June 27, 2025 • 14 mins
Our most frequent show guest, CU Physics Professor Paul Beale, joins the show to talk about a device that uses quantum mechanics to generate true random numbers. (Paul was part of the team that developed it!) We'll also discuss the new Vera C Rubin observatory that just released its first pictures about a week ago.
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Episode Transcript
Available transcripts are automatically generated. Complete accuracy is not guaranteed.
Speaker 1 (00:00):
My good friend and our favorite and most frequent show
guest back at his CEU physics professor Paul Beale, a
guy who makes me wish I had stayed in college
for a while or studied physics with him.
Speaker 2 (00:12):
And I know, I know it's I don't deny it.
I don't deny my nerdiness.
Speaker 1 (00:17):
And some of my best friends are nerds, because nerds
of a feather flock together.
Speaker 2 (00:22):
So a thing that's come up quite a.
Speaker 1 (00:25):
Few times in our conversations with Paul have been random numbers.
Speaker 2 (00:32):
And it just keeps coming up because.
Speaker 1 (00:35):
Random numbers have some uses that most people never think of,
but random numbers are shockingly difficult to generate. And so
Paul has been working with a team at NIST and
you know, folks affiliated with with CU as well, to
try to do something about this. And it looks like
(00:55):
you may have I shouldn't say stumbled, because that's not fair,
because you've been working on this real hard, but come
up with some solutions here. So, first of all, Paul,
good morning, and thanks for being here.
Speaker 3 (01:06):
Good morning.
Speaker 1 (01:08):
Before we get into what you and your team have done,
please explain.
Speaker 2 (01:16):
Two things, just briefly.
Speaker 1 (01:17):
Why are random numbers important, and why are they so
hard to generate?
Speaker 3 (01:24):
Okay?
Speaker 4 (01:24):
So, truly, random numbers are really useful in the sense of,
for example, in technology for cryptography, having random numbers that
are available on each computer allow different computers to talk
to each other in a secure way. So that's one
use of random numbers. And randomness appears everywhere in nature,
(01:48):
and being able to create them and use that to study.
Speaker 3 (01:52):
The properties of nature is very important.
Speaker 2 (01:54):
Okay. But or I should say, and.
Speaker 1 (02:01):
There's a function I remember when I was programming in
basic in the nineteen eighties on an Apple two plus
or a Trash eighty computer, if you remember those, there'd
be that one. Yeah, So there'd be a function like
rnd open parentheses, number of close parentheses, and that generates
a random number.
Speaker 3 (02:20):
Right.
Speaker 4 (02:21):
Well, those are called pseudorandom numbers, and that's something I
use all the time in my own work. You can
create them at an extraordinary rate, but they're come from
an algorithm, so they are unpredictable, but they are not
random in the sense. Sooner or later, the series of
numbers you get out of one of those will repeat
again and again and again, and they're very useful, but
(02:44):
they are not truly random, they are generated by an algorithm.
Speaker 1 (02:48):
And if they are not truly random, and if it
is something that would eventually repeat, does that imply that
to the extent you're going to use random numbers as
you said for cryptography, which means essentially encrypting messages so
that people or computers can communicate in a way where
(03:09):
if somebody intercepts the message that they can't understand what
it says, you can't read the message if they're using
one of these pseudorandom things, does that mean somebody with
a powerful enough computer may be able to guess what
the key is and decrypt a message that they shouldn't
be able to decrypt.
Speaker 3 (03:26):
That's exactly right.
Speaker 4 (03:27):
You would not want to use any sort of method
that generates the key using pseudorandom numbers because a sleuth
an adversary could much more easily guess what your key is.
Speaker 1 (03:40):
So I see a piece over at Nature, which is
one of the one of the top science publications quantum
physicists reveal unveil most trustworthy random number generator yet.
Speaker 2 (03:55):
And you're part of this group.
Speaker 1 (03:57):
So tell us about the group and tell us what
you've done and how you've done it.
Speaker 3 (04:01):
Okay, So the lead author is an this scientist.
Speaker 4 (04:04):
His name is Christer Scham and also on the paper
or a bunch of both NIST and CU employees. Jasper
Palfrey and Galtham Kaburi were the other sort of lead
authors of the paper.
Speaker 3 (04:18):
I played a very small role that I can describe later.
Speaker 4 (04:22):
And what they were doing is creating random numbers using
entangled photons, what the technologists might call a quantum two
point zero. It's using quantum mechanics to generate, which is
quantum mechanics generates things and measurements are always random and
unpredictable in quantum mechanics. And this is a means of
(04:42):
generating the numbers using the fundamental properties of the universe.
Speaker 1 (04:48):
How do you how do I want to put this,
How do you harness some fundamental property of the universe
in a way that you then turn into a random number?
Speaker 4 (04:56):
Okay, So what their technique is They use entangled photon.
So they take a laser and they shine it into
a crystal and what comes out or two photons, each
having half of the frequency of the input photon, and
they go in opposite directions, and they have properties that
(05:16):
photons have and one of the properties is polarization. So
when you put on polarizing sunglasses in your car, what
you're doing is you're filtering out light that's horizontally polarized.
So you're removing the photons that are horizontally polarized.
Speaker 3 (05:33):
And leaving in the ones that are verticallying.
Speaker 4 (05:35):
And the horizontally polarized ones are the ones mostly that
come from glare from the road and the brightness of
the sky, so the sky darkens without interfering with the
light just bouncing off of trees and everything else that
you're looking at. And so these polarized photons can be measured,
and so they send one photon to a detector they
(05:58):
call Alice and one to the one they call Bob.
And Alice and Bob are two characters that appear in
cryptography papers since nearly the beginning of cryptography, and so
they measure the polarization states of these two photons. And
since there came from the same source, they're entangled. So
(06:18):
if you measure one of them is vertically polarized, the
other one is guaranteed to be vertically polarized, and vice versa.
And so that connection this coupling between the polarization states
of the photons is inherently quantum, and excuse me. So
the detectors actually measure the polarization states and randomly vary
(06:41):
the direction in which they're measuring the polarizations, and the
sequence of whether you see the photons or not comes
out in a way that cannot be produced by any
adversary who's trying to create that sequence of events that
you measure in your detective.
Speaker 1 (06:59):
Okay, I understood a little bit of that. So is
the is the polarization of the photon?
Speaker 2 (07:08):
Infinitely variable?
Speaker 1 (07:10):
Is the polarization of the photon the random number or
what exactly is the random number that comes out of this.
Speaker 4 (07:18):
So when you measure a photon, let's call that a one,
and you don't and you don't see a photon in
the other detector, you would call that a zero. And
so the these numbers that come out of the two
detectors are correlated because of the fact they came from
the same entangled source and this correlation. The weird thing is,
(07:40):
when you're about to measure a photon, it doesn't know
which way you have your detector set up, so there
is no way to figure out a priori what the
measurement will give. But once one measurement happens, the other
one is going to be correlated with that. That's this
spooky action at a distance that I really bugged Einstein
(08:01):
in the nineteen thirties about the properties of quantum mechanics.
Speaker 1 (08:05):
All Right, I think I'll just dig myself into a
deeper hole if i keep going too much on this,
because I'm not really getting it, even though I'm still
I'm incredibly impressed that they've been able to do it.
Speaker 2 (08:15):
I do have one one more follow up, though.
Speaker 1 (08:17):
So you said that they randomize the position of the detectors.
Speaker 2 (08:24):
That right, How do.
Speaker 3 (08:25):
They randomizeization state of the detector?
Speaker 1 (08:28):
How do they randomize that in a way that's truly random.
Speaker 2 (08:31):
To make sure that the.
Speaker 1 (08:32):
Random number that comes out of this thing is actually random.
Speaker 4 (08:35):
So they use a physical random number generator. For example,
radio noise. If you tune your radio to some sort
of random frequency, you hear a bunch of hiss yeah,
And that is as random as you can get from
physical detectors. And so those are random numbers, but they
don't come from an inherently quantum source like the ones
(08:59):
that Christ and his team have created.
Speaker 2 (09:01):
Okay, all right, so now those.
Speaker 3 (09:03):
Kind of random numbers to set the detective.
Speaker 2 (09:05):
Okay, So.
Speaker 1 (09:08):
Would it be possible to create a true random number
generator from something that just listens to the noise when
you turn the radio in between frequencies and there's nothing there.
Speaker 3 (09:18):
Yeah.
Speaker 4 (09:18):
In fact, there are many there what are called randomness beacons,
and we'll come to that. There's one that based on
this experiment is that random dot Colorado dot edu. And
it generates and publishes the random numbers that it is creating.
And so there are a bunch of these all over
the world using all sorts of different random sources. I've
(09:41):
seen random number generators that are based on the patterns
created by lava lamps, all sorts of crazy. Anything that
is inherently long term random you can use as a
source for physical randomness.
Speaker 2 (09:57):
Wow. I'm looking at this.
Speaker 1 (10:00):
Colorado dot edu and it creates this incredibly. I don't
know how long this is, one hundred and twenty eight maybe,
I don't know. It's some very very long string of
hexadecimal whatever.
Speaker 4 (10:10):
Right, those are five hundred and twelve bits each time
it puts out an number.
Speaker 2 (10:14):
Wow. Okay, all right, let's do something else quickly.
Speaker 1 (10:18):
I'm going to need to read and drink more to
understand this a little better, but it is. It is
really incredible. Actually, what this team accomplished figuring out a
way to use to use quantum mechanics to generate real
random numbers pretty amazing stuff.
Speaker 2 (10:33):
So all right, let's just do two.
Speaker 1 (10:35):
Minutes on something else, even though it's worth more than
two minutes.
Speaker 2 (10:38):
Tell us about the Vira Sea Reuben Observatory.
Speaker 3 (10:42):
Okay, so, as the new observatories come online.
Speaker 4 (10:44):
It's in the mountains in Chile, about nine thousand feet
above sea level. And so they've generated a very huge
pixel detector that has three two billion pixels in the
detector and so that's the quote one hundreds and hundreds
(11:07):
of top end the iPhone type pixel measurements. And so
what they are able to do is scan an enormous
piece of sky every night. And in their first few
hours of observations, they observed ten million galaxies just by
pointing this telescope and following the spot across the sky
(11:29):
with this very high precision detector. And their goal is
to measure the locations of twenty billion galaxies over the
course of the next few years.
Speaker 2 (11:38):
Wow.
Speaker 1 (11:39):
Wow, And I have seen some of these initial pictures.
They're really quite incredible. One more question on that. Who's
Vera Rubin Oh.
Speaker 4 (11:49):
Vera Ruben's very interesting story. She was George Gamov's graduate
student in the nineteen fifties at s. In the nineteen sixties,
she and Kent Ford were the first people to measure
the existence of dark matter. And they were studying the
rotation rates of stars in nearby galaxies, and they noticed
that the stars on the far reaches of the galaxy
(12:11):
were moving much faster than they should have been just
based on the amount of mass that the galaxy appeared
to have from all the stars and everything in the
visible portion of the galaxy. And so dark matter makes
up something eighty five percent of all the matter in
the universe. Is this very mysterious dark matter? We don't
know what it is, but it is measurable. And every
(12:35):
galaxy in the universe appears to have a large collection
of dark matter that composes.
Speaker 3 (12:41):
Most of the mass of the galaxy.
Speaker 1 (12:43):
All right, last question, this comes from a listener, and
just give me a quick answer. Paul Ross. Please ask
Paul about the lava lamp wall.
Speaker 3 (12:52):
Oh, that's what I was referring to.
Speaker 4 (12:53):
Its people have a video cameras pointed at a whole
bunch of lava lamps and they're all doing the weird things.
Speaker 3 (13:00):
That lava lamps do that make them so mesmerizing.
Speaker 4 (13:04):
And so then they would take the video camera and
take that information from the dozens of lava lamps and
generate random bits and publish them. And so this is
called a randomness beacon, and random dot Colorado dot EEDU
is one of many many randomness beacons around the world.
And the fact that they're all generating random numbers in
(13:26):
very different ways by very different processes and are it
makes it very very difficult for someone to hack the
various random numbers are coming out because each random beacon
is used by other random beacons to sort of tie
the numbers together and give them a traceable output so
(13:49):
that you know if you choosing you look. For example,
you want to sign a document, you sign it using
the number that's most recently posted on some random the beacon,
and that time stamps the creation of that document within
the one minute that appear between the various random numbers.
Speaker 2 (14:09):
Absolutely amazing.
Speaker 1 (14:10):
See you, physics professor Paul Beal, I definitely need Bourbon
for that one for the random number thing, and as
always I'm very grateful for your time as fascinating conversation today.
Speaker 2 (14:21):
Thanks Paul.
Speaker 3 (14:23):
Hey, you have a nice weekend.
Speaker 2 (14:24):
Okay, you too, You too,
My good friend and our favorite and most frequent show
guest back at his CEU physics professor Paul Beale, a
guy who makes me wish I had stayed in college
for a while or studied physics with him.
Speaker 2 (00:12):
And I know, I know it's I don't deny it.
I don't deny my nerdiness.
Speaker 1 (00:17):
And some of my best friends are nerds, because nerds
of a feather flock together.
Speaker 2 (00:22):
So a thing that's come up quite a.
Speaker 1 (00:25):
Few times in our conversations with Paul have been random numbers.
Speaker 2 (00:32):
And it just keeps coming up because.
Speaker 1 (00:35):
Random numbers have some uses that most people never think of,
but random numbers are shockingly difficult to generate. And so
Paul has been working with a team at NIST and
you know, folks affiliated with with CU as well, to
try to do something about this. And it looks like
(00:55):
you may have I shouldn't say stumbled, because that's not fair,
because you've been working on this real hard, but come
up with some solutions here. So, first of all, Paul,
good morning, and thanks for being here.
Speaker 3 (01:06):
Good morning.
Speaker 1 (01:08):
Before we get into what you and your team have done,
please explain.
Speaker 2 (01:16):
Two things, just briefly.
Speaker 1 (01:17):
Why are random numbers important, and why are they so
hard to generate?
Speaker 3 (01:24):
Okay?
Speaker 4 (01:24):
So, truly, random numbers are really useful in the sense of,
for example, in technology for cryptography, having random numbers that
are available on each computer allow different computers to talk
to each other in a secure way. So that's one
use of random numbers. And randomness appears everywhere in nature,
(01:48):
and being able to create them and use that to study.
Speaker 3 (01:52):
The properties of nature is very important.
Speaker 2 (01:54):
Okay. But or I should say, and.
Speaker 1 (02:01):
There's a function I remember when I was programming in
basic in the nineteen eighties on an Apple two plus
or a Trash eighty computer, if you remember those, there'd
be that one. Yeah, So there'd be a function like
rnd open parentheses, number of close parentheses, and that generates
a random number.
Speaker 3 (02:20):
Right.
Speaker 4 (02:21):
Well, those are called pseudorandom numbers, and that's something I
use all the time in my own work. You can
create them at an extraordinary rate, but they're come from
an algorithm, so they are unpredictable, but they are not
random in the sense. Sooner or later, the series of
numbers you get out of one of those will repeat
again and again and again, and they're very useful, but
(02:44):
they are not truly random, they are generated by an algorithm.
Speaker 1 (02:48):
And if they are not truly random, and if it
is something that would eventually repeat, does that imply that
to the extent you're going to use random numbers as
you said for cryptography, which means essentially encrypting messages so
that people or computers can communicate in a way where
(03:09):
if somebody intercepts the message that they can't understand what
it says, you can't read the message if they're using
one of these pseudorandom things, does that mean somebody with
a powerful enough computer may be able to guess what
the key is and decrypt a message that they shouldn't
be able to decrypt.
Speaker 3 (03:26):
That's exactly right.
Speaker 4 (03:27):
You would not want to use any sort of method
that generates the key using pseudorandom numbers because a sleuth
an adversary could much more easily guess what your key is.
Speaker 1 (03:40):
So I see a piece over at Nature, which is
one of the one of the top science publications quantum
physicists reveal unveil most trustworthy random number generator yet.
Speaker 2 (03:55):
And you're part of this group.
Speaker 1 (03:57):
So tell us about the group and tell us what
you've done and how you've done it.
Speaker 3 (04:01):
Okay, So the lead author is an this scientist.
Speaker 4 (04:04):
His name is Christer Scham and also on the paper
or a bunch of both NIST and CU employees. Jasper
Palfrey and Galtham Kaburi were the other sort of lead
authors of the paper.
Speaker 3 (04:18):
I played a very small role that I can describe later.
Speaker 4 (04:22):
And what they were doing is creating random numbers using
entangled photons, what the technologists might call a quantum two
point zero. It's using quantum mechanics to generate, which is
quantum mechanics generates things and measurements are always random and
unpredictable in quantum mechanics. And this is a means of
(04:42):
generating the numbers using the fundamental properties of the universe.
Speaker 1 (04:48):
How do you how do I want to put this,
How do you harness some fundamental property of the universe
in a way that you then turn into a random number?
Speaker 4 (04:56):
Okay, So what their technique is They use entangled photon.
So they take a laser and they shine it into
a crystal and what comes out or two photons, each
having half of the frequency of the input photon, and
they go in opposite directions, and they have properties that
(05:16):
photons have and one of the properties is polarization. So
when you put on polarizing sunglasses in your car, what
you're doing is you're filtering out light that's horizontally polarized.
So you're removing the photons that are horizontally polarized.
Speaker 3 (05:33):
And leaving in the ones that are verticallying.
Speaker 4 (05:35):
And the horizontally polarized ones are the ones mostly that
come from glare from the road and the brightness of
the sky, so the sky darkens without interfering with the
light just bouncing off of trees and everything else that
you're looking at. And so these polarized photons can be measured,
and so they send one photon to a detector they
(05:58):
call Alice and one to the one they call Bob.
And Alice and Bob are two characters that appear in
cryptography papers since nearly the beginning of cryptography, and so
they measure the polarization states of these two photons. And
since there came from the same source, they're entangled. So
(06:18):
if you measure one of them is vertically polarized, the
other one is guaranteed to be vertically polarized, and vice versa.
And so that connection this coupling between the polarization states
of the photons is inherently quantum, and excuse me. So
the detectors actually measure the polarization states and randomly vary
(06:41):
the direction in which they're measuring the polarizations, and the
sequence of whether you see the photons or not comes
out in a way that cannot be produced by any
adversary who's trying to create that sequence of events that
you measure in your detective.
Speaker 1 (06:59):
Okay, I understood a little bit of that. So is
the is the polarization of the photon?
Speaker 2 (07:08):
Infinitely variable?
Speaker 1 (07:10):
Is the polarization of the photon the random number or
what exactly is the random number that comes out of this.
Speaker 4 (07:18):
So when you measure a photon, let's call that a one,
and you don't and you don't see a photon in
the other detector, you would call that a zero. And
so the these numbers that come out of the two
detectors are correlated because of the fact they came from
the same entangled source and this correlation. The weird thing is,
(07:40):
when you're about to measure a photon, it doesn't know
which way you have your detector set up, so there
is no way to figure out a priori what the
measurement will give. But once one measurement happens, the other
one is going to be correlated with that. That's this
spooky action at a distance that I really bugged Einstein
(08:01):
in the nineteen thirties about the properties of quantum mechanics.
Speaker 1 (08:05):
All Right, I think I'll just dig myself into a
deeper hole if i keep going too much on this,
because I'm not really getting it, even though I'm still
I'm incredibly impressed that they've been able to do it.
Speaker 2 (08:15):
I do have one one more follow up, though.
Speaker 1 (08:17):
So you said that they randomize the position of the detectors.
Speaker 2 (08:24):
That right, How do.
Speaker 3 (08:25):
They randomizeization state of the detector?
Speaker 1 (08:28):
How do they randomize that in a way that's truly random.
Speaker 2 (08:31):
To make sure that the.
Speaker 1 (08:32):
Random number that comes out of this thing is actually random.
Speaker 4 (08:35):
So they use a physical random number generator. For example,
radio noise. If you tune your radio to some sort
of random frequency, you hear a bunch of hiss yeah,
And that is as random as you can get from
physical detectors. And so those are random numbers, but they
don't come from an inherently quantum source like the ones
(08:59):
that Christ and his team have created.
Speaker 2 (09:01):
Okay, all right, so now those.
Speaker 3 (09:03):
Kind of random numbers to set the detective.
Speaker 2 (09:05):
Okay, So.
Speaker 1 (09:08):
Would it be possible to create a true random number
generator from something that just listens to the noise when
you turn the radio in between frequencies and there's nothing there.
Speaker 3 (09:18):
Yeah.
Speaker 4 (09:18):
In fact, there are many there what are called randomness beacons,
and we'll come to that. There's one that based on
this experiment is that random dot Colorado dot edu. And
it generates and publishes the random numbers that it is creating.
And so there are a bunch of these all over
the world using all sorts of different random sources. I've
(09:41):
seen random number generators that are based on the patterns
created by lava lamps, all sorts of crazy. Anything that
is inherently long term random you can use as a
source for physical randomness.
Speaker 2 (09:57):
Wow. I'm looking at this.
Speaker 1 (10:00):
Colorado dot edu and it creates this incredibly. I don't
know how long this is, one hundred and twenty eight maybe,
I don't know. It's some very very long string of
hexadecimal whatever.
Speaker 4 (10:10):
Right, those are five hundred and twelve bits each time
it puts out an number.
Speaker 2 (10:14):
Wow. Okay, all right, let's do something else quickly.
Speaker 1 (10:18):
I'm going to need to read and drink more to
understand this a little better, but it is. It is
really incredible. Actually, what this team accomplished figuring out a
way to use to use quantum mechanics to generate real
random numbers pretty amazing stuff.
Speaker 2 (10:33):
So all right, let's just do two.
Speaker 1 (10:35):
Minutes on something else, even though it's worth more than
two minutes.
Speaker 2 (10:38):
Tell us about the Vira Sea Reuben Observatory.
Speaker 3 (10:42):
Okay, so, as the new observatories come online.
Speaker 4 (10:44):
It's in the mountains in Chile, about nine thousand feet
above sea level. And so they've generated a very huge
pixel detector that has three two billion pixels in the
detector and so that's the quote one hundreds and hundreds
(11:07):
of top end the iPhone type pixel measurements. And so
what they are able to do is scan an enormous
piece of sky every night. And in their first few
hours of observations, they observed ten million galaxies just by
pointing this telescope and following the spot across the sky
(11:29):
with this very high precision detector. And their goal is
to measure the locations of twenty billion galaxies over the
course of the next few years.
Speaker 2 (11:38):
Wow.
Speaker 1 (11:39):
Wow, And I have seen some of these initial pictures.
They're really quite incredible. One more question on that. Who's
Vera Rubin Oh.
Speaker 4 (11:49):
Vera Ruben's very interesting story. She was George Gamov's graduate
student in the nineteen fifties at s. In the nineteen sixties,
she and Kent Ford were the first people to measure
the existence of dark matter. And they were studying the
rotation rates of stars in nearby galaxies, and they noticed
that the stars on the far reaches of the galaxy
(12:11):
were moving much faster than they should have been just
based on the amount of mass that the galaxy appeared
to have from all the stars and everything in the
visible portion of the galaxy. And so dark matter makes
up something eighty five percent of all the matter in
the universe. Is this very mysterious dark matter? We don't
know what it is, but it is measurable. And every
(12:35):
galaxy in the universe appears to have a large collection
of dark matter that composes.
Speaker 3 (12:41):
Most of the mass of the galaxy.
Speaker 1 (12:43):
All right, last question, this comes from a listener, and
just give me a quick answer. Paul Ross. Please ask
Paul about the lava lamp wall.
Speaker 3 (12:52):
Oh, that's what I was referring to.
Speaker 4 (12:53):
Its people have a video cameras pointed at a whole
bunch of lava lamps and they're all doing the weird things.
Speaker 3 (13:00):
That lava lamps do that make them so mesmerizing.
Speaker 4 (13:04):
And so then they would take the video camera and
take that information from the dozens of lava lamps and
generate random bits and publish them. And so this is
called a randomness beacon, and random dot Colorado dot EEDU
is one of many many randomness beacons around the world.
And the fact that they're all generating random numbers in
(13:26):
very different ways by very different processes and are it
makes it very very difficult for someone to hack the
various random numbers are coming out because each random beacon
is used by other random beacons to sort of tie
the numbers together and give them a traceable output so
(13:49):
that you know if you choosing you look. For example,
you want to sign a document, you sign it using
the number that's most recently posted on some random the beacon,
and that time stamps the creation of that document within
the one minute that appear between the various random numbers.
Speaker 2 (14:09):
Absolutely amazing.
Speaker 1 (14:10):
See you, physics professor Paul Beal, I definitely need Bourbon
for that one for the random number thing, and as
always I'm very grateful for your time as fascinating conversation today.
Speaker 2 (14:21):
Thanks Paul.
Speaker 3 (14:23):
Hey, you have a nice weekend.
Speaker 2 (14:24):
Okay, you too, You too,
The Ross Kaminsky Show News
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