles#_ Bruce PeretBruce Peret  !"#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcdefghijklmnopqrstuvwyz{|}~      !"#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcdefghijklmnopqrstuvwxyz{|}~      !"#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcdefghiklmnopqstuvwxy{|}~Root EntrydO)Pictures7Current UserzSummaryInformation(jPowerPoint Document(x DocumentSummaryInformation8r