Episode Transcript
Available transcripts are automatically generated. Complete accuracy is not guaranteed.
Speaker 1 (00:00):
One of our most frequent guests, most requested guests, and
actually had a listener who emailed a math thing that
we're going to get to with Paul in a little bit,
saying you should have Paul on to talk about this,
so we will, uh and and I will note in
advance because I will forget later if I if I
don't say it now that the listener who asked about
it lives in Abu Dhabi and listens to the show
(00:23):
from there.
Speaker 2 (00:24):
So so that's pretty cool. So Senio physics professor Paul
Biel is.
Speaker 1 (00:28):
As I say frequently, a guy who makes me wish
I were back in college and had a professor like him.
Speaker 2 (00:33):
I did enjoy physics in college.
Speaker 1 (00:35):
I only took I only took one semester of just
basic introductory physics.
Speaker 2 (00:39):
But Paul, I did.
Speaker 1 (00:40):
Get an A plus in college in basic introductory physics.
Speaker 2 (00:44):
But anyway, and.
Speaker 3 (00:48):
It didn't even take Electrictian magnanism.
Speaker 2 (00:50):
I didn't get that far.
Speaker 1 (00:52):
Oh God, long story, that would be fun though, right,
And Paul also runs the Buffalo Bicycle Classic, And just
give us seventeen seconds on how the Buffalo Bicycle Classic
was this year.
Speaker 3 (01:06):
It was fantastic. We had thirteen hundred riders, and we've
got lots of sponsors and people raised money, and so
we raised over one hundred thousand dollars for our scholarship fund.
Then we have twenty five students from Colorado high schools
who are at CU now because of the Buffalo Bicycle
Classic Scholarship Fund.
Speaker 2 (01:24):
Fantastic.
Speaker 1 (01:24):
All right, one quick thing before we talk about black holes.
One quick thing where I think, I think you're going
to be very proud of me. So I like to
do things at prime numbers, right. And we did a
thing earlier in the show where we gave away some
Broncos tickets and I had to tell listeners at what
time they could start texting in to try to win
the tickets. And the way I always do this is
(01:46):
whether I'm doing a time that's minutes and seconds with
a colon in between or whatever it is, I just
eliminate the colon and look at the whole number.
Speaker 2 (01:55):
Okay, So if it's like one oh one PM.
Speaker 1 (01:57):
Then I'm asking myself is the number one hundred and
one on prime?
Speaker 2 (02:00):
And if it is, then I can use that time?
Speaker 3 (02:02):
Right.
Speaker 1 (02:03):
So Dragon kept doing these stupid things like telling me
to use texture number four or eight or fifteen, and
I said no, and then anyway, and then I said
all right, and here's the time to text in.
Speaker 2 (02:15):
And I just picked off the top of my head.
Speaker 1 (02:17):
I said ten twenty eight and eleven seconds. I said
ten twenty eight and eleven second.
Speaker 2 (02:23):
I just made that up. And then I went to
the Google machine and I typed in, is one O
two eight one one a prime number? And the answer
is yes? How about that?
Speaker 1 (02:32):
Hey?
Speaker 3 (02:33):
Nice? Long?
Speaker 2 (02:34):
Yeah, yeah, better to be lucky than good.
Speaker 1 (02:36):
All right, you sent me, You sent me some physics
about black holes and black holes merging and stuff that
I really don't understand. And I found a couple of
web You sent me a website. I found another one
clearest signal of two merging black holes.
Speaker 2 (02:54):
So tell us about this.
Speaker 3 (02:56):
Okay, firstly, I'm checking to see how what was your
chain so that you got that? Right? So one chance
in eleven that you that that would be a prime number.
Speaker 2 (03:06):
Wait, but you got to narrow it down.
Speaker 1 (03:08):
Is it one chance in eleven that any that any
number that could represent a time so would have to
be within a certain number of digits? Right? Yeah?
Speaker 3 (03:19):
No, I took that fact number and just randomly if
you chose that number randomly. Yeahs a prime number and
the chance is one in eleven point five.
Speaker 1 (03:28):
All right, all right, not bad, I should go buy
a lottery ticket, all right. So tell us about merging
black holes.
Speaker 3 (03:34):
Okay, So about ten years ago a device that was
built in the United States called LEGO. It's a laser
interferometer which they use lasers to measure the link between
two mirrors that are ones in Louisiana and ones in Hanford, Washington.
And the whole goal of that was to try to
(03:56):
measure gravitational waves, which were first predicted by Einstein in
nineteen sixteen. And so something really cataclysmic has to happen
to generate a gravitational way big enough to be measurable.
And so what happens. This wave travels through space at
the speed of light, and in what it does, it
(04:17):
slightly changes the length between these two mirrors in a
and you can measure that using this interferometer. And so
the first measurement of a black hole collision and coalescence
happened in nineteen to twenty fifteen, and it won the
folks who built that the Nobel Prize in twenty seventeen.
(04:40):
So the black hole was about three or four solar
masses and another three or four solar masses and they combined,
and that was the first time in history anyone had
observer observed the universe using something other than electromagnetic waves
or particles.
Speaker 1 (04:56):
So the interferometer, it's really looked looking at light or is.
Speaker 2 (05:01):
It looking at something that? What's it looking at?
Speaker 3 (05:04):
It uses light, it uses lasers, But what it's looking
is the stretching and compressing of space time that happens
as a gravitational wave passes by. So gravitational wave is
a ripple on the fabric of space time.
Speaker 1 (05:20):
So does that work by deflecting a laser beam?
Speaker 2 (05:23):
Or how is it? How does it measure it?
Speaker 3 (05:25):
Well, it just measures. So these two mirrors can they
will differ, their distance between them will differ by less
than the diameter of one proton, and that's enough to
be measurable by this particular laser interferometer. And so this
ripple what you'll see as a little In fact, if
you turn it into a signal, you'll these things go
(05:47):
closer and farther apart, and it will create a little signal.
It sounds like and their first data set. When you
play it as an audio sounds exactly like that woo.
That characteristic that characteristic sound comes from the calculation that
Einstein could have done had he had supercomputers. And that's
(06:11):
what comes from the black hole merger.
Speaker 1 (06:13):
All right, this is going to be a dumb question,
but when two black holes merge to you just get
one more, one larger black hole. And also, if you
had a black hole of I don't know whether you
want to talk about diameters, circumference or volume, but let's
say you had a black hole of one of those
measures of X and another black hole of one of
(06:35):
those measures of why what what is the measure of
the combined black hole in terms of X and Y?
Speaker 3 (06:44):
Okay, So there's only three things you can literally a
black holes has in terms of measurable quantities. It's its mass,
it's charge and its spin Okay, and so mass and
its spin are related to what known as the area
of the black hole is in fact the important thing
that you can measure. And in this recent measurement, it
(07:07):
happened in early this year and has taken some months
of analysis for the researchers to antalyize exactly what happened
in this case, it was black holes of about thirty
or forty solar masses collided with each other and created
a black hole that was twice as big, and the
area of the final black hole is bigger than the
(07:28):
area of either of the beginning ones. But the important
thing that Einstein that excuse me, Stephen Hawking predicted in
the nineteen sixties was that the area has to increase
when two black holes come together, and so the final
area has to be bigger than the sum of the
areas of the two individuals. And that's what they were
(07:50):
able to measure from the exact details of the woo
that happens in the collision.
Speaker 1 (07:56):
Okay, so I'm going way, way way out of my
league here with this next question.
Speaker 2 (08:03):
This is probably going to be a really stupid question.
Speaker 1 (08:07):
I would have thought that it was at least possible
that when you combine these very very massive things, that
the increase in the gravitational field caused by the increase
in the mass of these two things would could cause
the area of the combined black holes to be smaller
(08:31):
than the sum of the areas.
Speaker 2 (08:33):
Is that a ridiculous concept.
Speaker 1 (08:37):
It's clearly wrong, as you just said it's wrong, But
is it ridiculous.
Speaker 3 (08:41):
No, not at all. And in fact, it took you know,
Stephen Hawking to prove that the area can only increase,
and so that caused him to start thinking, and he
worked with another mathematical physicist by the name of Beckenstein,
and they came up with a calculation in which showed, oh,
not only is this area interesting and measurable, but it
(09:05):
is proportional to the entropy of the black hole. So
the black hole and stuff goes down into it, it's
sucking in thermodynamic entropy, and the entropy is completely encoded
in the area of the black hole. Wow, we're talking
with all the way back to thermodynamics, the second law
of thermodynamics.
Speaker 1 (09:26):
We're talking with cup physics professor Paul Beal. I don't
know if there's some other term, some other units you
can put this in. A listener wants to know how
big is a solar mass?
Speaker 3 (09:37):
Oh solar mass, So solar mass is about ten to
the I'm gonna ten to the thirty something kilograms, okay,
and I forget whether it's thirty or thirty two or
thirty five that I can't.
Speaker 1 (09:54):
Remember, all right, Ed Paul didn't look that up by anyway.
That's just off the top of his head. So that's
how big a solar mass is. That's that's a lot. Okay,
one more listener question, even though it's way way off
topic and probably a question that you teach in all
of your most basic basic physics classes, but people ask
from time to time. So we'll do this one listener
(10:14):
question quickly, and then we'll do math. Can we travel
faster than the speed of light?
Speaker 3 (10:19):
Okay? So, as our theory of the universe does not
allow an object with mass to travel faster than the
speed of light because it would take an infinite amount
of energy to accelerate the particle, you know, exactly to
the speed of light. So the fastest anything we've ever
created is ninety nine point nine nine percent of the
(10:43):
speed of light. And that set the large Hadron collider
where they accelerate protons to very very close to the
speed of light.
Speaker 1 (10:51):
Wow, all right, excellent answer. Okay, let's do some math.
And this math thing is actually the thing that caused
me to reach out to you yesterday when a listener
in Abu Dhabi said, Hey, Ross, have you heard of this?
Have you heard of this thing called the Goldbach conjecture,
and I said no, and I looked it up, and
(11:12):
actually I probably have heard of it without that name,
just as the mathematical concept. But it's pretty interesting, as
you and I were talking about on the air. It's
a mathematical concept that's easy enough to understand that you
don't have to be a mathematician to understand the question.
But it turns out it's well nearly impossible, I guess,
because it hasn't been done yet to prove it.
Speaker 2 (11:32):
So can you can you elaborate please?
Speaker 3 (11:35):
Okay? So this was a conjecture made by Christian Goldbach,
and he was lived in the seventeen hundreds. He was
a contemporary of Leonard Euler, who I think is the
greatest mathematician in history, and they were communicating and talking
to each other, and Goldbach made this conjecture that every
even number bigger than four can be written as the
(11:58):
sum of two prime numbers. So, for example, six is
three plus three, and eight can be written as three
plus five ten, five plus five fourteen. It can be
written as seven plus seven or three plus eleven, So
you can always find two prime numbers that add up
to every even number. And I would say conjecture, cause
(12:21):
no one's proven it. But people, it's fairly easy with
a computer now to check two fairly large numbers and
up to numbers with eighteen digits, and them people have checked. Yes,
every even number is the sum of two prime numbers.
Speaker 1 (12:38):
Why is this so far for what two hundred and
eighty years impossible to prove?
Speaker 3 (12:46):
Well, I will say it's impossible. People are making progress.
There's a weaker form of the conjecture that says, oh,
let's look at odd numbers. Every odd number greater than seven,
it can be written as the sum of three prime numbers,
three odd prime numbers, and uh, and that is people
are it's it's a weaker conjecture because if gold box
(13:10):
and original conjecture is true, then this other one is
trivitally true. You can take any of the even numbers
that Goldbock referred to and just add three to it,
and that would give an odd number, and that would
count all of the odd number. And he and Eiler
figured that out immediately say ah, if we can prove this,
then uh uh, that would be maybe easier. But then
(13:33):
the first one, the strong conjecture, would actually have that
is a required element, that every odd numbers and some
of three odd primes.
Speaker 1 (13:44):
I mean there from time to time you run across
things like this in math, if you're even a little
bit of a math nerd, and I am a little
bit not not to your level, but two, but were
you where there are these these conjectures, these theorems with
you know, fair modern oiler and all these guys, and
all these famous theorems, and some of the theorems. Yeah,
almost have to be a mathematician to even understand the
(14:07):
question being posed. But this one is so easy, conceptually easy.
And I don't know whether that I don't know whether
I'm whether I should be surprised that a question that
is so conceptually easy has proven to be so theoretically
difficult to prove.
Speaker 3 (14:28):
And there are lots of things like this that seem
to be easy to state, and there's lots of them
we could talk about but have never been able to
be proven so far. But a lot of them have
fallen to the mathematicians who have proven some of these
very hard to prove theorems, like fair Ma's last theorem
was in the nineteen nineties, and that had stood the
(14:52):
test of three or four hundred years, and so this one,
this one could happen soon. Now there's a one million
dollar prize if someone can either prove it to be
true or to be false. If they can find an
example of a single even number that is not the
sum of two primes, then that's enough. That would be
(15:12):
the proof that, yeah, that conjecture is false because there's
a counterexample.
Speaker 2 (15:16):
All right, less, super quick question.
Speaker 1 (15:17):
Then I got to go, do you think your mathematical
skills are close to good enough that it would be
a good use of your time to try to win
that million dollars?
Speaker 3 (15:26):
H No way, no way. So even the weak conjecture,
there's like a two hundred page paper that's getting closer
to ward to proof, and mathematicians are pouring over that
two hundred page paper and trying to cross all the
t's and dot the i's and everything. I can't even
begin to read the math that's present in that paper.
Speaker 2 (15:48):
Wow.
Speaker 1 (15:49):
If Paul Beale can't even begin to read the math,
imagine the rest of us. See you, physics Professor Paul
bial Thanks so much. It's great to have you back
on the show. Sorry it's been so long. We'll do
it again soon.
Speaker 3 (15:59):
Okay, thank you all. Ry good one.
Speaker 2 (16:00):
Hey you too, have a great weekend.
One of our most frequent guests, most requested guests, and
actually had a listener who emailed a math thing that
we're going to get to with Paul in a little bit,
saying you should have Paul on to talk about this,
so we will, uh and and I will note in
advance because I will forget later if I if I
don't say it now that the listener who asked about
it lives in Abu Dhabi and listens to the show
(00:23):
from there.
Speaker 2 (00:24):
So so that's pretty cool. So Senio physics professor Paul
Biel is.
Speaker 1 (00:28):
As I say frequently, a guy who makes me wish
I were back in college and had a professor like him.
Speaker 2 (00:33):
I did enjoy physics in college.
Speaker 1 (00:35):
I only took I only took one semester of just
basic introductory physics.
Speaker 2 (00:39):
But Paul, I did.
Speaker 1 (00:40):
Get an A plus in college in basic introductory physics.
Speaker 2 (00:44):
But anyway, and.
Speaker 3 (00:48):
It didn't even take Electrictian magnanism.
Speaker 2 (00:50):
I didn't get that far.
Speaker 1 (00:52):
Oh God, long story, that would be fun though, right,
And Paul also runs the Buffalo Bicycle Classic, And just
give us seventeen seconds on how the Buffalo Bicycle Classic
was this year.
Speaker 3 (01:06):
It was fantastic. We had thirteen hundred riders, and we've
got lots of sponsors and people raised money, and so
we raised over one hundred thousand dollars for our scholarship fund.
Then we have twenty five students from Colorado high schools
who are at CU now because of the Buffalo Bicycle
Classic Scholarship Fund.
Speaker 2 (01:24):
Fantastic.
Speaker 1 (01:24):
All right, one quick thing before we talk about black holes.
One quick thing where I think, I think you're going
to be very proud of me. So I like to
do things at prime numbers, right. And we did a
thing earlier in the show where we gave away some
Broncos tickets and I had to tell listeners at what
time they could start texting in to try to win
the tickets. And the way I always do this is
(01:46):
whether I'm doing a time that's minutes and seconds with
a colon in between or whatever it is, I just
eliminate the colon and look at the whole number.
Speaker 2 (01:55):
Okay, So if it's like one oh one PM.
Speaker 1 (01:57):
Then I'm asking myself is the number one hundred and
one on prime?
Speaker 2 (02:00):
And if it is, then I can use that time?
Speaker 3 (02:02):
Right.
Speaker 1 (02:03):
So Dragon kept doing these stupid things like telling me
to use texture number four or eight or fifteen, and
I said no, and then anyway, and then I said
all right, and here's the time to text in.
Speaker 2 (02:15):
And I just picked off the top of my head.
Speaker 1 (02:17):
I said ten twenty eight and eleven seconds. I said
ten twenty eight and eleven second.
Speaker 2 (02:23):
I just made that up. And then I went to
the Google machine and I typed in, is one O
two eight one one a prime number? And the answer
is yes? How about that?
Speaker 1 (02:32):
Hey?
Speaker 3 (02:33):
Nice? Long?
Speaker 2 (02:34):
Yeah, yeah, better to be lucky than good.
Speaker 1 (02:36):
All right, you sent me, You sent me some physics
about black holes and black holes merging and stuff that
I really don't understand. And I found a couple of
web You sent me a website. I found another one
clearest signal of two merging black holes.
Speaker 2 (02:54):
So tell us about this.
Speaker 3 (02:56):
Okay, firstly, I'm checking to see how what was your
chain so that you got that? Right? So one chance
in eleven that you that that would be a prime number.
Speaker 2 (03:06):
Wait, but you got to narrow it down.
Speaker 1 (03:08):
Is it one chance in eleven that any that any
number that could represent a time so would have to
be within a certain number of digits? Right? Yeah?
Speaker 3 (03:19):
No, I took that fact number and just randomly if
you chose that number randomly. Yeahs a prime number and
the chance is one in eleven point five.
Speaker 1 (03:28):
All right, all right, not bad, I should go buy
a lottery ticket, all right. So tell us about merging
black holes.
Speaker 3 (03:34):
Okay, So about ten years ago a device that was
built in the United States called LEGO. It's a laser
interferometer which they use lasers to measure the link between
two mirrors that are ones in Louisiana and ones in Hanford, Washington.
And the whole goal of that was to try to
(03:56):
measure gravitational waves, which were first predicted by Einstein in
nineteen sixteen. And so something really cataclysmic has to happen
to generate a gravitational way big enough to be measurable.
And so what happens. This wave travels through space at
the speed of light, and in what it does, it
(04:17):
slightly changes the length between these two mirrors in a
and you can measure that using this interferometer. And so
the first measurement of a black hole collision and coalescence
happened in nineteen to twenty fifteen, and it won the
folks who built that the Nobel Prize in twenty seventeen.
(04:40):
So the black hole was about three or four solar
masses and another three or four solar masses and they combined,
and that was the first time in history anyone had
observer observed the universe using something other than electromagnetic waves
or particles.
Speaker 1 (04:56):
So the interferometer, it's really looked looking at light or is.
Speaker 2 (05:01):
It looking at something that? What's it looking at?
Speaker 3 (05:04):
It uses light, it uses lasers, But what it's looking
is the stretching and compressing of space time that happens
as a gravitational wave passes by. So gravitational wave is
a ripple on the fabric of space time.
Speaker 1 (05:20):
So does that work by deflecting a laser beam?
Speaker 2 (05:23):
Or how is it? How does it measure it?
Speaker 3 (05:25):
Well, it just measures. So these two mirrors can they
will differ, their distance between them will differ by less
than the diameter of one proton, and that's enough to
be measurable by this particular laser interferometer. And so this
ripple what you'll see as a little In fact, if
you turn it into a signal, you'll these things go
(05:47):
closer and farther apart, and it will create a little signal.
It sounds like and their first data set. When you
play it as an audio sounds exactly like that woo.
That characteristic that characteristic sound comes from the calculation that
Einstein could have done had he had supercomputers. And that's
(06:11):
what comes from the black hole merger.
Speaker 1 (06:13):
All right, this is going to be a dumb question,
but when two black holes merge to you just get
one more, one larger black hole. And also, if you
had a black hole of I don't know whether you
want to talk about diameters, circumference or volume, but let's
say you had a black hole of one of those
measures of X and another black hole of one of
(06:35):
those measures of why what what is the measure of
the combined black hole in terms of X and Y?
Speaker 3 (06:44):
Okay, So there's only three things you can literally a
black holes has in terms of measurable quantities. It's its mass,
it's charge and its spin Okay, and so mass and
its spin are related to what known as the area
of the black hole is in fact the important thing
that you can measure. And in this recent measurement, it
(07:07):
happened in early this year and has taken some months
of analysis for the researchers to antalyize exactly what happened
in this case, it was black holes of about thirty
or forty solar masses collided with each other and created
a black hole that was twice as big, and the
area of the final black hole is bigger than the
(07:28):
area of either of the beginning ones. But the important
thing that Einstein that excuse me, Stephen Hawking predicted in
the nineteen sixties was that the area has to increase
when two black holes come together, and so the final
area has to be bigger than the sum of the
areas of the two individuals. And that's what they were
(07:50):
able to measure from the exact details of the woo
that happens in the collision.
Speaker 1 (07:56):
Okay, so I'm going way, way way out of my
league here with this next question.
Speaker 2 (08:03):
This is probably going to be a really stupid question.
Speaker 1 (08:07):
I would have thought that it was at least possible
that when you combine these very very massive things, that
the increase in the gravitational field caused by the increase
in the mass of these two things would could cause
the area of the combined black holes to be smaller
(08:31):
than the sum of the areas.
Speaker 2 (08:33):
Is that a ridiculous concept.
Speaker 1 (08:37):
It's clearly wrong, as you just said it's wrong, But
is it ridiculous.
Speaker 3 (08:41):
No, not at all. And in fact, it took you know,
Stephen Hawking to prove that the area can only increase,
and so that caused him to start thinking, and he
worked with another mathematical physicist by the name of Beckenstein,
and they came up with a calculation in which showed, oh,
not only is this area interesting and measurable, but it
(09:05):
is proportional to the entropy of the black hole. So
the black hole and stuff goes down into it, it's
sucking in thermodynamic entropy, and the entropy is completely encoded
in the area of the black hole. Wow, we're talking
with all the way back to thermodynamics, the second law
of thermodynamics.
Speaker 1 (09:26):
We're talking with cup physics professor Paul Beal. I don't
know if there's some other term, some other units you
can put this in. A listener wants to know how
big is a solar mass?
Speaker 3 (09:37):
Oh solar mass, So solar mass is about ten to
the I'm gonna ten to the thirty something kilograms, okay,
and I forget whether it's thirty or thirty two or
thirty five that I can't.
Speaker 1 (09:54):
Remember, all right, Ed Paul didn't look that up by anyway.
That's just off the top of his head. So that's
how big a solar mass is. That's that's a lot. Okay,
one more listener question, even though it's way way off
topic and probably a question that you teach in all
of your most basic basic physics classes, but people ask
from time to time. So we'll do this one listener
(10:14):
question quickly, and then we'll do math. Can we travel
faster than the speed of light?
Speaker 3 (10:19):
Okay? So, as our theory of the universe does not
allow an object with mass to travel faster than the
speed of light because it would take an infinite amount
of energy to accelerate the particle, you know, exactly to
the speed of light. So the fastest anything we've ever
created is ninety nine point nine nine percent of the
(10:43):
speed of light. And that set the large Hadron collider
where they accelerate protons to very very close to the
speed of light.
Speaker 1 (10:51):
Wow, all right, excellent answer. Okay, let's do some math.
And this math thing is actually the thing that caused
me to reach out to you yesterday when a listener
in Abu Dhabi said, Hey, Ross, have you heard of this?
Have you heard of this thing called the Goldbach conjecture,
and I said no, and I looked it up, and
(11:12):
actually I probably have heard of it without that name,
just as the mathematical concept. But it's pretty interesting, as
you and I were talking about on the air. It's
a mathematical concept that's easy enough to understand that you
don't have to be a mathematician to understand the question.
But it turns out it's well nearly impossible, I guess,
because it hasn't been done yet to prove it.
Speaker 2 (11:32):
So can you can you elaborate please?
Speaker 3 (11:35):
Okay? So this was a conjecture made by Christian Goldbach,
and he was lived in the seventeen hundreds. He was
a contemporary of Leonard Euler, who I think is the
greatest mathematician in history, and they were communicating and talking
to each other, and Goldbach made this conjecture that every
even number bigger than four can be written as the
(11:58):
sum of two prime numbers. So, for example, six is
three plus three, and eight can be written as three
plus five ten, five plus five fourteen. It can be
written as seven plus seven or three plus eleven, So
you can always find two prime numbers that add up
to every even number. And I would say conjecture, cause
(12:21):
no one's proven it. But people, it's fairly easy with
a computer now to check two fairly large numbers and
up to numbers with eighteen digits, and them people have checked. Yes,
every even number is the sum of two prime numbers.
Speaker 1 (12:38):
Why is this so far for what two hundred and
eighty years impossible to prove?
Speaker 3 (12:46):
Well, I will say it's impossible. People are making progress.
There's a weaker form of the conjecture that says, oh,
let's look at odd numbers. Every odd number greater than seven,
it can be written as the sum of three prime numbers,
three odd prime numbers, and uh, and that is people
are it's it's a weaker conjecture because if gold box
(13:10):
and original conjecture is true, then this other one is
trivitally true. You can take any of the even numbers
that Goldbock referred to and just add three to it,
and that would give an odd number, and that would
count all of the odd number. And he and Eiler
figured that out immediately say ah, if we can prove this,
then uh uh, that would be maybe easier. But then
(13:33):
the first one, the strong conjecture, would actually have that
is a required element, that every odd numbers and some
of three odd primes.
Speaker 1 (13:44):
I mean there from time to time you run across
things like this in math, if you're even a little
bit of a math nerd, and I am a little
bit not not to your level, but two, but were
you where there are these these conjectures, these theorems with
you know, fair modern oiler and all these guys, and
all these famous theorems, and some of the theorems. Yeah,
almost have to be a mathematician to even understand the
(14:07):
question being posed. But this one is so easy, conceptually easy.
And I don't know whether that I don't know whether
I'm whether I should be surprised that a question that
is so conceptually easy has proven to be so theoretically
difficult to prove.
Speaker 3 (14:28):
And there are lots of things like this that seem
to be easy to state, and there's lots of them
we could talk about but have never been able to
be proven so far. But a lot of them have
fallen to the mathematicians who have proven some of these
very hard to prove theorems, like fair Ma's last theorem
was in the nineteen nineties, and that had stood the
(14:52):
test of three or four hundred years, and so this one,
this one could happen soon. Now there's a one million
dollar prize if someone can either prove it to be
true or to be false. If they can find an
example of a single even number that is not the
sum of two primes, then that's enough. That would be
(15:12):
the proof that, yeah, that conjecture is false because there's
a counterexample.
Speaker 2 (15:16):
All right, less, super quick question.
Speaker 1 (15:17):
Then I got to go, do you think your mathematical
skills are close to good enough that it would be
a good use of your time to try to win
that million dollars?
Speaker 3 (15:26):
H No way, no way. So even the weak conjecture,
there's like a two hundred page paper that's getting closer
to ward to proof, and mathematicians are pouring over that
two hundred page paper and trying to cross all the
t's and dot the i's and everything. I can't even
begin to read the math that's present in that paper.
Speaker 2 (15:48):
Wow.
Speaker 1 (15:49):
If Paul Beale can't even begin to read the math,
imagine the rest of us. See you, physics Professor Paul
bial Thanks so much. It's great to have you back
on the show. Sorry it's been so long. We'll do
it again soon.
Speaker 3 (15:59):
Okay, thank you all. Ry good one.
Speaker 2 (16:00):
Hey you too, have a great weekend.
The Ross Kaminsky Show News
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