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0.8701274588208152, -0.4051777247938366}, {-0.18784013719656167`, \ -0.7951722478530527}}}}, {{ Hold[Cell$$10472`universeScaleFunction$$], 1& }}}, Typeset`size$$ = { 350., {173., 177.}}, Typeset`update$$ = 0, Typeset`initDone$$, Typeset`skipInitDone$$ = False, Cell$$10472`universeType$832345$$ = False, Cell$$10472`fit$832346$$ = False, Cell$$10472`hubble$832347$$ = 0, Cell$$10472`normalFontSize$832348$$ = 0, Cell$$10472`t$832349$$ = 0}, DynamicBox[Manipulate`ManipulateBoxes[ 1, StandardForm, "Variables" :> { Cell$$10472`curTime$$ = 0, Cell$$10472`end1$$ = {-0.9, -0.9}, Cell$$10472`end2$$ = {-0.8, -0.9}, Cell$$10472`eventSource$$ = Cell$$10472`CANVAS, Cell$$10472`fit$$ = False, Cell$$10472`graphicScale$$ = Null, Cell$$10472`hubble$$ = 0.05, Cell$$10472`lastTime$$ = 0, Cell$$10472`mode$$ = Cell$$10472`INITIALIZED, Cell$$10472`modeBeforeRecentering$$ = Cell$$10472`INITIALIZED, Cell$$10472`mx$$ = 0, Cell$$10472`my$$ = 0, Cell$$10472`normalFontSize$$ = 12, Cell$$10472`objectPositions$$ = {{ 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Cell$$10472`recenterStartTime$$ = 3.431772327504175*^9, Cell$$10472`rulerLabel$$ = "0.1 units", Cell$$10472`scale$$ = 1, Cell$$10472`scaledEnd1$$ = {-0.9, -0.9}, Cell$$10472`scaledEnd2$$ = {-0.8, -0.9}, Cell$$10472`scaledRulerCenter$$ = {-0.85, -0.9}, Cell$$10472`t$$ = 0, Cell$$10472`targetCenter$$ = 0, Cell$$10472`universeScaleFunction$$ = 1& , Cell$$10472`universeType$$ = Cell$$10472`DeSitterUniverse, Cell$$10472`unscaledCenter$$ = {0, 0}}, "ControllerVariables" :> { Hold[ Cell$$10472`universeType$$, Cell$$10472`universeType$832345$$, False], Hold[Cell$$10472`fit$$, Cell$$10472`fit$832346$$, False], Hold[Cell$$10472`hubble$$, Cell$$10472`hubble$832347$$, 0], Hold[ Cell$$10472`normalFontSize$$, Cell$$10472`normalFontSize$832348$$, 0], Hold[Cell$$10472`t$$, Cell$$10472`t$832349$$, 0]}, "OtherVariables" :> { Typeset`show$$, Typeset`bookmarkList$$, Typeset`bookmarkMode$$, Typeset`animator$$, Typeset`animvar$$, Typeset`name$$, Typeset`specs$$, Typeset`size$$, Typeset`update$$, Typeset`initDone$$, Typeset`skipInitDone$$}, "Body" :> (Which[ And[ Cell$$10472`mode$$ =!= Cell$$10472`INITIALIZED, Cell$$10472`t$$ == 0], Cell$$10472`mode$$ = Cell$$10472`INITIALIZED; Cell$$10472`unscaledCenter$$ = {0, 0}; Cell$$10472`eventSource$$ = Cell$$10472`CANVAS; Cell$$10472`end1$$ = Cell$$10472`initialRulerEndPoint; Cell$$10472`end2$$ = Cell$$10472`initialRulerEndPoint + {Cell$$10472`rulerScale, 0}; Cell$$10472`perp$$ = {0, 1}; Cell$$10472`curTime$$ = 0; Cell$$10472`lastTime$$ = 0; Cell$$10472`objectPositions$$ = RandomReal[{-1, 1}, {Cell$$10472`numObjects, 2}]; Cell$$10472`universeScaleFunction$$ = 1& , And[ Or[ Cell$$10472`mode$$ === Cell$$10472`INITIALIZED, Cell$$10472`mode$$ === Cell$$10472`STOPPED], Cell$$10472`t$$ != Cell$$10472`lastTime$$], If[Cell$$10472`mode$$ === Cell$$10472`INITIALIZED, Cell$$10472`universeScaleFunction$$ = Cell$$10472`universeType$$; Null]; Cell$$10472`mode$$ = Cell$$10472`RUNNING; If[Cell$$10472`t$$ < Cell$$10472`lastTime$$, Cell$$10472`t$$ = Cell$$10472`lastTime$$], And[ Cell$$10472`mode$$ === Cell$$10472`RUNNING, Cell$$10472`t$$ === Cell$$10472`lastTime$$], Cell$$10472`mode$$ = Cell$$10472`STOPPED; AddTo[Cell$$10472`curTime$$, Cell$$10472`hubble$$ (Cell$$10472`t$$ - Cell$$10472`lastTime$$)]; Cell$$10472`lastTime$$ = Cell$$10472`t$$; Null]; Module[{Cell$$10472`fontScale$, Cell$$10472`scaledCenter$}, Switch[Cell$$10472`mode$$, Cell$$10472`RUNNING, AddTo[Cell$$10472`curTime$$, Cell$$10472`hubble$$ (Cell$$10472`t$$ - Cell$$10472`lastTime$$)]; Cell$$10472`lastTime$$ = Cell$$10472`t$$, Cell$$10472`RECENTERING, Module[{Cell$$10472`now$, Cell$$10472`dt$}, Cell$$10472`now$ = AbsoluteTime[]; Cell$$10472`dt$ = Min[Cell$$10472`now$ - Cell$$10472`recenterStartTime$$, Cell$$10472`recenteringTime]; Cell$$10472`unscaledCenter$$ = Cell$$10472`targetCenter$$ (Cell$$10472`dt$/ Cell$$10472`recenteringTime) + Cell$$10472`originalCenter$$ (1 - Cell$$10472`dt$/ Cell$$10472`recenteringTime); If[Cell$$10472`dt$ == Cell$$10472`recenteringTime, Cell$$10472`mode$$ = Cell$$10472`modeBeforeRecentering$$; Cell$$10472`lastTime$$ = Cell$$10472`t$$; Null]; Null]; Null]; Cell$$10472`scale$$ = Cell$$10472`universeScaleFunction$$[Cell$$10472`curTime$$]; Cell$$10472`scaledEnd1$$ = Cell$$10472`end1$$; If[Cell$$10472`fit$$, If[Head[Cell$$10472`scale$$] === Dynamic, Cell$$10472`scale$$ = Part[Cell$$10472`scale$$, 1]; Null]; Cell$$10472`fontScale$ = Cell$$10472`normalFontSize$$/Cell$$10472`scale$$; Cell$$10472`scaledEnd2$$ = Cell$$10472`end1$$ + (Cell$$10472`end2$$ - Cell$$10472`end1$$)/ Cell$$10472`scale$$; Cell$$10472`graphicScale$$ = 1; Null, Cell$$10472`fontScale$ = Cell$$10472`normalFontSize$$; Cell$$10472`graphicScale$$ = Cell$$10472`scale$$; Cell$$10472`scaledEnd2$$ = Cell$$10472`end2$$; Null]; Cell$$10472`scaledCenter$ = Cell$$10472`graphicScale$$ Cell$$10472`unscaledCenter$$; Cell$$10472`scaledRulerCenter$$ = (Cell$$10472`scaledEnd1$$ + Cell$$10472`scaledEnd2$$)/2; Cell$$10472`rulerLabel$$ = StringJoin[ ToString[ Norm[Cell$$10472`end2$$ - Cell$$10472`end1$$]/ Cell$$10472`rulerScale], " units"]; EventHandler[ Graphics[{ EventHandler[ Style[ Line[{Cell$$10472`scaledEnd1$$, Cell$$10472`scaledEnd2$$}], Red], "MouseDown" :> (Cell$$10472`eventSource$$ = Cell$$10472`BODY)], EventHandler[ Rotate[ Style[ Text[ Cell$$10472`rulerLabel$$, Cell$$10472`scaledRulerCenter$$, {0, 1}], Red], If[Part[Cell$$10472`perp$$, 2] != 0, -ArcTan[ Apply[Divide, Cell$$10472`perp$$]], Pi/2], Cell$$10472`scaledRulerCenter$$], "MouseDown" :> (Cell$$10472`eventSource$$ = Cell$$10472`BODY)], EventHandler[ Style[ Line[{Cell$$10472`scaledEnd1$$ + Cell$$10472`halfEndLength Cell$$10472`perp$$, Cell$$10472`scaledEnd1$$ - Cell$$10472`halfEndLength Cell$$10472`perp$$}], Red], "MouseDown" :> (Cell$$10472`eventSource$$ = Cell$$10472`END1)], EventHandler[ Style[ Line[{Cell$$10472`scaledEnd2$$ + Cell$$10472`halfEndLength Cell$$10472`perp$$, Cell$$10472`scaledEnd2$$ - Cell$$10472`halfEndLength Cell$$10472`perp$$}], Red], "MouseDown" :> (Cell$$10472`eventSource$$ = Cell$$10472`END2)], Apply[ Function[{ Cell$$10472`location$, Cell$$10472`label$, Cell$$10472`size$, Cell$$10472`color$, Cell$$10472`recenterTo$}, EventHandler[ Style[ Text[Cell$$10472`label$, Cell$$10472`location$], Cell$$10472`size$, Cell$$10472`color$], "MouseClicked" :> If[ And[ Cell$$10472`mode$$ =!= Cell$$10472`RECENTERING, Cell$$10472`unscaledCenter$$ != Cell$$10472`recenterTo$], Module[{ Cell$$10472`dc$ = (Cell$$10472`recenterTo$ - Cell$$10472`unscaledCenter$$)/ Cell$$10472`numRecenteringFrames, Cell$$10472`curCenter$ = Cell$$10472`unscaledCenter$$, Null$}, Cell$$10472`modeBeforeRecentering$$ = Cell$$10472`mode$$; Cell$$10472`mode$$ = Cell$$10472`RECENTERING; Cell$$10472`recenterStartTime$$ = AbsoluteTime[]; Cell$$10472`targetCenter$$ = Cell$$10472`recenterTo$; Cell$$10472`originalCenter$$ = Cell$$10472`unscaledCenter$$; Null$]], PassEventsUp -> False]], Join[{{{0, 0} - Cell$$10472`unscaledCenter$$, 0, Cell$$10472`normalFontSize$$, LightBlue, {0, 0}}}, MapIndexed[{# - Cell$$10472`unscaledCenter$$, Part[#2, 1], Cell$$10472`normalFontSize$$, LightGray, #}& , Cell$$10472`objectPositions$$], {{ Cell$$10472`graphicScale$$ ({0, 0} - Cell$$10472`unscaledCenter$$), 0, Cell$$10472`fontScale$, Blue, {0, 0}}}, MapIndexed[{ Cell$$10472`graphicScale$$ (# - Cell$$10472`unscaledCenter$$), Part[#2, 1], Cell$$10472`fontScale$, Black, #}& , Cell$$10472`objectPositions$$]], {1}]}, PlotRange -> {{-1, 1}, {-1, 1}}, PlotRangePadding -> None, ImageSize -> {350, 350}], { "MouseDown" :> ({Cell$$10472`mx$$, Cell$$10472`my$$} = MousePosition[Cell$$10472`MouseCoordinateSystem]), "MouseUp" :> (Cell$$10472`eventSource$$ = Cell$$10472`CANVAS), "MouseDragged" :> If[ And[Cell$$10472`mode$$ =!= Cell$$10472`RECENTERING, Apply[And, Map[ NumericQ, { Cell$$10472`mx$$, Cell$$10472`my$$, Cell$$10472`graphicScale$$}]]], Switch[ Cell$$10472`eventSource$$, Cell$$10472`CANVAS, SubtractFrom[ Cell$$10472`unscaledCenter$$, MousePosition[Cell$$10472`MouseCoordinateSystem] - { Cell$$10472`mx$$, Cell$$10472`my$$}]; { Cell$$10472`mx$$, Cell$$10472`my$$} = MousePosition[Cell$$10472`MouseCoordinateSystem], Alternatives[ Cell$$10472`BODY, Cell$$10472`END1, Cell$$10472`END2], Module[{ Cell$$10472`propEnd1$ = Cell$$10472`scaledEnd1$$, Cell$$10472`propEnd2$ = Cell$$10472`scaledEnd2$$, Cell$$10472`max1$, Cell$$10472`max2$, Cell$$10472`diffPt$}, Cell$$10472`diffPt$ = MousePosition[Cell$$10472`MouseCoordinateSystem] - { Cell$$10472`mx$$, Cell$$10472`my$$}; If[ MatchQ[Cell$$10472`eventSource$$, Alternatives[Cell$$10472`END1, Cell$$10472`BODY]], AddTo[Cell$$10472`propEnd1$, Cell$$10472`diffPt$]]; If[ MatchQ[Cell$$10472`eventSource$$, Alternatives[Cell$$10472`END2, Cell$$10472`BODY]], AddTo[Cell$$10472`propEnd2$, Cell$$10472`diffPt$]]; { Cell$$10472`max1$, Cell$$10472`max2$} = Table[ Max[ Abs[ Part[Cell$$10472`propEnd1$, Cell$$10472`i]], Abs[ Part[Cell$$10472`propEnd2$, Cell$$10472`i]]], { Cell$$10472`i, 2}]; If[Cell$$10472`max1$ > 1, SubtractFrom[Cell$$10472`diffPt$, (Cell$$10472`max1$ - 1) { Sign[ Part[Cell$$10472`diffPt$, 1]], 0}]]; If[Cell$$10472`max2$ > 1, SubtractFrom[ Cell$$10472`diffPt$, (Cell$$10472`max2$ - 1) {0, Sign[ Part[Cell$$10472`diffPt$, 2]]}]]; If[ MatchQ[Cell$$10472`eventSource$$, Alternatives[Cell$$10472`END1, Cell$$10472`BODY]], Cell$$10472`propEnd1$ = Cell$$10472`scaledEnd1$$ + Cell$$10472`diffPt$]; If[ MatchQ[Cell$$10472`eventSource$$, Alternatives[Cell$$10472`END2, Cell$$10472`BODY]], Cell$$10472`propEnd2$ = Cell$$10472`scaledEnd2$$ + Cell$$10472`diffPt$]; If[Norm[Cell$$10472`propEnd1$ - Cell$$10472`propEnd2$] < Cell$$10472`halfEndLength, SubtractFrom[ Cell$$10472`diffPt$, ((Cell$$10472`halfEndLength - Norm[ Cell$$10472`propEnd1$ - Cell$$10472`propEnd2$])/Norm[ Cell$$10472`diffPt$]) Cell$$10472`diffPt$]; Null]; If[ MatchQ[Cell$$10472`eventSource$$, Alternatives[Cell$$10472`END1, Cell$$10472`BODY]], AddTo[Cell$$10472`end1$$, Cell$$10472`diffPt$]]; If[ MatchQ[Cell$$10472`eventSource$$, Alternatives[Cell$$10472`END2, Cell$$10472`BODY]], AddTo[Cell$$10472`end2$$, Cell$$10472`diffPt$]]; If[Cell$$10472`fit$$, Switch[Cell$$10472`eventSource$$, Cell$$10472`END2, AddTo[ Cell$$10472`end2$$, (Cell$$10472`scale$$ - 1) Cell$$10472`diffPt$], Cell$$10472`END1, SubtractFrom[ Cell$$10472`end2$$, (Cell$$10472`scale$$ - 1) Cell$$10472`diffPt$]]]; AddTo[{Cell$$10472`mx$$, Cell$$10472`my$$}, Cell$$10472`diffPt$]; Cell$$10472`perp$$ = Dot[{{0, -1}, {1, 0}}, Cell$$10472`end2$$ - Cell$$10472`end1$$]/Norm[ Cell$$10472`end2$$ - Cell$$10472`end1$$]; Null]]]}]]), "Specifications" :> {{{ Cell$$10472`universeType$$, Cell$$10472`DeSitterUniverse, "type of universe"}, { Cell$$10472`DeSitterUniverse -> "inflating universe", Cell$$10472`OpenUniverse -> "open universe", Cell$$10472`FlatUniverse -> "flat universe", Cell$$10472`ClosedUniverse -> "closed universe"}, ControlType -> PopupMenu}, {{ Cell$$10472`fit$$, False, "rescale the universe\nto fit in the box"}, {True, False}}, {{ Cell$$10472`hubble$$, 0.05, "speed"}, 0.001, 1}, {{ Cell$$10472`normalFontSize$$, 12, "font size"}, 5, 20, 1}, {{ Cell$$10472`t$$, 0, ""}, 0, DirectedInfinity[1], ControlType -> Trigger, AnimationRate -> 1, AppearanceElements -> { "PlayPauseButton", "StepRightButton", "ResetButton"}, Enabled -> Dynamic[Cell$$10472`mode$$ =!= Cell$$10472`RECENTERING]}, { Cell$$10472`graphicScale$$, ControlType -> None}, {{ Cell$$10472`mode$$, Cell$$10472`INITIALIZED}, Null, ControlType -> None}, {{ Cell$$10472`modeBeforeRecentering$$, Cell$$10472`INITIALIZED}, ControlType -> None}, {{Cell$$10472`unscaledCenter$$, {0, 0}}, ControlType -> None}, {{Cell$$10472`scale$$, 1}, ControlType -> None}, {{Cell$$10472`targetCenter$$, 0}, ControlType -> None}, {{ Cell$$10472`recenterStartTime$$, 3.431772327504175*^9}, ControlType -> None}, {{Cell$$10472`originalCenter$$, {0, 0}}, ControlType -> None}, {{Cell$$10472`mx$$, 0}, ControlType -> None}, {{ Cell$$10472`my$$, 0}, ControlType -> None}, {{ Cell$$10472`eventSource$$, Cell$$10472`CANVAS}, ControlType -> None}, {{Cell$$10472`end1$$, {-0.9, -0.9}}, ControlType -> None}, {{ Cell$$10472`end2$$, {-0.8, -0.9}}, ControlType -> None}, {{ Cell$$10472`perp$$, {0, 1}}, ControlType -> None}, {{ Cell$$10472`rulerLabel$$, "0.1 units"}, ControlType -> None}, {{ Cell$$10472`scaledEnd1$$, {-0.9, -0.9}}, ControlType -> None}, {{ Cell$$10472`scaledEnd2$$, {-0.8, -0.9}}, ControlType -> None}, {{ Cell$$10472`scaledRulerCenter$$, {-0.85, -0.9}}, ControlType -> None}, {{Cell$$10472`curTime$$, 0}, ControlType -> None}, {{ Cell$$10472`lastTime$$, 0}, ControlType -> None}, {{ Cell$$10472`objectPositions$$, {{ 0.33720307431491436`, -0.19249241093935598`}, {0.6553520183620183, 0.08866216420106676}, {0.37813996078725687`, -0.8525855707365602}, { 0.9506476399161867, -0.4655541465590436}, {0.9548604355740595, 0.4141160840391782}, {-0.47860165271292976`, 0.32545000346077435`}, {-0.7034198672612475, \ -0.055144729948415794`}, {0.2947780437911969, -0.7124383450159355}, { 0.6401382332664523, 0.8139101543842049}, {-0.6908269270720226, -0.5431782842629254}, \ {-0.1010817362714942, -0.1552932653091088}, {-0.11069847262578403`, \ -0.32260596280155207`}, { 0.6736128284537455, -0.3209154115454411}, {-0.22792706383946237`, 0.2635325125147392}, {0.10127774214031326`, -0.2513920690644933}, { 0.47261321579485926`, 0.8986786173170596}, {-0.7409046624291808, -0.8074980117368784}, \ {-0.6792785768917251, 0.48521566673582317`}, { 0.8701274588208152, -0.4051777247938366}, {-0.18784013719656167`, \ -0.7951722478530527}}}, ControlType -> None}, {{ Cell$$10472`universeScaleFunction$$, 1& }, ControlType -> None}}, "Options" :> {Deployed -> True, AutorunSequencing -> {{5, 10}, {4, 5}}}, "DefaultOptions" :> {ControllerLinking -> True}], ImageSizeCache->{394., {269., 274.}}, SingleEvaluation->True], Deinitialization:>None, DynamicModuleValues:>{}, Initialization:>(({ Cell$$10472`initialRulerEndPoint = {-0.9, -0.9}, Cell$$10472`rulerScale = 0.1, Cell$$10472`numObjects = 20, Cell$$10472`recenteringTime = 3, Cell$$10472`halfEndLength = 0.02, Cell$$10472`MouseCoordinateSystem = "Graphics", Cell$$10472`DeSitterUniverse[ Pattern[Cell$$10472`time, Blank[]]] := E^Cell$$10472`time, Cell$$10472`OpenUniverse[ Pattern[Cell$$10472`time, Blank[]]] := 1 + Cell$$10472`time, Cell$$10472`FlatUniverse[ Pattern[Cell$$10472`time, Blank[]]] := (1 + Cell$$10472`time)^(2/3), Cell$$10472`ClosedUniverse[ Pattern[Cell$$10472`time$, Blank[]]] := Max[ Piecewise[{{ 1.505787061217049 (1 - Cos[Cell$$10472`time$ + Pi/4])^(1/3), And[Cell$$10472`time$ >= 0, Cell$$10472`time$ < (7 Pi)/4]}}], Cell$$10472`cutoff], Attributes[Cell$$10472`time$] = {Temporary}, Cell$$10472`cutoff = 1/100}; Typeset`initDone$$ = True); ReleaseHold[ HoldComplete[{($CellContext`DeSitterUniverse[ Pattern[$CellContext`time, Blank[]]] := E^$CellContext`time; Null) ($CellContext`OpenUniverse[ Pattern[$CellContext`time, Blank[]]] := 1 + $CellContext`time; Null) ($CellContext`FlatUniverse[ Pattern[$CellContext`time, Blank[]]] := (1 + $CellContext`time)^(2/3); Null) ( With[{$CellContext`const = (1 - 1/2.^Rational[1, 2])^((-1)/ 3.)}, $CellContext`ClosedUniverse[ Pattern[$CellContext`time, Blank[]]] := Max[ Piecewise[{{$CellContext`const (1 - Cos[$CellContext`time + Pi/4])^(1/3), And[$CellContext`time >= 0, $CellContext`time < 7 Pi/4]}}], $CellContext`cutoff]; Null]; Null) ($CellContext`numObjects = 20; Null) ($CellContext`cutoff = 10^(-2); Null) ($CellContext`recenteringTime = 3; Null) ( Protect[$CellContext`RUNNING, $CellContext`STOPPED, \ $CellContext`RECENTERING, $CellContext`INITIALIZED]; Null) ( Protect[$CellContext`CANVAS, $CellContext`BODY, $CellContext`END1, \ $CellContext`END2]; Null) ($CellContext`halfEndLength = 0.02; Null) ($CellContext`rulerScale = 0.1; Null) ($CellContext`initialRulerEndPoint = {-0.9, -0.9}; Null) ($CellContext`MouseCoordinateSystem = "Graphics"; Null)}]]; Typeset`initDone$$ = True), SynchronousInitialization->True, UnsavedVariables:>{Typeset`initDone$$}, UntrackedVariables:>{Typeset`size$$}], "Manipulate", Deployed->True, StripOnInput->False], Manipulate`InterpretManipulate[1]]], "Output", CellID->578966365], Cell[TextData[{ "In the 1920s, American astronomer Edwin Hubble", " discovered that the universe is expanding. Not only are distant stars and \ galaxies moving away from us, but further stars and galaxies move away from \ us faster than closer ones. This is because of the ", StyleBox["homogeneous", FontSlant->"Italic"], " nature of the expansion. Every distance in the universe expands by the \ same multiplicative factor, and so an object that is twice as far from us \ moves twice as far in a given time." }], "ManipulateCaption"], Cell["\<\ Our modern understanding of cosmology is based on Einstein's general theory \ of relativity. Shortly after the big bang, the universe underwent an \ inflationary epoch in which the universe expanded exponentially. After the \ inflationary epoch is complete, basic principles of general relativity tell \ us that there are three broad types of possible \"expansions\" of the \ universe. Loosely speaking, an open universe is one which continues to expand \ forever, and whose expansion never comes to a halt. A flat universe is one \ which continues to expand forever, but whose expansion is constantly slowing \ down. A closed universe eventually stops expanding and then starts \ contracting until the universe ends in a \"big crunch\"\[LongDash]the \ opposite of the big bang. For many years, physicists and astronomers could \ not tell from observation in which of these three broad types of universe we \ live, but recent observations of supernovas have given us sufficiently \ precise information on motion that we now know that we live in an open \ universe. (The open universe simulated in this Demonstration is only one of \ many possible types, however, and is not a perfect simulation of ours.)\ \>", "ManipulateCaption", CellID->3508661], Cell["DETAILS", "DetailsSection"], Cell["\<\ The numbers represent (randomly placed) clusters of galaxies in the universe; \ the blue \"0\" designates \"our\" location. As the universe's expansion is \ only visible on large scales the \"0\" encompasses the entire Milky Way \ galaxy which contains the Earth, plus some nearby galaxies.\ \>", "DetailNotes", CellID->1663795913], Cell["\<\ The Demonstration starts centered on the Milky Way, and, after clicking \ \"start\", the other objects in the universe begin to recede. The original \ position of the objects are shown in gray, to make it easy to see how far \ each object has gone.\ \>", "DetailNotes", CellID->1033342204], Cell["\<\ To see that the Earth is not a special point in the universe you can click on \ another object to re-center the Demonstration onto that object. This will \ pause the expansion so you can see the re-centering occurring without \ changing any distances between objects that are both black (current position) \ or both gray (original position), and then you will see that objects close to \ the new center have not moved as far away from the new center than further \ objects.\ \>", "DetailNotes", CellID->1197568101], Cell["\<\ To scroll to objects which have scrolled off the screen, drag the mouse on an \ empty part of the canvas.\ \>", "DetailNotes", CellID->988006958], Cell["\<\ To \"measure\" the distance between objects, drag the ruler, or each endpoint \ of the ruler, to objects you wish to measure.\ \>", "DetailNotes", CellID->1987234439], Cell["\<\ The \"rescale the universe to fit\" option changes the scale of the \ Demonstration while it runs so that objects never scroll out of the display. \ The effect is that everything in the universe gets smaller as the universe \ expands. Notice that this is true of the ruler, as well, so as the universe \ expands, the number of ruler-lengths between two objects increases. 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