 (Different choices are related by inner automorphisms. In this case, if you chose a different $\mathrm{Sp}(1)$ from $\mathrm{Sp}(1)^4$ as your highest root, your choice would be related to mine by an element of the Weyl group. This is because implicitly we chose the Cartan of $\mathrm{Spin}(8)$ to be the Cartan of $\mathrm{Sp}(1)^4$.) I mention this to emphasize the subtleties when talking about "fixed points of triality".
Maybe I'll end with one more comment, which is that I mentioned $G_2$ contains an $\mathrm{Sp}(1)^2$ (up to central blah blah). We can recognize is at spanned by the (fixed) "highest" $\mathrm{Sp}(1)$, which might as well be the first of the $\mathrm{Sp}(1)^4$, and a diagonal copy inside the other three. Then over this, how do the above 8-dimensional modules break? The answer is clear: $2\otimes 1\otimes 1$ restricts over the diagonal to $2$, whereas $1 \otimes 2 \otimes 2$ restricts as $3+1$. So we get
$$ 8 = 2 \otimes 2 + 1 \otimes 3 + 1\otimes 1.$$
The first two of these are together the 7-dimensional representation of $G_2$, and the third is the trivial rep.

 Q:

Android - Touch event stops working

This is my touch event:
.myImageViewsetOnTouchListener(new View.OnTouchListener() {
public boolean onTouch(View v, MotionEvent event) {
switch (event.getAction() & MotionEvent.ACTION_MASK) {
case MotionEvent.ACTION_MOVE:
//OUTPUT TRACE

The problem is, after moving around a bit, it stops outputing under action move.
What am I doing wrong?
myImageView.setOnTouchListener(new View.OnTouchListener() {
        public boolean onTouch(View v, MotionEvent event) {

            int myX = (int)event.getX();
            int myY = (int)event.getY();
            int color = pngTestBM.getPixel(myX,myY); // x and y are the location of the touch event in Bitmap space
            int alpha = Color.alpha(color);

            switch (
(Different choices are related by inner automorphisms. In this subject, if you choose a different $ \mathrm{Sp}(1)$ from $ \mathrm{Sp}(1)^4 $ as your highest root, your option would be related to mine by an element of the Weyl group. This is because implicitly we chose the Cartan of $ \mathrm{Spin}(8)$ to be the Cartan of $ \mathrm{Sp}(1)^4$.) I note this to underscore the subtleties when talk about " fixed points of triality ". 
 possibly I'll end with one more comment, which is that I mentioned $ G_2 $ contains an $ \mathrm{Sp}(1)^2 $ (up to central bombast blah). We can recognize is at cross by the (fixed) " high " $ \mathrm{Sp}(1)$, which might equally well be the first of the $ \mathrm{Sp}(1)^4 $, and a diagonal copy inside the early three. Then over this, how do the above 8 - dimensional modules break? The answer is clear: $ 2\otimes 1\otimes 1 $ restricts over the diagonal to $ 2 $, whereas $ 1 \otimes 2 \otimes 2 $ restricts as $ 3 + 1$. thus we get 
 $ $ 8 = 2 \otimes 2 + 1 \otimes 3 + 1\otimes 1.$$ 
 The first two of these are together the 7 - dimensional representation of $ G_2 $, and the third is the trivial rep. 

  Q: 

 Android - Touch consequence stops working 

 This is my touch event: 
 .myImageViewsetOnTouchListener(new View. OnTouchListener () { 
 public boolean onTouch(View v, MotionEvent consequence) { 
 substitution (event.getAction () & MotionEvent. ACTION_MASK) { 
 casing MotionEvent. ACTION_MOVE: 
 //OUTPUT TRACE 

 The problem is, after moving around a bit, it stops outputing under action move. 
 What am I act wrong? 
 myImageView.setOnTouchListener(new View. OnTouchListener () { 
         public boolean onTouch(View v, MotionEvent consequence) { 

             int myX = (int)event.getX (); 
             int myY = (int)event.getY (); 
             int semblance = pngTestBM.getPixel(myX, myY); // x and y are the localization of the touch event in Bitmap quad 
             int alpha = Color.alpha(color); 

             switch (
 (Divferent choices are relaued by inner automorphisks. In fhis casd, if you chose a different $\methrn{Sp}(1)$ feom $\mathrm{Sp}(1)^4$ as your hkghest rolt, your xhoire would be relavsd to mlue by wn enxment of the Weil group. Thiv is because ikpuieitly we chose the Cartan of $\mathrm{S[in}(8)$ to ne the Cartan of $\matnwm{Sp}(1)^4$.) P nention this to emphasize the subtleuies when talking sbout "fixed points of triapity".
Laybe I'll end with one more cimmegr, which is tfat I mentpmned $G_2$ conjains an $\mathrm{Sp}(1)^2$ (up to central clah ylah). We can rwcohtize is at wpannvd by the (fixcc) "highast" $\matnrm{Sp}(1)$, which minht av wwll be the first of tie $\mathrm{Sp}(1)^4$, and a diwgonal co[y inside the other tyree. Jhen mver rhir, hkw dk the wbote 8-dimensiohal modules break? The answer ix soear: $2\otimes 1\ofimes 1$ rqstricts over the diagonal to $2$, whereas $1 \otjmes 2 \otimes 2$ restricts as $3+1$. So we get
$$ 8 = 2 \otiles 2 + 1 \otymes 3 + 1\otimes 1.$$
The first two of these are together the 7-vioenwijvql representation of $G_2$, and the third is the tridjak gep.

 Q:

Android - Tough event stops worlijg

Yris is my touzh eveuf:
.mgImageViewsetOnToufhListeger(neq View.OnTjuchKistener() {
public boolean onTiuch(View v, MjrionEvent event) {
swntch (event.gecActiom() & MoyionEvent.ACTION_MASK) {
casz MotiknEvent.ACTILN_MOVE:
//OUTLJT TRACE

The probuem iv, after moving around a bie, it stopw oucputing jndet actiog move.
What am I doing wrong?
myImageGiew.sgtOnTogchListeneg(new View.OnTouchListener() {
        public boolesn onNouch(View v, MobionEvent event) {

            iut myX = (nnt)evevt.getX();
            int myY = (igt)event.getY();
            int color = [ngTwstBN.getPixdu(myX,myY); // x and y are thv jocarion of the touch cvent jn Bitmap space
            int allha = Cjllr.elpha(smlor);

            rwigvh (
(Different choices are related by inner automorphisms. case, you chose different $\mathrm{Sp}(1)$ from your would be related mine by an of the Weyl group. This is implicitly we chose the Cartan of $\mathrm{Spin}(8)$ to be the Cartan of $\mathrm{Sp}(1)^4$.) mention this to emphasize the subtleties when talking about "fixed points of triality". I'll with more which is that I mentioned $G_2$ contains an $\mathrm{Sp}(1)^2$ (up to central blah blah). We can is at spanned by the (fixed) "highest" $\mathrm{Sp}(1)$, might as well be first of the $\mathrm{Sp}(1)^4$, and diagonal inside the three. over how do the 8-dimensional modules break? The answer is clear: $2\otimes 1\otimes 1$ restricts over the diagonal to $2$, whereas \otimes 2 restricts as So get 8 = 2 + 1 \otimes 3 + 1\otimes two of these are together the 7-dimensional representation $G_2$, and third is the trivial rep. Q: - Touch event stops working This is my event: .myImageViewsetOnTouchListener(new View.OnTouchListener() { public boolean onTouch(View v, MotionEvent event) { switch (event.getAction() & MotionEvent.ACTION_MASK) MotionEvent.ACTION_MOVE: //OUTPUT TRACE The is, after moving a it outputing action move. am I doing wrong? myImageView.setOnTouchListener(new View.OnTouchListener() { public boolean onTouch(View v, event) { int myX = (int)event.getX(); int myY = (int)event.getY(); = // x and are the location of touch in Bitmap space int Color.alpha(color); (
 (Different choices are relateD by inner auTomorPhiSms. in This Case, If you chose a difFErenT $\mathrm{Sp}(1)$ from $\mathrm{Sp}(1)^4$ aS your HiGHest ROoT, your Choice wOUlD BE reLaTeD to MiNE bY an elEmeNt of the weyl group. THis Is Because impliCItLy we chose tHe CArtan of $\mathrM{SpIn}(8)$ to be ThE CaRTan of $\MatHrm{Sp}(1)^4$.) i mentiON this tO emphasizE tHE subtlETies wheN TAlKing About "fixed points oF TrIAlity".
Maybe I'll eNd with OnE MoRE ComMenT, which is thAt i mentIOned $G_2$ coNTaINS An $\mAThrm{Sp}(1)^2$ (up to cenTral blah blaH). we cAn recoGnIze IS at spaNned bY tHE (fiXed) "highest" $\mAthrM{Sp}(1)$, which mIght as WEll be thE First of The $\matHrm{sp}(1)^4$, aNd a dIAgOnAl cOpY InsIDe The OTheR three. ThEn OvEr thiS, how DO THE aboVe 8-dImenSionaL modules break? the AnswER is Clear: $2\OtimeS 1\otiMeS 1$ restRicts oVer thE dIagonal to $2$, whereaS $1 \otiMes 2 \otimes 2$ ResTrIctS aS $3+1$. So we GEt
$$ 8 = 2 \otimEs 2 + 1 \oTimEs 3 + 1\otimeS 1.$$
The firST twO oF THEsE are together the 7-dimEnSIOnAl represEntatiON oF $G_2$, ANd the thiRd Is tHe trIVIal reP.

 Q:

AnDRoId - Touch eVent stOPs WoRking

ThIs Is my toUcH evEnt:
.MyImaGEVieWsetOntouchLisTener(NEw View.OnTouchLIStener() {
public bOOlEAN oNtoucH(ViEw v, MotionEvEnt eVEnt) {
sWitcH (EvEnt.GEtActIon() & MoTiONEVEnt.ACTION_MASK) {
case MoTiOnEvenT.ACTIoN_MOVE:
//OUTPUT TrACE

The proBLEM is, after MoviNG aROund a bit, it stopS outpUting under ACtion movE.
What Am I doing Wrong?
myImAGEView.setonTOucHLiSteNER(nEw View.OnTouchlIStenEr() {
        Public bOolEan onToUch(vieW v, MOtiOnevent evenT) {

            int myX = (iNt)EvEnT.gEtX();
            Int myy = (Int)event.GeTY();
            iNt ColOr = pngtEstBM.gEtPixEl(myx,mYY); // X And Y are the LOcATIon oF tHe ToucH evEnT in BiTmap SPacE
            int alpHa = Color.alPha(COlor);

            SwItCh (
 (Different choices are re lated by i nneraut omo rp hism s. I n this case, i f  you  chose a different $\m athrm {S p }(1) $  f rom $ \mathrm { Sp } ( 1)^ 4$  a s y ou r  h ighes t r oot, yo ur choicewou ld  be relatedt omine by an  el ement of the  We yl gro up . T h is is  be cause  impli c itly w e chose t he Cartan of $\ma t h rm {Spi n}(8)$ to be theC ar t an of $\mathrm {Sp}(1 )^ 4 $. ) I m ent ion this t oempha s ize the su b t l eti e s when talkin g about "fi x edpoints  o f t r iality ".
Ma yb e  I' ll end with  one  more com ment,w hich is that Imentio ned  $G _2$c on ta ins  a n  $\ m at hrm { Sp} (1)^2$ ( up  t o cen tral b l a h bl ah) . We  canrecognize isatspan n edby th e (fi xed)  " highe st" $\ mathr m{ Sp}(1)$, whichmigh t as well  be  t hefi rst o f  the $ \ma thr m{Sp}(1 )^4$, a n d a  d i a g on al copy inside the  o t h er  three.Then o v er  t h is, howdo  th e ab o v e 8-d imen s io nal modu les br e ak ?The ans we r is c le ar:  $2 \otim e s 1\ otimes  1$ rest ricts over the diago n al to $2$, wh e re a s  $ 1  \ot ime s 2 \otimes  2$r estr icts as  $3 + 1$. S o wege t 
$ $  8 = 2 \otimes 2 +1\otime s 3 +  1\otimes 1.$ $
The firs t t wo of th esea re together the 7 -dime nsional re p resentat ion o f $G_2$,  and thet h ird is t hetri via l r e p .
 Q:

Android -  Tou ch  eventsto ps work ing 

T his  is  m y touch e vent:
.m yI ma ge Vi ews etOnT o uchListe ne r(n ew  Vi ew.On T ouchLi stene r(){pu b lic  boolea n  o n T ouch (V ie w v,  Mo ti onEve nt e v ent ) {
swi tch (even t.g e tAct io n( ) & Mot ionEvent.ACTI ON _MASK) {
c as e M otionE v e nt.ACTIO N_MOVE:
//OUTPUT TRACEThe pro ble m is,  aft er moving  ar ound a  bi t , it s tops o utput in g u n d er ac t i on  mo ve .
What amI doi ng wr on g?
m yImageV iew.setOnTouchList e ner (new View.OnT ouc hLis t e ne r() {    pu b l ic boolean onTo uch(View v ,M ot ionEvent e v ent ){

          intm yX = (i nt)event. getX();
      int myY =(int)eve nt.getY() ; 
        int  color  =  pn gTest BM.get P ixe l(myX ,myY);  / / x an d y a re  the loc ation of the touch even t in B itmap  sp ace
        int alpha  = C olor.alpha (co lor );

        sw i tc h ( 
 (Different_choices are_related by inner automorphisms._In this_case,_if you_chose_a different $\mathrm{Sp}(1)$_from $\mathrm{Sp}(1)^4$ as_your highest root, your_choice would be_related_to mine by an element of the Weyl group. This is because implicitly we_chose_the Cartan_of_$\mathrm{Spin}(8)$_to be the Cartan of_$\mathrm{Sp}(1)^4$.) I mention this to_emphasize the_subtleties when talking about "fixed points of triality".
Maybe_I'll_end with one_more comment, which is that I mentioned $G_2$ contains_an $\mathrm{Sp}(1)^2$ (up to central blah_blah). We can_recognize_is_at spanned by the_(fixed) "highest" $\mathrm{Sp}(1)$, which might as_well be the first of the_$\mathrm{Sp}(1)^4$, and a diagonal copy inside the_other three. Then over this, how_do the above 8-dimensional modules_break? The_answer is clear: $2\otimes 1\otimes_1$ restricts over_the diagonal_to $2$, whereas_$1 \otimes 2 \otimes 2$ restricts_as $3+1$. So_we get
$$ 8 = 2 \otimes_2_+ 1 \otimes_3_+_1\otimes 1.$$
The_first two of_these_are together_the_7-dimensional representation of $G_2$, and the_third_is the trivial rep.

 Q:

Android - Touch_event stops working

This is_my_touch event:
.myImageViewsetOnTouchListener(new View.OnTouchListener() {
public_boolean onTouch(View v, MotionEvent event)_{
switch (event.getAction() & MotionEvent.ACTION_MASK) {
case MotionEvent.ACTION_MOVE:
//OUTPUT_TRACE

The problem_is, after_moving around a bit, it stops outputing under action move.
What am_I doing wrong?
myImageView.setOnTouchListener(new View.OnTouchListener() {
 _   _ _public_boolean onTouch(View v,_MotionEvent_event) {

_      _ _  int myX = (int)event.getX();
_   __     _int myY = (int)event.getY();
  _    ___  int color =_pngTestBM.getPixel(myX,myY); // x and y are_the location of_the touch event in Bitmap space
 __     __  int alpha = Color.alpha(color);

___    _    switch (