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"" "  "" " ""  """" """ DDDDDDDDDDDDDDDDDDDDDDDD""""DDDDDDDDDDDDDDDDDDDDD""DDDDDDDDDDDDDDDDDDDDDDDDDDDD""DDDDDDDDDDD""""""""DDDDDDDDDDDDDDD""DDDDDDDDDD""""""""D3DDDDDDDDDDDD""""DDDDDDDDDD"""""""""D3DDDDDDDDDDDD"""03300DDDDDDDDD"""""""""33DDDDDDDDD"""3003DDDDDDDDD"""""""""33DDDDDDDDD""30300DDDDDD"""""""""3""3300DDDDDD"""""""""3"""""033300DDDDDDDDD"""""""""33DDDDDDDDDDD"""""DDDDDDDDD""""""""33DDDDDDDDDDD""DDDDD""""""""3DDDDDD""DDDDD"""""""""3DDDDDD"""""DDDDDD"""""""""DDDDDDDD"""DDDDDD"""""""""DDDDDDDDDDDDDDDDDDDD"""""""""DDDDDDDDDDDDDDDDDDDD"""""""""DDDDDDDDDDDDDDDDDDDD"""""""""DDDDDDDDDDDDDDDDDD"""""""""DDDDDDDDDDDDDDDDDD"""""""""DDDDDDDDDDDDDDDDDD"""""""""DDDDDDDDDDDDDDDDDD"""""""""DDDDDDDDDDDDDDDDDDD""""""""""DDDDDDDDDDDDDDDDDDD""""""""""DDDDDDDDDDDDDDDDDDD""""""""DDDDDDDDDDDDDDDDDDDD""""""""DDDDDDDDDDDDDDDDDDDD"""""""DDDDDDDDDDDDDDDDDDD"""""""DDDDDDDDDDDDDDDDDDD""""""""""""""""DDDDDDDDDDDDDDDDDD""""""""""""""""DDDDDDDDDDDDDDDDDDDDDDDDDDD !DDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDD$$DDDDDDDDDDDDD$ADDDDDDDDD""""""D"DDD"DDDDDDDDDDDD""""""D"DDD$DDDDDDDDDDDDD"""""""D""DDDDDDDDDDDDDDDD"""""""D"D"DDDDDDDDDDDDDDDD"""""""D"D"DDDDDDDDDDDDDDDD"""""""D"D"DDDDDDDDDDDDDDDD"""""""D"D"DDDDDDDDDDDDDDD""""""""D"DDDDDDDDDDDDDD"""""""D"D"DDDDDDDDDDDD"""""""D"D"DDDDDDDDDDDD"""""""DD"DDDDDDD$""DDDDDDD""""""D"DDD"DDDDDDD$DDDDDD"""""""D""DDD"DDDDDDD$ADDDDDD"""""""D""DDD" "DDDDDDD$DDDDDD"""""""D"D""DDDDDDD@DDDDD""""""""" ""DDDDDDD@DDDDD""""""""""""""""" ""DDDDDDDDDDDDDDDD"D""""""D"""""""""" """DDDDDDD@A@DDDDDDDDD"D""""""D""""D"""""""DD""DDDDDDDD433DDDDDD"DD""""""""""DD"""""""DDDDDDDDDD@A3333DDDDDD"DD""""""""""DD"""""""DDDDDDDDD@43333 DDDDDDDDD"D""""""""""D"""""""DDDDDDDDD@33333DDDDDDDDD"D"""""""""D"""""""DDDDDDDDDDDD@33333DDDDDDDDDD"DD"""""D""""D"""""""DDDDDDDDDDDD@<<<<DDDDDDDDDD"""""D"""D"""""DDDDDDDDDDDDD@DDDDDDDDDDD"""""DD"""DD"""""DDDDDDDDDDDDD@ DDDDDDDDDDD""""D""""""""""""""""DDD""D"""D"DDD"""""""""""DDDDDDDDDDDDDDDDDD""""""""""""""""""""DDD"""""D"DDD"""""""""""DDDDDDDDDDD!""""1""""""!""""""!""!!"!!!!!!!!   !!""""1""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""z ;; title: oh no! zeno's paradox ;; author: replicat ;; desc: a short "game" about one of zeno's paradoxes ;; site: matdombrock.com ;; license: GPL3 ;; version: 1.0 ;; script: scheme (define-macro (inc! x dx) `(set! ,x (+ ,x ,dx))) (define-macro (numh n) `(number->string (exact->inexact ,n))) (define-macro (loop n fn) `(let l ((i 0)) (when (< i ,n) (begin (,fn i)(l (+ i 1)))))) (define (any-key?) (define hit #f) (loop 128 (lambda (i) (when (t80::btnp i) (set! hit #t)) (when (t80::keyp i) (set! hit #t)))) hit) ;; global state (define phrases (list "Achilles is the fastest runner in all the land! Surely he can best the tortoise in a race to the flag! --press any key to continue--" "He may think he can give the tortoise quite the head start! For the tortoise is quite slow indeed! None the less it has already won the race!" "For before Achilles can catch the tortoise he must get half way to the tortoise!" "And before he can get half way, he must get one quarter of the way. Yet before that he must reach one eighth of the distance!" "ACHILLES CAN NOT MOVE AT ALL!! For before he can move any distance, he must cover the infinite amount of distances in between!" "The paradoxical conclusion then would be that travel over any finite distance can be neither completed nor begun! All motion must be an illusion!" "Yet Achilles can move!? He seems to have already covered half the distance between his starting point and the tortoise!" "However, the quickest runner can never overtake the slowest! Since the pursuer must first reach the point whence the pursued started, so that the slower must always hold a lead!" "Achilles is quite fast indeed! with each passing moment he covers half the distance between where he last was and where the tortoise is now!" "Yet is halfway there is ever enough?" "Even after reaching an infinite amount of halfway points there are an infinite amount left to cross!" "Achilles will never catch up!" "So long as the tortoise keeps advancing Achilles can never catch her!" "When Achilles arrives somewhere the tortoise has been, he always has some remaining distance to go before he can reach the tortoise!" "Achilles grows closer and closer to the tortoise in each passing moment!" "Yet it is now clear he will never pass her!" "He will only grow infinitely closer!" "Infinitely close is surely not passing!" "Yet, is there any difference between being infinitely close and being THERE?" "Let us try again!";; phase 2 "Suppose instead of trying to beat the tortoise, Achilles simply runs to the flag!" "Achilles will no longer be concerned with passing the tortoise. He will simply complete the race!" "He will only need to move halfway between the starting line and the flag!" "From there he can easily reach the halfway point between that halfway point and the flag!" "Surely the fastest runner in the world can complete such a simple task!" "Yet Achilles must wonder if he can complete an INFINITE amount of simple tasks?" "Achilles clears half of the race in a single bound! He is truly the fastest in the world!" "He bursts into the lead! Clearing the next halfway point without any signs of tiring!" "With each passing moment he crosses a new halfway point! There is no chance the tortoise can win the race now!" "Yet as the next halfway point approaches Achilles in his wisdom realizes he is not progressing as well as he had hoped!" "For the distance between each new halfway point grows smaller and smaller! Yet he must still pass each one!" "Achilles may be bested by the tortoise once again! She is gaining on him quickly now!" "But what of the tortoise? Can she complete the race herself? She is still far behind!" "However, she is not burdened with the knowledge of philosophy!" "She is not ruled by the tyrant of abstract thought!" "She moves discretely without regard for Zeno!" "She is not bothered to move only half way! She simply goes where she must!" "One step at a time, she approaches the lead!" "If only Achilles could move in discrete steps!" "Instead of converging on the flag he could simply pass it!" "There may still be time!" "Could Achilles simply attempt to move past the flag?" "Setting his goal to be twice the distance between his starting location on the flag could resolve him to the location of the flag by his first halfway point!" "While he must traverse an infinite amount of halfway points to get anywhere, he can get halfway to anywhere easily!" "Halfway to anywhere is every somewhere!" "Similarly, being infinitely close to a location is the same as being there!" "With this new mastery of the infinite is Achilles able to best the tortoise?" "Furthermore is that flag actually moving at all?")) (define t 0) (define moves 0) (define moves-real 0) (define ax 0) (define tx 0) (define flowers (list 210 0 220 0 230 0)) (define phase 0) (define phrase-index 0) (define input-time 120) (define input-timer input-time) (define (make-percent-string x) (define xx (* (/ x 200) 100)) (string-append (numh (min xx ;;99.99999999999999) 100)) (if (= xx 100) "...%" "%"))) (define (reset-phase!) (t80::sfx 0 16 30) (set! moves-real 0) (set! moves 0) (set! ax 0)) (define (handle-input!) (when (and (= input-timer 0) (any-key?)) (set! input-timer input-time) (inc! moves 1) (inc! phrase-index 1) (t80::sfx 0 (modulo (+ 32 moves) 98) 8 3 6) (set! tx (+ tx 4)) (when (> moves 5) (inc! moves-real 1) (when (= phase 0)(set! ax (- tx (/ (- tx ax) 2)))) (when (= phase 1)(set! ax (- 200 (/ (- 200 ax) 2)))) (when (= phase 2)(set! ax 0))) (when (= phase 3)(set! ax (- 420 (/ (- 420 ax) 2)))) (when (= phrase-index 20) (reset-phase!) (set! phase 1)) (when (= phrase-index 40) (reset-phase!) (set! phase 2)) (when (= phrase-index 46) (reset-phase!) (set! phase 3)))) (define (render) (define tt (floor (/ t 60))) (t80::cls 0) ;; !? (when (or (= phrase-index 6) (= phrase-index 19) (= phrase-index 26) (= phrase-index 32) (= phrase-index 40) (= phrase-index 46)) (t80::spr (+ 224 (* (modulo tt 2) 2)) 90 10 0 3 0 0 2 2)) ;; title (when (< phrase-index 6) ;; pillar (t80::spr 204 40 4 0 2 0 0 2 4) (t80::spr 204 110 4 0 2 0 0 2 4) ;; title (t80::spr 104 60 3 0 2 0 0 8 4) ;; arrow (t80::spr 192 (max (- 240 (* t 2)) 110) 8 0 2 0 0 3 1)) ;; tree (t80::spr 28 176 3 0 2 0 0 4 4) ;; Achilles (t80::spr (* (modulo moves-real 2) 2) (floor ax) 50 0 1 0 0 2 2) ;; tortoise (t80::spr (+ 6 (* (modulo moves 2) 2)) (floor tx) 50 0 1 0 0 2 2) ;; flag (t80::spr (+ 32 (* (modulo tt 4) 2)) 211 50 0 1 0 0 2 2) ;; flowers (loop 3 (lambda (i) (define ii (* i 2)) (define x (list-ref flowers ii)) (define y (list-ref flowers (+ 1 ii))) (t80::spr (+ 128 (modulo (+ tt i) 2)) x y 0 1 0 0 1 1) (when (= (modulo t 16) 0) (define rx (- (random 5) 2)) (define ry (random 3)) (list-set! flowers ii (+ x rx)) (if (> (+ y ry) 136) (begin (list-set! flowers ii (+ 210 (random 20))) (list-set! flowers (+ ii 1) 0)) (list-set! flowers (+ ii 1) (+ y ry)))))) ;; floor (loop 16 (lambda (i) (t80::spr 64 (* i 16) 67 0 1 0 0 2 2))) (when (> t 120) ;; input timer (t80::rect 0 132 (- 240 (* 2 input-timer)) 4 2) ;; Zeno (t80::spr (+ 96 (* (modulo tt 4) 2)) 0 75 0 1 0 0 2 2) (t80::print "ZENO:" 24 80 1 #f 2) ;;(t80::print (numh phrase-index) 0 20 1) (t80::print (list-ref phrases (min phrase-index (- (length phrases) 1))) 0 94 1) ;; stats (when (< phrase-index (length phrases)) (t80::print (make-percent-string ax) 0 0 2) (t80::print (make-percent-string tx) 0 10 3))) ;; Dev logo (when (< t 119) (t80::spr 204 132 (- 136 (min 42 t)) 0 2 0 0 2 4) (t80::spr 160 120 (- 120 (min 42 t)) 0 1 0 0 6 2)) (when (>= phrase-index (length phrases)) (t80::spr 160 42 4 0 3 0 0 6 2))) (t80::poke #x7FC3F 1 1) (t80::sfx 0 16 52) (define (TIC) (handle-input!) (render) (when (= t 60) (t80::sfx 2 16 16)) (when (= t 120) (set! input-timer input-time) (t80::music 0)) (inc! t 1) (when (> input-timer 0) (inc! input-timer -1)))