def show_value_at_zero(self):
arrow, x_equals_0 = ax0_group = self.get_arrow_x_equals_0_group()
ax0_group.next_to(
self.cosine_label, RIGHT,
align_using_submobjects = True
)
one = TexMobject("1")
one.next_to(arrow, RIGHT)
one.save_state()
one.move_to(self.cosine_label)
one.set_fill(opacity = 0)
v_line = self.get_vertical_line_to_graph(
0, self.cosine_graph,
line_class = DashedLine,
color = YELLOW
)
self.play(ShowCreation(v_line))
self.play(
ShowCreation(arrow),
Write(x_equals_0, run_time = 2)
)
self.play(one.restore)
self.dither()
self.v_line = v_line
self.equals_one_group = VGroup(arrow, x_equals_0, one)
def write_bayes_rule(self):
words = self.bayes_rule_words
words_rect = SurroundingRectangle(words)
rule = TexMobject("P(", "S", "|", "+", ")", "=", "P(", "S", ")", "{P(",
"+", "|", "S", ")", "\\over", "P(", "+", ")}")
rule.highlight_by_tex("S", SICKLY_GREEN)
rule.highlight_by_tex("+", YELLOW)
rule.to_corner(UP + RIGHT)
rule_rect = SurroundingRectangle(rule)
rule_rect.highlight(BLUE)
rule.save_state()
rule.replace(words_rect)
rule.scale_in_place(0.9)
rule.set_fill(opacity=0)
self.play(ShowCreation(words_rect))
self.play(ReplacementTransform(words_rect, rule_rect),
rule.restore,
run_time=2)
self.dither(3)
def construct(self):
num = 5
ordinals_cnt_base = OrdinalFiniteProd(OrdinalOmega,
num,
x1=-4 + num * 2.5)
ordinals_cnt = VGroup(
[VGroup(ordinals_cnt_base[:i]).copy() for i in range(1, num + 1)])
ordinals_cnt.save_state()
ordinals_cnt.arrange_submobjects(DOWN, center=False, coor_mask=Y_MASK)
ordinals_cnt.to_edge(UP)
self.play(ShowCreation(ordinals_cnt))
#self.wait_to(7)
self.dither()
self.play(ordinals_cnt.restore)
self.remove(ordinals_cnt)
self.add(ordinals_cnt_base)
omega1 = Omega1()
brace = BraceDesc(omega1, "\\omega_1", DOWN)
omega1.line.save_state()
omega1.line.behind_edge(RIGHT)
omega1_bars_src = make_ordinal_power(2)
omega1_bars_src.next_to(ordinals_cnt_base)
omega1_bars_src.add_to_back(*ordinals_cnt_base)
brace.desc.highlight(BLUE)
brace.save_state()
brace.shift_brace(omega1_bars_src)
brace.highlight(BLACK)
self.play(
brace.restore,
omega1.line.restore,
ReplacementTransform(omega1_bars_src, omega1.bars),
)
#self.wait_to(11)
self.dither()
aleph1 = TexMobject("\\aleph_1", "=|", "\omega_1", "|")
aleph1[2].highlight(BLUE)
aleph1[0].highlight(RED)
aleph1.shift(brace.desc.get_center() - aleph1[2].get_center())
aleph1.remove(aleph1[2])
self.play(Write(aleph1))
#self.wait_to(15)
self.dither()
ordinals_a1 = VGroup([omega1.copy() for _ in range(num)])
aleph1[0].save_state()
aleph1[0].next_to(omega1, LEFT, coor_mask=X_MASK)
self.play(
omega1.to_edge,
UP,
FadeOut(VGroup(brace, aleph1[1:])),
MoveFromSaved(aleph1[0]),
)
#self.wait_to(18.5)
self.dither()
aleph1 = aleph1[0]
scale_center = np.array(ordinals_a1[0].line.get_start())
for i, o in enumerate(ordinals_a1):
o.line.scale(1 + i * 0.2, about_point=scale_center)
ordinals_a1_lines_dest = VGroup([o.line for o in ordinals_a1]).copy()
ordinals_a1_bars_dest = VGroup([o.bars for o in ordinals_a1]).copy()
ordinals_a1.arrange_submobjects(DOWN, False, coor_mask=Y_MASK)
ordinals_a1.to_edge(UP)
ordinals_a1_lines = VGroup([o.line for o in ordinals_a1])
ordinals_a1_bars = VGroup([o.bars for o in ordinals_a1])
self.remove(omega1)
self.add(ordinals_a1[0])
self.play(FadeIn(VGroup(ordinals_a1[1:])))
self.play(
Transform(ordinals_a1_lines, ordinals_a1_lines_dest),
Transform(ordinals_a1_bars, ordinals_a1_bars_dest),
)
self.remove(*ordinals_a1[:-1])
omega2_src = ordinals_a1[-1]
omega2 = LongOrdinal(ordinal_end=0.3, line_start=0.2)
brace = BraceDesc(omega2, "\\omega_2", DOWN)
brace.desc.highlight(BLUE)
brace.save_state()
brace.shift_brace(omega2_src)
brace.highlight(BLACK)
self.play(
brace.restore,
ReplacementTransform(omega2_src, omega2),
)
#self.wait_to(24.5)
self.dither()
aleph2 = TexMobject("\\aleph_2", "=|", "\omega_2", "|")
aleph2[2].highlight(BLUE)
aleph2[0].highlight(RED)
aleph2.shift(brace.desc.get_center() - aleph2[2].get_center())
aleph2.remove(aleph2[2])
self.play(Write(aleph2))
#self.wait_to(28)
self.dither()
ordinal_fin = OrdinalFinite(7, x1=SPACE_WIDTH + 1).highlight(BLUE)
ord_labels = VGroup([
TexMobject("\\omega_{}".format(i + 1)).highlight(BLUE).next_to(
bar, UP) for i, bar in enumerate(ordinal_fin[:4])
])
card_labels = VGroup([
TexMobject("\\aleph_{}".format(i + 1)).highlight(RED).next_to(
bar, DOWN) for i, bar in enumerate(ordinal_fin[:4])
])
self.play(
FadeOut(VGroup(aleph2[1:], brace, omega2)),
ReplacementTransform(aleph1, card_labels[0]),
ReplacementTransform(aleph2[0], card_labels[1]),
)
for i, t in enumerate((29, 31, 35.5, 38)):
#self.wait_to(t)
self.play(FadeIn(ord_labels[i]), ShowCreation(ordinal_fin[i]))
if i >= 2: self.play(FadeIn(card_labels[i]))
#self.wait_to(41)
self.play(ShowCreation(VGroup(ordinal_fin[4:], rate_func=rush_into)))
omega = OrdinalOmega().highlight(BLUE)
omega_src = omega.copy()
omega_src.next_to(ordinal_fin, buff=1)
omega_src.add_to_back(*ordinal_fin)
label1 = VGroup(ord_labels[0], card_labels[0])
labels_to_fade = VGroup(list(zip(ord_labels[1:], card_labels[1:])))
labels_to_fade.save_state()
for l, bar in zip(labels_to_fade, omega[1:4]):
l.move_to(bar, coor_mask=X_MASK)
l.highlight(BLACK)
limit_bar = omega[0].copy().next_to(omega)
limit_lord = TexMobject("\\omega_\\omega").highlight(BLUE).next_to(
limit_bar, UP)
limit_lcard = TexMobject("\\aleph_\\omega").highlight(RED).next_to(
limit_bar, DOWN)
limit_g = VGroup(limit_bar, limit_lord, limit_lcard)
limit_g.next_to(omega, coor_mask=X_MASK)
limit_g.save_state()
limit_g.next_to(omega_src, coor_mask=X_MASK)
self.play(
MoveFromSaved(labels_to_fade),
ReplacementTransform(omega_src, omega),
Animation(label1),
limit_g.restore,
)
self.remove(labels_to_fade)
#self.wait_to(52)
plus1_bar = limit_bar.copy()
plus1_label = TexMobject("\\omega_{\\omega+1}").highlight(
BLUE).next_to(plus1_bar, UP)
plus1_g = VGroup(plus1_bar, plus1_label)
plus1_g.next_to(limit_g, coor_mask=X_MASK, buff=0.5)
self.play(FadeIn(plus1_label), ShowCreation(plus1_bar))
#self.wait_to(55)
omega_pow = make_ordinal_power(2, q=(0.8, 0.9, 0.9)).highlight(BLUE)
omega_pow_src = omega_pow.copy()
omega_pow_src.behind_edge(RIGHT)
omega_pow_src[0].add_to_back(limit_bar, plus1_bar)
omega_pow_src.add_to_back(omega)
limit_g.remove(limit_bar)
limit_g.save_state()
plus1_label.save_state()
limit_g.move_to(omega_pow[1][0], coor_mask=X_MASK)
plus1_label.move_to(omega_pow[1][1], coor_mask=X_MASK).highlight(BLACK)
pow_bar = limit_bar.copy()
pow_label = TexMobject("\\omega_{\\omega\\cdot\\omega}").highlight(
BLUE).next_to(pow_bar, UP)
pow_g = VGroup(pow_bar, pow_label)
pow_g.next_to(omega_pow, coor_mask=X_MASK, buff=-.2)
pow_g.save_state()
pow_g.next_to(omega_pow_src, coor_mask=X_MASK)
self.play(
MoveFromSaved(plus1_label),
ReplacementTransform(omega_pow_src, omega_pow),
MoveFromSaved(limit_g),
pow_g.restore,
)
self.remove(plus1_label)
#self.wait_to(59)
self.dither()
labels_to_fade = VGroup(label1, limit_g, pow_label)
labels_to_fade.save_state()
labels_to_fade.highlight(BLACK)
omega1 = Omega1(color=BLUE)
omega1_bar = pow_bar.copy()
omega1_label = TexMobject("\\omega_{\\omega_1}").highlight(
BLUE).next_to(omega1_bar, UP)
omega1_g = VGroup(omega1_bar, omega1_label)
omega1_g.shift(omega1.line.get_end() - omega1_bar.get_center())
omega1_g.add(omega1.line)
omega1_g.save_state()
omega1_g.behind_edge(RIGHT)
limit_g.move_to(omega1.bars[1][0], coor_mask=X_MASK)
pow_label.move_to(omega1.bars[-1], coor_mask=X_MASK)
pow_bar.save_state()
pow_bar.scale(0)
pow_bar.set_stroke(width=0)
pow_bar.move_to(omega1.bars[-1])
self.play(
MoveFromSaved(labels_to_fade, remover=True),
omega1_g.restore,
MoveFromSaved(pow_bar, remover=True),
ReplacementTransform(omega_pow, omega1.bars),
)
#self.wait_to(60+7.5)
self.dither()
ordinal_fin = OrdinalFinite(6, x1=SPACE_WIDTH + 1).highlight(BLUE)
omega1.save_state()
omega1.stretch_about_point(0, 0, ordinal_fin[0].get_center())
labels = VGroup([
TexMobject((i + 1) * "\\omega_{" + "\\omega_1" +
(i + 1) * "}").next_to(bar, UP)
for i, bar in enumerate(ordinal_fin[:3])
])
labels.highlight(BLUE)
next_bar = VGroup(labels[1], ordinal_fin[1])
next_bar.save_state()
next_bar.shift(8 * RIGHT)
self.play(
MoveFromSaved(omega1, remover=True),
next_bar.restore,
ReplacementTransform(omega1_label, labels[0]),
ReplacementTransform(omega1_bar, ordinal_fin[0]),
)
#self.wait_to(60+11)
self.play(FadeIn(labels[2]), ShowCreation(ordinal_fin[2]))
#self.wait_to(60+13)
self.play(ShowCreation(VGroup(ordinal_fin[3:]), rate_func=rush_into))
#self.wait_to(60+21.5)
self.dither(2)
conversation = Conversation(self)
conversation.add_bubble("What about the union of all the ordinals?")
self.play(FadeOut(VGroup(labels, ordinal_fin)),
Animation(conversation.dialog))
