WEBVTT
1
00:00:00.160 --> 00:00:03.759
One of our most frequent guests, most requested guests, and
2
00:00:03.839 --> 00:00:07.519
actually had a listener who emailed a math thing that
3
00:00:07.559 --> 00:00:09.320
we're going to get to with Paul in a little bit,
4
00:00:09.560 --> 00:00:11.839
saying you should have Paul on to talk about this,
5
00:00:12.000 --> 00:00:14.320
so we will, uh and and I will note in
6
00:00:14.359 --> 00:00:17.000
advance because I will forget later if I if I
7
00:00:17.000 --> 00:00:19.719
don't say it now that the listener who asked about
8
00:00:19.719 --> 00:00:23.359
it lives in Abu Dhabi and listens to the show
9
00:00:23.559 --> 00:00:24.280
from there.
10
00:00:24.480 --> 00:00:28.000
So so that's pretty cool. So Senio physics professor Paul
11
00:00:28.039 --> 00:00:28.519
Biel is.
12
00:00:28.800 --> 00:00:31.239
As I say frequently, a guy who makes me wish
13
00:00:31.280 --> 00:00:33.840
I were back in college and had a professor like him.
14
00:00:33.880 --> 00:00:35.439
I did enjoy physics in college.
15
00:00:35.479 --> 00:00:37.960
I only took I only took one semester of just
16
00:00:38.119 --> 00:00:39.600
basic introductory physics.
17
00:00:39.640 --> 00:00:40.439
But Paul, I did.
18
00:00:40.280 --> 00:00:43.880
Get an A plus in college in basic introductory physics.
19
00:00:44.479 --> 00:00:45.759
But anyway, and.
20
00:00:48.359 --> 00:00:50.280
It didn't even take Electrictian magnanism.
21
00:00:50.560 --> 00:00:51.759
I didn't get that far.
22
00:00:52.000 --> 00:00:56.840
Oh God, long story, that would be fun though, right,
23
00:00:57.240 --> 00:01:00.759
And Paul also runs the Buffalo Bicycle Classic, And just
24
00:01:00.799 --> 00:01:05.000
give us seventeen seconds on how the Buffalo Bicycle Classic
25
00:01:05.120 --> 00:01:05.560
was this year.
26
00:01:06.959 --> 00:01:10.040
It was fantastic. We had thirteen hundred riders, and we've
27
00:01:10.040 --> 00:01:12.640
got lots of sponsors and people raised money, and so
28
00:01:12.719 --> 00:01:16.120
we raised over one hundred thousand dollars for our scholarship fund.
29
00:01:16.200 --> 00:01:20.000
Then we have twenty five students from Colorado high schools
30
00:01:20.000 --> 00:01:22.719
who are at CU now because of the Buffalo Bicycle
31
00:01:22.760 --> 00:01:24.079
Classic Scholarship Fund.
32
00:01:24.239 --> 00:01:24.799
Fantastic.
33
00:01:24.799 --> 00:01:27.200
All right, one quick thing before we talk about black holes.
34
00:01:27.680 --> 00:01:29.959
One quick thing where I think, I think you're going
35
00:01:30.000 --> 00:01:32.920
to be very proud of me. So I like to
36
00:01:33.000 --> 00:01:36.400
do things at prime numbers, right. And we did a
37
00:01:36.439 --> 00:01:38.840
thing earlier in the show where we gave away some
38
00:01:38.920 --> 00:01:41.319
Broncos tickets and I had to tell listeners at what
39
00:01:41.519 --> 00:01:44.239
time they could start texting in to try to win
40
00:01:44.280 --> 00:01:45.959
the tickets. And the way I always do this is
41
00:01:46.000 --> 00:01:50.159
whether I'm doing a time that's minutes and seconds with
42
00:01:50.200 --> 00:01:52.640
a colon in between or whatever it is, I just
43
00:01:52.680 --> 00:01:54.799
eliminate the colon and look at the whole number.
44
00:01:55.159 --> 00:01:57.879
Okay, So if it's like one oh one PM.
45
00:01:57.599 --> 00:01:59.760
Then I'm asking myself is the number one hundred and
46
00:01:59.840 --> 00:02:00.640
one on prime?
47
00:02:00.680 --> 00:02:02.680
And if it is, then I can use that time?
48
00:02:02.799 --> 00:02:02.959
Right.
49
00:02:03.400 --> 00:02:06.280
So Dragon kept doing these stupid things like telling me
50
00:02:06.319 --> 00:02:09.639
to use texture number four or eight or fifteen, and
51
00:02:09.680 --> 00:02:12.479
I said no, and then anyway, and then I said
52
00:02:12.520 --> 00:02:15.360
all right, and here's the time to text in.
53
00:02:15.479 --> 00:02:17.400
And I just picked off the top of my head.
54
00:02:17.800 --> 00:02:21.719
I said ten twenty eight and eleven seconds. I said
55
00:02:21.759 --> 00:02:23.159
ten twenty eight and eleven second.
56
00:02:23.199 --> 00:02:25.120
I just made that up. And then I went to
57
00:02:25.159 --> 00:02:28.039
the Google machine and I typed in, is one O
58
00:02:28.280 --> 00:02:30.759
two eight one one a prime number? And the answer
59
00:02:30.800 --> 00:02:32.599
is yes? How about that?
60
00:02:32.719 --> 00:02:32.960
Hey?
61
00:02:33.240 --> 00:02:34.080
Nice? Long?
62
00:02:34.439 --> 00:02:36.759
Yeah, yeah, better to be lucky than good.
63
00:02:36.800 --> 00:02:40.280
All right, you sent me, You sent me some physics
64
00:02:40.719 --> 00:02:45.479
about black holes and black holes merging and stuff that
65
00:02:45.520 --> 00:02:48.759
I really don't understand. And I found a couple of
66
00:02:48.759 --> 00:02:50.719
web You sent me a website. I found another one
67
00:02:50.800 --> 00:02:53.919
clearest signal of two merging black holes.
68
00:02:54.000 --> 00:02:55.039
So tell us about this.
69
00:02:56.240 --> 00:02:59.719
Okay, firstly, I'm checking to see how what was your
70
00:02:59.800 --> 00:03:04.159
chain so that you got that? Right? So one chance
71
00:03:04.199 --> 00:03:06.639
in eleven that you that that would be a prime number.
72
00:03:06.800 --> 00:03:08.520
Wait, but you got to narrow it down.
73
00:03:08.680 --> 00:03:12.719
Is it one chance in eleven that any that any
74
00:03:12.840 --> 00:03:16.120
number that could represent a time so would have to
75
00:03:16.159 --> 00:03:19.800
be within a certain number of digits? Right? Yeah?
76
00:03:19.840 --> 00:03:23.439
No, I took that fact number and just randomly if
77
00:03:23.479 --> 00:03:26.800
you chose that number randomly. Yeahs a prime number and
78
00:03:26.800 --> 00:03:28.680
the chance is one in eleven point five.
79
00:03:28.800 --> 00:03:30.719
All right, all right, not bad, I should go buy
80
00:03:30.719 --> 00:03:32.960
a lottery ticket, all right. So tell us about merging
81
00:03:33.000 --> 00:03:33.840
black holes.
82
00:03:34.080 --> 00:03:38.159
Okay, So about ten years ago a device that was
83
00:03:38.159 --> 00:03:41.479
built in the United States called LEGO. It's a laser
84
00:03:41.520 --> 00:03:46.039
interferometer which they use lasers to measure the link between
85
00:03:46.120 --> 00:03:53.039
two mirrors that are ones in Louisiana and ones in Hanford, Washington.
86
00:03:53.599 --> 00:03:56.240
And the whole goal of that was to try to
87
00:03:56.280 --> 00:04:00.240
measure gravitational waves, which were first predicted by Einstein in
88
00:04:00.360 --> 00:04:05.879
nineteen sixteen. And so something really cataclysmic has to happen
89
00:04:05.960 --> 00:04:10.639
to generate a gravitational way big enough to be measurable.
90
00:04:11.080 --> 00:04:13.960
And so what happens. This wave travels through space at
91
00:04:13.960 --> 00:04:17.360
the speed of light, and in what it does, it
92
00:04:17.480 --> 00:04:22.600
slightly changes the length between these two mirrors in a
93
00:04:23.560 --> 00:04:26.600
and you can measure that using this interferometer. And so
94
00:04:26.680 --> 00:04:30.879
the first measurement of a black hole collision and coalescence
95
00:04:30.879 --> 00:04:36.279
happened in nineteen to twenty fifteen, and it won the
96
00:04:36.319 --> 00:04:39.560
folks who built that the Nobel Prize in twenty seventeen.
97
00:04:40.199 --> 00:04:42.959
So the black hole was about three or four solar
98
00:04:43.040 --> 00:04:46.680
masses and another three or four solar masses and they combined,
99
00:04:46.839 --> 00:04:49.879
and that was the first time in history anyone had
100
00:04:49.879 --> 00:04:54.439
observer observed the universe using something other than electromagnetic waves
101
00:04:54.560 --> 00:04:55.560
or particles.
102
00:04:56.560 --> 00:05:01.240
So the interferometer, it's really looked looking at light or is.
103
00:05:01.160 --> 00:05:03.879
It looking at something that? What's it looking at?
104
00:05:04.560 --> 00:05:07.639
It uses light, it uses lasers, But what it's looking
105
00:05:08.120 --> 00:05:12.639
is the stretching and compressing of space time that happens
106
00:05:12.680 --> 00:05:17.079
as a gravitational wave passes by. So gravitational wave is
107
00:05:17.120 --> 00:05:19.680
a ripple on the fabric of space time.
108
00:05:20.240 --> 00:05:23.040
So does that work by deflecting a laser beam?
109
00:05:23.199 --> 00:05:25.199
Or how is it? How does it measure it?
110
00:05:25.759 --> 00:05:29.240
Well, it just measures. So these two mirrors can they
111
00:05:29.279 --> 00:05:32.720
will differ, their distance between them will differ by less
112
00:05:32.759 --> 00:05:36.920
than the diameter of one proton, and that's enough to
113
00:05:36.959 --> 00:05:42.279
be measurable by this particular laser interferometer. And so this
114
00:05:42.399 --> 00:05:45.279
ripple what you'll see as a little In fact, if
115
00:05:45.319 --> 00:05:47.480
you turn it into a signal, you'll these things go
116
00:05:47.920 --> 00:05:50.120
closer and farther apart, and it will create a little signal.
117
00:05:50.120 --> 00:05:54.720
It sounds like and their first data set. When you
118
00:05:54.720 --> 00:05:57.600
play it as an audio sounds exactly like that woo.
119
00:05:59.120 --> 00:06:06.360
That characteristic that characteristic sound comes from the calculation that
120
00:06:06.480 --> 00:06:10.759
Einstein could have done had he had supercomputers. And that's
121
00:06:11.079 --> 00:06:13.040
what comes from the black hole merger.
122
00:06:13.720 --> 00:06:15.399
All right, this is going to be a dumb question,
123
00:06:15.879 --> 00:06:19.759
but when two black holes merge to you just get
124
00:06:20.000 --> 00:06:23.240
one more, one larger black hole. And also, if you
125
00:06:23.399 --> 00:06:27.000
had a black hole of I don't know whether you
126
00:06:27.040 --> 00:06:31.120
want to talk about diameters, circumference or volume, but let's
127
00:06:31.120 --> 00:06:33.000
say you had a black hole of one of those
128
00:06:33.040 --> 00:06:35.839
measures of X and another black hole of one of
129
00:06:35.879 --> 00:06:41.120
those measures of why what what is the measure of
130
00:06:41.160 --> 00:06:43.399
the combined black hole in terms of X and Y?
131
00:06:44.560 --> 00:06:47.920
Okay, So there's only three things you can literally a
132
00:06:47.920 --> 00:06:52.800
black holes has in terms of measurable quantities. It's its mass,
133
00:06:53.000 --> 00:06:56.800
it's charge and its spin Okay, and so mass and
134
00:06:57.959 --> 00:07:01.240
its spin are related to what known as the area
135
00:07:01.360 --> 00:07:03.600
of the black hole is in fact the important thing
136
00:07:03.639 --> 00:07:07.160
that you can measure. And in this recent measurement, it
137
00:07:07.240 --> 00:07:10.160
happened in early this year and has taken some months
138
00:07:10.160 --> 00:07:14.240
of analysis for the researchers to antalyize exactly what happened
139
00:07:14.279 --> 00:07:16.839
in this case, it was black holes of about thirty
140
00:07:16.879 --> 00:07:21.040
or forty solar masses collided with each other and created
141
00:07:21.079 --> 00:07:24.240
a black hole that was twice as big, and the
142
00:07:24.360 --> 00:07:28.040
area of the final black hole is bigger than the
143
00:07:28.160 --> 00:07:32.120
area of either of the beginning ones. But the important
144
00:07:32.160 --> 00:07:35.759
thing that Einstein that excuse me, Stephen Hawking predicted in
145
00:07:35.839 --> 00:07:41.399
the nineteen sixties was that the area has to increase
146
00:07:41.439 --> 00:07:44.360
when two black holes come together, and so the final
147
00:07:44.399 --> 00:07:46.360
area has to be bigger than the sum of the
148
00:07:46.480 --> 00:07:50.079
areas of the two individuals. And that's what they were
149
00:07:50.079 --> 00:07:53.199
able to measure from the exact details of the woo
150
00:07:54.319 --> 00:07:56.000
that happens in the collision.
151
00:07:56.639 --> 00:08:01.360
Okay, so I'm going way, way way out of my
152
00:08:01.480 --> 00:08:03.319
league here with this next question.
153
00:08:03.399 --> 00:08:05.399
This is probably going to be a really stupid question.
154
00:08:07.839 --> 00:08:12.120
I would have thought that it was at least possible
155
00:08:12.519 --> 00:08:15.959
that when you combine these very very massive things, that
156
00:08:16.040 --> 00:08:20.560
the increase in the gravitational field caused by the increase
157
00:08:21.040 --> 00:08:26.959
in the mass of these two things would could cause
158
00:08:27.079 --> 00:08:31.800
the area of the combined black holes to be smaller
159
00:08:31.839 --> 00:08:33.120
than the sum of the areas.
160
00:08:33.960 --> 00:08:36.720
Is that a ridiculous concept.
161
00:08:37.200 --> 00:08:39.720
It's clearly wrong, as you just said it's wrong, But
162
00:08:39.840 --> 00:08:40.679
is it ridiculous.
163
00:08:41.639 --> 00:08:43.960
No, not at all. And in fact, it took you know,
164
00:08:44.120 --> 00:08:49.360
Stephen Hawking to prove that the area can only increase,
165
00:08:50.279 --> 00:08:52.600
and so that caused him to start thinking, and he
166
00:08:52.679 --> 00:08:56.000
worked with another mathematical physicist by the name of Beckenstein,
167
00:08:56.759 --> 00:09:01.120
and they came up with a calculation in which showed, oh,
168
00:09:01.200 --> 00:09:05.000
not only is this area interesting and measurable, but it
169
00:09:05.120 --> 00:09:08.679
is proportional to the entropy of the black hole. So
170
00:09:08.759 --> 00:09:11.759
the black hole and stuff goes down into it, it's
171
00:09:11.840 --> 00:09:17.919
sucking in thermodynamic entropy, and the entropy is completely encoded
172
00:09:17.960 --> 00:09:21.879
in the area of the black hole. Wow, we're talking
173
00:09:21.919 --> 00:09:25.000
with all the way back to thermodynamics, the second law
174
00:09:25.000 --> 00:09:26.080
of thermodynamics.
175
00:09:26.200 --> 00:09:29.879
We're talking with cup physics professor Paul Beal. I don't
176
00:09:29.919 --> 00:09:33.159
know if there's some other term, some other units you
177
00:09:33.200 --> 00:09:35.080
can put this in. A listener wants to know how
178
00:09:35.080 --> 00:09:36.320
big is a solar mass?
179
00:09:37.279 --> 00:09:40.679
Oh solar mass, So solar mass is about ten to
180
00:09:40.840 --> 00:09:48.240
the I'm gonna ten to the thirty something kilograms, okay,
181
00:09:48.240 --> 00:09:52.080
and I forget whether it's thirty or thirty two or
182
00:09:52.120 --> 00:09:54.320
thirty five that I can't.
183
00:09:54.080 --> 00:09:56.960
Remember, all right, Ed Paul didn't look that up by anyway.
184
00:09:57.039 --> 00:09:58.639
That's just off the top of his head. So that's
185
00:09:58.639 --> 00:10:03.360
how big a solar mass is. That's that's a lot. Okay,
186
00:10:03.919 --> 00:10:06.000
one more listener question, even though it's way way off
187
00:10:06.039 --> 00:10:08.960
topic and probably a question that you teach in all
188
00:10:09.000 --> 00:10:12.759
of your most basic basic physics classes, but people ask
189
00:10:12.799 --> 00:10:14.399
from time to time. So we'll do this one listener
190
00:10:14.480 --> 00:10:17.000
question quickly, and then we'll do math. Can we travel
191
00:10:17.039 --> 00:10:18.279
faster than the speed of light?
192
00:10:19.679 --> 00:10:22.759
Okay? So, as our theory of the universe does not
193
00:10:22.919 --> 00:10:26.720
allow an object with mass to travel faster than the
194
00:10:26.759 --> 00:10:29.559
speed of light because it would take an infinite amount
195
00:10:29.600 --> 00:10:32.799
of energy to accelerate the particle, you know, exactly to
196
00:10:32.919 --> 00:10:36.159
the speed of light. So the fastest anything we've ever
197
00:10:36.240 --> 00:10:43.840
created is ninety nine point nine nine percent of the
198
00:10:43.879 --> 00:10:46.559
speed of light. And that set the large Hadron collider
199
00:10:47.480 --> 00:10:50.200
where they accelerate protons to very very close to the
200
00:10:50.240 --> 00:10:50.879
speed of light.
201
00:10:51.559 --> 00:10:56.039
Wow, all right, excellent answer. Okay, let's do some math.
202
00:10:56.600 --> 00:10:59.600
And this math thing is actually the thing that caused
203
00:10:59.600 --> 00:11:01.679
me to reach out to you yesterday when a listener
204
00:11:01.679 --> 00:11:05.279
in Abu Dhabi said, Hey, Ross, have you heard of this?
205
00:11:05.559 --> 00:11:09.960
Have you heard of this thing called the Goldbach conjecture,
206
00:11:10.279 --> 00:11:12.360
and I said no, and I looked it up, and
207
00:11:12.399 --> 00:11:14.519
actually I probably have heard of it without that name,
208
00:11:14.639 --> 00:11:17.519
just as the mathematical concept. But it's pretty interesting, as
209
00:11:17.559 --> 00:11:19.480
you and I were talking about on the air. It's
210
00:11:19.519 --> 00:11:22.720
a mathematical concept that's easy enough to understand that you
211
00:11:22.759 --> 00:11:25.039
don't have to be a mathematician to understand the question.
212
00:11:26.000 --> 00:11:30.480
But it turns out it's well nearly impossible, I guess,
213
00:11:30.480 --> 00:11:32.440
because it hasn't been done yet to prove it.
214
00:11:32.519 --> 00:11:34.279
So can you can you elaborate please?
215
00:11:35.519 --> 00:11:39.679
Okay? So this was a conjecture made by Christian Goldbach,
216
00:11:39.759 --> 00:11:42.759
and he was lived in the seventeen hundreds. He was
217
00:11:42.799 --> 00:11:46.360
a contemporary of Leonard Euler, who I think is the
218
00:11:46.360 --> 00:11:51.320
greatest mathematician in history, and they were communicating and talking
219
00:11:51.360 --> 00:11:54.840
to each other, and Goldbach made this conjecture that every
220
00:11:54.960 --> 00:11:58.639
even number bigger than four can be written as the
221
00:11:58.679 --> 00:12:03.240
sum of two prime numbers. So, for example, six is
222
00:12:03.320 --> 00:12:06.919
three plus three, and eight can be written as three
223
00:12:06.960 --> 00:12:12.360
plus five ten, five plus five fourteen. It can be
224
00:12:12.360 --> 00:12:15.519
written as seven plus seven or three plus eleven, So
225
00:12:15.559 --> 00:12:18.200
you can always find two prime numbers that add up
226
00:12:18.240 --> 00:12:21.679
to every even number. And I would say conjecture, cause
227
00:12:21.720 --> 00:12:25.080
no one's proven it. But people, it's fairly easy with
228
00:12:25.120 --> 00:12:28.480
a computer now to check two fairly large numbers and
229
00:12:28.720 --> 00:12:33.399
up to numbers with eighteen digits, and them people have checked. Yes,
230
00:12:33.480 --> 00:12:36.559
every even number is the sum of two prime numbers.
231
00:12:38.840 --> 00:12:43.519
Why is this so far for what two hundred and
232
00:12:43.519 --> 00:12:45.240
eighty years impossible to prove?
233
00:12:46.000 --> 00:12:49.320
Well, I will say it's impossible. People are making progress.
234
00:12:49.440 --> 00:12:53.919
There's a weaker form of the conjecture that says, oh,
235
00:12:54.000 --> 00:12:56.840
let's look at odd numbers. Every odd number greater than seven,
236
00:12:57.000 --> 00:12:59.679
it can be written as the sum of three prime numbers,
237
00:12:59.720 --> 00:13:05.240
three odd prime numbers, and uh, and that is people
238
00:13:05.279 --> 00:13:10.000
are it's it's a weaker conjecture because if gold box
239
00:13:10.039 --> 00:13:12.440
and original conjecture is true, then this other one is
240
00:13:12.440 --> 00:13:15.679
trivitally true. You can take any of the even numbers
241
00:13:15.679 --> 00:13:19.360
that Goldbock referred to and just add three to it,
242
00:13:19.679 --> 00:13:22.279
and that would give an odd number, and that would
243
00:13:22.279 --> 00:13:26.080
count all of the odd number. And he and Eiler
244
00:13:26.200 --> 00:13:28.720
figured that out immediately say ah, if we can prove this,
245
00:13:28.960 --> 00:13:32.679
then uh uh, that would be maybe easier. But then
246
00:13:33.879 --> 00:13:37.759
the first one, the strong conjecture, would actually have that
247
00:13:37.960 --> 00:13:42.559
is a required element, that every odd numbers and some
248
00:13:42.639 --> 00:13:44.240
of three odd primes.
249
00:13:44.559 --> 00:13:47.039
I mean there from time to time you run across
250
00:13:47.120 --> 00:13:49.480
things like this in math, if you're even a little
251
00:13:49.519 --> 00:13:51.120
bit of a math nerd, and I am a little
252
00:13:51.120 --> 00:13:53.799
bit not not to your level, but two, but were
253
00:13:53.840 --> 00:13:58.159
you where there are these these conjectures, these theorems with
254
00:13:58.240 --> 00:14:00.399
you know, fair modern oiler and all these guys, and
255
00:14:00.440 --> 00:14:04.360
all these famous theorems, and some of the theorems. Yeah,
256
00:14:04.559 --> 00:14:07.480
almost have to be a mathematician to even understand the
257
00:14:07.600 --> 00:14:13.240
question being posed. But this one is so easy, conceptually easy.
258
00:14:13.840 --> 00:14:17.360
And I don't know whether that I don't know whether
259
00:14:17.440 --> 00:14:21.039
I'm whether I should be surprised that a question that
260
00:14:21.159 --> 00:14:25.879
is so conceptually easy has proven to be so theoretically
261
00:14:25.879 --> 00:14:26.679
difficult to prove.
262
00:14:28.399 --> 00:14:31.519
And there are lots of things like this that seem
263
00:14:31.600 --> 00:14:33.919
to be easy to state, and there's lots of them
264
00:14:33.960 --> 00:14:36.639
we could talk about but have never been able to
265
00:14:36.639 --> 00:14:39.840
be proven so far. But a lot of them have
266
00:14:40.000 --> 00:14:43.200
fallen to the mathematicians who have proven some of these
267
00:14:43.320 --> 00:14:47.559
very hard to prove theorems, like fair Ma's last theorem
268
00:14:47.879 --> 00:14:52.080
was in the nineteen nineties, and that had stood the
269
00:14:52.120 --> 00:14:56.000
test of three or four hundred years, and so this one,
270
00:14:56.279 --> 00:15:00.360
this one could happen soon. Now there's a one million
271
00:15:00.399 --> 00:15:03.440
dollar prize if someone can either prove it to be
272
00:15:03.559 --> 00:15:06.159
true or to be false. If they can find an
273
00:15:06.159 --> 00:15:09.000
example of a single even number that is not the
274
00:15:09.000 --> 00:15:12.360
sum of two primes, then that's enough. That would be
275
00:15:12.440 --> 00:15:15.240
the proof that, yeah, that conjecture is false because there's
276
00:15:15.279 --> 00:15:16.039
a counterexample.
277
00:15:16.080 --> 00:15:17.799
All right, less, super quick question.
278
00:15:17.840 --> 00:15:20.240
Then I got to go, do you think your mathematical
279
00:15:20.279 --> 00:15:23.039
skills are close to good enough that it would be
280
00:15:23.080 --> 00:15:24.720
a good use of your time to try to win
281
00:15:24.759 --> 00:15:25.639
that million dollars?
282
00:15:26.279 --> 00:15:31.000
H No way, no way. So even the weak conjecture,
283
00:15:31.080 --> 00:15:34.519
there's like a two hundred page paper that's getting closer
284
00:15:34.559 --> 00:15:38.080
to ward to proof, and mathematicians are pouring over that
285
00:15:38.120 --> 00:15:41.639
two hundred page paper and trying to cross all the
286
00:15:41.720 --> 00:15:45.320
t's and dot the i's and everything. I can't even
287
00:15:45.360 --> 00:15:48.360
begin to read the math that's present in that paper.
288
00:15:48.399 --> 00:15:48.639
Wow.
289
00:15:49.240 --> 00:15:51.279
If Paul Beale can't even begin to read the math,
290
00:15:51.320 --> 00:15:54.120
imagine the rest of us. See you, physics Professor Paul
291
00:15:54.200 --> 00:15:55.960
bial Thanks so much. It's great to have you back
292
00:15:55.960 --> 00:15:57.799
on the show. Sorry it's been so long. We'll do
293
00:15:57.840 --> 00:15:58.440
it again soon.
294
00:15:59.240 --> 00:16:00.720
Okay, thank you all. Ry good one.
295
00:16:00.759 --> 00:16:02.080
Hey you too, have a great weekend.
1
00:00:00.160 --> 00:00:03.759
One of our most frequent guests, most requested guests, and
2
00:00:03.839 --> 00:00:07.519
actually had a listener who emailed a math thing that
3
00:00:07.559 --> 00:00:09.320
we're going to get to with Paul in a little bit,
4
00:00:09.560 --> 00:00:11.839
saying you should have Paul on to talk about this,
5
00:00:12.000 --> 00:00:14.320
so we will, uh and and I will note in
6
00:00:14.359 --> 00:00:17.000
advance because I will forget later if I if I
7
00:00:17.000 --> 00:00:19.719
don't say it now that the listener who asked about
8
00:00:19.719 --> 00:00:23.359
it lives in Abu Dhabi and listens to the show
9
00:00:23.559 --> 00:00:24.280
from there.
10
00:00:24.480 --> 00:00:28.000
So so that's pretty cool. So Senio physics professor Paul
11
00:00:28.039 --> 00:00:28.519
Biel is.
12
00:00:28.800 --> 00:00:31.239
As I say frequently, a guy who makes me wish
13
00:00:31.280 --> 00:00:33.840
I were back in college and had a professor like him.
14
00:00:33.880 --> 00:00:35.439
I did enjoy physics in college.
15
00:00:35.479 --> 00:00:37.960
I only took I only took one semester of just
16
00:00:38.119 --> 00:00:39.600
basic introductory physics.
17
00:00:39.640 --> 00:00:40.439
But Paul, I did.
18
00:00:40.280 --> 00:00:43.880
Get an A plus in college in basic introductory physics.
19
00:00:44.479 --> 00:00:45.759
But anyway, and.
20
00:00:48.359 --> 00:00:50.280
It didn't even take Electrictian magnanism.
21
00:00:50.560 --> 00:00:51.759
I didn't get that far.
22
00:00:52.000 --> 00:00:56.840
Oh God, long story, that would be fun though, right,
23
00:00:57.240 --> 00:01:00.759
And Paul also runs the Buffalo Bicycle Classic, And just
24
00:01:00.799 --> 00:01:05.000
give us seventeen seconds on how the Buffalo Bicycle Classic
25
00:01:05.120 --> 00:01:05.560
was this year.
26
00:01:06.959 --> 00:01:10.040
It was fantastic. We had thirteen hundred riders, and we've
27
00:01:10.040 --> 00:01:12.640
got lots of sponsors and people raised money, and so
28
00:01:12.719 --> 00:01:16.120
we raised over one hundred thousand dollars for our scholarship fund.
29
00:01:16.200 --> 00:01:20.000
Then we have twenty five students from Colorado high schools
30
00:01:20.000 --> 00:01:22.719
who are at CU now because of the Buffalo Bicycle
31
00:01:22.760 --> 00:01:24.079
Classic Scholarship Fund.
32
00:01:24.239 --> 00:01:24.799
Fantastic.
33
00:01:24.799 --> 00:01:27.200
All right, one quick thing before we talk about black holes.
34
00:01:27.680 --> 00:01:29.959
One quick thing where I think, I think you're going
35
00:01:30.000 --> 00:01:32.920
to be very proud of me. So I like to
36
00:01:33.000 --> 00:01:36.400
do things at prime numbers, right. And we did a
37
00:01:36.439 --> 00:01:38.840
thing earlier in the show where we gave away some
38
00:01:38.920 --> 00:01:41.319
Broncos tickets and I had to tell listeners at what
39
00:01:41.519 --> 00:01:44.239
time they could start texting in to try to win
40
00:01:44.280 --> 00:01:45.959
the tickets. And the way I always do this is
41
00:01:46.000 --> 00:01:50.159
whether I'm doing a time that's minutes and seconds with
42
00:01:50.200 --> 00:01:52.640
a colon in between or whatever it is, I just
43
00:01:52.680 --> 00:01:54.799
eliminate the colon and look at the whole number.
44
00:01:55.159 --> 00:01:57.879
Okay, So if it's like one oh one PM.
45
00:01:57.599 --> 00:01:59.760
Then I'm asking myself is the number one hundred and
46
00:01:59.840 --> 00:02:00.640
one on prime?
47
00:02:00.680 --> 00:02:02.680
And if it is, then I can use that time?
48
00:02:02.799 --> 00:02:02.959
Right.
49
00:02:03.400 --> 00:02:06.280
So Dragon kept doing these stupid things like telling me
50
00:02:06.319 --> 00:02:09.639
to use texture number four or eight or fifteen, and
51
00:02:09.680 --> 00:02:12.479
I said no, and then anyway, and then I said
52
00:02:12.520 --> 00:02:15.360
all right, and here's the time to text in.
53
00:02:15.479 --> 00:02:17.400
And I just picked off the top of my head.
54
00:02:17.800 --> 00:02:21.719
I said ten twenty eight and eleven seconds. I said
55
00:02:21.759 --> 00:02:23.159
ten twenty eight and eleven second.
56
00:02:23.199 --> 00:02:25.120
I just made that up. And then I went to
57
00:02:25.159 --> 00:02:28.039
the Google machine and I typed in, is one O
58
00:02:28.280 --> 00:02:30.759
two eight one one a prime number? And the answer
59
00:02:30.800 --> 00:02:32.599
is yes? How about that?
60
00:02:32.719 --> 00:02:32.960
Hey?
61
00:02:33.240 --> 00:02:34.080
Nice? Long?
62
00:02:34.439 --> 00:02:36.759
Yeah, yeah, better to be lucky than good.
63
00:02:36.800 --> 00:02:40.280
All right, you sent me, You sent me some physics
64
00:02:40.719 --> 00:02:45.479
about black holes and black holes merging and stuff that
65
00:02:45.520 --> 00:02:48.759
I really don't understand. And I found a couple of
66
00:02:48.759 --> 00:02:50.719
web You sent me a website. I found another one
67
00:02:50.800 --> 00:02:53.919
clearest signal of two merging black holes.
68
00:02:54.000 --> 00:02:55.039
So tell us about this.
69
00:02:56.240 --> 00:02:59.719
Okay, firstly, I'm checking to see how what was your
70
00:02:59.800 --> 00:03:04.159
chain so that you got that? Right? So one chance
71
00:03:04.199 --> 00:03:06.639
in eleven that you that that would be a prime number.
72
00:03:06.800 --> 00:03:08.520
Wait, but you got to narrow it down.
73
00:03:08.680 --> 00:03:12.719
Is it one chance in eleven that any that any
74
00:03:12.840 --> 00:03:16.120
number that could represent a time so would have to
75
00:03:16.159 --> 00:03:19.800
be within a certain number of digits? Right? Yeah?
76
00:03:19.840 --> 00:03:23.439
No, I took that fact number and just randomly if
77
00:03:23.479 --> 00:03:26.800
you chose that number randomly. Yeahs a prime number and
78
00:03:26.800 --> 00:03:28.680
the chance is one in eleven point five.
79
00:03:28.800 --> 00:03:30.719
All right, all right, not bad, I should go buy
80
00:03:30.719 --> 00:03:32.960
a lottery ticket, all right. So tell us about merging
81
00:03:33.000 --> 00:03:33.840
black holes.
82
00:03:34.080 --> 00:03:38.159
Okay, So about ten years ago a device that was
83
00:03:38.159 --> 00:03:41.479
built in the United States called LEGO. It's a laser
84
00:03:41.520 --> 00:03:46.039
interferometer which they use lasers to measure the link between
85
00:03:46.120 --> 00:03:53.039
two mirrors that are ones in Louisiana and ones in Hanford, Washington.
86
00:03:53.599 --> 00:03:56.240
And the whole goal of that was to try to
87
00:03:56.280 --> 00:04:00.240
measure gravitational waves, which were first predicted by Einstein in
88
00:04:00.360 --> 00:04:05.879
nineteen sixteen. And so something really cataclysmic has to happen
89
00:04:05.960 --> 00:04:10.639
to generate a gravitational way big enough to be measurable.
90
00:04:11.080 --> 00:04:13.960
And so what happens. This wave travels through space at
91
00:04:13.960 --> 00:04:17.360
the speed of light, and in what it does, it
92
00:04:17.480 --> 00:04:22.600
slightly changes the length between these two mirrors in a
93
00:04:23.560 --> 00:04:26.600
and you can measure that using this interferometer. And so
94
00:04:26.680 --> 00:04:30.879
the first measurement of a black hole collision and coalescence
95
00:04:30.879 --> 00:04:36.279
happened in nineteen to twenty fifteen, and it won the
96
00:04:36.319 --> 00:04:39.560
folks who built that the Nobel Prize in twenty seventeen.
97
00:04:40.199 --> 00:04:42.959
So the black hole was about three or four solar
98
00:04:43.040 --> 00:04:46.680
masses and another three or four solar masses and they combined,
99
00:04:46.839 --> 00:04:49.879
and that was the first time in history anyone had
100
00:04:49.879 --> 00:04:54.439
observer observed the universe using something other than electromagnetic waves
101
00:04:54.560 --> 00:04:55.560
or particles.
102
00:04:56.560 --> 00:05:01.240
So the interferometer, it's really looked looking at light or is.
103
00:05:01.160 --> 00:05:03.879
It looking at something that? What's it looking at?
104
00:05:04.560 --> 00:05:07.639
It uses light, it uses lasers, But what it's looking
105
00:05:08.120 --> 00:05:12.639
is the stretching and compressing of space time that happens
106
00:05:12.680 --> 00:05:17.079
as a gravitational wave passes by. So gravitational wave is
107
00:05:17.120 --> 00:05:19.680
a ripple on the fabric of space time.
108
00:05:20.240 --> 00:05:23.040
So does that work by deflecting a laser beam?
109
00:05:23.199 --> 00:05:25.199
Or how is it? How does it measure it?
110
00:05:25.759 --> 00:05:29.240
Well, it just measures. So these two mirrors can they
111
00:05:29.279 --> 00:05:32.720
will differ, their distance between them will differ by less
112
00:05:32.759 --> 00:05:36.920
than the diameter of one proton, and that's enough to
113
00:05:36.959 --> 00:05:42.279
be measurable by this particular laser interferometer. And so this
114
00:05:42.399 --> 00:05:45.279
ripple what you'll see as a little In fact, if
115
00:05:45.319 --> 00:05:47.480
you turn it into a signal, you'll these things go
116
00:05:47.920 --> 00:05:50.120
closer and farther apart, and it will create a little signal.
117
00:05:50.120 --> 00:05:54.720
It sounds like and their first data set. When you
118
00:05:54.720 --> 00:05:57.600
play it as an audio sounds exactly like that woo.
119
00:05:59.120 --> 00:06:06.360
That characteristic that characteristic sound comes from the calculation that
120
00:06:06.480 --> 00:06:10.759
Einstein could have done had he had supercomputers. And that's
121
00:06:11.079 --> 00:06:13.040
what comes from the black hole merger.
122
00:06:13.720 --> 00:06:15.399
All right, this is going to be a dumb question,
123
00:06:15.879 --> 00:06:19.759
but when two black holes merge to you just get
124
00:06:20.000 --> 00:06:23.240
one more, one larger black hole. And also, if you
125
00:06:23.399 --> 00:06:27.000
had a black hole of I don't know whether you
126
00:06:27.040 --> 00:06:31.120
want to talk about diameters, circumference or volume, but let's
127
00:06:31.120 --> 00:06:33.000
say you had a black hole of one of those
128
00:06:33.040 --> 00:06:35.839
measures of X and another black hole of one of
129
00:06:35.879 --> 00:06:41.120
those measures of why what what is the measure of
130
00:06:41.160 --> 00:06:43.399
the combined black hole in terms of X and Y?
131
00:06:44.560 --> 00:06:47.920
Okay, So there's only three things you can literally a
132
00:06:47.920 --> 00:06:52.800
black holes has in terms of measurable quantities. It's its mass,
133
00:06:53.000 --> 00:06:56.800
it's charge and its spin Okay, and so mass and
134
00:06:57.959 --> 00:07:01.240
its spin are related to what known as the area
135
00:07:01.360 --> 00:07:03.600
of the black hole is in fact the important thing
136
00:07:03.639 --> 00:07:07.160
that you can measure. And in this recent measurement, it
137
00:07:07.240 --> 00:07:10.160
happened in early this year and has taken some months
138
00:07:10.160 --> 00:07:14.240
of analysis for the researchers to antalyize exactly what happened
139
00:07:14.279 --> 00:07:16.839
in this case, it was black holes of about thirty
140
00:07:16.879 --> 00:07:21.040
or forty solar masses collided with each other and created
141
00:07:21.079 --> 00:07:24.240
a black hole that was twice as big, and the
142
00:07:24.360 --> 00:07:28.040
area of the final black hole is bigger than the
143
00:07:28.160 --> 00:07:32.120
area of either of the beginning ones. But the important
144
00:07:32.160 --> 00:07:35.759
thing that Einstein that excuse me, Stephen Hawking predicted in
145
00:07:35.839 --> 00:07:41.399
the nineteen sixties was that the area has to increase
146
00:07:41.439 --> 00:07:44.360
when two black holes come together, and so the final
147
00:07:44.399 --> 00:07:46.360
area has to be bigger than the sum of the
148
00:07:46.480 --> 00:07:50.079
areas of the two individuals. And that's what they were
149
00:07:50.079 --> 00:07:53.199
able to measure from the exact details of the woo
150
00:07:54.319 --> 00:07:56.000
that happens in the collision.
151
00:07:56.639 --> 00:08:01.360
Okay, so I'm going way, way way out of my
152
00:08:01.480 --> 00:08:03.319
league here with this next question.
153
00:08:03.399 --> 00:08:05.399
This is probably going to be a really stupid question.
154
00:08:07.839 --> 00:08:12.120
I would have thought that it was at least possible
155
00:08:12.519 --> 00:08:15.959
that when you combine these very very massive things, that
156
00:08:16.040 --> 00:08:20.560
the increase in the gravitational field caused by the increase
157
00:08:21.040 --> 00:08:26.959
in the mass of these two things would could cause
158
00:08:27.079 --> 00:08:31.800
the area of the combined black holes to be smaller
159
00:08:31.839 --> 00:08:33.120
than the sum of the areas.
160
00:08:33.960 --> 00:08:36.720
Is that a ridiculous concept.
161
00:08:37.200 --> 00:08:39.720
It's clearly wrong, as you just said it's wrong, But
162
00:08:39.840 --> 00:08:40.679
is it ridiculous.
163
00:08:41.639 --> 00:08:43.960
No, not at all. And in fact, it took you know,
164
00:08:44.120 --> 00:08:49.360
Stephen Hawking to prove that the area can only increase,
165
00:08:50.279 --> 00:08:52.600
and so that caused him to start thinking, and he
166
00:08:52.679 --> 00:08:56.000
worked with another mathematical physicist by the name of Beckenstein,
167
00:08:56.759 --> 00:09:01.120
and they came up with a calculation in which showed, oh,
168
00:09:01.200 --> 00:09:05.000
not only is this area interesting and measurable, but it
169
00:09:05.120 --> 00:09:08.679
is proportional to the entropy of the black hole. So
170
00:09:08.759 --> 00:09:11.759
the black hole and stuff goes down into it, it's
171
00:09:11.840 --> 00:09:17.919
sucking in thermodynamic entropy, and the entropy is completely encoded
172
00:09:17.960 --> 00:09:21.879
in the area of the black hole. Wow, we're talking
173
00:09:21.919 --> 00:09:25.000
with all the way back to thermodynamics, the second law
174
00:09:25.000 --> 00:09:26.080
of thermodynamics.
175
00:09:26.200 --> 00:09:29.879
We're talking with cup physics professor Paul Beal. I don't
176
00:09:29.919 --> 00:09:33.159
know if there's some other term, some other units you
177
00:09:33.200 --> 00:09:35.080
can put this in. A listener wants to know how
178
00:09:35.080 --> 00:09:36.320
big is a solar mass?
179
00:09:37.279 --> 00:09:40.679
Oh solar mass, So solar mass is about ten to
180
00:09:40.840 --> 00:09:48.240
the I'm gonna ten to the thirty something kilograms, okay,
181
00:09:48.240 --> 00:09:52.080
and I forget whether it's thirty or thirty two or
182
00:09:52.120 --> 00:09:54.320
thirty five that I can't.
183
00:09:54.080 --> 00:09:56.960
Remember, all right, Ed Paul didn't look that up by anyway.
184
00:09:57.039 --> 00:09:58.639
That's just off the top of his head. So that's
185
00:09:58.639 --> 00:10:03.360
how big a solar mass is. That's that's a lot. Okay,
186
00:10:03.919 --> 00:10:06.000
one more listener question, even though it's way way off
187
00:10:06.039 --> 00:10:08.960
topic and probably a question that you teach in all
188
00:10:09.000 --> 00:10:12.759
of your most basic basic physics classes, but people ask
189
00:10:12.799 --> 00:10:14.399
from time to time. So we'll do this one listener
190
00:10:14.480 --> 00:10:17.000
question quickly, and then we'll do math. Can we travel
191
00:10:17.039 --> 00:10:18.279
faster than the speed of light?
192
00:10:19.679 --> 00:10:22.759
Okay? So, as our theory of the universe does not
193
00:10:22.919 --> 00:10:26.720
allow an object with mass to travel faster than the
194
00:10:26.759 --> 00:10:29.559
speed of light because it would take an infinite amount
195
00:10:29.600 --> 00:10:32.799
of energy to accelerate the particle, you know, exactly to
196
00:10:32.919 --> 00:10:36.159
the speed of light. So the fastest anything we've ever
197
00:10:36.240 --> 00:10:43.840
created is ninety nine point nine nine percent of the
198
00:10:43.879 --> 00:10:46.559
speed of light. And that set the large Hadron collider
199
00:10:47.480 --> 00:10:50.200
where they accelerate protons to very very close to the
200
00:10:50.240 --> 00:10:50.879
speed of light.
201
00:10:51.559 --> 00:10:56.039
Wow, all right, excellent answer. Okay, let's do some math.
202
00:10:56.600 --> 00:10:59.600
And this math thing is actually the thing that caused
203
00:10:59.600 --> 00:11:01.679
me to reach out to you yesterday when a listener
204
00:11:01.679 --> 00:11:05.279
in Abu Dhabi said, Hey, Ross, have you heard of this?
205
00:11:05.559 --> 00:11:09.960
Have you heard of this thing called the Goldbach conjecture,
206
00:11:10.279 --> 00:11:12.360
and I said no, and I looked it up, and
207
00:11:12.399 --> 00:11:14.519
actually I probably have heard of it without that name,
208
00:11:14.639 --> 00:11:17.519
just as the mathematical concept. But it's pretty interesting, as
209
00:11:17.559 --> 00:11:19.480
you and I were talking about on the air. It's
210
00:11:19.519 --> 00:11:22.720
a mathematical concept that's easy enough to understand that you
211
00:11:22.759 --> 00:11:25.039
don't have to be a mathematician to understand the question.
212
00:11:26.000 --> 00:11:30.480
But it turns out it's well nearly impossible, I guess,
213
00:11:30.480 --> 00:11:32.440
because it hasn't been done yet to prove it.
214
00:11:32.519 --> 00:11:34.279
So can you can you elaborate please?
215
00:11:35.519 --> 00:11:39.679
Okay? So this was a conjecture made by Christian Goldbach,
216
00:11:39.759 --> 00:11:42.759
and he was lived in the seventeen hundreds. He was
217
00:11:42.799 --> 00:11:46.360
a contemporary of Leonard Euler, who I think is the
218
00:11:46.360 --> 00:11:51.320
greatest mathematician in history, and they were communicating and talking
219
00:11:51.360 --> 00:11:54.840
to each other, and Goldbach made this conjecture that every
220
00:11:54.960 --> 00:11:58.639
even number bigger than four can be written as the
221
00:11:58.679 --> 00:12:03.240
sum of two prime numbers. So, for example, six is
222
00:12:03.320 --> 00:12:06.919
three plus three, and eight can be written as three
223
00:12:06.960 --> 00:12:12.360
plus five ten, five plus five fourteen. It can be
224
00:12:12.360 --> 00:12:15.519
written as seven plus seven or three plus eleven, So
225
00:12:15.559 --> 00:12:18.200
you can always find two prime numbers that add up
226
00:12:18.240 --> 00:12:21.679
to every even number. And I would say conjecture, cause
227
00:12:21.720 --> 00:12:25.080
no one's proven it. But people, it's fairly easy with
228
00:12:25.120 --> 00:12:28.480
a computer now to check two fairly large numbers and
229
00:12:28.720 --> 00:12:33.399
up to numbers with eighteen digits, and them people have checked. Yes,
230
00:12:33.480 --> 00:12:36.559
every even number is the sum of two prime numbers.
231
00:12:38.840 --> 00:12:43.519
Why is this so far for what two hundred and
232
00:12:43.519 --> 00:12:45.240
eighty years impossible to prove?
233
00:12:46.000 --> 00:12:49.320
Well, I will say it's impossible. People are making progress.
234
00:12:49.440 --> 00:12:53.919
There's a weaker form of the conjecture that says, oh,
235
00:12:54.000 --> 00:12:56.840
let's look at odd numbers. Every odd number greater than seven,
236
00:12:57.000 --> 00:12:59.679
it can be written as the sum of three prime numbers,
237
00:12:59.720 --> 00:13:05.240
three odd prime numbers, and uh, and that is people
238
00:13:05.279 --> 00:13:10.000
are it's it's a weaker conjecture because if gold box
239
00:13:10.039 --> 00:13:12.440
and original conjecture is true, then this other one is
240
00:13:12.440 --> 00:13:15.679
trivitally true. You can take any of the even numbers
241
00:13:15.679 --> 00:13:19.360
that Goldbock referred to and just add three to it,
242
00:13:19.679 --> 00:13:22.279
and that would give an odd number, and that would
243
00:13:22.279 --> 00:13:26.080
count all of the odd number. And he and Eiler
244
00:13:26.200 --> 00:13:28.720
figured that out immediately say ah, if we can prove this,
245
00:13:28.960 --> 00:13:32.679
then uh uh, that would be maybe easier. But then
246
00:13:33.879 --> 00:13:37.759
the first one, the strong conjecture, would actually have that
247
00:13:37.960 --> 00:13:42.559
is a required element, that every odd numbers and some
248
00:13:42.639 --> 00:13:44.240
of three odd primes.
249
00:13:44.559 --> 00:13:47.039
I mean there from time to time you run across
250
00:13:47.120 --> 00:13:49.480
things like this in math, if you're even a little
251
00:13:49.519 --> 00:13:51.120
bit of a math nerd, and I am a little
252
00:13:51.120 --> 00:13:53.799
bit not not to your level, but two, but were
253
00:13:53.840 --> 00:13:58.159
you where there are these these conjectures, these theorems with
254
00:13:58.240 --> 00:14:00.399
you know, fair modern oiler and all these guys, and
255
00:14:00.440 --> 00:14:04.360
all these famous theorems, and some of the theorems. Yeah,
256
00:14:04.559 --> 00:14:07.480
almost have to be a mathematician to even understand the
257
00:14:07.600 --> 00:14:13.240
question being posed. But this one is so easy, conceptually easy.
258
00:14:13.840 --> 00:14:17.360
And I don't know whether that I don't know whether
259
00:14:17.440 --> 00:14:21.039
I'm whether I should be surprised that a question that
260
00:14:21.159 --> 00:14:25.879
is so conceptually easy has proven to be so theoretically
261
00:14:25.879 --> 00:14:26.679
difficult to prove.
262
00:14:28.399 --> 00:14:31.519
And there are lots of things like this that seem
263
00:14:31.600 --> 00:14:33.919
to be easy to state, and there's lots of them
264
00:14:33.960 --> 00:14:36.639
we could talk about but have never been able to
265
00:14:36.639 --> 00:14:39.840
be proven so far. But a lot of them have
266
00:14:40.000 --> 00:14:43.200
fallen to the mathematicians who have proven some of these
267
00:14:43.320 --> 00:14:47.559
very hard to prove theorems, like fair Ma's last theorem
268
00:14:47.879 --> 00:14:52.080
was in the nineteen nineties, and that had stood the
269
00:14:52.120 --> 00:14:56.000
test of three or four hundred years, and so this one,
270
00:14:56.279 --> 00:15:00.360
this one could happen soon. Now there's a one million
271
00:15:00.399 --> 00:15:03.440
dollar prize if someone can either prove it to be
272
00:15:03.559 --> 00:15:06.159
true or to be false. If they can find an
273
00:15:06.159 --> 00:15:09.000
example of a single even number that is not the
274
00:15:09.000 --> 00:15:12.360
sum of two primes, then that's enough. That would be
275
00:15:12.440 --> 00:15:15.240
the proof that, yeah, that conjecture is false because there's
276
00:15:15.279 --> 00:15:16.039
a counterexample.
277
00:15:16.080 --> 00:15:17.799
All right, less, super quick question.
278
00:15:17.840 --> 00:15:20.240
Then I got to go, do you think your mathematical
279
00:15:20.279 --> 00:15:23.039
skills are close to good enough that it would be
280
00:15:23.080 --> 00:15:24.720
a good use of your time to try to win
281
00:15:24.759 --> 00:15:25.639
that million dollars?
282
00:15:26.279 --> 00:15:31.000
H No way, no way. So even the weak conjecture,
283
00:15:31.080 --> 00:15:34.519
there's like a two hundred page paper that's getting closer
284
00:15:34.559 --> 00:15:38.080
to ward to proof, and mathematicians are pouring over that
285
00:15:38.120 --> 00:15:41.639
two hundred page paper and trying to cross all the
286
00:15:41.720 --> 00:15:45.320
t's and dot the i's and everything. I can't even
287
00:15:45.360 --> 00:15:48.360
begin to read the math that's present in that paper.
288
00:15:48.399 --> 00:15:48.639
Wow.
289
00:15:49.240 --> 00:15:51.279
If Paul Beale can't even begin to read the math,
290
00:15:51.320 --> 00:15:54.120
imagine the rest of us. See you, physics Professor Paul
291
00:15:54.200 --> 00:15:55.960
bial Thanks so much. It's great to have you back
292
00:15:55.960 --> 00:15:57.799
on the show. Sorry it's been so long. We'll do
293
00:15:57.840 --> 00:15:58.440
it again soon.
294
00:15:59.240 --> 00:16:00.720
Okay, thank you all. Ry good one.
295
00:16:00.759 --> 00:16:02.080
Hey you too, have a great weekend.
