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254.667 273.333 509.333 273.333 254.667 136.668 509.333 136.668 509.333 273.333 764 273.333 509.333 136.668 764 136.668 0 136.668 254.667 136.668 0 0 254.667 0 254.667 136.668 509.333 136.668 254.667 0 509.333 0 509.333 136.668 764 136.668 509.333 0 764 0 CPBorderColorProperty 0.18254 0.102222 0.0791005 version 1 CPVerticalAlignmentProperty 2 CPFillProperty dictionary 675 87 dictionary 0 0 650 420 root Region 1 Region 2 2001 17 55 2002 26 43 2003 53 70 2004 96 58 0.403922 0.341176 0.243137 0.3 g0.666667 0.2 0.2 0.211765 0.66 0.18254 0.102222 0.0791005 0.403922 0.341176 0.243137 0.3 0.403922 0.341176 0.243137 0.3 0.403922 0.341176 0.243137 0.3 0.18254 0.102222 0.0791005 0.18254 0.102222 0.0791005 0.254902 0.192157 0.113725 0.18254 0.102222 0.0791005 0.431373 0.364706 0.266667 0.18254 0.102222 0.0791005 0.156863 0.12549 0.0745098 0.18254 0.102222 0.0791005 0.411765 0.309804 0.160784 0.18254 0.102222 0.0791005 0.792157 0.631373 0.431373 0.18254 0.102222 0.0791005 0.666667 0.623529 0.509804 0.18254 0.102222 0.0791005 g1 dictionary 0 0 650 420 dictionary 0 0 650 420 dictionary 675 87 string VerticalBar dictionary 661 87 dictionary 824 37 dictionary 0 0 650 420 dictionary 675 87 <styles> <fill-style fill-type="none"/> <dash-style pattern="none"/> <shadow-style opacity="0" radius="0"/> </styles> dictionary 0 0 618 346 dictionary 0 0 618 346 dictionary 0 0 618 346 CPTextProperty CPStrokePatternProperty CPCellOpacityProperty 1 CPStrokeWidthProperty 2 CPBorderOpacityProperty 1 TableNodeSnapShotProperty1 1.2 822 458 0 458 274.001 458 0 305.332 274.001 305.332 274.001 458 547.999 458 274.001 305.332 547.999 305.332 547.999 458 822 458 547.999 305.332 822 305.332 0 305.332 274.001 305.332 0 152.669 274.001 152.669 274.001 305.332 547.999 305.332 274.001 152.669 547.999 152.669 547.999 305.332 822 305.332 547.999 152.669 822 152.669 0 152.669 274.001 152.669 0 0 274.001 0 274.001 152.669 547.999 152.669 274.001 0 547.999 0 547.999 152.669 822 152.669 547.999 0 822 0 CPBorderColorProperty 0.18254 0.102222 0.0791005 version 1 CPVerticalAlignmentProperty 2 CPFillProperty dictionary 0 0 618 346 dictionary 0 0 618 346 dictionary 824 44 dictionary 0 0 618 346 dictionary 0 0 618 346 dictionary 0 0 618 346 <styles> <fill-style fill-type="none"/> <dash-style pattern="none"/> <shadow-style opacity="0" radius="0"/> </styles> dictionary 0 0 305 274 dictionary 0 0 305 274 dictionary 0 0 305 274 CPTextProperty CPStrokePatternProperty CPCellOpacityProperty 1 CPStrokeWidthProperty 2 CPBorderOpacityProperty 1 TableNodeSnapShotProperty1 1.2 341 464 0 464 113.667 464 0 309.333 113.667 309.333 113.667 464 227.333 464 113.667 309.333 227.333 309.333 227.333 464 341 464 227.333 309.333 341 309.333 0 309.333 113.667 309.333 0 154.669 113.667 154.669 113.667 309.333 227.333 309.333 113.667 154.669 227.333 154.669 227.333 309.333 341 309.333 227.333 154.669 341 154.669 0 154.669 113.667 154.669 0 0 113.667 0 113.667 154.669 227.333 154.669 113.667 0 227.333 0 227.333 154.669 341 154.669 227.333 0 341 0 CPBorderColorProperty 0.18254 0.102222 0.0791005 version 1 CPVerticalAlignmentProperty 2 CPFillProperty dictionary 0 0 305 274 dictionary 0 0 305 274 dictionary 456 44 dictionary 0 0 305 274 dictionary 0 0 305 274 dictionary 0 0 306 275 <styles> <fill-style fill-type="none"/> <dash-style pattern="none"/> <shadow-style opacity="0" radius="0"/> </styles> dictionary 0 0 305 274 dictionary 0 0 305 274 dictionary 0 0 305 274 CPTextProperty CPStrokePatternProperty CPCellOpacityProperty 1 CPStrokeWidthProperty 2 CPBorderOpacityProperty 1 TableNodeSnapShotProperty1 1.2 341 464 0 464 113.667 464 0 309.333 113.667 309.333 113.667 464 227.333 464 113.667 309.333 227.333 309.333 227.333 464 341 464 227.333 309.333 341 309.333 0 309.333 113.667 309.333 0 154.669 113.667 154.669 113.667 309.333 227.333 309.333 113.667 154.669 227.333 154.669 227.333 309.333 341 309.333 227.333 154.669 341 154.669 0 154.669 113.667 154.669 0 0 113.667 0 113.667 154.669 227.333 154.669 113.667 0 227.333 0 227.333 154.669 341 154.669 227.333 0 341 0 CPBorderColorProperty 0.18254 0.102222 0.0791005 version 1 CPVerticalAlignmentProperty 2 CPFillProperty dictionary 0 0 305 274 dictionary 0 0 305 274 dictionary 456 44 dictionary 0 0 305 274 dictionary 0 0 305 274 dictionary 0 0 306 275 <styles> <fill-style fill-type="none"/> <dash-style pattern="none"/> <shadow-style opacity="0" radius="0"/> </styles> dictionary 0 0 728 481 dictionary 0 0 728 481 dictionary 0 0 728 481 CPTextProperty CPStrokePatternProperty CPCellOpacityProperty 1 CPStrokeWidthProperty 2 CPBorderOpacityProperty 1 TableNodeSnapShotProperty1 1.2 822 595 0 595 274.001 595 0 396.666 274.001 396.666 274.001 595 547.999 595 274.001 396.666 547.999 396.666 547.999 595 822 595 547.999 396.666 822 396.666 0 396.666 274.001 396.666 0 198.336 274.001 198.336 274.001 396.666 547.999 396.666 274.001 198.336 547.999 198.336 547.999 396.666 822 396.666 547.999 198.336 822 198.336 0 198.336 274.001 198.336 0 0 274.001 0 274.001 198.336 547.999 198.336 274.001 0 547.999 0 547.999 198.336 822 198.336 547.999 0 822 0 CPBorderColorProperty 0.18254 0.102222 0.0791005 version 1 CPVerticalAlignmentProperty 2 CPFillProperty dictionary 0 0 728 481 dictionary 0 0 728 481 dictionary 824 44 dictionary 0 0 728 481 dictionary 0 0 728 481 dictionary 0 0 728 481 <styles> <fill-style fill-type="none"/> <dash-style pattern="none"/> <shadow-style opacity="0" radius="0"/> </styles> dictionary 0 0 618 346 dictionary 0 0 618 346 dictionary 0 0 618 346 CPTextProperty CPStrokePatternProperty CPCellOpacityProperty 1 CPStrokeWidthProperty 2 CPBorderOpacityProperty 1 TableNodeSnapShotProperty1 1.2 822 458 0 458 274.001 458 0 305.332 274.001 305.332 274.001 458 547.999 458 274.001 305.332 547.999 305.332 547.999 458 822 458 547.999 305.332 822 305.332 0 305.332 274.001 305.332 0 152.669 274.001 152.669 274.001 305.332 547.999 305.332 274.001 152.669 547.999 152.669 547.999 305.332 822 305.332 547.999 152.669 822 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822 305.332 547.999 152.669 822 152.669 0 152.669 274.001 152.669 0 0 274.001 0 274.001 152.669 547.999 152.669 274.001 0 547.999 0 547.999 152.669 822 152.669 547.999 0 822 0 CPBorderColorProperty 0.18254 0.102222 0.0791005 version 1 CPVerticalAlignmentProperty 2 CPFillProperty dictionary 0 0 618 346 dictionary 0 0 618 346 dictionary 824 44 dictionary 0 0 618 346 dictionary 0 0 618 346 dictionary 0 0 618 346 <styles> <fill-style fill-type="none"/> <dash-style pattern="none"/> <shadow-style opacity="0" radius="0"/> </styles> dictionary 0 0 618 346 dictionary 0 0 618 346 dictionary 0 0 618 346 CPTextProperty CPStrokePatternProperty CPCellOpacityProperty 1 CPStrokeWidthProperty 2 CPBorderOpacityProperty 1 TableNodeSnapShotProperty1 1.2 822 458 0 458 274.001 458 0 305.332 274.001 305.332 274.001 458 547.999 458 274.001 305.332 547.999 305.332 547.999 458 822 458 547.999 305.332 822 305.332 0 305.332 274.001 305.332 0 152.669 274.001 152.669 274.001 305.332 547.999 305.332 274.001 152.669 547.999 152.669 547.999 305.332 822 305.332 547.999 152.669 822 152.669 0 152.669 274.001 152.669 0 0 274.001 0 274.001 152.669 547.999 152.669 274.001 0 547.999 0 547.999 152.669 822 152.669 547.999 0 822 0 CPBorderColorProperty 0.18254 0.102222 0.0791005 version 1 CPVerticalAlignmentProperty 2 CPFillProperty dictionary 0 0 618 346 dictionary 0 0 618 346 dictionary 824 44 dictionary 0 0 618 346 dictionary 0 0 618 346 dictionary 0 0 618 346 <styles> <fill-style fill-type="none"/> <dash-style pattern="none"/> <shadow-style opacity="0" radius="0"/> </styles> dictionary 0 0 305 274 dictionary 0 0 305 274 dictionary 0 0 305 274 CPTextProperty CPStrokePatternProperty CPCellOpacityProperty 1 CPStrokeWidthProperty 2 CPBorderOpacityProperty 1 TableNodeSnapShotProperty1 1.2 341 464 0 464 113.667 464 0 309.333 113.667 309.333 113.667 464 227.333 464 113.667 309.333 227.333 309.333 227.333 464 341 464 227.333 309.333 341 309.333 0 309.333 113.667 309.333 0 154.669 113.667 154.669 113.667 309.333 227.333 309.333 113.667 154.669 227.333 154.669 227.333 309.333 341 309.333 227.333 154.669 341 154.669 0 154.669 113.667 154.669 0 0 113.667 0 113.667 154.669 227.333 154.669 113.667 0 227.333 0 227.333 154.669 341 154.669 227.333 0 341 0 CPBorderColorProperty 0.18254 0.102222 0.0791005 version 1 CPVerticalAlignmentProperty 2 CPFillProperty dictionary 0 0 305 274 dictionary 0 0 305 274 dictionary 456 44 dictionary 0 0 305 274 dictionary 0 0 305 274 dictionary 0 0 306 275 <styles> <fill-style fill-type="none"/> <dash-style pattern="none"/> <shadow-style opacity="0" radius="0"/> </styles> dictionary 0 0 305 274 dictionary 0 0 305 274 dictionary 0 0 305 274 CPTextProperty CPStrokePatternProperty CPCellOpacityProperty 1 CPStrokeWidthProperty 2 CPBorderOpacityProperty 1 TableNodeSnapShotProperty1 1.2 341 464 0 464 113.667 464 0 309.333 113.667 309.333 113.667 464 227.333 464 113.667 309.333 227.333 309.333 227.333 464 341 464 227.333 309.333 341 309.333 0 309.333 113.667 309.333 0 154.669 113.667 154.669 113.667 309.333 227.333 309.333 113.667 154.669 227.333 154.669 227.333 309.333 341 309.333 227.333 154.669 341 154.669 0 154.669 113.667 154.669 0 0 113.667 0 113.667 154.669 227.333 154.669 113.667 0 227.333 0 227.333 154.669 341 154.669 227.333 0 341 0 CPBorderColorProperty 0.18254 0.102222 0.0791005 version 1 CPVerticalAlignmentProperty 2 CPFillProperty dictionary 0 0 305 274 dictionary 0 0 305 274 dictionary 456 44 dictionary 0 0 305 274 dictionary 0 0 305 274 dictionary 0 0 306 275 <styles> <fill-style fill-type="none"/> <dash-style pattern="none"/> <shadow-style opacity="0" radius="0"/> </styles> dictionary 0 0 305 274 dictionary 0 0 305 274 dictionary 0 0 305 274 CPTextProperty CPStrokePatternProperty CPCellOpacityProperty 1 CPStrokeWidthProperty 2 CPBorderOpacityProperty 1 TableNodeSnapShotProperty1 1.2 341 464 0 464 113.667 464 0 309.333 113.667 309.333 113.667 464 227.333 464 113.667 309.333 227.333 309.333 227.333 464 341 464 227.333 309.333 341 309.333 0 309.333 113.667 309.333 0 154.669 113.667 154.669 113.667 309.333 227.333 309.333 113.667 154.669 227.333 154.669 227.333 309.333 341 309.333 227.333 154.669 341 154.669 0 154.669 113.667 154.669 0 0 113.667 0 113.667 154.669 227.333 154.669 113.667 0 227.333 0 227.333 154.669 341 154.669 227.333 0 341 0 CPBorderColorProperty 0.18254 0.102222 0.0791005 version 1 CPVerticalAlignmentProperty 2 CPFillProperty dictionary 0 0 305 274 dictionary 0 0 305 274 dictionary 456 44 dictionary 0 0 305 274 dictionary 0 0 305 274 dictionary 0 0 306 275 <styles> <fill-style fill-type="none"/> <dash-style pattern="none"/> <shadow-style opacity="0" radius="0"/> </styles> dictionary 0 0 305 274 dictionary 0 0 305 274 dictionary 0 0 305 274 CPTextProperty CPStrokePatternProperty CPCellOpacityProperty 1 CPStrokeWidthProperty 2 CPBorderOpacityProperty 1 TableNodeSnapShotProperty1 1.2 341 464 0 464 113.667 464 0 309.333 113.667 309.333 113.667 464 227.333 464 113.667 309.333 227.333 309.333 227.333 464 341 464 227.333 309.333 341 309.333 0 309.333 113.667 309.333 0 154.669 113.667 154.669 113.667 309.333 227.333 309.333 113.667 154.669 227.333 154.669 227.333 309.333 341 309.333 227.333 154.669 341 154.669 0 154.669 113.667 154.669 0 0 113.667 0 113.667 154.669 227.333 154.669 113.667 0 227.333 0 227.333 154.669 341 154.669 227.333 0 341 0 CPBorderColorProperty 0.18254 0.102222 0.0791005 version 1 CPVerticalAlignmentProperty 2 CPFillProperty dictionary 0 0 305 274 dictionary 0 0 305 274 dictionary 450 44 dictionary 0 0 305 274 dictionary 0 0 305 274 dictionary 0 0 306 275 How to Model Tom Carter CSSS 2004 <body visibility="hidden" vertical-alignment="tracks-master"/> </drawables> <transition-style type="inherited"/> <thumbnails> <thumbnail byte-size="8370" size="60 45" file="thumbs/st0.tiff"/> </thumbnails> <bullets> <bullet level="0" marker-type="inherited"> <content font-color="0.18254 0.102222 0.0791005" paragraph-alignment="left" tab-stops="L 96" font-size="72" font-name="Papyrus"/> </bullet> </bullets> </slide> <slide master-slide-id="master-slide-1"> <drawables> <title visibility="tracks-master" location="100 117" size="824 273" vertical-alignment="tracks-master"/> <body visibility="hidden" location="143 362" size="824 308" vertical-alignment="tracks-master"/> </drawables> <transition-style type="inherited"/> <thumbnails> <thumbnail byte-size="8370" size="60 45" file="thumbs/st1.tiff"/> </thumbnails> <bullets> <bullet level="0" marker-type="inherited"> <content font-color="0.18254 0.102222 0.0791005" paragraph-alignment="center" tab-stops="L 96" font-size="72" font-name="Papyrus">Most Random Number</content> </bullet> <bullet level="1" marker-type="inherited"> <content font-color="0.18254 0.102222 0.0791005" paragraph-alignment="center" tab-stops="L 96" font-size="48" font-name="Papyrus">Tom Carter</content> </bullet> <bullet level="1" marker-type="inherited"> <content font-color="0.18254 0.102222 0.0791005" paragraph-alignment="center" tab-stops="L 96" font-size="48" font-name="Papyrus">CSSS</content> </bullet> <bullet level="1" marker-type="inherited"> <content font-color="0.18254 0.102222 0.0791005" paragraph-alignment="center" tab-stops="L 96" font-size="48" font-name="Papyrus">2004</content> </bullet> </bullets> </slide> <slide master-slide-id="master-slide-2"> <drawables> <title visibility="tracks-master" location="100 50" size="824 284" vertical-alignment="tracks-master"/> <body visibility="tracks-master" vertical-alignment="tracks-master"/> </drawables> <transition-style type="inherited"/> <thumbnails> <thumbnail byte-size="8370" size="60 45" file="thumbs/st11.tiff"/> </thumbnails> <bullets> <bullet level="0" marker-type="inherited"> <content font-color="0.18254 0.102222 0.0791005" paragraph-alignment="center" tab-stops="L 96" font-size="64" font-name="Papyrus">Here’s a somewhat strange question . . .</content> </bullet> <bullet level="1" marker-type="inherited"> <content font-color="0.18254 0.102222 0.0791005" paragraph-head-indent="17" paragraph-first-line-indent="17" tab-stops="L 53" font-size="64" font-name="Papyrus">What is the most random number between 1 and 1000?</content> </bullet> </bullets> </slide> <slide master-slide-id="master-slide-2"> <drawables> <title visibility="tracks-master" location="100 101" size="824 166" vertical-alignment="tracks-master"/> <body visibility="tracks-master" vertical-alignment="tracks-master"/> </drawables> <transition-style type="inherited"/> <thumbnails> <thumbnail byte-size="8370" size="60 45" file="thumbs/st2.tiff"/> </thumbnails> <bullets> <bullet level="0" marker-type="inherited"> <content font-color="0.18254 0.102222 0.0791005" paragraph-alignment="center" tab-stops="L 96" font-size="64" font-name="Papyrus">How to go at it?</content> </bullet> <bullet level="1" marker-type="inherited"> <content font-color="0.18254 0.102222 0.0791005" paragraph-head-indent="17" paragraph-first-line-indent="17" tab-stops="L 53" font-size="42" font-name="Papyrus"> <![CDATA[Let’s try to develop a “probability distribution function” representing some general notion of a “randomness” property for numbers . . . :-)]]> </content> </bullet> </bullets> </slide> <slide master-slide-id="master-slide-2"> <drawables> <title visibility="tracks-master" location="100 36" size="824 225" vertical-alignment="tracks-master"/> <image byte-size="63376" display-name="normal-500-167.jpg" transformation="0.58724 0 0 0.58724 211 252" lock-aspect-ratio="true" image-data="normal-500-167.jpg" natural-size="1024 768"/> <body visibility="hidden" vertical-alignment="tracks-master"/> </drawables> <transition-style type="inherited"/> <thumbnails> <thumbnail byte-size="6118" size="60 45" file="thumbs/st3.tiff"/> </thumbnails> <bullets> <bullet level="0" marker-type="inherited"> <content font-color="0.18254 0.102222 0.0791005" paragraph-alignment="center" tab-stops="L 96" font-size="48" font-name="Papyrus">First guess: everything is normal, right?</content> </bullet> </bullets> </slide> <slide master-slide-id="master-slide-2"> <drawables> <body visibility="tracks-master" location="100 71" size="824 611" vertical-alignment="tracks-master"/> <title visibility="hidden" vertical-alignment="tracks-master"/> </drawables> <transition-style type="inherited"/> <thumbnails> <thumbnail byte-size="8370" size="60 45" file="thumbs/st4.tiff"/> </thumbnails> <bullets> <bullet level="0" marker-type="inherited"> <content font-color="0.18254 0.102222 0.0791005" paragraph-alignment="left" tab-stops="L 96" font-size="72" font-name="Papyrus"/> </bullet> <bullet level="1" marker-type="inherited"> <content font-color="0.18254 0.102222 0.0791005" paragraph-head-indent="17" paragraph-first-line-indent="17" tab-stops="L 53" font-size="42" font-name="Papyrus">Too simple. We do get a unique maximum at 500, but that can’t be right.</content> </bullet> <bullet level="1" marker-type="inherited"> <content font-color="0.18254 0.102222 0.0791005" paragraph-head-indent="17" paragraph-first-line-indent="17" tab-stops="L 53" font-size="42" font-name="Papyrus"> <![CDATA[As everybody knows, you never get the actual data value. There are always “errors” that push you away from the real value.]]> </content> </bullet> <bullet level="1" marker-type="inherited"> <content font-color="0.18254 0.102222 0.0791005" paragraph-head-indent="17" paragraph-first-line-indent="17" tab-stops="L 53" font-size="42" font-name="Papyrus">So, we should overlay a repelling “error dark-force” on top.</content> </bullet> </bullets> </slide> <slide master-slide-id="master-slide-2"> <drawables> <title visibility="tracks-master" vertical-alignment="tracks-master"/> <image byte-size="62895" display-name="error-force.jpg" transformation="0.631836 0 0 0.631836 188 209" lock-aspect-ratio="true" image-data="error-force.jpg" natural-size="1024 768"/> <body visibility="hidden" vertical-alignment="tracks-master"/> </drawables> <transition-style type="inherited"/> <thumbnails> <thumbnail byte-size="5852" size="60 45" file="thumbs/st5.tiff"/> </thumbnails> <bullets> <bullet level="0" marker-type="inherited"> <content font-color="0.18254 0.102222 0.0791005" paragraph-alignment="center" tab-stops="L 96" font-size="48" font-name="Papyrus">Error dark-force</content> </bullet> </bullets> </slide> <slide master-slide-id="master-slide-2"> <drawables> <title visibility="tracks-master" location="100 50" size="824 213" vertical-alignment="tracks-master"/> <image byte-size="73961" display-name="normal-w-error-force.jpg" transformation="0.597656 0 0 0.597656 206 238" lock-aspect-ratio="true" image-data="normal-w-error-force.jpg" natural-size="1024 768"/> <body visibility="hidden" vertical-alignment="tracks-master"/> </drawables> <transition-style type="inherited"/> <thumbnails> <thumbnail byte-size="6244" size="60 45" file="thumbs/st6.tiff"/> </thumbnails> <bullets> <bullet level="0" marker-type="inherited"> <content font-color="0.18254 0.102222 0.0791005" paragraph-alignment="center" tab-stops="L 96" font-size="48" font-name="Papyrus">Overlay the dark-force on the normal distribution:</content> </bullet> </bullets> </slide> <slide master-slide-id="master-slide-2"> <drawables> <body visibility="tracks-master" location="100 87" size="824 593" vertical-alignment="tracks-master"/> <title visibility="hidden" vertical-alignment="tracks-master"/> </drawables> <transition-style type="inherited"/> <thumbnails> <thumbnail byte-size="8370" size="60 45" file="thumbs/st7.tiff"/> </thumbnails> <bullets> <bullet level="0" marker-type="inherited"> <content font-color="0.18254 0.102222 0.0791005" paragraph-alignment="left" tab-stops="L 96" font-size="72" font-name="Papyrus"/> </bullet> <bullet level="1" marker-type="inherited"> <content font-color="0.18254 0.102222 0.0791005" paragraph-head-indent="17" paragraph-first-line-indent="17" tab-stops="L 53" font-size="42" font-name="Papyrus">Now we’re getting somewhere!</content> </bullet> <bullet level="1" marker-type="inherited"> <content font-color="0.18254 0.102222 0.0791005" paragraph-head-indent="17" paragraph-first-line-indent="17" tab-stops="L 53" font-size="42" font-name="Papyrus">But, we don’t have a unique maximum any more.</content> </bullet> <bullet level="1" marker-type="inherited"> <content font-color="0.18254 0.102222 0.0791005" paragraph-head-indent="17" paragraph-first-line-indent="17" tab-stops="L 53" font-size="42" font-name="Papyrus">There must be a bias in one direction or the other, mustn’t there?</content> </bullet> </bullets> </slide> <slide master-slide-id="master-slide-2"> <drawables> <body visibility="tracks-master" location="92 62" size="840 643" vertical-alignment="tracks-master"/> <title visibility="hidden" vertical-alignment="tracks-master"/> </drawables> <transition-style type="inherited"/> <thumbnails> <thumbnail byte-size="8370" size="60 45" file="thumbs/st8.tiff"/> </thumbnails> <bullets> <bullet level="0" marker-type="inherited"> <content font-color="0.18254 0.102222 0.0791005" paragraph-alignment="left" tab-stops="L 96" font-size="72" font-name="Papyrus"/> </bullet> <bullet level="1" marker-type="inherited"> <content font-color="0.18254 0.102222 0.0791005" paragraph-head-indent="17" paragraph-first-line-indent="17" tab-stops="L 53" font-size="42" font-name="Papyrus">Aha! We forgot about Benford’s law on the distribution of significant digits.</content> </bullet> <bullet level="1" marker-type="inherited"> <content font-color="0.18254 0.102222 0.0791005" paragraph-head-indent="17" paragraph-first-line-indent="17" tab-stops="L 53" font-size="42" font-name="Papyrus"> <![CDATA[One form of Benford’s law says that on average, the proportion of numbers having first digit less than d will be about log(d+1) for d = 1, 2, . . ., 9.]]> </content> </bullet> <bullet level="1" marker-type="inherited"> <content font-color="0.18254 0.102222 0.0791005" paragraph-head-indent="17" paragraph-first-line-indent="17" tab-stops="L 53" font-size="42" font-name="Papyrus"> <![CDATA[Another way to say this is that the distribution will be approximately 1/(d+1), so we’ll overlay a power law]]> </content> </bullet> </bullets> </slide> <slide master-slide-id="master-slide-2"> <drawables> <title visibility="tracks-master" vertical-alignment="tracks-master"/> <image byte-size="60439" display-name="first-digit-dist.jpg" transformation="0.662109 0 0 0.662109 173 180" lock-aspect-ratio="true" image-data="first-digit-dist.jpg" natural-size="1024 768"/> <body visibility="hidden" vertical-alignment="tracks-master"/> </drawables> <transition-style type="inherited"/> <thumbnails> <thumbnail byte-size="5538" size="60 45" file="thumbs/st9.tiff"/> </thumbnails> <bullets> <bullet level="0" marker-type="inherited"> <content font-color="0.18254 0.102222 0.0791005" paragraph-alignment="center" tab-stops="L 96" font-size="48" font-name="Papyrus">1/(x/100 + 1)</content> </bullet> </bullets> </slide> <slide master-slide-id="master-slide-2"> <drawables> <title visibility="tracks-master" location="100 55" size="824 202" vertical-alignment="tracks-master"/> <image byte-size="71002" display-name="mrn.jpg" transformation="0.595703 0 0 0.595703 207 247" lock-aspect-ratio="true" image-data="mrn.jpg" natural-size="1024 768"/> <body visibility="hidden" vertical-alignment="tracks-master"/> </drawables> <transition-style type="inherited"/> <thumbnails> <thumbnail byte-size="6240" size="60 45" file="thumbs/st10.tiff"/> </thumbnails> <bullets> <bullet level="0" marker-type="inherited"> <content font-color="0.18254 0.102222 0.0791005" paragraph-alignment="center" tab-stops="L 96" font-size="48" font-name="Papyrus"> <![CDATA[Normal, with dark-force and digit overlay]]> </content> </bullet> </bullets> </slide> <slide master-slide-id="master-slide-2"> <drawables> <body visibility="tracks-master" location="100 75" size="824 618" vertical-alignment="tracks-master"/> <title visibility="hidden" vertical-alignment="tracks-master"/> </drawables> <transition-style type="inherited"/> <thumbnails> <thumbnail byte-size="8370" size="60 45" file="thumbs/st111.tiff"/> </thumbnails> <bullets> <bullet level="0" marker-type="inherited"> <content font-color="0.18254 0.102222 0.0791005" paragraph-alignment="left" tab-stops="L 96" font-size="72" font-name="Papyrus"/> </bullet> <bullet level="1" marker-type="inherited"> <content font-color="0.18254 0.102222 0.0791005" paragraph-head-indent="17" paragraph-first-line-indent="17" tab-stops="L 53" font-size="42" font-name="Papyrus"> <![CDATA[Now we’re almost done. We have a single maximum, and it is not the simplistic 500.]]> </content> </bullet> <bullet level="1" marker-type="inherited"> <content font-color="0.18254 0.102222 0.0791005" paragraph-head-indent="17" paragraph-first-line-indent="17" tab-stops="L 53" font-size="42" font-name="Papyrus">One more piece. Random numbers must not have “special properties,” right?</content> </bullet> <bullet level="1" marker-type="inherited"> <content font-color="0.18254 0.102222 0.0791005" paragraph-head-indent="17" paragraph-first-line-indent="17" tab-stops="L 53" font-size="42" font-name="Papyrus">So, they probably won’t be divisible by small primes like 2 or 3 or 5.</content> </bullet> <bullet level="1" marker-type="inherited"> <content font-color="0.18254 0.102222 0.0791005" paragraph-head-indent="17" paragraph-first-line-indent="17" tab-stops="L 53" font-size="42" font-name="Papyrus">Let’s write a couple of small MatLab functions for all this.</content> </bullet> </bullets> </slide> <slide master-slide-id="master-slide-2"> <drawables> <textbox size="626.5 124" transformation="1 0 0 1 198.5 96"> <content font-color="0.18254 0.102222 0.0791005" paragraph-alignment="left" tab-stops="L 84" font-size="20" font-name="Papyrus"> <![CDATA[function r = mrn(x) %"most random number" function :-) r = (1/((x/100) + 1)) * (1 - normpdf(x, 500, 70) normpdf(500,500,70)) * normpdf(x, 500, 167);]]> </content> </textbox> <textbox size="639 341" transformation="1 0 0 1 192 273"> <content font-color="0.18254 0.102222 0.0791005" paragraph-alignment="left" tab-stops="L 84" font-size="20" font-name="Papyrus"> <![CDATA[function r = maxrn % search for "most random number" using mrn(x) maxval = 0; maxrn = 0; for n = 1:1000 if rem(n,2) ~= 0 & rem(n,3) ~= 0 & rem(n,5) ~= 0 & mrn(n) > maxval maxval = mrn(n); maxrn = n; end end r = maxrn;]]> </content> </textbox> <title visibility="hidden" vertical-alignment="tracks-master"/> <body visibility="hidden" vertical-alignment="tracks-master"/> </drawables> <transition-style type="inherited"/> <thumbnails> <thumbnail byte-size="8370" size="60 45" file="thumbs/st12.tiff"/> </thumbnails> <bullets> <bullet level="0" marker-type="inherited"> <content font-color="0.18254 0.102222 0.0791005" paragraph-alignment="left" tab-stops="L 96" font-size="72" font-name="Papyrus">Our distribution:</content> </bullet> </bullets> </slide> <slide master-slide-id="master-slide-2"> <drawables> <title visibility="tracks-master" location="100 50" size="824 253" vertical-alignment="tracks-master"/> <textbox size="416 297" transformation="1 0 0 1 304 320"> <content font-color="0.18254 0.102222 0.0791005" paragraph-alignment="left" tab-stops="L 84" font-size="64" font-name="Papyrus"> <![CDATA[>> maxrn ans = 347]]> </content> </textbox> <body visibility="hidden" vertical-alignment="tracks-master"/> </drawables> <transition-style type="inherited"/> <thumbnails> <thumbnail byte-size="8370" size="60 45" file="thumbs/st13.tiff"/> </thumbnails> <bullets> <bullet level="0" marker-type="inherited"> <content font-color="0.18254 0.102222 0.0791005" paragraph-alignment="left" tab-stops="L 96" font-size="48" font-name="Papyrus"> <![CDATA[Now we run our function, and there it is, the most random number between 1 and 1000:]]> </content> </bullet> </bullets> </slide> <slide master-slide-id="master-slide-2"> <drawables> <body visibility="tracks-master" location="100 154" size="824 460" vertical-alignment="tracks-master"/> <title visibility="hidden" vertical-alignment="tracks-master"/> </drawables> <transition-style type="inherited"/> <thumbnails> <thumbnail byte-size="8370" size="60 45" file="thumbs/st15.tiff"/> </thumbnails> <bullets> <bullet level="0" marker-type="inherited"> <content font-color="0.18254 0.102222 0.0791005" paragraph-alignment="left" tab-stops="L 96" font-size="72" font-name="Papyrus"/> </bullet> <bullet level="1" marker-type="inherited"> <content font-color="0.18254 0.102222 0.0791005" paragraph-head-indent="17" paragraph-first-line-indent="17" tab-stops="L 53" font-size="42" font-name="Papyrus">What about more general versions of this?</content> </bullet> <bullet level="1" marker-type="inherited"> <content font-color="0.18254 0.102222 0.0791005" paragraph-head-indent="17" paragraph-first-line-indent="17" tab-stops="L 53" font-size="42" font-name="Papyrus"> <![CDATA[In other words, what about the most random number between 1 and 10, 1 and 100, 1 and 10000, etc.?]]> </content> </bullet> </bullets> </slide> <slide master-slide-id="master-slide-2"> <drawables> <textbox size="651.5 124" transformation="1 0 0 1 177.5 100"> <content font-color="0.18254 0.102222 0.0791005" paragraph-alignment="left" tab-stops="L 84" font-size="20" font-name="Papyrus"> <![CDATA[function r = mrng(x,maxn) %"most random number" function :-) r = (1/((10*x/maxn) + 1)) * (1 - normpdf(x, maxn/2, 0.07*maxn)/normpdf(maxn/2,maxn/2,0.07*maxn)) * normpdf(x, maxn/2, maxn/6);]]> </content> </textbox> <textbox size="693 341" transformation="1 0 0 1 177 281"> <content font-color="0.18254 0.102222 0.0791005" paragraph-alignment="left" tab-stops="L 84" font-size="20" font-name="Papyrus"> <![CDATA[function r = maxrng(maxn) % search for "most random number" using mrng(x,maxn) maxval = 0; maxrn = 0; for n = 1:maxn if rem(n,2) ~= 0 & rem(n,3) ~= 0 & rem(n,5) ~= 0 & mrng(n,maxn) > maxval maxval = mrng(n,maxn); maxrn = n; end end r = maxrn;]]> </content> </textbox> <title visibility="hidden" vertical-alignment="tracks-master"/> <body visibility="hidden" vertical-alignment="tracks-master"/> </drawables> <transition-style type="inherited"/> <thumbnails> <thumbnail byte-size="8370" size="60 45" file="thumbs/st151.tiff"/> </thumbnails> <bullets> <bullet level="0" marker-type="inherited"> <content font-color="0.18254 0.102222 0.0791005" paragraph-alignment="left" tab-stops="L 96" font-size="72" font-name="Papyrus"/> </bullet> </bullets> </slide> <slide master-slide-id="master-slide-2" hidden="true"> <drawables> <title visibility="tracks-master" location="100 58" size="824 80" vertical-alignment="tracks-master"/> <body visibility="tracks-master" location="196 125" size="632 560" vertical-alignment="tracks-master"/> </drawables> <transition-style type="inherited"/> <thumbnails> <thumbnail byte-size="8370" size="60 45" file="thumbs/st16.tiff"/> </thumbnails> <bullets> <bullet level="0" marker-type="inherited"> <content font-color="0.18254 0.102222 0.0791005" paragraph-alignment="left" tab-stops="L 96" font-size="48" font-name="Papyrus">Summary of most random numbers:</content> </bullet> <bullet level="1" marker-type="inherited"> <content font-color="0.18254 0.102222 0.0791005" paragraph-head-indent="17" paragraph-first-line-indent="17" tab-stops="L 53" font-size="36" font-name="Papyrus">1 to 10: 7</content> </bullet> <bullet level="1" marker-type="inherited"> <content font-color="0.18254 0.102222 0.0791005" paragraph-head-indent="17" paragraph-first-line-indent="17" tab-stops="L 53" font-size="36" font-name="Papyrus">1 to 50: 17</content> </bullet> <bullet level="1" marker-type="inherited"> <content font-color="0.18254 0.102222 0.0791005" paragraph-head-indent="17" paragraph-first-line-indent="17" tab-stops="L 53" font-size="36" font-name="Papyrus">1 to 100: 37</content> </bullet> <bullet level="1" marker-type="inherited"> <content font-color="0.18254 0.102222 0.0791005" paragraph-head-indent="17" paragraph-first-line-indent="17" tab-stops="L 53" font-size="36" font-name="Papyrus">1 to 500: 173</content> </bullet> <bullet level="1" marker-type="inherited"> <content font-color="0.18254 0.102222 0.0791005" paragraph-head-indent="17" paragraph-first-line-indent="17" tab-stops="L 53" font-size="36" font-name="Papyrus">1 to 1000: 347</content> </bullet> <bullet level="1" marker-type="inherited"> <content font-color="0.18254 0.102222 0.0791005" paragraph-head-indent="17" paragraph-first-line-indent="17" tab-stops="L 53" font-size="36" font-name="Papyrus">1 to 10,000: 3,479</content> </bullet> <bullet level="1" marker-type="inherited"> <content font-color="0.18254 0.102222 0.0791005" paragraph-head-indent="17" paragraph-first-line-indent="17" tab-stops="L 53" font-size="36" font-name="Papyrus">1 to 100,000: 34,799</content> </bullet> <bullet level="1" marker-type="inherited"> <content font-color="0.18254 0.102222 0.0791005" paragraph-head-indent="17" paragraph-first-line-indent="17" tab-stops="L 53" font-size="36" font-name="Papyrus">1 to 1,000,000: 347,971</content> </bullet> </bullets> </slide> <slide master-slide-id="master-slide-2"> <drawables> <textbox size="824 74" transformation="1 0 0 1 128 76"> <content font-color="0.18254 0.102222 0.0791005" paragraph-alignment="left" tab-stops="L 96" font-size="48" font-name="Papyrus">Summary of most random numbers:</content> </textbox> <textbox grow-horizontally="true" size="139 56" transformation="1 0 0 1 155.5 157"> <content font-color="0.184314 0.101961 0.0784314" paragraph-head-indent="17" paragraph-first-line-indent="17" tab-stops="L 53" font-size="36" font-name="Papyrus">1 to 10: </content> </textbox> <textbox id="textbox-1" grow-horizontally="true" size="52 56" transformation="1 0 0 1 325 157"> <content font-color="0.184314 0.101961 0.0784314" paragraph-head-indent="17" paragraph-first-line-indent="17" tab-stops="L 53" font-size="36" font-name="Papyrus"> 7</content> </textbox> <textbox grow-horizontally="true" size="237 56" transformation="1 0 0 1 140.5 436"> <content font-color="0.184314 0.101961 0.0784314" paragraph-head-indent="17" paragraph-first-line-indent="17" tab-stops="L 53" font-size="36" font-name="Papyrus">1 to 10,000: </content> </textbox> <textbox id="textbox-6" grow-horizontally="true" size="114 56" transformation="1 0 0 1 384 436"> <content font-color="0.184314 0.101961 0.0784314" paragraph-head-indent="17" paragraph-first-line-indent="17" tab-stops="L 53" font-size="36" font-name="Papyrus">3,479</content> </textbox> <textbox grow-horizontally="true" size="236 56" transformation="1 0 0 1 141 491"> <content font-color="0.184314 0.101961 0.0784314" paragraph-head-indent="17" paragraph-first-line-indent="17" tab-stops="L 53" font-size="36" font-name="Papyrus">1 to 100,000:</content> </textbox> <textbox id="textbox-7" grow-horizontally="true" size="133 56" transformation="1 0 0 1 414.5 491"> <content font-color="0.184314 0.101961 0.0784314" paragraph-head-indent="17" paragraph-first-line-indent="17" tab-stops="L 53" font-size="36" font-name="Papyrus">34,799</content> </textbox> <textbox grow-horizontally="true" size="270 56" transformation="1 0 0 1 140 545"> <content font-color="0.184314 0.101961 0.0784314" paragraph-head-indent="17" paragraph-first-line-indent="17" tab-stops="L 53" font-size="36" font-name="Papyrus">1 to 1,000,000:</content> </textbox> <textbox id="textbox-8" grow-horizontally="true" size="148 56" transformation="1 0 0 1 427 545"> <content font-color="0.184314 0.101961 0.0784314" paragraph-head-indent="17" paragraph-first-line-indent="17" tab-stops="L 53" font-size="36" font-name="Papyrus"> 347,971</content> </textbox> <textbox id="textbox-9" grow-horizontally="true" size="110 56" transformation="1 0 0 1 699 597"> <content font-color="0.184314 0.101961 0.0784314" paragraph-head-indent="17" paragraph-first-line-indent="17" tab-stops="L 53" font-size="36" font-name="Papyrus">done</content> </textbox> <textbox grow-horizontally="true" size="139 56" transformation="1 0 0 1 156.5 216"> <content font-color="0.184314 0.101961 0.0784314" paragraph-head-indent="17" paragraph-first-line-indent="17" tab-stops="L 53" font-size="36" font-name="Papyrus">1 to 50:</content> </textbox> <textbox id="textbox-2" grow-horizontally="true" size="61 56" transformation="1 0 0 1 319.5 216"> <content font-color="0.184314 0.101961 0.0784314" paragraph-head-indent="17" paragraph-first-line-indent="17" tab-stops="L 53" font-size="36" font-name="Papyrus"> 17</content> </textbox> <textbox grow-horizontally="true" size="163 56" transformation="1 0 0 1 154.5 267"> <content font-color="0.184314 0.101961 0.0784314" paragraph-head-indent="17" paragraph-first-line-indent="17" tab-stops="L 53" font-size="36" font-name="Papyrus">1 to 100: </content> </textbox> <textbox id="textbox-3" grow-horizontally="true" size="61 56" transformation="1 0 0 1 318.5 267"> <content font-color="0.184314 0.101961 0.0784314" paragraph-head-indent="17" paragraph-first-line-indent="17" tab-stops="L 53" font-size="36" font-name="Papyrus">37</content> </textbox> <textbox grow-horizontally="true" size="171 56" transformation="1 0 0 1 149.5 325"> <content font-color="0.184314 0.101961 0.0784314" paragraph-head-indent="17" paragraph-first-line-indent="17" tab-stops="L 53" font-size="36" font-name="Papyrus">1 to 500: </content> </textbox> <textbox id="textbox-4" grow-horizontally="true" size="70 56" transformation="1 0 0 1 345 325"> <content font-color="0.184314 0.101961 0.0784314" paragraph-head-indent="17" paragraph-first-line-indent="17" tab-stops="L 53" font-size="36" font-name="Papyrus">173</content> </textbox> <textbox grow-horizontally="true" size="186 56" transformation="1 0 0 1 143 380"> <content font-color="0.184314 0.101961 0.0784314" paragraph-head-indent="17" paragraph-first-line-indent="17" tab-stops="L 53" font-size="36" font-name="Papyrus">1 to 1000: </content> </textbox> <textbox id="textbox-5" grow-horizontally="true" size="85 56" transformation="1 0 0 1 336.5 380"> <content font-color="0.184314 0.101961 0.0784314" paragraph-head-indent="17" paragraph-first-line-indent="17" tab-stops="L 53" font-size="36" font-name="Papyrus">347</content> </textbox> <title visibility="hidden" vertical-alignment="tracks-master"/> <body visibility="hidden" vertical-alignment="tracks-master"/> </drawables> <transition-style type="inherited"/> <thumbnails> <thumbnail byte-size="8370" size="60 45" file="thumbs/st19.tiff"/> </thumbnails> <bullets> <bullet level="0" marker-type="inherited"> <content font-color="0.18254 0.102222 0.0791005" paragraph-alignment="left" tab-stops="L 96" font-size="72" font-name="Papyrus"/> </bullet> </bullets> <events> <build type="apple:move in" duration="1" delivery="1" target-id="textbox-1"> <property name="direction" value="1"/> <property name="animationType" value="1"/> </build> <build type="apple:move in" duration="1" 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