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Further uncertainty progress
This commit is contained in:
Grant Sanderson
parent
8224b9ba3f
commit
94c67e1fe7
1 changed files with 317 additions and 24 deletions
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@ -28,6 +28,7 @@ from mobject.vectorized_mobject import *
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from mobject.svg_mobject import *
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from mobject.tex_mobject import *
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from topics.graph_scene import *
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from topics.light import *
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from active_projects.fourier import *
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@ -238,6 +239,82 @@ class RadarPulse(ContinualAnimation):
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def is_finished(self):
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return all([ps.is_finished() for ps in self.pulse_singletons])
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class Flash(AnimationGroup):
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CONFIG = {
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"line_length" : 0.2,
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"num_lines" : 12,
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"flash_radius" : 0.3,
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"line_stroke_width" : 3,
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}
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def __init__(self, mobject, color = YELLOW, **kwargs):
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digest_config(self, kwargs)
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original_color = mobject.get_color()
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on_and_off = UpdateFromAlphaFunc(
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mobject.copy(), lambda m, a : m.highlight(
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color if a < 0.5 else original_color
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),
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remover = True
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)
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lines = VGroup()
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for angle in np.arange(0, TAU, TAU/self.num_lines):
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line = Line(ORIGIN, self.line_length*RIGHT)
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line.shift((self.flash_radius - self.line_length)*RIGHT)
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line.rotate(angle, about_point = ORIGIN)
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lines.add(line)
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lines.move_to(mobject)
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lines.highlight(color)
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line_anims = [
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ShowCreationThenDestruction(
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line, rate_func = squish_rate_func(smooth, 0, 0.5)
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)
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for line in lines
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]
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fade_anims = [
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UpdateFromAlphaFunc(
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line, lambda m, a : m.set_stroke(
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width = self.line_stroke_width*(1-a)
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),
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rate_func = squish_rate_func(smooth, 0, 0.75)
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)
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for line in lines
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]
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AnimationGroup.__init__(
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self, on_and_off, *line_anims+fade_anims, **kwargs
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)
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class MultipleFlashes(Succession):
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CONFIG = {
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"run_time_per_flash" : 1.0,
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"num_flashes" : 3,
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}
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def __init__(self, *args, **kwargs):
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digest_config(self, kwargs)
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kwargs["run_time"] = self.run_time_per_flash
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Succession.__init__(self, *[
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Flash(*args, **kwargs)
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for x in range(self.num_flashes)
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])
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class TrafficLight(SVGMobject):
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CONFIG = {
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"file_name" : "traffic_light",
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"height" : 0.7,
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"post_height" : 2,
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"post_width" : 0.05,
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}
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def __init__(self, **kwargs):
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SVGMobject.__init__(self, **kwargs)
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post = Rectangle(
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height = self.post_height,
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width = self.post_width,
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stroke_width = 0,
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fill_color = WHITE,
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fill_opacity = 1,
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)
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self.move_to(post.get_top(), DOWN)
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self.add_to_back(post)
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###################
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class MentionUncertaintyPrinciple(TeacherStudentsScene):
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@ -339,8 +416,9 @@ class FourierTradeoff(Scene):
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y_axis_config = {"unit_size" : 0.5}
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)
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time_label = TextMobject("Time")
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time_label.scale(1.5)
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time_label.next_to(
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time_axes.x_axis.get_right(), UP,
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time_axes.x_axis.get_right(), UP+LEFT,
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buff = MED_SMALL_BUFF,
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)
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time_axes.add(time_label)
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@ -360,8 +438,9 @@ class FourierTradeoff(Scene):
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color = TEAL,
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)
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frequency_label = TextMobject("Frequency")
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frequency_label.scale(1.5)
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frequency_label.next_to(
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frequency_axes.x_axis.get_right(), UP,
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frequency_axes.x_axis.get_right(), UP+LEFT,
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buff = MED_SMALL_BUFF,
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)
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frequency_label.highlight(FREQUENCY_COLOR)
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@ -397,7 +476,7 @@ class FourierTradeoff(Scene):
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t_max = time_mean + time_radius,
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n_samples = 2*time_radius*17,
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# complex_to_real_func = abs,
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complex_to_real_func = lambda z : z.real,
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complex_to_real_func = abs,
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color = FREQUENCY_COLOR,
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)
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@ -416,8 +495,8 @@ class FourierTradeoff(Scene):
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wave_packet, frequency_axes.coords_to_point(4, 10),
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color = FREQUENCY_COLOR,
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)
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fourier_words = TextMobject("Fourier Transform")
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fourier_words.next_to(arrow, RIGHT, buff = MED_LARGE_BUFF)
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fourier_words = TextMobject("$|$Fourier Transform$|$")
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fourier_words.next_to(arrow, LEFT, buff = MED_LARGE_BUFF)
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sub_words = TextMobject("(To be explained shortly)")
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sub_words.highlight(BLUE)
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sub_words.scale(0.75)
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@ -454,8 +533,8 @@ class ShowPlan(PiCreatureScene):
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self.add_title()
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words = self.get_words()
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self.play_sound_anims(words[0])
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self.play_doppler_anims(words[1], words[0])
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self.play_quantum_anims(words[2], words[1])
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self.play_doppler_anims(words[1])
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self.play_quantum_anims(words[2])
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def add_title(self):
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title = TextMobject("The plan")
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@ -466,14 +545,19 @@ class ShowPlan(PiCreatureScene):
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self.add(title, h_line)
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def get_words(self):
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colors = [YELLOW, GREEN, BLUE]
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topics = ["sound waves", "Doppler radar", "quantum particles"]
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trips = [
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("sound waves", "(time vs. frequency)", YELLOW),
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("Doppler radar", "(distance vs. velocity)", GREEN),
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("quantum particles", "(position vs. momentum)", BLUE),
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]
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words = VGroup()
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for topic, color in zip(topics, colors):
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word = TextMobject("Uncertainty for", topic)
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word[1].highlight(color)
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for topic, tradeoff, color in trips:
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word = TextMobject("Uncertainty for", topic, tradeoff)
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word[1:].highlight(color)
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word[2].scale(0.75)
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word[2].next_to(word[1], DOWN, buff = 1.5*SMALL_BUFF)
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words.add(word)
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words.arrange_submobjects(DOWN, aligned_edge = LEFT, buff = LARGE_BUFF)
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words.arrange_submobjects(DOWN, aligned_edge = LEFT, buff = MED_LARGE_BUFF)
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words.to_edge(LEFT)
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return words
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@ -517,7 +601,7 @@ class ShowPlan(PiCreatureScene):
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self.add(word)
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self.wait()
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def play_doppler_anims(self, word, to_fade):
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def play_doppler_anims(self, word):
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morty = self.pi_creature
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radar_dish = RadarDish()
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@ -533,7 +617,6 @@ class ShowPlan(PiCreatureScene):
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self.add(target_movement)
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self.play(
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to_fade.fade, 0.5,
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Write(word),
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DrawBorderThenFill(radar_dish),
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UpdateFromAlphaFunc(
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@ -542,7 +625,6 @@ class ShowPlan(PiCreatureScene):
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morty.change, "pondering",
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run_time = 1
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)
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self.wait()
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self.add(pulse)
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count = it.count() #TODO, this is not a great hack...
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while not pulse.is_finished() and count.next() < 15:
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@ -560,25 +642,236 @@ class ShowPlan(PiCreatureScene):
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)
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self.wait()
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def play_quantum_anims(self, word):
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morty = self.pi_creature
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dot_cloud = ProbabalisticDotCloud()
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gdw = dot_cloud.gaussian_distribution_wrapper
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gdw.next_to(word, DOWN, MED_LARGE_BUFF)
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gdw.rotate(5*DEGREES)
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gdw.save_state()
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gdw.scale(0)
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checkmark = self.get_checkmark(word)
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ish = TextMobject("$\\dots$ish")
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ish.next_to(checkmark, RIGHT, -SMALL_BUFF, DOWN)
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self.add(dot_cloud)
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self.play(
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Write(word),
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FadeIn(dot_cloud.mobject),
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morty.change, "confused",
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)
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self.play(gdw.restore, run_time = 2)
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self.play(Write(checkmark))
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self.wait()
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self.play(
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Write(ish),
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morty.change, 'maybe'
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)
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self.wait(6)
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def play_quantum_anims(self, word, to_fade):
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pass
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##
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def get_checkmark(self, word):
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checkmark = TexMobject("\\checkmark")
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checkmark.highlight(GREEN)
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checkmark.scale(1.5)
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checkmark.next_to(word, UP+RIGHT, buff = 0)
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checkmark.scale(1.25)
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checkmark.next_to(word[1], UP+RIGHT, buff = 0)
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return checkmark
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class StartWithIntuition(TeacherStudentsScene):
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def construct(self):
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self.teacher_says(
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"You already \\\\ have this \\\\ intuition",
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bubble_kwargs = {
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"height" : 3.5,
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"width" : 3,
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},
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)
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self.change_student_modes("pondering", "erm", "maybe")
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self.look_at(VectorizedPoint(4*LEFT + 2*UP))
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self.wait(5)
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class TwoCarsAtRedLight(Scene):
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def construct(self):
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self.pull_up_behind()
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self.flash_in_sync_short_time()
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self.show_low_confidence()
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self.flash_in_sync_long_time()
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self.mention_uncertainty_principle()
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def pull_up_behind(self):
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#Setup Traffic light
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traffic_light = TrafficLight()
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traffic_light.move_to(6*RIGHT + 2*DOWN, DOWN)
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source_point = VectorizedPoint(
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traffic_light[6].get_right()
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)
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screen = Line(ORIGIN, UP)
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screen.next_to(source_point, RIGHT, LARGE_BUFF)
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red_light = Spotlight(
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color = RED,
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source_point = source_point,
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radius = 0.5,
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screen = screen,
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num_levels = 20,
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opacity_function = lambda r : 1/(10*r**2+1)
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)
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red_light.fade(0.5)
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red_light.rotate(TAU/2, about_edge = LEFT)
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self.add(red_light, traffic_light)
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#Setup cars
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car1, car2 = cars = self.cars = VGroup(*[
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Car() for x in range(2)
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])
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cars.arrange_submobjects(RIGHT, buff = LARGE_BUFF)
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cars.next_to(
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traffic_light, LEFT,
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buff = LARGE_BUFF, aligned_edge = DOWN
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)
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car2.pi_creature.highlight(GREY_BROWN)
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car1.start_point = car1.get_corner(DOWN+RIGHT)
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car1.shift(SPACE_WIDTH*LEFT)
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#Pull up car
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self.add(cars)
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self.play(
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SwitchOn(
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red_light,
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rate_func = squish_rate_func(smooth, 0, 0.3),
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),
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Animation(traffic_light),
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self.get_flashes(car2, num_flashes = 3),
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MoveCar(
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car1, car1.start_point,
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run_time = 3,
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rate_func = rush_from,
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)
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)
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def flash_in_sync_short_time(self):
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car1, car2 = cars = self.cars
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#Setup axes
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axes = Axes(
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x_min = 0,
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x_max = 5,
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y_min = 0,
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y_max = 2,
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y_axis_config = {
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"tick_frequency" : 0.5,
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},
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)
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time_label = TextMobject("Time")
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time_label.scale(0.75)
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time_label.next_to(
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axes.x_axis.get_right(),
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DOWN + LEFT
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)
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y_title = TextMobject("Signal")
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y_title.scale(0.75)
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y_title.next_to(axes.y_axis, UP, SMALL_BUFF)
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axes.add(time_label, y_title)
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axes.to_corner(UP+LEFT, buff = MED_SMALL_BUFF)
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graph = axes.get_graph(
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lambda x : sum([
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1.25*np.exp(-100*(x-m)**2)
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for m in range(1, 4)
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]),
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x_min = 0.8,
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x_max = 3.8,
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)
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graph.highlight(YELLOW)
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#Label short duration
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brace = Brace(Line(
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axes.input_to_graph_point(1, graph),
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axes.input_to_graph_point(3, graph),
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), UP)
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text = TextMobject("Short duration observation")
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text.scale(0.75)
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text.next_to(brace, UP, SMALL_BUFF)
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text.align_to(
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axes.coords_to_point(0.25, 0), LEFT
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)
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self.play(
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self.get_flashes(car1, num_flashes = 2),
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self.get_flashes(car2, num_flashes = 2),
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LaggedStart(FadeIn, VGroup(
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axes, time_label, y_title,
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))
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)
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self.play(
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self.get_flashes(car1, num_flashes = 3),
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self.get_flashes(car2, num_flashes = 3),
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ShowCreation(graph, rate_func = None, run_time = 3)
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)
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self.play(
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self.get_flashes(car1, num_flashes = 10),
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self.get_flashes(car2, num_flashes = 10, run_time_per_flash = 0.98),
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GrowFromCenter(brace),
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Write(text),
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)
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self.time_axes = axes
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self.time_graph = graph
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self.time_graph_label = VGroup(
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brace, text
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)
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def show_low_confidence(self):
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car1, car2 = cars = self.cars
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time_axes = self.time_axes
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frequency_axes = Axes(
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x_min = 0,
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x_max = 3.5,
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y_min = 0,
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y_max = 1.5,
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y_axis_config = {
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"tick_frequency" : 0.5,
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}
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)
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frequency_axes.next_to(time_axes, DOWN, LARGE_BUFF, LEFT)
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frequency_axes.highlight(LIGHT_GREY)
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frequency_label = TextMobject("Frequency")
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frequency_label.scale(0.75)
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frequency_label.next_to(
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frequency_axes.x_axis.get_right(),
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DOWN
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)
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frequency_axes.add(frequency_label)
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frequency_axes.x_axis.add_numbers(1, 2)
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fourier_graph = get_fourier_graph(
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frequency_axes,
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self.time_graph.underlying_function,
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t_min = 0,
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t_max = 4,
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)
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self.add(frequency_axes, fourier_graph)
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def flash_in_sync_long_time(self):
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pass
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def mention_uncertainty_principle(self):
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pass
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###
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def get_flashes(self, car, colors = [YELLOW, RED], num_flashes = 1, **kwargs):
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return AnimationGroup(*[
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MultipleFlashes(light, color, num_flashes = num_flashes, **kwargs)
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for light, color in zip(car.get_lights(), colors)
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])
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