mirror of
https://github.com/3b1b/manim.git
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End of independence project
This commit is contained in:
Grant Sanderson
parent
25bd813486
commit
887565a5df
2 changed files with 400 additions and 33 deletions
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@ -56,11 +56,20 @@ def get_quiz(*questions):
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rect.shift(MED_SMALL_BUFF*DOWN)
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rect.highlight(WHITE)
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quiz = VGroup(rect, content)
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quiz.questions = q_mobs
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quiz.scale(0.7)
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return quiz
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def get_slot_group(bool_list, buff = MED_LARGE_BUFF, include_qs = True):
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def get_slot_group(
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bool_list,
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buff = MED_LARGE_BUFF,
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include_qs = True,
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min_bool_list_len = 3,
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):
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if len(bool_list) < min_bool_list_len:
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bool_list += [None]*(min_bool_list_len - len(bool_list))
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n = len(bool_list)
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lines = VGroup(*[
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Line(ORIGIN, MED_LARGE_BUFF*RIGHT)
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for x in range(n)
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@ -102,7 +111,7 @@ def get_slot_group(bool_list, buff = MED_LARGE_BUFF, include_qs = True):
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return slot_group
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def get_probability_of_slot_group(bool_list, conditioned_list = None):
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filler_tex = "Fi"*len(bool_list)
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filler_tex = "Fi"*max(len(bool_list), 3)
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if conditioned_list is None:
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result = TexMobject("P(", filler_tex, ")")
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else:
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@ -735,6 +744,33 @@ class AssociatePatternsWithScores(BreakDownQuestionPatterns):
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self.play(row.highlight, YELLOW)
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self.dither(4)
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class BeforeCounting(TeacherStudentsScene):
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def construct(self):
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triangle = PascalsTriangle(nrows = 7)
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triangle.scale_to_fit_height(4)
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triangle.next_to(self.teacher, UP+LEFT)
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prob = get_probability_of_slot_group([True, True, False])
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prob.to_edge(UP)
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brace = Brace(prob, DOWN)
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q_marks = brace.get_text("???")
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self.teacher.change_mode("raise_right_hand")
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self.add(triangle)
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self.change_student_modes(*["hooray"]*3)
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self.play(
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triangle.scale, 0.5,
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triangle.to_corner, UP+RIGHT,
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self.teacher.change_mode, "sassy"
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)
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self.change_student_modes(*["confused"]*3)
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self.play(Write(prob))
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self.play(
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GrowFromCenter(brace),
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LaggedStart(FadeIn, q_marks)
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)
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self.dither(2)
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class TemptingButWrongCalculation(BreakDownQuestionPatterns):
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def construct(self):
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self.add_title()
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@ -745,6 +781,7 @@ class TemptingButWrongCalculation(BreakDownQuestionPatterns):
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title.scale(1.5)
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title.to_edge(UP)
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self.add(title)
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self.title = title
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def write_simple_product(self):
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lhs = TexMobject("P\\big(", "Filler Blah", "\\big)", "= ")
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@ -807,6 +844,9 @@ class TemptingButWrongCalculation(BreakDownQuestionPatterns):
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)
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self.dither(3)
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self.question = question
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self.rhs = rhs
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class ThousandPossibleQuizzes(Scene):
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CONFIG = {
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"n_quiz_rows" : 25,
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@ -820,6 +860,7 @@ class ThousandPossibleQuizzes(Scene):
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def construct(self):
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self.draw_all_quizzes()
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self.show_division_by_first_question()
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self.ask_about_second_question()
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self.show_uncorrelated_division_by_second()
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self.increase_second_correct_slice()
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self.second_division_among_first_wrong()
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@ -852,8 +893,8 @@ class ThousandPossibleQuizzes(Scene):
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full_quizzes.arrange_submobjects(RIGHT)
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target_quizzes = VGroup(*quizzes[:len(full_quizzes)])
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self.add(full_quizzes)
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self.dither()
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for quiz in full_quizzes:
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self.play(FadeIn(quiz, run_time = 3, submobject_mode = "lagged_start"))
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self.play(
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Transform(full_quizzes, target_quizzes),
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FadeIn(title)
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@ -904,6 +945,43 @@ class ThousandPossibleQuizzes(Scene):
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self.splits = VGroup(top_split, bottom_split)
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self.q1_split_labels = labels
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def ask_about_second_question(self):
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top_split = self.splits[0]
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sg1, sg2 = slot_groups = VGroup(*[
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get_slot_group(
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[True, b],
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include_qs = False,
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buff = SMALL_BUFF
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)
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for b in True, False
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])
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question = VGroup(
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TextMobject("Where are"), sg1,
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TextMobject("and"), sg2, TextMobject("?"),
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)
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question.arrange_submobjects(RIGHT, aligned_edge = DOWN)
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question[-1].next_to(question[-2], RIGHT, SMALL_BUFF)
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question.next_to(top_split, UP, MED_LARGE_BUFF)
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slot_groups.shift(SMALL_BUFF*DOWN)
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little_rects = VGroup(*[
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SurroundingRectangle(
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VGroup(sg.lines[1], sg.content[1])
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)
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for sg in slot_groups
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])
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big_rect = SurroundingRectangle(top_split)
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self.play(Write(question))
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self.play(ShowCreation(little_rects))
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self.dither()
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self.play(FadeOut(little_rects))
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self.play(ShowCreation(big_rect))
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self.play(
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FadeOut(big_rect),
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FadeOut(question),
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)
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self.dither()
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def show_uncorrelated_division_by_second(self):
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top_split = self.splits[0]
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top_label = self.q1_split_labels[0]
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@ -1168,6 +1246,86 @@ class ThousandPossibleQuizzes(Scene):
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quizzes.shift(MED_LARGE_BUFF*DOWN)
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return quizzes
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class ExampleConditional(Scene):
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def construct(self):
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prob = get_probability_of_slot_group(
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[True, True], [True]
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)
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rhs = TexMobject("=", "0.925", ">", "0.8")
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rhs.highlight_by_tex("0.925", YELLOW)
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rhs.next_to(prob, RIGHT)
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expression = VGroup(prob, rhs)
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expression.scale_to_fit_width(2*SPACE_WIDTH - 1)
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expression.center().to_edge(DOWN)
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self.play(Write(expression))
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self.dither()
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class HarderQuizzes(Scene):
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def construct(self):
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quizzes = VGroup(
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get_quiz(
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"Find all primes $p$ \\\\ where $p+2$ is prime.",
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"Find all primes $p$ \\\\ where $2^{p}-1$ is prime.",
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"Solve $\\zeta(s) = 0$",
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),
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get_quiz(
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"Find $S$ such that \\\\ $\\#\\mathds{N} < \\#S < \\#\\mathcal{P}(\\mathds{N})$",
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"Describe ``forcing''",
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"Prove from ZFC that $S \\notin S$.",
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),
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)
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quizzes.arrange_submobjects(RIGHT)
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quizzes.to_edge(DOWN)
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crosses = VGroup(*[
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Cross(quiz.questions[0])
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for quiz in quizzes
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])
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for quiz in quizzes:
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self.play(FadeIn(quiz))
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self.dither()
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for cross in crosses:
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self.play(ShowCreation(cross))
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self.dither()
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class WritePSecond(Scene):
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def construct(self):
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prob = get_probability_of_slot_group([None, True, None])
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rhs = TexMobject("= 0.8")
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rhs.next_to(prob, RIGHT)
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prob.add(rhs)
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prob.scale_to_fit_width(2*SPACE_WIDTH - 1)
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prob.center().to_edge(DOWN)
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self.play(Write(prob))
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class SubmitToTemptation(TemptingButWrongCalculation):
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def construct(self):
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self.force_skipping()
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TemptingButWrongCalculation.construct(self)
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self.revert_to_original_skipping_status()
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title = self.title
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question = self.question
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title.generate_target()
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title.target.scale_in_place(1./1.5)
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new_words = TextMobject("and", "okay", "assuming independence.")
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new_words.highlight_by_tex("okay", GREEN)
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new_words.next_to(title.target, RIGHT)
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VGroup(title.target, new_words).center().to_edge(UP)
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self.play(
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MoveToTarget(title),
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FadeOut(question)
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)
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self.play(
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Write(new_words, run_time = 2),
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self.randy.change, "hooray"
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)
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for part in self.rhs:
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self.play(Indicate(part.value))
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self.dither()
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class AccurateProductRule(SampleSpaceScene, ThreeDScene):
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def construct(self):
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self.setup_terms()
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@ -1742,12 +1900,17 @@ class ProbablyWrong(TeacherStudentsScene):
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class ShowTrueDistribution(PiCreatureScene):
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def construct(self):
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self.force_skipping()
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self.remove(self.randy)
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self.add_title()
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self.show_distributions()
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self.show_emotion()
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self.imagine_score_0()
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self.revert_to_original_skipping_status()
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self.get_angry()
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def add_title(self):
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title = TexMobject("P(", "\\text{Correct}", ")", "=", "0.65")
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title.to_edge(UP)
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@ -1816,6 +1979,17 @@ class ShowTrueDistribution(PiCreatureScene):
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self.dither()
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self.play(FadeOut(bar_rect))
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def get_angry(self):
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randy = self.randy
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self.play(randy.change, "angry")
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self.dither(2)
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self.play(PiCreatureSays(
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randy, "It's not representative!",
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target_mode = "pleading",
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bubble_kwargs = {"fill_opacity" : 1}
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))
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self.dither(2)
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#####
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@ -2031,9 +2205,48 @@ class CorrelationsWith35Percent(ThousandPossibleQuizzes):
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)
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self.dither()
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class WeighingIndependenceAssumption(PiCreatureScene):
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def construct(self):
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randy = self.randy
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title = TextMobject("Independence")
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title.scale(1.5)
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title.to_edge(UP)
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self.add(title)
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formula = TexMobject(
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"P(", "A", "B", ")", "="
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"P(", "A", ")", "P(", "B", ")"
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)
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formula.highlight_by_tex("A", BLUE)
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formula.highlight_by_tex("B", GREEN)
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clean = TextMobject("Clean")
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clean.next_to(formula, UP)
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VGroup(clean, formula).next_to(randy, UP+LEFT)
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clean.save_state()
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clean.shift(2*(DOWN+RIGHT))
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clean.set_fill(opacity = 0)
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self.play(
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randy.change, "raise_left_hand", clean,
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clean.restore
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)
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self.play(Write(formula))
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self.play(
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randy.change, "raise_right_hand",
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randy.look, UP+RIGHT,
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)
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self.dither(2)
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####
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def create_pi_creature(self):
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self.randy = Randolph().to_edge(DOWN)
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return self.randy
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class NameBinomial(Scene):
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CONFIG = {
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"flip_indices" : [1, 2, 4, 5, 7, 9],
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"flip_indices" : [0, 2, 4, 5, 6, 7],
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}
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def construct(self):
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self.name_distribution()
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@ -2178,10 +2391,11 @@ class NameBinomial(Scene):
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GrowFromCenter(brace),
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FadeIn(words)
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)
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for m1, m2 in (self.checkmarks, girls), (self.crosses, boys):
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for m1, m2 in (self.crosses, boys), (self.checkmarks, girls):
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self.play(ReplacementTransform(
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m1, m2,
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submobject_mode = "lagged_start"
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submobject_mode = "lagged_start",
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run_time = 3
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))
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self.dither()
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@ -2230,6 +2444,18 @@ class NameBinomial(Scene):
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buff = SMALL_BUFF
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)
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prob = TexMobject(
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"P(", "\\# \\text{Girls}", "=", "6", ")"
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)
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prob.highlight_by_tex("Girls", MAROON_B)
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arrow = Arrow(UP, ORIGIN, tip_length = 0.15)
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arrow.highlight(MAROON_B)
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arrow.next_to(prob, DOWN)
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prob.add(arrow)
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prob.next_to(chart_rect, UP)
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girls = VGroup(*[self.girls[i] for i in self.flip_indices])
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self.play(ShowCreation(chart_rect))
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self.play(LaggedStart(
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ShowCreation, girl_rects,
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@ -2238,6 +2464,16 @@ class NameBinomial(Scene):
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))
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self.dither()
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self.play(Write(prob))
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self.play(LaggedStart(
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Indicate, girls,
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run_time = 3,
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lag_ratio = 0.3,
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rate_func = there_and_back
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))
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self.play(FadeOut(prob))
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self.dither()
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self.chart_rect = chart_rect
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self.girl_rects = girl_rects
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@ -2413,30 +2649,39 @@ class ProbabilityOfAGivenBoyGirlPattern(CycleThroughPatterns):
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prob.submobjects[1] = pattern
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prob.next_to(self.count, DOWN, LARGE_BUFF)
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gp = TexMobject("(0.49)").highlight(MAROON_B)
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bp = TexMobject("(0.51)").highlight(BLUE)
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gp = TexMobject("P(\\female)")
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gp[2].highlight(MAROON_B)
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bp = TexMobject("P(\\male)")
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bp[2].highlight(BLUE)
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gp_num = TexMobject("(0.49)").highlight(MAROON_B)
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bp_num = TexMobject("(0.51)").highlight(BLUE)
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gp_nums = VGroup()
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bp_nums = VGroup()
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factored = VGroup()
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gps = VGroup()
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bps = VGroup()
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factored_in_nums = VGroup()
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for i in range(10):
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if i in indices:
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mob = gp.copy()
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gps.add(mob)
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num_mob = gp_num.copy()
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gp_nums.add(num_mob)
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p_mob = gp.copy()
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else:
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mob = bp.copy()
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bps.add(mob)
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factored.add(mob)
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factored.arrange_submobjects(RIGHT, buff = SMALL_BUFF)
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factored.next_to(prob, DOWN, MED_LARGE_BUFF)
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gps.save_state()
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bps.save_state()
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num_mob = bp_num.copy()
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bp_nums.add(num_mob)
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p_mob = bp.copy()
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factored_in_nums.add(num_mob)
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factored.add(p_mob)
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for group in factored, factored_in_nums:
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group.arrange_submobjects(RIGHT, buff = SMALL_BUFF)
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group.next_to(prob, DOWN, MED_LARGE_BUFF)
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gp_nums.save_state()
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bp_nums.save_state()
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final_probability = TexMobject(
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"(0.49)^6", "(0.51)^4"
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)
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final_probability.highlight_by_tex("0.49", MAROON_B)
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final_probability.highlight_by_tex("0.51", BLUE)
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final_probability.next_to(factored, DOWN, LARGE_BUFF)
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final_probability.next_to(factored_in_nums, DOWN, LARGE_BUFF)
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self.play(FadeIn(prob))
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self.dither()
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@ -2445,7 +2690,13 @@ class ProbabilityOfAGivenBoyGirlPattern(CycleThroughPatterns):
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run_time = 1.5,
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))
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self.dither(2)
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for group, tex in (gps, "0.49"), (bps, "0.51"):
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self.play(ReplacementTransform(
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factored, factored_in_nums,
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run_time = 2,
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submobject_mode = "lagged_start"
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))
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self.dither(2)
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for group, tex in (gp_nums, "0.49"), (bp_nums, "0.51"):
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part = final_probability.get_part_by_tex(tex)
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self.play(group.shift, MED_LARGE_BUFF*DOWN)
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self.play(
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@ -2510,7 +2761,7 @@ class GeneralBinomialDistributionValues(Scene):
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)
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full_probability.next_to(chart, UP, aligned_edge = LEFT)
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self.add(chart, full_probability)
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self.add(chart)
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self.chart = chart
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self.full_probability = full_probability
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|
|
@ -2541,6 +2792,12 @@ class GeneralBinomialDistributionValues(Scene):
|
|||
|
||||
self.play(FadeIn(shown_prob))
|
||||
self.dither()
|
||||
self.play(LaggedStart(
|
||||
FadeIn, self.full_probability,
|
||||
run_time = 4,
|
||||
lag_ratio = 0.5,
|
||||
))
|
||||
self.dither()
|
||||
last_k = 6
|
||||
for k in 3, 8, 5, 9, 6:
|
||||
self.play(Transform(
|
||||
|
|
@ -2877,12 +3134,43 @@ class ButWhatsTheAnswer(TeacherStudentsScene):
|
|||
self.play(self.teacher.change, "pondering")
|
||||
self.dither(3)
|
||||
|
||||
class PermuteQuizQuestions(Scene):
|
||||
def construct(self):
|
||||
quiz = get_quiz(
|
||||
"Define ``Brachistochrone''",
|
||||
"Define ``Tautochrone''",
|
||||
"Define ``Cycloid''",
|
||||
)
|
||||
questions = [
|
||||
VGroup(*q[2:])
|
||||
for q in quiz.questions
|
||||
]
|
||||
colors = [BLUE, GREEN, RED]
|
||||
for color, question in zip(colors, questions):
|
||||
question.highlight(color)
|
||||
quiz.scale(2)
|
||||
|
||||
self.add(quiz)
|
||||
self.dither()
|
||||
for m1, m2 in it.combinations(questions, 2):
|
||||
self.play(
|
||||
m1.move_to, m2, LEFT,
|
||||
m2.move_to, m1, LEFT,
|
||||
path_arc = np.pi
|
||||
)
|
||||
self.dither()
|
||||
|
||||
class AssumeOrderDoesntMatter(Scene):
|
||||
def construct(self):
|
||||
self.force_skipping()
|
||||
|
||||
self.add_title()
|
||||
self.show_equality()
|
||||
self.mention_correlation()
|
||||
|
||||
self.revert_to_original_skipping_status()
|
||||
self.coming_soon()
|
||||
|
||||
def add_title(self):
|
||||
title = TextMobject(
|
||||
"Softer simplifying assumption: " +\
|
||||
|
|
@ -2933,18 +3221,50 @@ class AssumeOrderDoesntMatter(Scene):
|
|||
self.prob_groups = prob_groups
|
||||
|
||||
def mention_correlation(self):
|
||||
everything = VGroup(*self.get_top_level_mobjects())
|
||||
question = TextMobject("But what is ``correlation''?")
|
||||
assumption_group = VGroup(*self.get_top_level_mobjects())
|
||||
question = TextMobject(
|
||||
"But what is ", "``correlation''", "?",
|
||||
arg_separator = ""
|
||||
)
|
||||
question.highlight(BLUE)
|
||||
question.to_edge(UP)
|
||||
bottom = question.get_bottom()
|
||||
|
||||
self.play(
|
||||
Write(question),
|
||||
everything.next_to, bottom, DOWN, LARGE_BUFF
|
||||
assumption_group.next_to, bottom, DOWN, LARGE_BUFF
|
||||
)
|
||||
self.dither()
|
||||
|
||||
self.assumption_group = assumption_group
|
||||
self.question = question
|
||||
|
||||
def coming_soon(self):
|
||||
self.play(
|
||||
LaggedStart(
|
||||
ApplyMethod, self.assumption_group,
|
||||
lambda m : (m.shift, 2*SPACE_HEIGHT*DOWN),
|
||||
remover = True,
|
||||
),
|
||||
ApplyMethod(
|
||||
self.question.center,
|
||||
rate_func = squish_rate_func(smooth, 0.5, 1),
|
||||
run_time = 2
|
||||
)
|
||||
)
|
||||
|
||||
part = self.question.get_part_by_tex("correlation")
|
||||
brace = Brace(part, UP)
|
||||
words = brace.get_text("Coming soon!")
|
||||
self.play(
|
||||
GrowFromCenter(brace),
|
||||
part.highlight, YELLOW
|
||||
)
|
||||
self.play(Write(words))
|
||||
self.dither()
|
||||
|
||||
|
||||
|
||||
class FormulaCanBeRediscovered(PointOutSimplicityOfFormula):
|
||||
def construct(self):
|
||||
prob = self.get_probability_expression(full = False)
|
||||
|
|
@ -3223,6 +3543,48 @@ class IndependencePatreonThanks(PatreonThanks):
|
|||
],
|
||||
}
|
||||
|
||||
class Thumbnail(DangerInProbability):
|
||||
def construct(self):
|
||||
n, p = 15, 0.5
|
||||
dist = get_binomial_distribution(n, p)
|
||||
values = np.array(map(dist, range(n+1)))
|
||||
values *= 2
|
||||
chart = BarChart(
|
||||
values = values,
|
||||
label_y_axis = False,
|
||||
width = 2*SPACE_WIDTH - 3,
|
||||
height = 1.5*SPACE_HEIGHT
|
||||
)
|
||||
chart.to_edge(DOWN)
|
||||
self.add(chart)
|
||||
|
||||
|
||||
warning = self.get_warning_sign()
|
||||
warning.scale_to_fit_height(2)
|
||||
warning.to_edge(UP)
|
||||
self.add(warning)
|
||||
|
||||
|
||||
words = TextMobject("Independence")
|
||||
words.scale(2.5)
|
||||
words.next_to(warning, DOWN)
|
||||
self.add(words)
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
|
|
|
|||
|
|
@ -307,7 +307,6 @@ class BarChart(VGroup):
|
|||
x_axis = Line(self.tick_width*LEFT/2, self.width*RIGHT)
|
||||
y_axis = Line(MED_LARGE_BUFF*DOWN, self.height*UP)
|
||||
ticks = VGroup()
|
||||
labels = VGroup()
|
||||
heights = np.linspace(0, self.height, self.n_ticks+1)
|
||||
values = np.linspace(0, self.max_value, self.n_ticks+1)
|
||||
for y, value in zip(heights, values):
|
||||
|
|
@ -315,15 +314,21 @@ class BarChart(VGroup):
|
|||
tick.scale_to_fit_width(self.tick_width)
|
||||
tick.move_to(y*UP)
|
||||
ticks.add(tick)
|
||||
label = TexMobject(str(np.round(value, 2)))
|
||||
label.scale_to_fit_height(self.y_axis_label_height)
|
||||
label.next_to(tick, LEFT, SMALL_BUFF)
|
||||
labels.add(label)
|
||||
y_axis.add(ticks)
|
||||
|
||||
self.add(x_axis, y_axis, labels)
|
||||
self.add(x_axis, y_axis)
|
||||
self.x_axis, self.y_axis = x_axis, y_axis
|
||||
self.y_axis_labels = labels
|
||||
|
||||
if self.label_y_axis:
|
||||
labels = VGroup()
|
||||
for tick, value in zip(ticks, values):
|
||||
label = TexMobject(str(np.round(value, 2)))
|
||||
label.scale_to_fit_height(self.y_axis_label_height)
|
||||
label.next_to(tick, LEFT, SMALL_BUFF)
|
||||
labels.add(label)
|
||||
self.y_axis_labels = labels
|
||||
self.add(labels)
|
||||
|
||||
|
||||
def add_bars(self, values):
|
||||
buff = float(self.width) / (2*len(values) + 1)
|
||||
|
|
|
|||
Loading…
Add table
Reference in a new issue